\documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[version=4]{mhchem} \usepackage{stmaryrd} \usepackage{hyperref} \hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,} \urlstyle{same} \usepackage{graphicx} \usepackage[export]{adjustbox} \graphicspath{ {./images/} } \title{Frequency Domain Measurements of Melt Pool Recoil Force using Modal Analysis } \author{Tristan Cullom¹, Cody Lough'1, Nicholas Altese ${ }^{1}$, Douglas Bristow ${ }^{1}$, Robert\\ Landers $^{1}$, Ben Brown'2, Troy Hartwig'2, Andrew Barnard ${ }^{3}$, Jason Blough',\\ Kevin Johnson ${ }^{3}$, Edward Kinzel ${ }^{4, *}$} \date{} %New command to display footnote whose markers will always be hidden \let\svthefootnote\thefootnote \newcommand\blfootnotetext[1]{% \let\thefootnote\relax\footnote{#1}% \addtocounter{footnote}{-1}% \let\thefootnote\svthefootnote% } %Overriding the \footnotetext command to hide the marker if its value is `0` \let\svfootnotetext\footnotetext \renewcommand\footnotetext[2][?]{% \if\relax#1\relax% \ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else% \if?#1\ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else\svfootnotetext[#1]{#2}\fi% \fi } \begin{document} \maketitle Recoil pressure is a critical factor affecting the melt pool dynamics during Laser Powder Bed Fusion (LPBF) processes. Recoil pressure depresses the melt pool, providing layer-to-layer fusion without introducing porosity. If the recoil pressure is too low, the process operates in a conduction mode where layers will not properly fuse, while excessive recoil pressure leads to a keyhole mode, which results in gas porosity. Direct recoil pressure measurements are challenging because it is localized over an area proportionate to the laser spot size producing a force in the $\mathbf{m N}$ range. This paper reports a vibration-based approach to quantify the recoil force exerted on a part in a commercial LPBF machine. The measured recoil force is consistent with estimates from high speed synchrotron imaging of entrained particles, and the results show that the recoil force scales with applied laser power and is inversely related to the laser scan speed. These results facilitate further studies of melt pool dynamics and have the potential to aid process development for new materials. Understanding the complex melt pool dynamics in Laser Powder Bed Fusion (LPBF) processes is critical to maintaining quality of printed parts. Tight quality control is necessary as parts created by LPBF are used in demanding biomedical, aerospace, and defense applications. In the LPBF process a focused laser spot follows a computer generated path over a thin powder layer. The powder is heated by the absorbed laser irradiation to the point that it melts and fuses with the underlying part. Variations in the melt pool dynamics lead to changes in microstructure, notably porosity. Specifically, insufficient laser fluence produces a lack of fusion between layers while excessive power leads to gas entrapment as the melt pool solidifies. The influence of the recoil pressure can be seen with the different melt pool modes. If the recoil pressure is too low, heat transfer in the melt pool operates in the conduction mode ${ }^{1}$, leading to poor fusion between the molten material and the previous layer and resulting in brittle parts. Conversely, if the recoil pressure is too high, convection in the melt pool is the dominant heat transfer mode, depressing the melt pool into multiple previous layers and potentially creating keyhole porosity due to increased laser absorptivity and making the melt pool less stable ${ }^{2,3}$. This melt pool mode is referred to as the keyhole mode ${ }^{4}$. Since part quality is primarily driven by these defects, it is important to understand recoil pressure to operate the LPBF process between the conduction and keyhole modes, thus, minimizing the potential for these defects. For most commercial processes, the temperature of the top of the melt pool exceeds the vaporization point of the metal. This produces a recoil pressure that depresses the melt pool ${ }^{5}$ which drives the melt pool deeper and enhances the heat transfer allowing for adequate layer-to-layer fusion. The melt pool dynamics are driven by Marangoni ${ }^{6,7,8}$, capillary ${ }^{9,10}$ and buoyancy ${ }^{11}$ forces, in addition to the recoil pressure. These forces all significantly influence the shape of the melt $\mathrm{pool}^{7,8}$ as well as its stability ${ }^{6}$ and overall fluid transport. However, the recoil force magnitude is significantly greater than the other forces acting on the melt pool once it starts to vaporize. For example, using the definitions of these forces described in Heeling et al. ${ }^{12}$ and typical processing parameters for 304L stainless steel ${ }^{13}$, the recoil force is at least an order of magnitude larger than the net Marangoni force, and more than eight orders of magnitude larger than the capillary and buoyancy forces. \footnotetext{${ }^{1}$ Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO 65409. ${ }^{2}$ Kansas City National Security Campus, Kansas City, MO 64147. ${ }^{3}$ Department of Mechanical Engineering - Engineering Mechanics, Michigan Technological University, Houghton, MI 49931. ${ }^{4}$ Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556 *Correspondence to: \href{mailto:ekinzel@nd.edu}{ekinzel@nd.edu} } The effects of the recoil pressure in depressing the melt pool has been studied numerically ${ }^{7,14,15}$. While modeling recoil pressure is computationally expensive, an estimate for the recoil pressure can be made using the Clausius-Clapeyron model and via the simulation results in Khairallah et al. ${ }^{16}$. The recoil pressure was estimated to be $86 \mathrm{kPa}$ for a 316L stainless steel simulation with a laser power of $200 \mathrm{~W}$ and a scan speed of $1.5 \mathrm{~m} / \mathrm{s}$. Simulations have also shown that as material is vaporized, changes in the thermal and fluid transport within the melt pool lead to surface defects known as humps ${ }^{10,17}$. This is an effect of the backflow generated by the recoil pressure as the exposed area of the melt pool is displaced away from the center. In addition, the recoil pressure driven melt pool depression has been experimentally shown to be correlated with the formation of spatter ${ }^{18-24,32}$. Recently, there have been a few attempts to measure recoil pressure using particle tracking techniques. This requires in-situ high-speed imaging of the melt pool. Zhao et al. used a custom built 2D setup illuminated with synchrotron radiation to estimate an average pressure above the melt pool of $60 \mathrm{kPa}$ for Ti-6Al-4V powder melted with a laser power of $210 \mathrm{~W}$ and a scan speed $0.5 \mathrm{~m} / \mathrm{s}^{25}$. Yin et al. calculated a vapor pressure of $49 \mathrm{kPa}$ for Inconel powder processed with a laser power of $1150 \mathrm{~W}$, a scan speed of 1 $\mathrm{m} / \mathrm{s}$, and a spot size of $159 \mu \mathrm{m}$ by observing spatter tracks using high-speed visible camera imaging ${ }^{26}$. These studies pose instrumentation challenges and require the assumption that the particles are moving parallel to the imaging plane. In addition, significant complications arise with the presence of the gas that flows over the build plate (i.e., shielding gas) to create an inert atmosphere as it substantially modifies particle velocities. Shielding gas was present during the experiment in the Inconel study ${ }^{26}$ to prevent melt pool oxidation while the Ti-6Al-4V study was performed in vacuum ${ }^{25}$. A possible alternative to measuring the laser spatter trajectories is to directly measure the reaction force generated by the recoil pressure. Both experimental and numerical studies give an expectation for the recoil pressure on the order of $50-90 \mathrm{kPa}$. This is equivalent to a recoil force acting on the melt pool in the sub $\mathrm{mN}$ range. Measuring this force in the time domain is difficult given the noise inherent in LPBF environments (e.g., shielding gas, chiller). However, if the experiments can be conducted in the frequency domain, spectral filtering techniques can be employed to significantly improve the Signal to Noise Ratio (SNR). This paper presents a study in a commercial LPBF system using an accelerometer to measure part vibration and quantify recoil force in the frequency domain. Modal analysis is used in this study by exciting parts with a laser at resonance to calculate the recoil force. This approach is used to measure the recoil force for various ranges of process parameters to evaluate their relationship with recoil pressure. Finally, the dependence of the microstructure and melt-pool depth on recoil pressure for typical LPBF of SS304L parts is presented. Experimental Approach The experiments in this paper are conducted using a commercial LPBF machine (AM250, Renishaw). This machine stabilizes the melt pool using an Acousto-Optic Modulator (AOM) to pulse the laser. During processing, the laser is pulsed for duration $\tau_{\text {pulse }} \sim 85 \mu$ s while being held stationary at a point. At the conclusion of the pulse, galvo scanners move the beam along the scan path by a point distance, $P D^{27,28}$. The point distance and pulse duration can both be adjusted to provide an equivalent velocity, $V=P D / \tau_{\text {pulse }}$. Adjusting the pulse length corresponds to specifying the pulse repetition frequency (PRF) of the laser modulation, $1 / \tau_{\text {pulse }}$, and can be adjusted from $1-25 \mathrm{kHz}$ with $\tau_{\text {pulse }}$ adjustable in $10 \mu \mathrm{s}$ increments. Figure 1 shows a part being excited by the laser. In the LPBF process, the laser energy is absorbed by the layer of unfused powder on top of the part. The powder is melted and then vaporized. The metallic vapor exerts a recoil pressure on the melt pool, deforming it and producing a net force normal to the surface. In addition to the vaporized metal, particles can be entrained by the local pressure field and ejected away from the melt pool. This is depicted in Fig. $1 \mathrm{~b}$.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_4726529c9ddd3a76690dg-03} Figure 1: Illustrations of (a) laser excitation of tuning fork with accelerometer (Accel) mounted on tuning fork prong, (b) laser interaction with powder on top of tuning fork during laser excitation, and (c) example FRFs and mode shapes. The experiments conducted in this paper use 304L stainless steel powder. Tuning forks are printed directly on the build plate. After printing, the unfused powder is removed from the chamber and an accelerometer is fixed to the tuning forks as illustrated in Fig. 1a and shown in Fig. 2. Experiments show that the powder ordinarily surrounding the part increases structural damping by a factor of 14 , which would significantly lower the sensitivity of the experiment. After fixing the accelerometer to the tuning fork with superglue, a new $50 \mu \mathrm{m}$ thick layer of powder is placed on the top surface of the part. The force generated by the laser interaction at the melt pool produces a strong acceleration response when the part is forced at resonance. This requires both the force and the accelerometer to be coupled to a common resonant mode. To accomplish this, the tuning forks are printed at $60^{\circ}$ relative to horizontal so the laser would excite the bending modes and the parts could be printed without support structures. The force/acceleration coupling of the tuning forks was simulated using ANSYS as shown Fig. 1c and is quantified by the Frequency Response Function (FRF) \begin{equation*} F R F(f)=a(f) / F(f) \tag{1} \end{equation*} where $f$ is the frequency, $a$ is the part acceleration, and $F$ is the force applied to the part. The tuning fork modes in Figure 1c were determined using ANSYS. The accelerometer mass was not included in the ANSYS simulations. Experimentally, the force acting on the part consists of all of the melt pool forces; including capillary (i.e., surface tension), thermo-capillary (i.e., Marangoni), and recoil ${ }^{5,29,30}$. However, as discussed earlier, the recoil force magnitude is expected to dominate those of the other forces. The FRF of each tuning fork was measured experimentally with a modal impact test by striking each prong with an impact hammer and measuring the corresponding acceleration. The impact hammer strikes the same surface that is irradiated by the laser and as normal to the surface as possible (see Fig. 1a). This test occurs with the build plate inside the LPBF chamber. Powder is than added to the top surface of part, the chamber is evacuated and back filled with Argon, and the acceleration measured while the part is scanned by the laser with the accelerometer in the same position. After the test, the FRF was measured again to ensure that any changes resulting from the laser interaction (e.g., additional mass fused to the tip of the tuning fork) are negligible. Multiple tuning forks are fabricated in order to have resonant frequencies spanning a wide range of laser PRFs. Because the FRF of the individual parts are known (after modal impact hammer testing), the PRF used to excite an individual tuning fork is adjusted to match the tuning fork's resonant frequency. Figure 2 shows a photograph of 40 tuning forks, 12 of which used in the experiments. During the experiment, the accelerometer remained in the same location during the laser excitation and the impact test afterwards. Since the location of the accelerometer did not change during the test, the relative effect of the mass loading is effectively cancelled out. The tuning forks are printed using $P=175 \mathrm{~W}, V=0.8 \mathrm{~m} / \mathrm{s}$, exposure time of $75 \mu \mathrm{s}$, hatch spacing of $85 \mu \mathrm{m}$, and $P D=60 \mu \mathrm{m}$. The resonant frequencies of the 12 turning forks are given in Table I of the Methods section. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_4726529c9ddd3a76690dg-04} \end{center} Figure 2: Tuning fork build with arrows indicating beginning and ending tuning forks for each row, where tuning fork numbers linearly increment. Tuning forks used in experiments are tabulated in Table I in Methods section. The laser power modulation in the AM250 does not produce an ideal rectangular wave. Figure 3a shows the response from a photodiode exposed to scattered laser radiation. The measured laser/AOM response has rise and fall times of $\sim 10 \mu \mathrm{s}$. In the experiment shown in Fig. 3a, the laser is scanned over an alumina disk using $\tau_{\text {Pulse }}=100 \mu \mathrm{s}$. Between pulses, there is a delay time of $\tau_{\text {Delay }}=10 \mu \mathrm{s}$. The duty cycle is $1-$ $\tau_{\text {Delay }} / \tau_{\text {Pulse. }}$. The figure also shows that at $t=310 \mu$ s the effect of the laser as it reverses its travel as part of the raster scan process (scan path illustrated in the inset). This introduces a slightly longer delay ( $\tau_{\text {Delay+Corner }}$ $\sim 20 \mu \mathrm{s}$ ) before the next pulse. The variable $\tau_{\text {Delay }}$ is a function of the point distance but is constant for $\mathrm{PD}<$ $60 \mu \mathrm{m}$, while $\tau_{\text {Delay+Corner }}$ is a function of point distance and hatch spacing. Both $\tau_{\text {Delay }}$ and $\tau_{\text {Delay+Corner }}$ are kept constant in this paper. The addition of the intermittent delay associated with cornering introduces a phase delay in the frequency domain. Figure $3 \mathrm{~b}$ shows the Fourier transform of the measured laser/AOM response from a single line with and without cornering. The fundamental frequency without cornering occurs at $f_{0}=$ $10 \mathrm{kHz}$ with harmonics at integer multiples of the fundamental frequency (red curve). However, the Fourier transform of a waveform including raster scanning (i.e., with cornering) shows a shift in the fundamental frequency and a slight (0.5\%) decrease in magnitude. This energy loss is shifted to side bands (blue curve).\\ \includegraphics[max width=\textwidth, center]{2024_03_10_4726529c9ddd3a76690dg-04(1)} Figure 3: (a) Normalized experimental photodiode waveform with inset showing raster scan path for $\tau_{\text {Pulse }}$ $=100 \mu \mathrm{s}$ and (b) corresponding signal in the frequency domain with and without cornering. A range of laser powers, pulse durations, and scan paths were recorded. As Fig. 3b shows, much of the laser energy is outside of the measurement range. Assuming that the recoil force has the same frequency content as the laser/AOM response, the measured recoil force at the fundamental frequency can be scaled by the ratio of the laser energy at the fundamental frequency to the total laser energy. This fraction varies\\ with the duty cycle and the scaling is described in the Methods section. Further, for the experiments conducted in this study, to prevent aliasing of the PRF peak magnitude, the frequency resolution, $d f$, is selected such that it is an integer multiple of the PRF, i.e., $\operatorname{rem}(\mathrm{PRF} / \mathrm{d} f)=0$. \section*{Results and Discussion} Single Line Scan Path without Powder. The simplest case occurs when no powder, i.e., $h=0$ $\mu \mathrm{m}$, is added to the exposed surface of the tuning fork and the scan path consists of a single line to avoid cornering. A laser PRF of $f_{0}=10 \mathrm{kHz}$ and a point distance of $P D=1 \mu \mathrm{m}$, corresponding to a scan speed of $V=10 \mathrm{~mm} / \mathrm{s}$, are used. This scan speed is well below the range typical for 304L stainless steel ${ }^{13,31}$; however, it was selected to gather sufficient data when processing a single line (i.e., the laser did not need to reverse its direction of travel). Figure 4 shows experimental results for Tuning Fork \#16 using various laser powers. Because of the atypically high laser fluence, the FRF was measured after each experiment to determine if the sample was physically modified (i.e., its frequency response changed). Figure 4a shows that the resonant frequency changed over a range of only $8.7 \mathrm{~Hz}$ during the five experiments. Further, the peak response at $f_{r}=10.03 \mathrm{kHz}$ is approximately $18 \mathrm{~dB}$ larger than the next highest peak, demonstrating that most of the energy is contained at this frequency. The measured acceleration during laser excitation is shown in Fig. 4b. While there is energy at other frequencies, this shows a very sharp peak at the excitation frequency which matched the resonant frequency of the part. The value of the acceleration also scales with the laser power, whereas the energy at other frequencies does not. This is due to the fact that the laser is only providing energy at $10 \mathrm{kHz}$ and the subsequent harmonics; therefore, the only portion of the acceleration that should be changing with laser power is at $10 \mathrm{kHz}$. Figure 4c shows the force response calculated by solving Eq. 1 for $F(f)$ using the measured FRF and acceleration. A Noise Equivalent Force (NEF), the ratio of the measured accelerometer noise to the difference between the FRF signal and the measured FRF noise as described in the Methods section, is used to calculate an equivalent Signal to Noise Ratio (SNR). Figure $4 \mathrm{c}$ shows that this is much higher near the part resonance and supports the confidence of the magnitude of the force at the laser PRF (more than five orders of magnitude greater SNR at $f=10 \mathrm{kHz}$ than $f=5.25 \mathrm{kHz}$ ). \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_4726529c9ddd3a76690dg-06} \end{center} Figure 4: Results for Tuning Fork \#16 (a) measured FRFs for various laser powers, (b) measured acceleration spectrum with inset showing single line scanning strategy schematic, and (c) calculated forcing spectrum with SNR spectrum (gray line). $\mathrm{V}=10 \mathrm{~mm} / \mathrm{s}$. To examine the part independence of this result, the experiment is repeated with different tuning forks using the same laser powers. The different tuning forks have slightly different FRFs with resonant frequencies listed in Table I in the Methods section. Figure 5 shows the total recoil force as a function of laser power after correcting for the fraction of the force at the fundamental PRF frequency. The corrective measure for the fraction of force at the PRF frequency is shown in the Methods section in Figure 12. Figure 5 shows that the recoil force scales with the laser power with good agreement across multiple specimens. The increase in recoil force is due to the fact that as the laser power increases a greater amount of material will be vaporized. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_4726529c9ddd3a76690dg-07} \end{center} Figure 5: Recoil force versus applied laser power for single line scanning strategies using Tuning Forks \#15, \#16, \#17, and \#20. Rasters with Powder. The slow scan speed and the lack of powder in Figs. 4 and 5 does not correspond to typical LPBF processing conditions. Figure 6 shows the recoil force for a range of characteristic process parameters for 304L stainless steel ${ }^{34}$. Powder was spread across the surface of the tuning forks using two $50 \mu \mathrm{m}$ thick metal shims to create a uniform layer. The laser was rastered with scan speeds varied by changing the point distance. The higher scan speeds, compared to that used in the previous section, required rastering the laser; therefore, the recoil force was corrected using the measurement at the fundamental frequency to account for the delay time introduced by cornering. The force correction for the additional delay time is shown in the Methods section in Figure 12. Figure 6a shows the variance in the measured recoil force with respect to scan speed and laser power when the PRF is maintained at $6.25 \mathrm{kHz}$. The force magnitude is inversely proportional to scan speed, which agrees with the results in Figs. 4 and 5 where an order of magnitude slower scan speed produced recoil forces that were an order of magnitude higher. It is significant to note that the recoil force does not depend appreciably on the PRF. This is illustrated in Fig. 6b where the scan speed is constant while varying laser PRF and laser power and demonstrates that when the PRF is varied but the scan speed remains constant the material vaporization remains constant in the process parameter range considered in this study.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_4726529c9ddd3a76690dg-07(1)} Figure 6: (a) Recoil force as function of laser power and scan speed for constant PRF and (b) recoil force as function of applied laser power for constant scan speed. Uncertainty is detailed in Methods section. Figure 7 shows the data in Figs. 4-6 replotted as a function of the linear energy data, $P / V$. Single line scans at slow scan speeds with powder are also included in the figure. There is minimal recoil force at very low linear energy densities (notably, the data between $P / V=2$ and $5 \mathrm{~J} / \mathrm{mm}$ is generated using a laser power of $P=40 \mathrm{~W}$ ). However, lager linear energy densities, $P / V>9.2 \mathrm{~J} / \mathrm{mm}$, produce a significantly greater recoil force. This is consistent with models of the LPBF process in Trapp et $\mathrm{al} .^{3}$, predicting that the greater\\ temperatures produced by higher linear energy densities increase the vaporization rate. The greater vaporization rate produces a higher recoil pressure, forming a cavity which traps more laser energy to further increase the absorptivity of the melt pool. This positive feedback on the recoil pressure leads to formation of keyholes. In general, the figure shows that the addition of powder increases the recoil force by a factor of 1.33 from the case without powder. This can be attributed to a greater absorptivity of the loose powder bed and the fact that isolated powder particles are more readily vaporized because of reduced thermal conductance to surrounding material.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_4726529c9ddd3a76690dg-08} Figure 7: (a) Recoil force as function of linear energy density for both powder and no powder and (b) recoil force magnitude comparison for both powder and no powder. Measurements of Melt Pool after Solidification. The recoil force significantly affects the melt pool morphology. Figure 8 shows melt pool metallographic micrographs for different process parameters obtained from an auxiliary set of experiments (different substrates but the same processing conditions as the samples in Figs. 2-7, see Methods section). The melt pool depth, $\delta$, and half-width, $w / 2$, are defined in the close up of the metallograph for $P=200 \mathrm{~W}$ and $V=200 \mathrm{~mm} / \mathrm{s}$ in Fig. 8. As expected, the melt pool width and depth increase with increasing laser powers and decrease with increasing scan speed. Most significantly, gas porosity can be seen with lower scan speeds. These are plotted as a function of fluence in Fig. 9. It is interesting to note that the melt pool dimensions produced in experiments with and without powder are linearly related. This is plotted in the insets of Fig. 9 where the melt pool depth for experiments with powder is 1.11 times the melt pool depth for experiments without powder, and the melt pool width for experiments with powder is 1.12 times the melt pool width for experiments without powder. This agrees with the increased recoil forces measured for experiments with powder. The results indicate that increasing melt pool dimensions without keyholing or significant recoil pressure for experiments with powder can be attributed to increased absorptance of the powder bed, which leads to greater heating, and thus size, of the melt pool. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_4726529c9ddd3a76690dg-09(1)} \end{center} Figure 8: Sample micrographs for different laser powers, scan speeds, and PRFs with melt pool dimensions annotated in side picture that is portion of melt pool indicated by dashed box.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_4726529c9ddd3a76690dg-09} Figure 9: Melt pool (a) depth and (b) width as function of laser fluence for experiments with powder and without powder. Insets show melt pool dimensions for experiments with powder versus experiments without powder. The melt pool aspect ratio (AR), $\delta / w$, has been shown to be correlated with different melting modes ${ }^{1,33}$. Specifically, Qi et al. ${ }^{33}$ gives ranges for the conduction, transition, and keyhole modes of $A R \leq 0.5,0.5<$ $A R<1.1$, and $1.1 \leq A R$, respectively. Figure 10 shows the measured aspect ratio as a function of the measured recoil forces. Vertical dashed lines show the ranges of recoil forces producing each mode. Again, this agrees with the metallography in Fig. 8 (close-ups shown in the insets of Fig. 10) showing the gas porosity resulting for slow scan speeds and void size scaling with laser power. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_4726529c9ddd3a76690dg-10} \end{center} Figure 10: Melt pool aspect ratio as function of recoil force with horizontal lines indicating dominant melting modes and vertical lines representing recoil force magnitudes at melting mode boundaries with insets showing micrographs that were collected at $V=120 \mathrm{~mm} / \mathrm{s}$ and $P R F=2 \mathrm{kHz}$. None of the process parameters produced $A R<0.5$, which corresponds to conduction mode. For process parameters with $A R \sim 0.5$, the recoil force was measured to be less than $0.5 \mathrm{mN}$. This appears to be a threshold between conduction and transition melting modes, and recoil forces between 0.5 and $8 \mathrm{mN}$ produced aspect ratios in the range between 0.5 and 1.1 ; therefore, these forces indicated the process was in the transition region. Beyond $10 \mathrm{mN}$, the melting mode is in the keyhole region. It is significant to note that the presence of powder during processing does not significantly appear to change these thresholds. \section*{Summary and Conclusions} This paper demonstrated a method to measure the recoil force produced by the recoil pressure in LPBF using a vibration response approach. While subject to well bounded error, the results correlate well with microstructure analysis. The following conclusions can be drawn from the study: \begin{itemize} \item Recoil force is proportionate to the laser fluence past a threshold where the powder begins to be melted. \item The recoil force increases by $33 \%$ with the addition of a $50 \mu$ m layer of powder on the part surface compared to a part surface without powder. \item Melt pool depth and width scale with laser fluence for experiments both with and without powder. \item The process is hypothesized to operate in the conduction, transition, and keyholing modes for recoil force values less than $0.5 \mathrm{mN}$, between 0.5 and $8 \mathrm{mN}$, and greater than $10 \mathrm{mN}$, respectively. \end{itemize} \section*{Methods} Equipment. The accelerometer used in this study was model 352C34 from PCB Piezotronics. The accelerometer bandwidth was $0.005-12 \mathrm{kHz}$. The impact hammer used to measure the sample FRFs was model 086E80 from PCB Piezotronics. This impact hammer is rated to typically excite frequencies up to $12 \mathrm{kHz}$ given a metal tip. The coherence spectrum to support this is shown in Figure 11, which was the coherence plot for the response from Tuning Fork \#15. The coherence response has notches which correlate to the anti-resonances in the FRF response. Aside from the anti-resonances, the magnitude of the coherence is above 0.95 , indicating good correlation between the impact and the resulting acceleration.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_4726529c9ddd3a76690dg-11} Figure 11: (a) Coherence spectrum and (b) FRF for tuning fork 15. The photodiode used to capture the waveforms was model PDA100A2 from Thorlabs. The bandwidth of the photodiode was $11 \mathrm{MHz}$. Tuning Fork Dimensions. The prong lengths and resonant frequencies of the samples used in the experiments are tabulated in Table I. Table I: Tuning forks used in experiments, resonant frequencies, and prong lengths. \begin{center} \begin{tabular}{cccc} \hline Tuning Fork & Resonant Frequency $[\mathrm{kHz}]$ & $L[\mathrm{~mm}]$ & Mode Number \\ \hline 15 & 10.05 & 35 & 7 \\ 16 & 10.03 & 36 & 8 \\ 17 & 9.930 & 37 & 12 \\ 20 & 9.800 & 41 & 12 \\ 27 & 6.300 & 49 & 11 \\ 29 & 6.300 & 51 & 10 \\ 30 & 6.175 & 52 & 10 \\ 31 & 11.02 & 53 & 14 \\ 32 & 5.200 & 54 & 11 \\ 33 & 5.490 & 56 & 9 \\ 34 & 6.256 & 57 & 12 \\ 39 & 2.050 & 62 & 7 \\ \end{tabular} \end{center} Materials. The material used in this study was 304L stainless steel purchased from LPW Technology. Recoil Force Magnitude Correction. For most of the samples in Table I, the higher harmonics lie outside of the accelerometer bandwidth. The total energy can be inferred from the energy in the first harmonic assuming that the force response scales with the laser energy as measured by a photodiode\\ response. This gives the fractional energy in the first harmonic a dependence on the duty cycle of the laser's pulse train. The fractional energy was calculated by taking the ratio of the magnitude at the fundamental frequency to the rms magnitude of the input signal i.e., $M_{\text {Fund }} / M_{\text {Input. }}$. Figure 12 shows the fraction of energy in the first harmonic relative to the total energy of the measured photodiode signal for various laser duty cycles. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_4726529c9ddd3a76690dg-12} \end{center} Figure 12: Percentage of energy located in fundamental frequency for various duty cycles and both straight (red) and raster (blue) paths. Using the data in Figure 12, the total estimated recoil force is \begin{equation*} F=\frac{a_{f_{1}}(f)}{F R F_{f_{1}}(f)} \frac{M_{\text {Input }}}{M_{\text {Fund }}} \tag{2} \end{equation*} where $a$ is the measured tuning fork acceleration magnitude during the laser excitation at the first harmonic, and FRF is the experimentally measured tuning fork FRF magnitude at the first harmonic. Uncertainty Calculation. The uncertainty in the recoil force measurements was defined using the following propagation of uncertainty \begin{equation*} F_{\text {Unc }}(f)=|F| \sqrt{\left(\frac{E_{\text {Accel }}(f)}{A(f)}\right)^{2}+\left(\frac{E_{\text {Force }}(f)}{F(f)}\right)^{2}} \tag{3} \end{equation*} where $E_{\text {accel }}$ and $E_{\text {Force }}$ are the margins of error for a 95\% confidence interval, defined below, for the measured FRFs and how the acceleration spectrums were processed. The margin of error is defined as \begin{equation*} E=Z_{\alpha / 2} \frac{\sigma}{\sqrt{N}}=1.96 \frac{\sigma}{\sqrt{N}} \tag{4} \end{equation*} where $Z$ is the normal distribution indexed at the confidence level of interest, $\sigma$ is the standard deviation of the FRFs, and $N$ is the number of FRFs taken. Auxiliary Experimental Procedure for Melt Pool Dimensions. Rectangular prisms were printed of dimensions $6.35 \times 3.85 \times 5 \mathrm{~mm}$. The process parameters used to print the specimens were $P=200$ $\mathrm{W}, V=0.8 \mathrm{~m} / \mathrm{s}$, exposure time of $75 \mu \mathrm{s}$, hatch spacing of $85 \mu \mathrm{m}$, and $P D=60 \mu \mathrm{m}$. After they were printed,\\ their top surfaces were scanned with the same laser powers, scan speeds, and PRFs as the ones seen in Figures 6-8a. After scanning, the specimens were removed from the build plate, mounted using a Simplimet 1000, polished using an AutoMet 250 Grinder-Polisher, and then subsequently etched using a 40/60 nitric acid solution. The melt pool dimensions were measured using a Hirox KH-8700 digital microscope. \section*{References} \begin{enumerate} \item King, W. E., Barth, H. D., Castillo, V. M., Gallegos, G. F., Gibbs, J. W., Hahn, D. E., Kamath, C. \& Rubenchik, A. M. Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J. Mater. Process. Technol. 214, 2915-2925 (2014). \item Madison, J. D. \& Aagesen, L. K. Quantitative characterization of porosity in laser welds of stainless steel. Scr. Mater. 67, 783-786 (2012). \item Trapp, J., Rubenchik, A. M., Guss, G. \& Matthews, M. J. In situ absorptivity measurements of metallic powders during laser powder-bed fusion additive manufacturing. Appl. Mater. Today 9, 341-349 (2017). \item Rai, R., Elmer, J. W., Palmer, T. A. \& Debroy, T. Heat transfer and fluid flow during keyhole mode laser welding of tantalum, Ti-6Al-4V, 304L stainless steel and vanadium. J. Phys. D. Appl. Phys. 40, 5753-5766 (2007). \item Mazumder, J., Ki, H. \& Mohanty, P. S. Role of recoil pressure, multiple reflections, and free surface evolution during laser keyhole welding. ICALEO 2002 - 21st Int. Congr. Appl. Laser Electro-Optics, Congr. Proc. 33, (2002). \item Chen, Q., Guillemot, G., Gandin, C. A. \& Bellet, M. Numerical modelling of the impact of energy distribution and Marangoni surface tension on track shape in selective laser melting of ceramic material. Addit. Manuf. 21, 713-723 (2018). \item Wu, Y. C., San, C., Chang, C., Lin, H., Marwan, R., Baba, S. \& Hwang, W. Numerical modeling of melt-pool behavior in selective laser melting with random powder distribution and experimental validation. J. Mater. Process. Technol. 254, 72-78 (2018). \item Zhang, W. Probing Heat Transfer, Fluid Flow and Microstructural Evolution During Fusion Welding of Alloys. PhD Diss. 312 (2004). \item Panwisawas, C., Qiu, C. L., Sovani, Y., Brooks, J. W., Attallah, M. M. \& Basoalto, H. C. On the role of thermal fluid dynamics into the evolution of porosity during selective laser melting. Scr. Mater. 105, 14-17 (2015). \item Tang, C., Le, K. Q. \& Wong, C. H. Physics of humping formation in laser powder bed fusion. Int. J. Heat Mass Transf. 149, (2020). \item Xiao, B. \& Zhang, Y. Marangoni and Buoyancy effects on direct metal laser sintering with a moving laser beam. Numer. Heat Transf. Part A Appl. 51, 715-733 (2007). \item Heeling, T., Cloots, M. \& Wegener, K. Melt pool simulation for the evaluation of process parameters in selective laser melting. Addit. Manuf. 14, 116-125 (2017). \item Lough, C. S., Wang, X., Smith, C. C., Landers, R. G., Bristow, D. A., Drallmeier, J. A., Brown, B. \& Kinzel, E. C. Correlation of SWIR imaging with LPBF 304 L stainless steel part properties. Addit. Manuf. 35, 101359 (2020). \item Aggarwal, A., Patel, S. \& Kumar, A. Selective laser melting of 316L stainless steel: physics of melting mode transition and its influence on microstructural and mechanical behavior. Jom 71, 1105-1116 (2019). \item Sharma, S., Mandal, V., Ramakrishna, S. A. \& Ramkumar, J. Numerical simulation of melt pool oscillations and protuberance in pulsed laser micro melting of SS304 for surface texturing applications. J. Manuf. Process. 39, 282-294 (2019). \item Khairallah, S. A., Anderson, A. T., Rubenchik, A. \& King, W. E. Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater. 108, 36-45 (2016). \item Le, K. Q., Tang, C. \& Wong, C. H. On the study of keyhole-mode melting in selective laser melting process. Int. J. Therm. Sci. 145, (2019). \item Zhang, M. J., Chen, G. Y., Zhou, Y., Li, S. C. \& Deng, H. Observation of spatter formation mechanisms in high-power fiber laser welding of thick plate. Appl. Surf. Sci. 280, 868-875 (2013). \item Taheri Andani, M., Dehghani, R., Karamooz-Ravari, M. R., Mirzaeifar, R. \& Ni, J. Spatter formation in selective laser melting process using multi-laser technology. Mater. Des. 131, 460-469 (2017). \item Ly, S., Rubenchik, A. M., Khairallah, S. A., Guss, G. \& Matthews, M. J. Metal vapor micro-jet controls material redistribution in laser powder bed fusion additive manufacturing. Sci. Rep. 7, 1-12 (2017). \item Zhao, C., Fezzaa, K., Cunningham, R. W., Wen, H., Carlo, F. D., Chen. L., Rollett, A. D. \& Sun, T. Real-time monitoring of laser powder bed fusion process using high-speed X-ray imaging and diffraction. Sci. Rep. 7, 1-11 (2017). \item Zhang, Y., Fuh, J. Y. H., Ye, D. \& Hong, G. S. In-situ monitoring of laser-based PBF via off-axis vision and image processing approaches. Addit. Manuf. 25, 263-274 (2019). \item Taheri Andani, M., Dehghani, R., Karamooz-Ravari, M. R., Mirzaeifar, R. \& Ni, J. A study on the effect of energy input on spatter particles creation during selective laser melting process. Addit. Manuf. 20, 33-43 (2018). \item Guo, Q., Zhao, C., Escano, L. I., Young, Z., Xiong, L., Fezzaa, K., Everhart, W., Brown, B., Sun, T. \& Chen. L. Transient dynamics of powder spattering in laser powder bed fusion additive manufacturing process revealed by in-situ high-speed high-energy x-ray imaging. Acta Mater. 151, 169-180 (2018). \item Zhao, C., Guo, Q., Li, X., Parab, N., Fezzaa, K., Tan, W., Chen, L \& Sun, T. Bulk-explosion-induced metal spattering during laser processing. Phys. Rev. X 9, 21052 (2019). \item Yin, J., Wang, D., Yang, L., Wei, H., Dong, P., Ke, L., Wang, G., Zhu, H. \& Zeng, X. Correlation between forming quality and spatter dynamics in laser powder bed fusion. Addit. Manuf. 31, 100958 (2019). \item Fischer, P., Leber, H., Romano, V., Weber, H. P., Karapatis, N. P., Andre, C. \& Glardon, R. Microstructure of near-infrared pulsed laser sintered titanium samples. Appl. Phys. A Mater. Sci. Process. 78, 1219-1227 (2004). \item Fischer, P., Romano, V., Weber, H. P., Karapatis, N. P., Boillat, E. \& Glardon, R. Sintering of commercially pure titanium powder with a Nd:YAG laser source. Acta Mater. 51, 1651-1662 (2003). \item Qiu, C., Panwisawas, C., Ward, M., Basoalto, H. C., Brooks, J. W. \& Attallah, M. M. On the role of melt flow into the surface structure and porosity development during selective laser melting. Acta Mater. 96, 72-79 (2015). \item Shrestha, S., Rauniyar, S. \& Chou, K. Thermo-fluid modeling of selective laser melting: single-track formation incorporating metallic powder. J. Mater. Eng. Perform. 28, 611-619 (2019). \item West, B. M., Capps, N. E., Urban, J. S., Pribe, J. D., Hartwig, T. J., Lunn, T. D., Brown, B., Bristow, D. A., Landers, R. G. \& Kinzel, E. C. Modal analysis of metal additive manufactured parts. Manuf. Lett. 13, 30-33 (2017). \item Sutton, A. T., Kriewall, C. S., Leu, M. C., Newkirk, J. W. \& Brown, B. Characterization of laser spatter and condensate generated during the selective laser melting of 304L stainless steel powder. Addit. Manuf. 31. (2020). \item Qi, T., Zhu, H., Zhang, H., Yin, J., Ke, L. \& Zeng, X. Selective laser melting of Al7050 powder: Melting mode transition and comparison of the characteristics between the keyhole and conduction mode. Mater. Des. 135, 257-266 (2017). \item Lough, C. S., Wang, X., Smith, C. C., Landers, R. G., Bristow, D. A., Drallmeier, J. A., Brown, B., \& Kinzel, E. C. Correlation of SWIR imaging with LBPF 304L stainless steel part properties. Addit. Manuf. 35. (2020). \end{enumerate} \section*{Acknowledgements} This work was funded by Honeywell Federal Manufacturing \& Technologies under Contract No. DENA0002839 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. \end{document} \documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[version=4]{mhchem} \usepackage{stmaryrd} \usepackage{hyperref} \hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,} \urlstyle{same} \usepackage{graphicx} \usepackage[export]{adjustbox} \graphicspath{ {./images/} } \title{Single-track investigation of IN738LC superalloy fabricated by laser powder bed fusion: Track morphology, bead characteristics and part quality } \author{Chuan Guo ${ }^{\text {a,b,c }}$, Zhen Xu ${ }^{\text {a,b }}$, Yang Zhou ${ }^{\text {a,b }}$, Shi Shi ${ }^{\text {d }}$, Gan Li ${ }^{\text {a,b }}$, Hongxing Lu ${ }^{\text {a,b }}$, Qiang Zhu ${ }^{\text {a, b, *, }}$\\ R. Mark Ward ${ }^{\mathrm{C}, * *}$\\ a Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China\\ ${ }^{\mathrm{b}}$ Shenzhen Key Laboratory for Additive Manufacturing of High-Performance Materials, Shenzhen 518055, PR China\\ c School of Metallurgy and Materials, University of Birmingham, Edgbaston, Birmingham B152TT, UK\\ ${ }^{\mathrm{d}}$ College of Civil and Transportation Engineering, Shenzhen University, Shenzhen, 518060 Guangdong, PR China} \date{} %New command to display footnote whose markers will always be hidden \let\svthefootnote\thefootnote \newcommand\blfootnotetext[1]{% \let\thefootnote\relax\footnote{#1}% \addtocounter{footnote}{-1}% \let\thefootnote\svthefootnote% } %Overriding the \footnotetext command to hide the marker if its value is `0` \let\svfootnotetext\footnotetext \renewcommand\footnotetext[2][?]{% \if\relax#1\relax% \ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else% \if?#1\ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else\svfootnotetext[#1]{#2}\fi% \fi } \begin{document} \maketitle \section*{A R T I C L E I N F O} Associate Editor: M. Merklein \section*{Keywords:} Single-track experiment Laser powder bed fusion Track morphology Bead characteristics Part quality \begin{abstract} A B S T R A C T Single-track experiments were performed to investigate how the scan speed and the laser power affected the behavior of the single tracks during laser powder bed fusion, including the track stability, the melt pool dimension and the bead mode, using the nickel-based superalloy IN738LC. The processing parameters had an evident effect on the track morphology and the bead features in the experimental conditions investigated. The balling phenomenon was studied by a competitive model between the spread and the solidification of droplets. The analysis and experimental results clearly demonstrated that the track lost its stability when the droplets solidified before they spread out on the substrate with a contact angle greater than $90^{\circ}$. The keyhole mode was investigated by establishing the relationship between the normalized enthalpy and the normalized bead depth. The conduction mode would convert to the keyhole mode as normalized enthalpy was greater than $\sim 50$. Finally, bulk samples were built with the same parameters as the single-track testing. It can be seen that the parts with high porosity appeared at both low and high energy input densities due to the un-melted powders and the keyhole pores, respectively. \end{abstract} \section*{1. Introduction} Additive manufacturing (AM) has become an advanced manufacturing technology, attracting increasing attention from both enterprise and educational circles. Laser powder bed fusion (LPBF), also known as selective laser melting (SLM), is the most widely used technology in the metallic additive manufacturing process, where a component with complex geometry can be nearly net-shaped formed using metallic powders in a layer by layer manner. The process of LPBF is schematically illustrated in Fig. 1(a). A 3D CAD model of the objective is prepared and sliced into a sequence of $2 \mathrm{D}$ profiles with a certain thickness, which acts as the source file input into the computer control system. A laser beam with high scan speeds passes through a beam expander, a scanning galvanometer and lenses, and irradiates on the powder bed selectively according to the current slice of the input 3D CAD model. Subsequently, the powders melt to form a strong metallurgical bond within a layer during a rapid cooling process. After the current layer is finished, the building station piston drives the substrate to lower down by the thickness of a layer in the building chamber. Simultaneously, the powder bed in the powder supply chamber rises a certain height, and another layer of powder is added to the building chamber with a recoater. This process is repeated until the whole part is completed. The whole fabrication work is conducted in an argon-filled atmosphere. $\mathrm{Ni}$-based superalloys are widely used in the energy, aerospace and automobile industries since they have excellent creep property and oxidation resistance at high temperatures. Inconel 738LC (IN738LC) is one of the most capable superalloys to be used for turbine blades, discs and other applications in the aero-engine system. It is primarily strengthened by $\gamma^{\prime}$ precipitates with $\mathrm{L1}_{2}$ crystal structure and $\mathrm{Ni}_{3}(\mathrm{Al}, \mathrm{Ti})$ basic composition. However, a relatively large amount of $\mathrm{Al}$ and $\mathrm{Ti}$ $(\mathrm{Al}+\mathrm{Ti}>6 \%)$ in this alloy indicates that it is difficult to be welded and LPBFed due to a strong cracking tendency, as reported by Rickenbacher et al. (2013). Some internal defects like pores and cracks are believed to \footnotetext{\begin{itemize} \item Corresponding author at: Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China. \end{itemize} $* *$ Corresponding author at: School of Metallurgy and Materials, University of Birmingham, Edgbaston, Birmingham B152TT, UK. E-mail addresses: \href{mailto:zhuq@sustech.edu.cn}{zhuq@sustech.edu.cn} (Q. Zhu), \href{mailto:R.M.Ward@bham.ac.uk}{R.M.Ward@bham.ac.uk} (R.M. Ward). } greatly restrict its application in fabricating parts requiring nearly full density and excellent mechanical performance. In order to study the formation mechanism of these defects in the LPBF process, investigation of the solidification behavior and the fluid dynamics of the local melt is highly necessary. Heat transportation phenomena (including heat conduction, convection and radiation), metallurgical phenomena (including melting, solidification, re-melting and re-solidification), laser-matter interaction phenomena (including recoil pressure, vapor and plasma) and melt flowing phenomena (including fluid dynamics and wetting behavior) determine the complexity of the reaction between the powder bed and the laser beam, posing the major hurdles to study the LPBF process. Most researches have focused on the parameter control and the posttreatment, etc., of the IN738LC alloy during LPBF. However, there are very few investigations on the fluid dynamics and the solidification behavior in bulk printed parts of IN738LC. This is mainly because little information can be revealed due to the overlapping between the previously fabricated tracks and layers. In this case, it is even difficult to measure the geometry of the melt pools. Therefore, a single-track experiment method is necessarily applied in order to directly reveal the printing behavior and the reaction between the powder bed and the laser beam. Yadroitsev et al. (2010) investigated the single-track formation using the SS grade $904 \mathrm{~L}$ alloy in the process of LPBF. They remarked that low scan speed led to the instability of the laser track to form irregularities and distortions, and considerably high speed was favorable for the formation of balling. Sadowski et al. (2016) tried to optimize the quality of Inconel 718 in the LPBF process using a single-track method. Laser energy density was used to analyze the effects of scan speed and laser power. The energy density $>0.21 \mathrm{~J} / \mathrm{mm}$ was found to be desired for a continuous and filled track. Mumtaz and Hopkinson (2009) used side and top surfaces' roughness to characterize the quality of the single track of Inconel 625 using LPBF. They reported that both top and side roughness tended to reduce with increasing the laser power. Wang et al. (2012) found 4 different track types associated with different energy inputs, including regularly thin track, regularly thick track, regularly broken track and irregularly pre-balling track in the LPBFed $316 \mathrm{~L}$ stainless steel process. They also suggested that the shape of regular and thin track was considered to be desirable for LPBF fabrication with adequate overlapping referred to the fabrication efficiency. Since the heat history in the bulk sample printing process is complex, the single-track method was also widely used in numerical modeling in some previous studies. Matthews et al. (2016) performed finite element model simulations of Ti6Al4V alloy in a single-track process and found that the melt pools tended to direct vapor backward and normal to the laser scanning direction, which was consistent with observation using high-speed imaging. Gusarov and Smurov (2010) numerically simulated the heat transfer in the interaction region between the laser beam and the powder bed by the proposed model to correlate radiation and heat transfer with the LPBFed single-track method. They remarked that the thermal conductivity and radiative properties of the powders significantly depended on the size distribution of the powders. The relationship between spatter and scan speed in LPBF of Ti6Al4V was established by Qiu et al. (2015) using single-track computational fluid dynamics (CFD) calculation. Higher laser scan speed increased the Marangoni force and the instability of the melt flow, thus enhancing the spatter of the powders. In more recent work of Rubenchik et al. (2018), the linear energy density concept has been extended to include the effects of the thermal diffusivity and enthalpy of the material, helping to normalize the results from a range of materials and increase the predictive power of the criterion for predicting keyhole formation in a single-track thermal model. In the present work, single tracks of IN738LC with different scan speeds and laser powers were used to understand how the processing parameters influence the track morphology, the bead dimension and the bead mode. In addition, bulk samples were built with the same parameters as the single-track testing in order to associate the track behavior with the printed part quality. Results would be helpful in selecting suitable parameters to fabricate not only IN738LC but also other alloys using LPBF. \section*{2. Material and experiment method} \subsection*{2.1. IN738LC powder} The mean size of the gas atomized IN738LC powders from SNDVARY POWDER Co., Lt was $\mathrm{D}_{50}=30.7 \mu \mathrm{m}$. The powder morphology was observed using a scanning electron microscope (ZEISS Merlin SEM), as presented in Fig. 1(b). Table 1 lists the chemical components of the powders. The flowability was measured through the Hall cup technique, and the time for $50 \mathrm{~g}$ powders to flow from the Hall cup was $14.3 \pm 0.5 \mathrm{~s}$. \subsection*{2.2. Experiment setup} The LPBF experiment was performed by a BLT-S200 system with a continuous laser mode. The maximum power could reach $400 \mathrm{~W}$, and the scan speed ranged from $100 \mathrm{~mm} / \mathrm{s}$ to $7000 \mathrm{~mm} / \mathrm{s}$. The size of the substrate was $105 \mathrm{~mm} \times 105 \mathrm{~mm}$, and the capacity of building depth was $200 \mathrm{~mm}$. Since the machine had no function to directly scan single tracks, a block substrate was fabricated firstly in order to hold the single tracks on its top. The block substrates were fabricated as cubes with side length $10 \mathrm{~mm}$, and a single layer with a hatching space of $400 \mu \mathrm{m}$ and a thickness of $30 \mu \mathrm{m}$ was scanned on the top of the block substrates to attain single tracks, as shown in Fig. 2(a). Fig. 2(b) is a schematic diagram of the building part to exhibit that a single layer was deposited. Fig. 2(c) is an example of a printed part, where the bright single tracks can be seen on the top. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-02} \end{center} Fig. 1. (a) Schematic diagram of the LPBF process, (b) SEM image showing the morphology of the powders. Table 1 Chemical components of the IN738LC powders (wt\%). \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline $\mathrm{Ni}$ & $\mathrm{Cr}$ & Co & $\mathrm{Ta}$ & W & $\mathrm{Al}$ & $\mathrm{Ti}$ & $\mathrm{Nb}$ & Mo & B & $\mathrm{Zr}$ & C \\ \hline Bal. & 15.83 & 8.47 & 1.63 & 2.67 & 3.36 & 3.41 & 0.74 & 1.71 & 0.009 & 0.03 & 0.1 \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-03(1)} \end{center} (b)\\ \includegraphics[max width=\textwidth, center]{2024_03_10_b157ebe2add5a8848f75g-03} Fig. 2. (a) Illustration showing the LPBF process to obtain the single tracks, (b) schematic diagram of the block substrate and the single tracks, (c) an example of the printed single tracks. Table 2 presents the details of the parameters for the single-track testing (P1 referred to the sample with the first group of parameters, and so on). All the block substrates were manufactured using the same parameters (scan speed $2000 \mathrm{~mm} / \mathrm{s}$, laser power $250 \mathrm{~W}$, hatching space $50 \mu \mathrm{m}$, layer thickness $30 \mu \mathrm{m}$ ). The $90^{\circ}$ raster scan strategy was used to build them, as shown in Fig. 2(a). Secondly, in order to directly reflect the relationship between the printing quality and the single tracks, bulk cubic samples with side length $10 \mathrm{~mm}$ were fabricated using the same parameters (scan speed and laser power) as the various single tracks. Other parameters used to build the bulk samples were hatching space $50 \mu \mathrm{m}$, layer thickness $30 \mu \mathrm{m}$ and $90^{\circ}$ raster scan strategy. \subsection*{2.3. Analysis procedure} The morphology of the tracks was observed by an Axio Observer 3.0 Optical microscope (OM). The single tracks and the bulk samples were cut vertically to the tracks and parallel to the building direction, respectively, using a wire-electrode cutting machine. The cut sections were hot mounted by conductive resin powders and ground by 400 grit 1500 grit abrasive paper. Finally, they were finely polished in $0.5 \mu \mathrm{m}$ diamond and $0.04 \mu \mathrm{m}$ colloidal silica suspension. All the track sections were etched electrolytically in a $10 \%$ phosphoric acid solution under $4 \mathrm{~V}$ for $10 \mathrm{~s}$ to reveal the melt pools. Dimensions of the melt pools were measured by an Axio Vision SE64 Rel. 4.9 software. The final results of the dimensions were the average by measuring 8 different melt pools with the same parameter. The details of the melt pools were observed using SEM. Porosity measurements were performed by an image threshold method using software Image $\mathrm{J}$ in the bulk samples, and 5 sections were measured to obtain the averages. \section*{3. Results} \subsection*{3.1. Single-track morphology} The morphology of the tracks built with the different parameters on Table 2 Parameters used for the single-track and bulk-sample testing. \begin{center} \begin{tabular}{llllll} \hline & $500 \mathrm{~mm} / \mathrm{s}$ & $1000 \mathrm{~mm} / \mathrm{s}$ & $1500 \mathrm{~mm} / \mathrm{s}$ & $2000 \mathrm{~mm} / \mathrm{s}$ & $2500 \mathrm{~mm} / \mathrm{s}$ \\ \hline $370 \mathrm{~W}$ & P21 & P22 & P23 & P24 & P25 \\ $290 \mathrm{~W}$ & P16 & P17 & P18 & P19 & P20 \\ $210 \mathrm{~W}$ & P11 & P12 & P13 & P14 & P15 \\ $130 \mathrm{~W}$ & P6 & P7 & P8 & P9 & P10 \\ $50 \mathrm{~W}$ & P1 & P2 & P3 & P4 & P5 \\ \hline \end{tabular} \end{center} the block substrates is shown in Fig. 3. According to the morphology, the tracks could be classified into 4 types, i.e., the wide-continuous track (WCT), the narrow-continuous track (NCT), the fluctuating track (FT) and the balling track (BT). The summary of the track types vs. the processing parameters within the current processing conditions investigated is mapped in Fig. 4. The track with a width larger than $200 \mu \mathrm{m}$ was defined as WCT. It exhibited a continuous and straight morphology, i.e., with almost uniform width along the whole scanning direction. At high magnification, as presented in Fig. 5, a clear ripple shape going against the direction of the laser beam was visible. Mumtaz and Hopkinson (2009) suggested that the ripple morphology was primarily attributed to the surface tension exerting a resultant shear force on the melt pool, which was affected by the processing parameters and the atmosphere in the building chamber. The WCT appeared at high laser powers, i.e., $370 \mathrm{~W}$ and $290 \mathrm{~W}$ with low scan speeds, i.e., from $500 \mathrm{~mm} / \mathrm{s}$ to $1500 \mathrm{~mm} / \mathrm{s}$. The NCT covered a large range of the processing parameters in the left top of the track type map in Fig. 4. The width of the track in this type was relatively small $\sim 100 \mu \mathrm{m}$. The track showed a continuous and straight morphology deposited on the block substrate without any ripple trace on the surface. The FT only occurred at the combinations of the laser power of $290 \mathrm{~W}$ and the scan speed of $2500 \mathrm{~mm} / \mathrm{s}$ (P20), the laser power of $210 \mathrm{~W}$ and the scan speed of $1500 \mathrm{~mm} / \mathrm{s}$ (P13). In this type, the track started to fluctuate with a non-uniform width along the whole track length. Discontinuity of the track was also observed occasionally, as shown in Fig. 6. Gunenthiram et al. (2017) remarked that the track lost its stability through the humping phenomenon due to the periodic shrinkage of the track caused by the lateral surface tension of the molten liquid. A very low energy input density (laser power/scan speed), i.e., extremely low laser power and/or extremely high scan speed, was favorable for the formation of BTs, as shown in the right bottom corner of Fig. 4. In this instance, the BT tended to break up into small droplets, leading to a severe discontinuity of the track, as shown in Fig. 3. \subsection*{3.2. Bead morphology} The bead type was classified according to the cross-sections of the tracks, as shown in Fig. 7. The shape, the dimension and the wetting behavior of the beads varied obviously as the different parameters were applied. With the decrease of the laser power and/or the increase of the scan speed, the bead shape changed from a smooth morphology to necking down, balling, and finally, the bead detached from the block\\ \includegraphics[max width=\textwidth, center]{2024_03_10_b157ebe2add5a8848f75g-04(1)} Fig. 3. OM images of the 25 single tracks made by the laser powers of $50 \mathrm{~W}-370 \mathrm{~W}$ and the scan speeds of $500 \mathrm{~mm} / \mathrm{s}-2500 \mathrm{~mm} / \mathrm{s}$, showing the 4 types of tracks, $\mathrm{i}$. e., the wide-continuous track (WCT), the narrow-continuous track (NCT), the fluctuating track (FT) and the balling track (BT). \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-04} \end{center} Fig. 4. Map of the track types vs. the processing parameters. substrate. These beads could be classified into 4 types, i.e., the widekeyhole bead (WKB), the narrow-keyhole bead (NKB), the conduction bead (CB) and the shallow-ball bead (SBB), as shown in Fig. 7. Figs. 8 and 9 summarize the bead type vs. the laser power and the scan speed within the current processing conditions investigated. The WKBs occurred at high laser powers i.e., $210 \mathrm{~W}-370 \mathrm{~W}$ with the minimum scan speed of $500 \mathrm{~mm} / \mathrm{s}$. In this type, the whole melt pool could be separated into 2 parts. The width of the upper part was $\sim 150 \%$ greater than that of the lower part, and the lower part was a keyhole with a relatively deep and narrow morphology, as shown in Fig. 7(a). The NKB was observed at the maximum laser power, i.e., $370 \mathrm{~W}$ with the scan speeds of $1000 \mathrm{~mm} / \mathrm{s}-2000 \mathrm{~mm} / \mathrm{s}$, or when the scan speed was low, i.e., $1000 \mathrm{~mm} / \mathrm{s}$ with the laser powers of $210 \mathrm{~W}-370 \mathrm{~W}$. The bead in this type had a depth similar to that of the WKB and could also be separated into 2 parts, as shown in Fig. 7(b). The difference from the WKB was that the edge of the upper part of the NKB was nearly tangent to the lower part with the top having a width of no more than $150 \%$ of the lower part. The CB appeared when the scan speed and the laser power were combined to give a moderate energy input density, i.e., high laser power with high scan speed or low laser power with low scan speed. The melt pool in the CB type was nearly elliptic with a short longitudinal length and a larger width, as shown in Fig. 7(c). The occurrence of SBB was associated with relatively low energy input density, i.e., low laser power with the combination of high scan speed, as depicted in Fig. 8. Fig. 7(d) shows that the bead in this type had a round shape with a poor wettability with the block substrate. The "ball" touched the block substrate with a relatively small area, resulting in a rather shallow and narrow melt pool. And the bead tended to break away from the block substrate at the laser power of $50 \mathrm{~W}$ and the scan speed of $2500 \mathrm{~mm} / \mathrm{s}$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-05(1)} \end{center} Fig. 5. OM image at high magnification of the WCT (P21) showing the ripple morphology on the surface of the track. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-05} \end{center} Fig. 6. OM image of the FT (P13) showing the humping phenomenon and the discontinuity of the track. \subsection*{3.3. Bead dimension} Fig. 10(a) shows the bead width as a function of the processing parameters. The bead width is the distance between the 2 contact points of the melt pool edge and the block substrate, indicated by the insert picture of Fig. 10(a). It is apparent that the bead width was positively correlated to the laser power and negatively correlated to scan speed. It is worth noting that the bead width was considerably large when the laser powers were $290 \mathrm{~W}$ and $370 \mathrm{~W}$ at the scan speed of $500 \mathrm{~mm} / \mathrm{s}$. This was consistent with the WKB, whose upper part was extremely large in width.\\ The bead depth is the length from the top of the block substrate to the deepest point of the bead. Fig. 10(b) shows that the bead depth increased with the increase of the laser power and decreased with the increase of the scan speed. The bead depth at low scan speed was much larger than that at high scan speed, especially for the moderate laser power $(210 \mathrm{~W}$, 290 W), which was attributed to the keyhole formation in the lower part of the WKB and the NKB in these conditions. The bead height is the length from the top of the block substrate to the top of the bead. Fig. 10(c) suggests that there was no distinct relationship between the bead height and the processing parameters. The contact angle is the average of the 2 angles between the block substrate surface and the bead edge, as indicated by the insert picture of Fig. 10(d). It is evident that the contact angle increased with increasing the scan speed and decreased with increasing the laser power. The contact angles were larger than $90^{\circ}$ at low laser power with the combination of high scan speed, indicating a poor wettability of the bead with the occurrence of the SBB type. It is worthy of note that the maximum contact angle was $180^{\circ}$ at the laser power of $50 \mathrm{~W}$ and the scan speed of $2500 \mathrm{~mm} / \mathrm{s}$, where the bead left from the block substrate. The smallest contact angle was attained at the laser power of $370 \mathrm{~W}$ and the scan speed of $500 \mathrm{~mm} / \mathrm{s}$, and the corresponding value was $\sim 26^{\circ}$. \subsection*{3.4. Porosity of bulk samples} The processing parameters had a great impact on the pore condition in the printed bulk samples, as shown in Fig. 11. The pores with a regularly round shape appeared in the left top corner of the parameter map, i.e., high laser power combined with low scan speed (marked with yellow blocks). It is worth mentioning that the sample at the scan speed of $500 \mathrm{~mm} / \mathrm{s}$ and the laser power of $370 \mathrm{~W}$ failed to be fabricated due to severe warping on the substrate. The maximum porosity was $10.929 \%$ at the scan speed of $500 \mathrm{~mm} / \mathrm{s}$ and the laser power of $290 \mathrm{~W}$ among this condition. Green blocks had marked off the parts of high quality with nearly full density in Fig. 11, which were obtained at relatively moderate energy input densities, i.e., high scan speed combined with high laser power or low scan speed combined with low laser power. More than half the parameter map was occupied by the parts with irregularshaped pores in the right bottom corner (marked with red blocks). In this instance, parts were unable to be built at high scan speeds $(1500 \mathrm{~mm} / \mathrm{s}-2500 \mathrm{~mm} / \mathrm{s})$ with the minimum laser power, i.e., $50 \mathrm{~W}$. Relatively low porosity of $0.103 \%$ was attained at $500 \mathrm{~mm} / \mathrm{s}$ with the combination of $130 \mathrm{~W}$. While the part density at the scan speed of $1000 \mathrm{~mm} / \mathrm{s}$ and the laser power of $50 \mathrm{~W}$ was almost only half $(100 \%$ $45.716 \%=54.284 \%$ ). \section*{4. Discussion} \subsection*{4.1. Effect of parameters on track stability} Track characteristics can reflect the flowing behavior of the melt in the LPBF process, which can directly determine the quality of the printed components. In the current work, the relationship between the track stability and the processing parameters was studied. It is apparent in Fig. 3 that the straight track fluctuated and tended to break into small droplets with the decrease of the laser power and/or the increase of the scan speed. It is described as balling in the LPBF process. Rombouts et al. (2006) thought that there were 2 potential causes for the balling known as the Rayleigh instability and the Marangoni convection regarding the melt flow process. In the Rayleigh instability theory, the melt track is regarded as a liquid cylinder, and the critical condition for the instability is described as the wavelength of the axial harmonic disturbance being larger than the circumference of the cylinder, i.e., $L / W>\pi$, as shown in Fig. 12(a), where $W$ is the diameter, and $L$ is the wavelength. Under this unstable condition, Tian et al. (2017) found that the cylinder would break up into metallic droplets to reduce the surface energy, leading to the balling \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-06} \end{center} Fig. 7. OM images showing the 4 types of beads, namely (a) the wide-keyhole bead (WKB), (b) the narrow-keyhole bead (NKB), (c) the conduction bead (CB) and (d) the shallow-ball bead (SBB). \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-06(1)} \end{center} Fig. 8. OM images of the 25 beads made by the laser powers of $50 \mathrm{~W}-370 \mathrm{~W}$ and the scan speeds of $500 \mathrm{~mm} / \mathrm{s}-2500 \mathrm{~mm} / \mathrm{s}$. phenomenon, as depicted in Fig. 12(b). Rombouts et al. (2006) remarked that increasing the scan speed could increase the length to width ratio of the melt pool, and the trend of the Rayleigh instability was further enhanced. For example, P14 was in the BT type, and its scan speed was higher than that of P13, while P13 was in the FT type. In addition, by comparing P20 (FT, 290 W @ 2500 mm/s) with P15 (BT, $210 \mathrm{~W} @ 2500 \mathrm{~mm} / \mathrm{s})$, it is apparent that decreasing the laser power also favored the formation of the Rayleigh instability. This is ascribed to \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-07(1)} \end{center} Fig. 9. Map of the bead types vs. the processing parameters. the decrease in track width $W$ with decreasing the laser power (Fig. 10 (a)), inducing an increase of $L / W$ and accordingly aggravating the Rayleigh instability. Apart from the Rayleigh instability, Zhou et al. (2015) believed that the Marangoni convection also contributed to the balling phenomenon. The surface tension of a liquid varies with temperature, and if there is a temperature gradient across its surface, the resultant variation in surface tension force will drive the Marangoni convection. Because the spatial derivative of temperature drives this, additive manufacturing processes with their extremely high local energy density can create strong Marangoni flow. Rombouts et al. (2006) reported the direction of the Marangoni convection was from the low surface tension region to the high surface tension region, determined by the gradient of the surface tension to the temperature $d \gamma_{L V} / d T$. Generally, the value of $d \gamma_{L V} / d T$ is negative, implying that high temperature leads to low surface tension. A higher\\ \includegraphics[max width=\textwidth, center]{2024_03_10_b157ebe2add5a8848f75g-07} temperature is normally obtained in the center of the melt pool as a Gaussian-profile laser beam is applied. In this case, the melt will flow from the center to the edge of the melt pool, and the mass transfer of the melt to the neighboring tracks is correspondingly formed in most cases, as reported by Guo et al. (2020). On the contrary, if the Marangoni convection flows reversely, the resultant big agglomeration of the melt leads to an obvious stacking of materials on the melt pool, leading to the balling phenomenon, as depicted in Fig. 13(a). The directional change of the Marangoni flow is crucially caused by the high contents of surface-active elements, which can significantly reduce the surface intension, making $d \gamma_{L V} / d T$ change to a positive value. Li and Gu (2014) showed that the thermal gradient would increase along the building direction when a high scan speed was applied, and Tan et al. (2018) argued that a higher thermal gradient can result in a higher gradient of the surface tension, implying the Marangoni convection could be enhanced at high scan speed. An apparent trace of the Marangoni convection in the melt pool was visible at a relatively high scan speed (P20, scan speed 2500 mm/s) in this investigation, as presented in Fig. 13(b). \subsection*{4.2. Effect of parameters on bead dimension} Fig. 8 shows that as the scan speed increased and/or the laser power decreased, the penetration of the bead became less, and then lateral shrinking happened. Finally, the bead no longer penetrated the block substrate at the maximum scan speed combined with the minimum laser power. As seen in Fig. 10(a) and (b), both bead depth and width were positively correlated to the laser power and negatively correlated to the scan speed. This is ascribed to that the combination of low scan speed and high laser power induced a higher energy input per unit length, increasing the working temperature, thus favoring the formation of a broader and deeper melt pool.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_b157ebe2add5a8848f75g-07(2)} Fig. 10. (a) The bead width, (b) the bead depth, (c) the bead height and (d) the contact angle as a function of the laser power and the scan speed. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-08(3)} \end{center} Fig. 11. OM images of the metallographs displaying the pore condition vs. the processing parameters and the corresponding porosity. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-08(2)} \end{center} (b) Fig. 12. Schematic diagram showing the development process of the Rayleigh instability. (a) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-08(1)} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-08} \end{center} Fig. 13. (a) Schematic diagram showing the formation process of the balling attributed to the Marangoni convection, (b) SEM image of the Marangoni convection trace in the melt pool (P20, laser power $290 \mathrm{~W}$, scan speed $2500 \mathrm{~mm} / \mathrm{s}$ ). For bead height, low laser power and high scan speed are unfavorable for a good wettability of the bead with the block substrate, as studied by Tian et al. (2017), contributing to a large bead height. However, when the laser power is low and the scan speed is high, a relatively small number of the powders are melted by the laser beam due to the low energy input density, leading to a decrease in the bead height. Due to the opposite effects of these 2 factors, the bead height was independent of the processing parameters. The contact angle can directly reflect the wettability of the bead. At low laser power and/or high scan speed, the contact angle increases, indicating a poor wettability of the bead. The working temperature in the melt pool decreases with decreasing the energy input density. The viscosity of the melt in the pool is temperature-dependent. Xia et al. (2017) believed that a low energy input density was likely to lead to cooler liquid with a higher viscosity, in turn inducing a poor flowability of the melt, and a high contact angle could be obtained. In addition, by comparing Fig. 4 and Fig. 9, it is evident that the BTs always presented accompanied by the SBBs with the contact angles larger than $90^{\circ}$, implying that the track lost its stability by the balling phenomenon. This is consistent with the investigation of Schiaffino and Sonin (1997). They suggested that the molten droplet was unstable at the contact angle greater than $90^{\circ}$. It is worth noting that the FTs had the contact angles slightly larger than $90^{\circ}$. For instance, the contact angles of P13 and P20 were $91.66^{\circ}$ and $91.32^{\circ}$, respectively. It indicates that the fluctuation of the track was a transitionally unstable condition before the balling phenomenon occurred. \subsection*{4.3. Spreading vs. solidification} The balling phenomenon can be considered as a competitive process between the spread and the solidification of molten liquid, which is controlled by the capillary force and the heat loss during LPBF. Fig. 14 demonstrates that a droplet attaches to a solid surface with the irradiation of a laser beam. The droplet solidifies with a solidification angle $\theta_{a}$, and spreads with a spread angle $\theta_{b}$ on a solid basis. As the wetting behavior continues, $\theta_{b}$ decreases because the droplet tends to spread out on the solid surface, and $\theta_{a}$ correspondingly increases due to that the melt is solidifying. It stops when $\theta_{a}$ is equal to $\theta_{b}$, and the whole bead is formed. It is reasonable to infer that if the melt can spread out on the block substrate before it solidifies, then the balling may be avoided, and a smooth surface and a stable track can be obtained. It requires the solidification time to be greater than the spread time. The model of the time for a droplet to spread on a surface is reported by Zhou et al. (2015): $t=\left(\frac{\rho_{m} a^{3}}{\sigma}\right)^{0.5}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-09} \end{center} Fig. 14. Schematic diagram demonstrating the competitive relationship between the spread and the solidification of a droplet. where $\rho_{m}$ is the melting density, $a$ is the radius of the droplet, and $\sigma$ is the surface tension. For alloys that have high viscosity near their liquidus, it may be useful to add a viscosity term into this in the future. The solidification time of the droplet can be calculated based on the investigation of Gao and Sonin (1994) as: $\tau=2\left(\frac{a^{2}}{3 \alpha}\right) \ln \left(\frac{T_{p}-T_{t}}{T_{f}-T_{t}}\right)$ where $a$ is the radius of the droplet, $\alpha$ is the thermal diffusivity, $T_{p}$ is the superheat temperature, $T_{f}$ is the fusion temperature, also known as liquidus temperature, and $T_{t}$ is the ambient temperature. Note that this doesn't include the increasing ease of heat loss as the droplet spreads out, but it's a useful approximation. $T_{p}$ can be obtained by the wellknown Rosenthal equation from Rosenthal (1946), which is related to a point heat source to move in the $\mathrm{x}$-direction as: $T_{p}(x, R)=T_{0}+\frac{A P}{2 \pi k}\left(\frac{1}{R}\right) \exp \left[-\frac{v}{2 \alpha}(R+x)\right]$ where $T_{0}$ is the initial temperature, $A$ is the absorptivity of powder, $k$ is the thermal conductivity, $P$ is the laser power, $v$ is the scan speed, and $R$ is the distance from the beam location to the point of interest as $R=$ $\sqrt{x^{2}+y^{2}+z^{2}}$. In the model, $a$ is usually $\sim 50 \mu \mathrm{m}$. The average peak temperature point is selected right between the laser beam and the droplet edge, i.e., $R=x=25 \mu \mathrm{m}$. $T_{0}$ is equal to $T_{f}$ showing that the laser beam irradiates on melt as it moves in the scanning direction during the wetting process. The other relevant material properties and temperatures are given in Table 3. The calculated solidification time vs. the contact angle is shown in Fig. 15. References for constants: ${ }^{a}$ Quested et al. (2013), ${ }^{b}$ Ragnhild et al. (2005), ${ }^{\text {C}}$ Tolochko et al. (2000). It can be found that the contact angle increased with decreasing the solidification time, implying that the time for a molten droplet to spread on the block substrate is reduced. Using Eq. (1), the spread time was calculated to be $22.25 \mu$ s. Fig. 15 demonstrates that the predicted solidification times of the FTs and the BTs were less than $22.25 \mu$ s, indicating the droplets under these parameters solidified before they spread out on the block substrate, thus losing their stability by fluctuating or balling. The solidification time and the contact angle are significantly influenced by the temperature and the fluid dynamic behavior in the melt pool. By carefully selecting the processing parameters, a stable track can be obtained in order to avoid defects such as balling, low overlapping and pores in printed components. \subsection*{4.4. Keyhole and conduction mode transition} The keyhole phenomenon was widely studied in the welding processes of metals, such as Fabbro (2010). Kasperovich et al. (2016) believed that the keyhole occurred when the energy input was high enough to form material vaporization, and a cavity was generated in the molten material exerted by the recoil force. Rai et al. (2007) thought that the formation of the keyhole could improve the efficiency of the laser beam due to the multiple reflections in the cavity. However, King et al. (2014) believed that it was an unstable condition of the melt pool and a cause of pores, as indicated by the circle in Fig. 7(a), which should be prevented in this case. The formation mechanism of the keyhole pore is schematically presented in Fig. 16. A considerably high working temperature induced by high energy density causes substantial metallic vaporization, and the recoil pressure can be generated towards the melt Table 3 Constants used to calculate the solidification time and the spread time. \begin{center} \begin{tabular}{lllllll} \hline $\rho_{m}\left(\mathrm{~kg} / \mathrm{m}^{3}\right)^{\mathrm{a}}$ & $\sigma(\mathrm{N} / \mathrm{m})^{\mathrm{b}}$ & $\alpha\left(\mathrm{m}^{2} / \mathrm{s}\right)^{\mathrm{a}}$ & $k\left(\mathrm{~W} / \mathrm{m} \mathrm{K}^{\mathrm{a}}\right.$ & $A^{\mathrm{c}}$ & $T_{f}(\mathrm{~K})^{\mathrm{a}}$ & $T_{t}(\mathrm{~K})$ \\ \hline 7324 & 1.85 & $4.87 \times 10^{-6}$ & 24.9 & 0.72 & 1628 & 298 \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-10} \end{center} Fig. 15. Relationship between the solidification time and the contact angle, the spread time and the critical contact angle are marked with dotted lines. pool, as shown in Fig. 16(a). Once the recoil pressure exceeds the hydrostatic pressure and the surface tension, the molten liquid is pressed downward to the melt pool bottom. As a result, the melt pool is relatively deep and narrow, as depicted in Fig. 16(b). Subsequently, the downwards flow driven by the recoil pressure and the gravity and the upwards flow driven by the surface tension collide, inducing the inward collapse to be generated with the participation of the hydrostatic pressure at the waist of the keyhole, as shown in Fig. 16(c). The collapses the molten liquid on both sides joint together, and strong metallic bonding is formed after solidification, leaving a large void with vapor entrapping at the bottom of the keyhole, see Fig. 16(d). This process is also clearly elucidated by Tan et al. (2020) in the LPBFed $2024 \mathrm{Al}$ alloy. By investigating different materials and welding parameters, Hann et al. (2011) found that the normalized bead depth was a function of the normalized energy density, which was given by Rubenchik et al. (2018) as: $\frac{\Delta H}{h_{s}}=\frac{2^{3 / 4} A P}{h_{s} \sqrt{\pi \alpha v d^{3}}}$ where $\Delta H$ is the deposited energy density, $A$ is the absorptivity of powder, $\alpha$ is the thermal diffusivity, $P$ is the laser power, $v$ is the scan speed, $d$ is the laser beam spot size, and $h_{s}$ is the enthalpy at melting. The normalized bead depth is $D /(a d / v)^{1 / 2}$, and $D$ is the bead depth. Other relevant material properties and the laser beam size are listed in Table 4. Similar to Hann et al. (2011), the normalized bead depth vs. the normalized enthalpy is shown in Fig. 17. It can be seen that the SBBs had Table 4 Constants used to calculate the normalized enthalpy. \begin{center} \begin{tabular}{lllll} \hline $\rho\left(\mathrm{kg} / \mathrm{m}^{3}\right)^{\mathrm{a}}$ & $\alpha\left(\mathrm{m}^{2} / \mathrm{s}\right)^{\mathrm{a}}$ & $h_{s}(\mathrm{~J} / \mathrm{g})^{\mathrm{b}}$ & $A^{\mathrm{c}}$ & $d(\mu \mathrm{m})$ \\ \hline 8177 & $4.87 \times 10^{-6}$ & 1071.8 & 0.72 & 30 \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-10(1)} \end{center} Fig. 16. Schematic diagram showing the formation mechanism of the keyhole pore.\\ a relatively low normalized bead depth below 10 , and the corresponding normalized enthalpy was also at a low level. When the value of normalized enthalpy increased gradually to $\sim 50$, the bead would convert from the conduction type to the keyhole type. Hence, when the deposited energy was $\sim 50$ times larger than the enthalpy for melting, the keyhole mode occurred for IN738LC in the LPBF process. References for constants: ${ }^{a}$ Quested et al. (2013), ${ }^{\text {b }}$ Chapman et al. (2008), ${ }^{\text {c }}$ Tolochko et al. (2000). \subsection*{4.5. Track behavior vs. part quality} High laser power companying with low scan speed was found to lead to stable and continuous tracks (Fig. 3). Given such tracks (WCTs and NCTs), with sufficient overlap between them, it should be possible to produce dense solid using raster scanning. However, it can be seen in Fig. 4 and Fig. 9 that a large proportion of the continuous tracks included keyhole beads (WKBs, NKBs). In this case, a large number of keyhole pores appeared, and would likely be presented in the raster-scanned solid, as shown in Fig. 11. On the contrary, low power and high scan speed resulted in BTs and SBBs. Low bead width and track instability could induce low overlapping between tracks, and the balling hindered the continuity of the melt within a single laser track, both of which led to irregular-shaped pores attributed to un-melted powders or lack of fusion. The parts with the highest quality were obtained in the overlap of NCTs and CBs in Fig. 4 and Fig. 9, such as P6 and P18. Among these parameters, moderate energy input density favored the stability of the melt track, and the keyhole pores and the lack of fusion could be effectively avoided. Considering the part quality and the fabrication efficiency, the parameters with higher scan speed like P19 (290 W @ $2000 \mathrm{~mm} / \mathrm{s}$ ) and P25 (370 W @ $2500 \mathrm{~mm} / \mathrm{s}$ ) might be more desirable for the part fabrication in the current LPBF system. \section*{5. Conclusion} Single-track experiments using IN738LC processed by LPBF were performed to investigate the relationship between the track morphology, bead characteristics and the printed part quality: \begin{itemize} \item The tracks could be classified into 4 types, namely the widecontinuous track, the narrow-continuous track, the fluctuating track and the balling track regarding their morphology and stability. The continuous (stable) tracks appeared at high energy input density. On the contrary, when energy input density was low, the track started to fluctuate and broke into metallic droplets. \item The bead width and depth increased with increasing the laser power and decreased with increasing the scan speed due to the different energy input densities. The bead height was largely independent of the processing parameters. The contact angle decreased with increasing the energy input density, indicating a good wettability. The contact angle for the fluctuating and balling track was greater than $90^{\circ}$ \item A model for a competitive process between the spread and the solidification of the melt was proposed to justify the relationship between the balling and the processing parameters. It suggested that if the solidification time was less than the spread time, the molten droplet would solidify before it spreads out on the block substrate. In this case, the balling was correspondingly formed. \item The beads were classified into 4 types, namely the wide-keyhole bead, the narrow-keyhole bead, the conduction bead and the shallow-ball bead. The normalized bead depth was found to increase with the normalized enthalpy. When the deposited energy was $\sim 50$ times greater than the enthalpy for melting, the bead changed from the conduction mode to the keyhole mode. \item Both high and low energy densities could lead to high porosity in bulk samples due to the keyhole pores and the un-melted powders, respectively. \end{itemize} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_b157ebe2add5a8848f75g-11} \end{center} Fig. 17. Relationship between the normalized enthalpy and the bead depth normalized by beam size, the critical value for the occurrence of the keyhole is marked with a dotted line. \section*{CRediT authorship contribution statement} Chuan Guo: Conceptualization, Data curation, Investigation, Methodology, Writing - original draft. Zhen Xu: Data curation, Resources. Yang Zhou: Data curation, Formal analysis. Shi Shi: Writing review \& editing, Methodology. Gan Li: Conceptualization, Writing review \& editing. Hongxing Lu: Conceptualization, Writing - review \& editing. Qiang Zhu: Project administration, Supervision, Funding acquisition, Writing - review \& editing, Methodology. R. Mark Ward: Project administration, Supervision, Writing - review \& editing, Methodology. \section*{Declaration of Competing Interest} The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. \section*{Acknowledgments} National Natural Science Foundation of China (No.91860131), National Key Research and Development Program of China (No. 2017YFB0702901), Shenzhen Science and Technology Innovation Commission (No.JCYJ20170817111811303, No.KQTD20170328154443162, No.ZDSYS201703031748354), and dual-education Ph.D. project (No. FEFE/GAS1792) financially supported this investigation. \section*{References} Chapman, L., Morrell, R., Quested, P.N., Brooks, R.F., 2008. Properties of alloys and moulds relevant to investment casting. NPL Report MATC 141 Fabbro, R., 2010. Melt pool and keyhole behaviour analysis for deep penetration laser welding. Journal of Physics D: Appl. Phys. 43 (44). Gao, F., Sonin Ain, A., 1994. Precise deposition of molten microdrops: the physics of digital microfabrication. Proc. R. Soc. Lond. A 444, 533-554. Gunenthiram, V., Peyre, P., Schneider, M., Dal, M., Coste, F., Fabbro, R., 2017. Analysis of laser-melt pool-powder bed interaction during the selective laser melting of a stainless steel. J. Laser Appl. 29 (2). Guo, C., Li, S., Shi, S., Li, X., Hu, X., Zhu, Q., Ward, R.M., 2020. Effect of processing parameters on surface roughness, porosity and cracking of as-built IN738LC parts fabricated by laser powder bed fusion. J. Mater. Process. Technol. 285, 116788. Gusarov, A.V., Smurov, I., 2010. Modeling the interaction of laser radiation with powder bed at selective laser melting. Phys. Procedia 5 (Part B), 381-394. Hann, D.B., Iammi, J., Folkes, J., 2011. A simple methodology for predicting laser-weld properties from material and laser parameters. J. Phys. D-Appl. Phys. 44 (44), 445401. Kasperovich, G., Haubrich, J., Gussone, J., Requena, G., 2016. Correlation between porosity and processing parameters in TiAl6V4 produced by selective laser melting. Mater. Des. 105, 160-170. King, W.E., Barth, H.D., Castillo, V.M., Gallegos, G.F., Gibbs, J.W., Hahn, D.E., Kamath, C., Rubenchik, A.M, 2014 Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J. Mater. Process. Technol. 214 (12), 2915-2925. Li, Y., Gu, D., 2014. Thermal behavior during selective laser melting of commercially pure titanium powder: numerical simulation and experimental study. Addit. Manuf. $1-4,99-109$. Matthews, M.J., Guss, G., Khairallah, S.A., Rubenchik, A.M., Depond, P.J., King, W.E., 2016. Denudation of metal powder layers in laser powder bed fusion processes. Acta Mater. 114, 33-42. Mumtaz, K., Hopkinson, N., 2009. Top surface and side roughness of Inconel 625 parts processed using selective laser melting. Rapid Prototyp. J. 15 (2), 96-103. Qiu, C., Panwisawas, C., Ward, M., Basoalto, H.C., Brooks, J.W., Attallah, M.M., 2015. On the role of melt flow into the surface structure and porosity development during selective laser melting. Acta Mater. 96, 72-79. Quested, P.N., Brooks, R.F., Chapman, L., Morrell, R., Youssef, Y., Mills, K.C., 2013. Measurement and estimation of thermophysical properties of nickel based superalloys. Mater. Sci. Technol. 25 (2), 154-162. Ragnhild, E.A., Livio, B., Brooks, R., Ivan, E., Hans-Jörg, F., Jean-Paul, G., et al., 2005. Thermophysical properties of IN738LC, MM247LC and CMSX-4 in the liquid and high temperature solid phase. In: 6th International Superalloys Symposium. Pittsburgh, pp. 625-706. Rai, R., Elmer, J.W., Palmer, T.A., DebRoy, T., 2007. Heat transfer and fluid flow during keyhole mode laser welding of tantalum, Ti-6Al-4V, 304L stainless steel and vanadium. J. Phys. D-Appl. Phys. 40 (18), 5753-5766. Rickenbacher, L., Etter, T., Hövel, S., Wegener, K., 2013. High-temperature material properties of IN738LC processed by selective laser melting (LPBF) technology. Rapid Prototyp. J. 19 (4), 282-290. Rombouts, M., Kruth, J.P., Froyen, L., Mercelis, P., 2006. Fundamentals of Selective Laser Melting of alloyed steel powders. Cirp Ann-Manuf. Techn. 55 (1), 187-192. Rosenthal, D., 1946. The theory of moving source of heat and its application to metal treatments. Transactions of the American Society of Mechanical Engineering Nov 1964, 849-866.\\ Rubenchik, A.M., King, W.E., Wu, S.S., 2018. Scaling laws for the additive manufacturing. J. Mater. Process. Technol. 257, 234-243. Sadowski, M., Ladani, L., Brindley, W., Romano, J., 2016. Optimizing quality of additively manufactured Inconel 718 using powder bed laser melting process. Addit. Manuf. 11, 60-70. Schiaffino, S., Sonin, A.A., 1997. Formation and stability of liquid and molten beads on a solid surface. J. Fluid Mech. 343, 95-110. Tan, C., Zhou, K., Ma, W., Min, L., 2018. Interfacial characteristic and mechanical performance of maraging steel-copper functional bimetal produced by selective laser melting based hybrid manufacture. Mater. Des. 155, 77-85. Tan, Q., Liu, Y., Fan, Z., Zhang, J., Zhang, M.X., 2020. Effect of processing parameters on the densification of an additively manufactured $2024 \mathrm{Al}$ alloy. J. Mater. Sci. Technol. 58, 34-45. Tian, Y., Tomus, D., Rometsch, P., Wu, X., 2017. Influences of processing parameters on surface roughness of Hastelloy X produced by selective laser melting. Addit. Manuf. 13, 103-112. Tolochko, N.K., Khlopkov, Y.V., Mozzharov, S.E., Ignatiev, M.B., Laoui, T., et al., 2000. Absorptance of powder materials suitable for laser sintering. Rapid Prototyp. J. 6 (3), 155-161. Wang, D., Yang, Y., Su, X., Chen, Y., 2012. Study on energy input and its influences on single-track,multi-track, and multi-layer in SLM. Int. J. Adv. Manuf. Tech. 58 (9-12), 1189-1199. Xia, M., Gu, D., Yu, G., Dai, D., Chen, H., Shi, Q., 2017. Porosity evolution and its thermodynamic mechanism of randomly packed powder-bed during selective laser melting of Inconel 718 alloy. Int. J. Mach. Tool. Manu. 116, 96-106. Yadroitsev, I., Gusarov, A., Yadroitsava, I., Smurov, I., 2010. Single track formation in selective laser melting of metal powders. J. Mater. Process. Technol. 210 (12), 1624-1631. Zhou, X., Liu, X., Zhang, D., Shen, Z., Liu, W., 2015. Balling phenomena in selective laser melted tungsten. J. Mater. Process. Technol. 222, 33-42. \begin{itemize} \item \end{itemize} \end{document} \documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[version=4]{mhchem} \usepackage{stmaryrd} \usepackage{hyperref} \hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,} \urlstyle{same} \usepackage{graphicx} \usepackage[export]{adjustbox} \graphicspath{ {./images/} } \title{3D multi-layer grain structure simulation of powder bed fusion additive manufacturing } \author{Johannes A. Koepf a, * , Martin R. Gotterbarm ${ }^{\text {b }}$, Matthias Markl a, Carolin Körner ${ }^{\text {a, b }}$\\ ${ }^{a}$ Chair of Materials Science and Engineering for Metals (WTM), Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstr. 5, 91058 Erlangen,\\ Germany\\ b Joined Institute of Advanced Materials and Processes (ZMP), Friedrich-Alexander-Universität Erlangen-Nürnberg Dr.-Mack-Str. 81, 90762 Fürth, Germany} \date{} %New command to display footnote whose markers will always be hidden \let\svthefootnote\thefootnote \newcommand\blfootnotetext[1]{% \let\thefootnote\relax\footnote{#1}% \addtocounter{footnote}{-1}% \let\thefootnote\svthefootnote% } %Overriding the \footnotetext command to hide the marker if its value is `0` \let\svfootnotetext\footnotetext \renewcommand\footnotetext[2][?]{% \if\relax#1\relax% \ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else% \if?#1\ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else\svfootnotetext[#1]{#2}\fi% \fi } \begin{document} \maketitle Full length article \section*{A R T I C L E I N F O} \section*{Article history:} Received 26 January 2018 Received in revised form 11 April 2018 Accepted 13 April 2018 Available online 16 April 2018 \section*{Keywords:} Grain structure Cellular automata Numerical modeling Grain growth Crystal growth Additive manufacturing \begin{abstract} A B S T R A C T In powder bed fusion (PBF) additive manufacturing, powder layers are locally melted with a laser or an electron beam to build a component. Hatching strategies and beam parameters as beam power, scan velocity and line offset significantly affect the grain structure of the manufactured part. While experiments reveal the result of specific parameter combinations, the precise impact of distinct parameters on the resulting grain structure is widely unknown. This knowledge is necessary for a reliable prediction of the microstructure and consequently the mechanical properties of the manufactured part.\\ We introduce the adaption of a three-dimensional model for the prediction of dendritic growth for use with PBF. The heat input is calculated using an analytical solution of the transient heat conduction equation. Massively parallel processing on a high-performance cluster computer allows the computation of the grain structure on the scale of small parts within reasonable times.\\ The model is validated by accurately reproducing experimental grain structures of Inconel 718 test specimens manufactured by selective electron beam melting. The grain selection zone within the first layers as well as the subsequent microstructure in several millimeters build height is modeled in unprecedented level of detail. This model represents the cutting-edge of grain structure simulation in PBF and enables a reliable numerical prediction of appropriate beam parameters for arbitrary applications. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. This is an open access article under the CC BY-NCND license (\href{http://creativecommons.org/licenses/by-nc-nd/4.0/}{http://creativecommons.org/licenses/by-nc-nd/4.0/}). \end{abstract} \section*{1. Introduction} In powder bed fusion (PBF) additive manufacturing, a part is built in layers by successively consolidating small partitions of powder previously deposited in a powder bed [1]. The necessary energy for melting is provided either by a laser (Selective Laser Melting, SLM [2]) or an electron beam (Selective Electron Beam Melting, SEBM [3,4]). The resulting grain structure is of special interest not only because of its influence on the mechanical properties of the final part. Especially the possibility of grain selection for the growth as well as the repair of single crystals is highly favorable [5]. The dimension and geometry of the melt pool localize the solidification and growth of the grains. The resulting as-built grain structure neglecting recrystallization and solid phase \footnotetext{\begin{itemize} \item Corresponding author. \end{itemize} E-mail addresses: \href{mailto:johannes.koepf@fau.de}{johannes.koepf@fau.de} (J.A. Koepf), \href{mailto:martin.gotterbarm@fau.de}{martin.gotterbarm@fau.de} (M.R. Gotterbarm), \href{mailto:matthias.markl@fau.de}{matthias.markl@fau.de} (M. Markl), \href{mailto:carolin.koerner@fau.de}{carolin.koerner@fau.de} (C. Körner). } transformations is mainly influenced by the topology of the melt pool as well as the thermal gradient and the velocity of the solidification front [6-8]. There are three major approaches for grain structure modeling resulting from a transient thermal gradient [8]. The phase field method describes the microstructure of a material by using a set of conserved and non-conserved field variables that are continuous across the liquid-solid-interface [9,10]. While this method shows remarkable results in modeling of dendritic growth [11,12], the requirement of extremely fine spatial resolutions almost prevents modeling of big domains with a huge number of grains $[8,13]$. Averaging methods try to overcome this limitation by coupling the microstructure formation to macroscopic continuity equations [14]. This approach enables modeling of microscopic phenomena of dendritic growth with computational costs several orders of magnitude lower than that of phase field methods [15-17], but they lack the prediction of grain competition. Cellular automata (CA) methods have been developed to resolve this issue [8,18,19], albeit with loss of detail. In their original formulation, these methods predict grain boundaries excluding the dendritic structure [20]. By\\ coupling a numerical model solving solute diffusion, the dendritic morphology is included in two as well as three dimensions [20-22]. The development of CA models substantially progressed in the last years, especially for two dimensions [23-26]. The requirement of one perpendicular growth direction to the simulation plane as well as the inability to model the grain selection out of this plane is limiting their usability. Enormous computational costs impeded the application of CA models in three dimensions until recently. Song et al. [27]. coupled a CA model with a proprietary casting code to determine the grain structure of ingot castings. Chen et al. $[28,29]$. coupled a finite element model for the heat input with a CA model to simulate the solidification grain structure in arc-welding. Low process velocities in combination with high powers allow the use of much coarser computational grids compared to PBF. Zinovieva et al. [30] recently applied CA models for the grain structure prediction in SLM within the first layers of a part made of Ti-6Al-4V. They reduced the computational costs by using a simplified model alleged to cause grid dependencies in the growth directions of the grains. The goal of our work is to predict the three-dimensional grain structure resulting from specific beam parameters of PBF processes on the scale of full sized parts. Previously we introduced an adaption of the model for the prediction of dendritic growth from Gandin and Rappaz [18] for PBF technologies [31]. In the current contribution, we extend this work by accurately reproducing the grain structure of an Inconel 718 test specimen consisting of hundreds of layers manufactured by SEBM. Each layer is formed by the superposition of multiple beam traversals, where the scanning direction is rotated every layer. The computational effort is distributed by Message Passing Interface (MPI) parallelization on a highperformance cluster computer with thousands of computational nodes. The fine temporal and spatial resolution, enabled by the efficient implementation and computational power, results in a degree of accuracy of the grain structure prediction unmatched in any work published so far. \section*{2. Model description} \subsection*{2.1. Hatching strategies} In PBF, a part is build layer-by-layer by successively melting powder. The build of each layer consists of four repetitive steps: Preheating, selective melting, lowering of the build platform and applying a new powder bed [32]. Crucial for the grain structure evolution is the melting step, where the desired area of the current layer is molten with a high-energy beam. The scanning pattern of the beam across the surface in this step is referred to as hatching strategy. Besides material properties like thermal conductivity or diffusivity, the hatching strategy as well as the beam parameters like the power $P$ or velocity $v$ influence the melt pool dimensions and thus the resulting microstructure [33-36]. The beam scans across the surface of the powder bed back and forth in a snake-like pattern. In a standard hatching strategy, the hatching direction is rotated every layer by $90^{\circ}$ (Fig. 1, left). An important parameter in characterizing different manufacturing conditions is the line energy $E_{1}$ [37]. It refers to the energy brought in per unit length $E_{1}=P / v$. When comparing different hatching strategies, the line energy is usually related to the line offset $l_{\text {off }}$, i.e. the distance between two lines resulting in the area energy $E_{\mathrm{A}}=E_{\mathrm{l}} / l_{\mathrm{off}}$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_3dcbe7431bd7efc1478ag-2} \end{center} Fig. 1. Illustration of the hatching strategy (left) and the analytical heat source model (right). The resulting thermal field is a superposition of individual heat sources positioned to meet at the turning point of the real beam. \subsection*{2.2. Thermal model} A reliable heat input model is prerequisite for predicting the grain structure. There is a variety of analytical as well as numerical approaches dealing with a thermal field resulting from a transient heat source [20-24]. While numerical solutions are indispensable for the computation of the thermal field resulting from complex beam paths, they are slow in comparison to analytical solutions. The applied analytical heat source model approximates the thermal field emerging from the hatching strategy (Fig. 1, left) with computational costs significantly smaller than numerical solutions. \subsection*{2.2.1. Single pass melting} The analytical heat source model is based upon Rosenthal's solution for the temperature distribution resulting from a point heat source traversing the surface with constant speed $v$ [38]. It assumes a quasi-stationary temperature distribution and uses a moving coordinate system centered at the origin of the beam. With the beam traversing in $x$-direction and the distance $\xi$ of any given point along the $x$-axis to the origin of the beam, the coordinate transformation from the fixed to the moving coordinate system is $\xi=x-v \cdot t$. This coordinate transformation is used in the analytical solution for the thermal field induced by a traversing beam [39]. $T(\xi, y, z)=T_{0}+\frac{q / v}{2 \pi \lambda} \exp \left(-\frac{v \cdot(\xi+r(y, z))}{2 \alpha}\right)$. $T_{0}$ depicts the start temperature, $q$ and $v$ the power and velocity of the beam, $r(y, z)$ the distance from a given point to the beam and $\lambda$ the thermal conductivity. The thermal diffusivity $\alpha$ is calculated from the thermal conductivity $\lambda$, the density $\rho$ and the specific heat capacity $c_{p}$ by $\alpha=\lambda / \rho c_{p}$. \subsection*{2.2.2. Hatching} In the melting step, the beam scans the surface of the powder bed repeatedly in opposing directions (Fig. 1, left). Each scan line of the beam across the surface is calculated as an individual beam with its own time $t$. The total number of beams is computed by $n_{B}=$ $l_{\text {Build }} / l_{\text {off }}+1$, where $l_{\text {Build }}$ is the length of the build domain. The resulting thermal field is the superposition of all individual beams $T=\sum_{i=1}^{n_{B}} T\left(\xi_{i}, y, z\right)$. The calculation of the thermal field resulting from three scan lines of a cuboid simulation domain is depicted in Fig. 1 (right). The\\ individual beams are started at times calculated in advance to ensure that two successive beams meet exactly at the turning point of the beam. The resulting thermal field is depicted in color only for the simulation domain. The outer regions are grayed for clarity. The inlet (right) shows the relationship of the individual beams with the hatching strategy (left). \subsection*{2.2.3. Reduced simulation domain} The high computational costs of the microstructure evolution model described below usually result in simulation domains being significantly smaller than the build domain. The simulation domain in these cases represents an arbitrarily positioned excerpt within the build domain. Fig. 2 depicts the case of a simulation domain located in the center of the build domain. When the simulation domain is significantly smaller than the build domain, the total number of beams $n_{B}$ can be reduced. Instead of considering the build length, the number of beams is calculated with the simulation length $l_{\operatorname{sim}}$ as well as the domain parameters $\zeta$ and $\eta$ according to $n_{S}=\left(l_{\text {Sim }}+\zeta+\eta\right) / l_{\text {off }}+1$. The domain parameters $\zeta$ and $\eta$ mimic an additional heating although the beam is scanning outside the simulation domain. This treatment ensures a stable melt pool as it is expected in the center of the build domain. \subsection*{2.3. Modeling microstructure evolution} Since the underlying model is well documented in literature $[18,40,41]$, the general procedure is only repeated in brief with an emphasis on the adaptions for PBF. Besides the heat input discussed in 2.2, these adaptions concern the grain initialization, the remelting of the grains as well as the layered buildup. \subsection*{2.3.1. Basic algorithm} The algorithm is based on a CA model reproducing the growth of fcc dendrites. The preferential $<100>$ growth direction is maintained by approximating the dendrite envelopes with octahedra, each of them coupled to a distinct cell. Each octahedron grows along its main diagonals corresponding to the $<100>$ crystallographic orientations of the dendrite [42]. The growth velocity depends on the undercooling of its cell approximated by a polynomial law [19]. $v(\cdot T)=A \cdot \Delta T^{2}+B \cdot \Delta T^{3}$, where $\Delta T$ is the undercooling to the melting temperature and $A$ and $B$ are material dependent parameters. Once an octahedron comprises the center of an adjacent liquid cell, this cell is captured, i.e., it is associated with the grain properties of the capturing cell and a \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_3dcbe7431bd7efc1478ag-3} \end{center} Fig. 2. Correlation of simulated and build domain. The amount of calculated beams can be reduced in cases where the simulated domain is significantly smaller than the build domain. new octahedron with the same orientation is initiated. Octahedra grow independently until all adjacent cells are captured. Cells with no liquid neighbors are no longer considered in the algorithm. \subsection*{2.3.2. Grain initialization} Unlike the model from Gandin and Rappaz [19,40], where individual grains nucleate from single cells and grow into an undercooled melt, a PBF process starts with solid particles forming a powder bed. These particles fill the volume only imperfectly leaving gaps in between. By concentrating on the repeatedly re-melted bulk material and leaving aside boundary effects, the powder bed is approximated as continuous media with material properties like density and thermal diffusivity based on that of the powder material. Multiple cells are combined and initialized as an individual grain reflecting the initial grain size within the powder particles. The octahedra of these cells share the same orientation, which is defined by three Euler angles [43]. Due to this definition, the rotation of the octahedron in any direction of the threedimensional space is possible. The three Euler angles are thereby randomly generated using a mersenne twister pseudo random generator [44]. \subsection*{2.3.3. Re-melting} In PBF, solidified cells are repeatedly re-melted, i.e., an already solidified cell becomes liquid and capturable by adjacent cells again. While the octahedron of liquefied cells is deleted, that of solidified cells has to be stored and reactivated. There are three possibilities to modify the octahedron of a solid cell when a neighboring cell liquefies again: (a) Re-initialization to a negligible size; (b) Reactivation with the size when the cell became solid; (c) Dynamic size adaption depending on the current undercooling. These possibilities are summarized in $L_{\mu}^{0}=c(\Delta T) \cdot L_{\mu}^{t}$, where $L_{\mu}^{0}$ depicts the size of the re-initialized octahedron, $L_{\mu}^{t}$ its size at the time $t$ when it became solid and $c$ a weighting factor with $0 \leq$ $c \leq 1$ depending on the local undercooling $\Delta T$. Preliminary tests revealed this parameter is not negligible. The exact determination of this coefficient requires detailed investigations that will be subject to further studies. For all calculations in this paperc $=1$. \subsection*{2.3.4. Layered build-up} With a volume of several cube decimeters [45], the build domain in PBF exceeds the computational feasibility by magnitudes. However, crystal growth occurs only within the re-melted section, if solid phase transformations and recrystallization are disregarded. Consequently, only the re-melted section is relevant for the development of the microstructure of the build-up part. Instead of modeling the complete building tank, only the remelted zone at the top of the specimen is considered. After each layer, all cells corresponding to one layer thickness are stored, the cells above are shifted downwards and an equal number of new cells are initialized on top. By repeating this procedure each layer, an arbitrary build height with constant computational effort per layer is possible. After completion of calculation, the results are reassembled, i.e., the stored cells are merged showing the whole build volume again. \section*{3. Validation} The application of the basic algorithm described in 2.3.1 with transient thermal fields has already been demonstrated [28,29]. Here, we focus on the usability of the thermal model described in section 2.2 for SEBM. Experimentally determined melt pool depths resulting from a wide range of beam power and velocity combinations are compared with numerical predictions. \subsection*{3.1. Single pass melting} Hartmann investigated the impact of line energies between $0.15 \mathrm{~J} / \mathrm{mm}$ and $2.4 \mathrm{~J} / \mathrm{mm}$ on the geometry of the melt pool of a single line using CMSX-4 [46]. The beam power ranged from $300 \mathrm{~W}$ up to $1200 \mathrm{~W}$ and the beam velocity from $0.5 \mathrm{~m} / \mathrm{s}$ to $2 \mathrm{~m} / \mathrm{s}$. The material properties of CMSX-4 used for the thermal model are listed in Table 1 [47]. All parameters are specified at the solidus temperature and are assumed temperature-independent. Fig. 3 depicts the melt pool depth predicted by the analytical solution compared with experimental data. The measurements show the nonlinear correlation between line energy and melt pool depth. Equal line energies result in different melt pool depths depending on the beam velocity and power. This phenomenon is not reproduced by the analytical solution due to restrictions on constant material parameters, the disregard of evaporation in congruent melt pools for distinct line energies and a seamless transition between different scan speeds (dotted line in Fig. 3). Due to the exclusion of the enthalpy of fusion, the melt pool depth is overestimated with decreasing line energies. \subsection*{3.2. Hatching} Helmer investigated the impact of different area energies on the melt pool depths analyzing additively build parts using Inconel 718 [48]. The measurements were performed with a standard hatching strategy, a line offset of $100 \mu \mathrm{m}$ and layer thickness of $50 \mu \mathrm{m}$. The beam power was adjusted in a range from $510 \mathrm{~W}$ to $855 \mathrm{~W}$ and the velocity from $3.0 \mathrm{~m} / \mathrm{s}$ to $4.5 \mathrm{~m} / \mathrm{s}$, resulting in area energies ranging from $1.6 \mathrm{~J} / \mathrm{mm}^{2}$ to $2.0 \mathrm{~J} / \mathrm{mm}^{2}$. The material properties of Inconel 718 and the simulation parameters used for the thermal model are listed in Table 2 and Table 3, respectively. The melt pool is measured after completion of the last layer. Fig. 4 shows a comparison of the calculated and measured maximum melt pool depths resulting from hatching a single layer. The discontinuous behavior of the melt pool depths is observable similar to the single line results. Hatching strategies with equal area energy but different velocities result in different melt pool depths. To ensure comparability, the powder shrinkage has to be considered. The effective melt pool depth has to be measured from the height of the rake and is adjusted by doubling the layer thickness. When comparing the analytical and the effective melt pool depths, the overestimation is similar to the single line investigation showed in 3.1. \section*{4. Results and discussion} The model verification is demonstrated by comparing the grain structure of additively build specimens and the simulated counterpart. Table 1 Material properties of CMSX-4 used for thermal model [47]. \begin{center} \begin{tabular}{lll} \hline Quantity & value & unit \\ \hline Liquidus temperature & 1,380 & ${ }^{\circ} \mathrm{C}$ \\ Density $\rho$ & $8.1 \cdot 10^{3}$ & $\mathrm{~kg} / \mathrm{m}^{3}$ \\ Thermal conductivity $\lambda$ & $4.5 \cdot 10^{1}$ & $\mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$ \\ Thermal diffusivity $\alpha$ & $5.5 \cdot 10^{-6}$ & $\mathrm{~m}^{2} / \mathrm{s}$ \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_3dcbe7431bd7efc1478ag-4} \end{center} Fig. 3. Comparison of the melt pool depth of a single scan line predicted by the analytical solution (open symbols) with experimental data (filled symbols) [44]. The analytical solution shows a seamless transition between different scan speeds (dotted line) and overestimates the melt pool depth with decreasing line energy. Table 2 Material properties of Inconel 718 used for thermal model. \begin{center} \begin{tabular}{lll} \hline Quantity & value & unit \\ \hline Liquidus temperature & 1340 & ${ }^{\circ} \mathrm{C}$ \\ Density $\rho$ & 7700 & $\mathrm{~kg} / \mathrm{m}^{3}$ \\ Specific heat capacity $c_{\mathrm{p}}$ & 650 & $\mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$ \\ Thermal conductivity $\lambda$ & 30 & $\mathrm{~J} /(\mathrm{m} \cdot \mathrm{K})$ \\ \hline \end{tabular} \end{center} Table 3 Simulation parameters used for thermal model. \begin{center} \begin{tabular}{lll} \hline Quantity & value & unit \\ \hline Dimension & $1.0 \times 1.0 \times 0.4$ & $\mathrm{~mm}^{3}$ \\ Line offset $\mathrm{l}_{\text {off }}$ & 100.0 & $\mu \mathrm{m}$ \\ Line length $\mathrm{l}_{\text {Build }}$ & 15.0 & $\mathrm{~mm}$ \\ Simulated length $\mathrm{l}_{\text {Sim }}$ & 1.0 & $\mathrm{~mm}$ \\ Domain parameters $\zeta, \eta$ & 0.4 & $\mathrm{~mm}$ \\ \hline \end{tabular} \end{center} \subsection*{4.1. Experiments} Three samples were built on an Arcam $^{\mathrm{TM}}$ A2 SEBM machine using $60 \mathrm{kV}$ acceleration voltage. For each sample 25 supports where additively raised in a $5 \times 5$ matrix inside an Inconel 718 powder bed from a polycrystalline base plate of Inconel $718(17 \mathrm{~mm}$ thick and $136 \mathrm{~mm}$ in diameter). Based on the supports, a cuboid was built with the dimensions $15 \mathrm{~mm} \times 15 \mathrm{~mm} \times 20 \mathrm{~mm}$ using the hatching strategy depicted in Fig. 1 together with the build parameters stated in Table 4. The specimens were prepared by means of longitudinal microsections. Additionally, cross sections were taken in $5 \mathrm{~mm}$ steps beginning from bottom of the specimen. After cold mounting in Technovit 4071 and grinding with 320-2500 grit SiC-paper the samples were polished using first $3 \mu \mathrm{m}$ and $1 \mu \mathrm{m}$ diamond suspension and afterwards $0.04 \mu \mathrm{m}$ colloidal silica suspension. Finally, the microsections were etched $15 \mathrm{~s}$ using a mixture of $32 \% \mathrm{HCl}$ and $5 \% \mathrm{H}_{2} \mathrm{O}$. Fig. 5 shows details of the microsections, taken from the bottom (left) as well as from the top of the specimen (right). Obviously, the grain selection is finished within the first millimeter of the build. Melt pool depth $[\mu \mathrm{m}]$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_3dcbe7431bd7efc1478ag-5(1)} \end{center} Fig. 4. Comparison of the maximum melt pool depth resulting from hatching predicted by the analytical solution (open symbols) with experimentally determined values (filled symbols). Considering the powder shrinkage, the measured melt pool depths were adjusted resulting in the effective depth. Table 4 Build parameters for cuboid samples. \begin{center} \begin{tabular}{lll} \hline Quantity & value & unit \\ \hline Power P & 800 & $\mathrm{~W}$ \\ Beam velocity v & 5 & $\mathrm{~m} / \mathrm{s}$ \\ Line offset $\mathrm{l}_{\text {off }}$ & 100 & $\mu \mathrm{m}$ \\ Preheat temperature $\mathrm{T}_{0}$ & 950 & ${ }^{\circ} \mathrm{C}$ \\ Layer thickness & 50 & $\mu \mathrm{m}$ \\ \hline \end{tabular} \end{center} Unfavorably orientated grains are quickly overgrown and above the first millimeter all grains are aligned in build direction with minimal misorientations. The width of the grains increases within the first millimeter to approximately $50 \mu \mathrm{m}$ and remains nearly constant dominating the microstructure throughout the specimen (Fig. 5, right). Based on the cross sections, EBSD measurements were carried out using a FEI Helios 600i dual-beam SEM. At the lower end of the\\ Table 5 Simulation Parameters used for grain structure calulation \begin{center} \begin{tabular}{lll} \hline Quantity & value & unit \\ \hline Grid size & $240 \times 240 \times 30$ & cells \\ Cell size & 10 & $\mu \mathrm{m}$ \\ Time step size & 1 & $\mu \mathrm{s}$ \\ Initial grain size & 20 & $\mu \mathrm{m}$ \\ Line length $\mathrm{l}_{\text {Build }}$ & 15 & $\mathrm{~mm}$ \\ Domain length $\mathrm{l}_{\text {Sim }}$ & 2.4 & $\mathrm{~mm}$ \\ Domain parameters $\zeta, \eta$ & 0.8 & $\mathrm{~mm}$ \\ Growth parameter A & 0.0001 & \\ Growth parameter B & 0 & \\ Number of layers & 200 & $\mathrm{~mm}$ \\ Final build height & 10 & \\ \hline \end{tabular} \end{center} longitudinal cross section, a variety of scans was conducted and combined in a $1.5 \times 5 \mathrm{~mm}^{2}$ EBSD image to visualize the grain selection process. $1.0 \times 1.0 \mathrm{~mm}^{2}$ images were taken from each transversal cross section for grain size measurements (see Fig. 5). The step size in all cases was $5 \mu \mathrm{m}$. \subsection*{4.2. Simulations} The simulations were carried out on a high performance cluster computer located at the Erlangen Regional Computing Center (RRZE). 720 computational cores required $200 \mathrm{~h}$ of computing time to simulate the first $10 \mathrm{~mm}$ of the build. A $2.4 \times 2.4 \mathrm{~mm}^{2}$ polycrystalline baseplate with random orientation was used for grain initialization. The details of the numerical setup are stated in Table 5. The material parameters of Inconel 718 used for the simulation are shown in Table 2. Fig. 6 depicts the simulated grain structure by cutting along the $x$ - and $y$-axis through the simulation domain. A comparison of the simulated grain structure with the EBSD measurements carried out on the longitudinal sections is shown on the right side of Fig. 6. The occurring grain selection as well as the columnar grain structure becomes apparent: The base is dominated by a wide variety of randomly orientated grains. Within the first $500 \mu \mathrm{m}$ of the build, misorientated grains are overgrown and a columnar grain structure evolves. This comparison confirms the simulation results in the height of the grain selection zone as well as in the columnar growth of the remaining grains. The accumulations of many small new grains observable in the EBSD-measurements originate from powder impurities or \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_3dcbe7431bd7efc1478ag-5} \end{center} Fig. 5. Position of traversal and longitudinal cross section cuts. The microsections taken from the bottom (left) as well as the top (right) of the specimen show a uniform columnar grain structure.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_3dcbe7431bd7efc1478ag-6} Fig. 6. Three-dimensional view of the simulated grain structure with a build height of $10 \mathrm{~mm}$ (left) and comparison of a detailed two -dimensional view of the simulation results with EBSD-measurements taken from the first $5 \mathrm{~mm}$ of the longitudinal section cut (right). discrepancies in the powder deposition. These grains impede the growth of already well-oriented grains resulting in a very fine columnar microstructure. This phenomenon is not yet implemented in the numerical model and will be considered in further studies. The development of the microstructure is compared by transversal section cuts within the first millimeter (bottom) and after $10 \mathrm{~mm}$ (top) of the build in Fig. 7. In both cases, the simulated as well as the measured grain structure and orientation is depicted. Within the first millimeter, the randomly distributed orientations and nearly regular shaped grains are obvious. After $10 \mathrm{~mm}$, there is an excellent agreement of the size and shape of the grains as well as the orientation of the primary growth direction. Pole figures were derived from the simulation results using the matlab toolbox MTEX [49]. The corresponding pole figures confirm the completion of the grain selection according to the primary build direction leading to a strong (001)-fiber texture with no further grain coarsening.\\ Additionally, the pole figures reveal a slight secondary anisotropy relating to the orientation of the crystallographic [100]- and [010]direction. However, there is an orientation discrepancy between the simulated and measured secondary anisotropy. The possibility of a correlation between this variance and the overestimation of the melt pool by the analytical heat model is currently investigated and will be addressed in future works. \section*{5. Conclusion and perspectives} The present work describes a three-dimensional crystal growth model for PBF processes. A thermal heat model based on an analytical solution for the transient heat source is presented that enables an efficient calculation of the beam induced thermal field. Validation with previously published experiments indicate the analytical solution to overestimate the depth of the melt pool by a constant factor. This effect mainly vanishes in simulations based on\\ \includegraphics[max width=\textwidth, center]{2024_03_10_3dcbe7431bd7efc1478ag-7} Fig. 7. Comparison of grain structure and orientation of the simulation (left) with EBSD measurements (right) the thermal model due to the iterative re-melting of already solidified regions verified by comparing numerical simulations with EBSD measurements. The grain selection at the bottom of the specimen was as accurately reproduced as the microstructure in several millimeters build height. This outstanding accuracy was enabled by a very fine spatial and temporal resolution as well as a massively parallelization. The execution on a high-performance cluster computer ensured the enormous computational load to finish in reasonable time. Simulations of microstructure prediction encompassing several millimeters build height in the presented level of detail are unreached by any grain structure simulation published so far. This predictive power enables a wide range of possibilities, beginning from tailoring the microstructure for specific applications to\\ subsequent determination of the resulting mechanical properties or the analysis of process strategies. Finally, the beam parameters can be computationally optimized for any desired resulting microstructure. These applications will be addressed in future works. \section*{Declarations of interest} None. \section*{Acknowledgment} The authors want to thank the German Research Foundation (DFG) for funding the Collaborative Research Center 814 (CRC 814) - Additive Manufacturing, sub-project B4. The authors gratefully acknowledge the compute resources and support provided by the Erlangen Regional Computing Center (RRZE). \section*{References} [1] L.E. Murr, S.M. Gaytan, D.A. Ramirez, E. Ramirez, J. Hernandez, K.N. Amato, P.W. Shindo, F.R. Medina, R.B. Wicker, Metal fabrication by additive manufacturing using laser and electron beam melting technologies, J. Mater. Sci. Technol. 28 (2012) 1. [2] D. Gu, W. Meiners, K.R.P. Wissenbach, Laser additive manufacturing of metallic components: materials, processes and mechanisms, Int. Mater. Rev. 57 (2012) 133 [3] S.M. Gaytan, L.E. Murr, F. Medina, E. Martinez, M.I. Lopez, R.B. Wicker, Advanced metal powder based manufacturing of complex components by electron beam melting, Mater. Technol. 24 (2009) 180. [4] C. Körner, Additive manufacturing of metallic components by selective electron beam melting - a review, Int. Mater. Rev. 61 (2016) 361. [5] M. Gäumann, S. Henry, F. Cleton, J.-D. Wagniere, W. Kurz, Epitaxial laser metal forming: analysis of microstructure formation, Mater. Sci. Eng. 271 (1999) 232. [6] R. Trivedi, W. Kurz, Solidification microstructures: a conceptual approach, Acta Metall. Mater. 42 (1994) 15 [7] M.F. Zäh, S. Lutzmann, Modelling and simulation of electron beam melting, Prod. Eng. Res. Devel. 4 (2010) 15. [8] W.J. Böttinger, S.R. Coriell, A.L. Greer, A. Karma, W. Kurz, M. Rappaz, R. Trivedi, Solidification microstructures: recent developments, future directions, Acta Mater. 48 (2000) 43. [9] S.A. David, Vitek Jm, Correlation between solidification parameters and weld microstructures, Int. Mater. Rev. 34 (1989) 213 [10] N. Moelans, B. Blanpain, P. Wollants, An introduction to phase-field modeling of microstructure evolution, Computer Coupling of Phase Diagrams ans Thermochemestry 32 (2008) 268. [11] D. Tourret, A. Karma, Growth competition of columnar dendritic grains: a phase-field study, Acta Mater. 82 (2015) 64. [12] S. Sahoo, K. CHou, Phase-field simulation of microstructure evolution of Ti$6 \mathrm{Al}-4 \mathrm{~V}$ in electron beam additive manufacturing process, Add. Man. 9 (2016) 14. [13] V. Plochikhine, Modelling of the Grain Structure Formation by Laser Beam Welding, 1998. [14] M. Rappaz, Modelling of microstructure formation in solidification processes, Int. Mater. Rev. 34 (1989) 93. [15] I. Steinbach, C. Beckermann, B. Kauerauf, Q. Li, J. Guo, Three- dimensional modeling of equiaxed dendritic growth on a mesoscopic scale, Acta Mater. 47 (1998) 971. [16] P. Thevoz, J.L. Desbiolles, M. Rappaz, Modeling of equiaxed microstructure formation in casting, Metall. Trans. A 20A (1989) 311. [17] C.Y. Wang, C. Beckermann, Equiaxed dendritic solidification with convection part i. multiscale/multiphase modeling, Metall. Mat. Trans. A 27A (1996) 2754. [18] C.-A. Gandin, M.A. Rappaz, 3D Cellular automaton algorithm for the prediction of dendritic grain growth, Acta Mater. 45 (1996) 2187. [19] C.-A. Gandin, M. Rappaz, R. Tintiller, 3- dimensional simulation of the grain formation in investment casting, Metall. Mat. Trans. A 25A (1994) 629. [20] W. Wang, P.D. Lee, M. McLean, A model of solidification microstructures in nickel-based superalloys: predicting primary dendrite spacing selection, Acta Mater. 51 (2003) 2971 [21] R.C. Atwood, P.D. Lee, Simulation of the three-dimensional morphology of solidification porosity in an aluminium-silicon alloy, Acta Mater. 51 (2003) 5447 . [22] H.B. Dong, P.D. Lee, Simulation of the columnar-to-equiaxed transition in directionally solidified Al-Cu alloys, Acta Mater. 53 (2005) 659. [23] A. Rai, C. Körner, H. Helmer, Simulation of grain structure evolution during powder bed based additive manufacturing, Add. Manu. 13 (2017) 124. [24] H.W. Bergmann, S. Mayer, V.V. Ploshikin, Grian selection and texture evolution during solidification of laser beams welding, Mater. Sci. Forum 273-275 (1998) 345. [25] O. Zinovieva, A. Zinoviev, V.V. Ploshikhin, V. Romanova, R. Balokhonov, Two dimensional cellular automata simulation of grain growth during solidification and recrystallization, IOP Conf. Series: Mat. Sci. Eng. 71 (2015) p.1. [26] A. Rai, M. Markl, C. Körner, A coupled cellular automaton-lattice Boltzmann model for grain structure simulation during additive manufacturing, Comput Mater. Sci. 124 (2016) 37. [27] W. Song, J-m Zhang, S-x Wang, B. Wang, L-l. Han, Simulation of Solidification microstructure of Fe-6.5\% Si Alloy using cellular automton-finite element method, J. Cent. South Univ. vol. 23 (2016) 2156. [28] S. Chen, G. Guillemot, C.-A. Gandin, 3D coupled cellular automaton (CA)- finite element (FE) modeling for solidification grain structures in Gas Tungsten arc welding (GTAW), ISIL Intern. 54 (2014) 401. [29] S. Chen, G. Guillemot, C.-A. Gandin, Three-dimensional cellular automatonfinite element modeling of solidification grain structures for arc-welding processes, Acta Mater. 115 (2016) 448. [30] O. Zinovieva, A. Zinoviev, V. Ploshikhin, Three-dimensional modeling of the microstructure evolution during metal additive manufacturing, Comput Mater. Sci. 141 (2018) 207. [31] J. Koepf, A. Rai, M. Markl, C. Körner, in: I. Drstevensek, D. Drummer M. Schmidt (Eds.), 3D Grain Structure Simulation for Beam- Based Additive Manufacturing, 6th International Conference on Additive Technologies iCAT2016, Nuremberg, 2016. [32] P. Heinl, C. Körner, R.F. Singer, Selective electron beammelting of cellular titanium: mechanical properties, Adv. Eng. Mat. 10 (2008) 882. [33] H. Helmer, A. Bauereiß, R.F. Singer, C. Körner, Grain structure evolution in Inconel 718 during selective electron beam melting, Mat. Sci. Eng. A 668 (2016) 180. [34] N. Hrabe, T. Quinn, Effects of processing on microstructure and mechanical properties of a titanium alloy( $\mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V})$ fabricated using electron beam melting (EBM), Part 2:Energy input, orientation, and location, Mat. Sci. Eng. A 573 (2013) 271 [35] M. Markl, R. Ammer, U. Rüde, C. Körner, Numerical Investigations on hatching process strategies for powder bed based additive manufacturing using an electron beam, Int. J. Adv. Manuf. Technol. 78 (2014) 1. [36] L. Thijs, F. Verhaeghe, T. Craeghs, Humbeeck Jv, J.-P. Kruth, A study of the microstructural evolution during selective laser melting of $\mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V}$, Acta Mater. 58 (2010) 3303. [37] C. Körner, E. Attar, P. Heinl, Mesoscopic simulation of selective beam melting processes, J. Mater. Process. Technol. 211 (2011) 978. [38] D. Rosenthal, The theory of moving sources of heat and its application of metal treatments, Trans. ASME 68 (1946) 849. [39] K. Easterling, Introduction to the Physical Metallurgy of Welding, Elsevier, 2013. [40] C.-A. Gandin, R.J. Schaefer, M. Rappaz, Analytical and numerical predictions of dendritic grain envelopes, Acta Mater. 44 (1996) 3339. [41] M. Rappaz, C.-A. Gandin, Probabilistic modelling of microstructure formation in solidification processes, Acta Metall. Mater 41 (1993) 345 [42] C.-A. Gandin, J.-L. Desbiolles, M. Rappaz, P. Thevoz, A Three-dimensiona cellular automaton - finite element model for the prdiction of solidification grain structures, Metall. Mater. Trans. 30A (1999) 3153. [43] H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 2000. [44] D.B. Thomas, W. Luk, P.H.W. Leong, J.D. Villasenor, Gaussian random number generators, ACM Comput. Surv. 39 (2007) 1. [45] W.E. Frazier, Metal additive manufacturing: a review, J. Mater. Eng. Perform. 23 (2014) 1917 [46] O. Hartmann, Modellierung der Kornbildung vor der Erstarrungsfront bei der additiven Fertigung mit dem Elektronenstrahl, Chair of Materials Science and Engineering for Metals, Friedrich Alexander University Erlangen-Nürnberg, 2014. [47] K.C. Mills, Recommended Values of Thermophysical Properties for Selected Commercial Alloys, Woodhead Publishing, 2002. [48] H. Helmer, Additive Fertigung durch Selektives Elektronenstrahlschmelzen der Nickelbasis Superlegierung IN718: Prozessfenster, Mikrostruktur und mechanische Eigenschaften. Chair of Materials Science and Engineering fo Metals, vol. Dr.-Ing. Erlangen, Friedrich Alexander Iniversität Erlangen, Nürnberg, 2017. [49] A.D. Rollett, Texture Analysis with MTEX inside Matlab, 2016. \begin{itemize} \item \end{itemize} \end{document} \documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[version=4]{mhchem} \usepackage{stmaryrd} \usepackage{graphicx} \usepackage[export]{adjustbox} \graphicspath{ {./images/} } \title{Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods } \author{Alexander Klassen, Thorsten Scharowsky and Carolin Körner\\ Chair of Metals Science and Technology, University of Erlangen-Nuremberg, Martensstr. 5, D-91058\\ Erlangen, Germany\\ E-mail: alexander.klassen@ww.uni-erlangen.de} \date{} \begin{document} \maketitle PAPER \section*{Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods} To cite this article: Alexander Klassen et al 2014 J. Phys. D: Appl. Phys. 47275303 View the article online for updates and enhancements. Recent citations \begin{itemize} \item Preventing Evaporation Products for High-\\ Quality Metal Film in Directed Energy\\ Deposition: A Review\\ Kang-Hyung Kim et al \item Semi-coupled resolved CFD-DEM\\ $\frac{\text { simulation of powder-based selective laser }}{\text { melting for additive manufacturing }}$\\ Tao Yu and Jidong Zhao \item Modified Cellular Automaton Simulation of\\ $\frac{\text { Metal Additive Manufacturing }}{\text { Jun Kubo et al }}$ \end{itemize} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9f4c77949db3cee9cebfg-01} \end{center} \section*{IOP ebooks"} Bringing together innovative digital publishing with leading authors from the global scientific community. Start exploring the collection-download the first chapter of every title for free. Received 24 January 2014, revised 28 April 2014 Accepted for publication 12 May 2014 Published 13 June 2014 \begin{abstract} Evaporation plays an important role in many technical applications including beam-based additive manufacturing processes, such as selective electron beam or selective laser melting (SEBM/SLM). In this paper, we describe an evaporation model which we employ within the framework of a two-dimensional free surface lattice Boltzmann method. With this method, we solve the hydrodynamics as well as thermodynamics of the molten material taking into account the mass and energy losses due to evaporation and the recoil pressure acting on the melt pool. Validation of the numerical model is performed by measuring maximum melt depths and evaporative losses in samples of pure titanium and Ti-6Al-4V molten by an electron beam. Finally, the model is applied to create processing maps for an SEBM process. The results predict that the penetration depth of the electron beam, which is a function of the acceleration voltage, has a significant influence on evaporation effects. \end{abstract} Keywords: evaporation, thermal lattice Boltzmann method, free surfaces, selective electron beam melting (Some figures may appear in colour only in the online journal) \section*{1. Introduction} The adaptation of optical or particle beams to materials processing applications allows the precise machining of parts and the manufacturing of arbitrary components and devices. These processes are limited by thermal conduction at low and medium irradiances and by evaporation at high irradiances. This applies, for example, to the selective melting by an electron or laser beam (SEBM/SLM), welding or cladding, where heating and melting are inherent to the process. Apart from mass and energy transfer to the vapour phase, evaporation also generates recoil onto the melt surface. These effects can be taken advantage of, e.g. for deep penetration welding, or they can unintentionally impact the process itself by forming melt pool instabilities. Thus, the properties of the fabricated product such as bulk porosity or local alloy composition can be adversely influenced. As the interplay between beam absorption, conduction and phase changes is complex and depends on the process parameters, predictions based on numerical methods require a rigorous mathematical description of evaporation on the macroscopic scale. The kinetics of evaporation is well determined theoretically since the original work of Hertz in 1882 [1] and has been further elaborated upon by Anisimov [2], Ytrehus [3] and Knight [4]. The Knudsen layer that forms at the direct interface between the condensed matter and the vapour phase and that, in a macroscopic sense, constitutes a contact discontinuity is thereby described by analytical jump conditions. Following the literature on beam-based manufacturing processes, this theoretical approach is widely used for numerical computations of evaporation effects, particularly in laser keyhole welding, e.g. [5-7]. In this paper, we implement the evaporation model in an existing code based on the lattice Boltzmann method (LBM) with free surfaces. The main field of application is additive manufacturing by SEBM/SLM. Intense evaporation is not expected in the irradiance regime of interest, so that the emerging vapour plume and the gas phase do not have to be \section*{(a) Subsonic flow} (b) Supersonic flow \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9f4c77949db3cee9cebfg-03} \end{center} Figure 1. Schematic of the flow structure generated by an expanding vapour plume for (a) subsonic and sonic and (b) supersonic flow. Encircled letters denote flow regions of interest and are used as subscripts in the equations throughout this paper. resolved numerically. The model is hence simplified to the point that evaporation is represented by a local loss of mass and energy inducing a recoil pressure acting normal to the free surface. The theoretical approach is then validated against SEBM experiments in terms of melt pool depth and evaporative mass loss. Since the numerical model is currently limited to single-component evaporation, both a pure metal (titanium) and an alloy (Ti-6Al-4V) are considered in the experiments, in which the alloy has effective physical properties. Finally, an SEBM process conducted under given conditions is evaluated using numerically generated processing maps. In addition to the $60 \mathrm{kV}$ electron gun of the deployed SEBM machine, the impact of the beam acceleration voltage on the process window is numerically predicted. \section*{2. Mathematical model} \subsection*{2.1. Flow structure of the vapour plume} The evaporation of condensed matter under conditions imposed by heating using a laser or electron beam induces a vapour flow, as depicted in figure 1. The emerging vapour plume is characterized by a total of three transition layers across which the properties of the medium change from one equilibrium state to another and which separate the region of undisturbed ambient gas from the vapour at the surface of the target. In a macroscopic sense, these disturbances can be mathematically treated as gas dynamic discontinuities. The first upstream discontinuity in the immediate vicinity of the evaporating surface is the Knudsen layer. It typically has a thickness of the order of a few molecular mean free paths within which the evaporated particles approach translational equilibrium. The front of the expanding plume is a shock wave that propagates into the stagnant ambient gas. The shock wave causes a sharp increase in temperature and pressure of the ambient gas just behind it [8]. The regions of compressed ambient gas and expanding vapour phase are separated by a third contact discontinuity across which the pressure and velocity field is uniform, but the temperature and density undergo significant changes $[9,10]$. This flow structure as shown in figure 1(a) is typical of SLM processes, since these are generally conducted at atmospheric pressure using medium laser intensities, so that the vapour flow remains subsonic. In an expansion into a vacuum as is the case for SEBM processes or under conditions of intense evaporation (e.g. laser welding or drilling), though, a non-equilibrium rarefaction fan develops between the Knudsen layer and the vapour phase [3], see figure 1(b). The flow field in front of the Knudsen layer thus expands at supersonic speeds, while the flow at the outer boundary of the Knudsen layer is choked [4,11]. How the expanding vapour acts upon the condensed phase in terms of mass, momentum and energy is predominantly determined by the processes within the Knudsen layer. Therefore, an analytical solution of the Knudsen layer will be introduced into the evaporation model. The vapour phase in front of the Knudsen layer, on the other hand, will be disregarded in the numerical model. For manufacturing processes using an electron beam as energy source the neglect of the vapour phase is justified by the fact that the density of the vapour is much lower than that of its condensed phase. Thus, the interaction of free electrons with the vapour is considered to be insignificant. This holds for selective electron beam melting (SEBM) and electron beam welding where maximum temperatures are typically well below the critical temperature of the sample material, $T_{\text {crit }}$. In this regard, however, it is worth noting that the occurrence of a vapour plume may be of importance to laser-based manufacturing technologies as it can strongly affect laser attenuation and absorption. \subsection*{2.2. Evaporation and condensation fluxes} The evaporation of condensed matter can be rigorously described by the flux of particles leaving the surface of the condensed phase, $j^{+}$, and the flux of particles returning to the surface, $j^{-}$. The net mass transport from the evaporating surface per unit time is then given by \begin{equation*} j^{\mathrm{net}}=j^{+}-j^{-}=\left(\frac{j^{+}-j^{-}}{j^{+}}\right) \cdot j^{+}=\phi \cdot j^{+} \tag{1} \end{equation*} The evaporation coefficient $\phi$ yields the fraction of the net flux of particles that are able to escape into the half space with respect to the evaporation flux $j^{+}$. The accommodation coefficients for upstream and downstream flow are taken to be unity and are thus not included in equation (1) $[12,13]$. These coefficients define the probability of a particle to be emitted from the surface or to stick onto the surface upon impingement and not being scattered back into the corresponding half space, respectively. The fluxes may be found by assuming a half-range Maxwellian distribution function in the velocity space for evaporating particles and a full-range Maxwellian for condensing particles and by applying the principles of conservation of mass, momentum and translational energy. The basic procedure outlined in the following is based on a one-dimensional formulation of the problem. Furthermore, the vapour phase is expected to obey the ideal gas law. From\\ this, the evaporation flux is given by [1] \begin{equation*} j^{+}=p_{\mathrm{s}} \sqrt{\frac{m_{\mathrm{A}}}{2 \pi \cdot k_{\mathrm{B}} T_{\mathrm{s}}}} \tag{2} \end{equation*} where $m_{\mathrm{A}}$ is the atomic mass, $k_{\mathrm{B}}$ is Boltzmann's constant and $p_{\mathrm{s}}$ and $T_{\mathrm{s}}$ are the pressure and temperature at the vapour side of the phase interface, respectively. The pressure $p_{\mathrm{s}}$ can be interpreted as the saturated vapour pressure at surface temperature $T_{\mathrm{s}}$, which follows from the assumption that prior to vaporization the particles were in equilibrium with their condensed phase. This holds for pure metals. In the case of an alloy, the evaporation fluxes of each alloying element have to be considered individually taking into account the different partial vapour pressures [5]. In this paper, though, alloys are treated as pure materials having effective physical properties. The saturated vapour pressure is derived using the ClausiusClapeyron equation in its approximate form: \begin{equation*} \frac{1}{p_{\mathrm{s}}} \mathrm{d} p_{\mathrm{s}}=\frac{L_{\mathrm{vap}}\left(T_{\mathrm{s}}\right) \cdot m_{\mathrm{A}}}{k_{\mathrm{B}}} \cdot \frac{1}{T_{\mathrm{s}}^{2}} \mathrm{~d} T_{\mathrm{s}} \tag{3} \end{equation*} Introducing the temperature-dependent latent heat of vaporization, $L_{\text {vap }}\left(T_{\mathrm{s}}\right)$, as [14] \begin{equation*} L_{\text {vap }}\left(T_{\mathrm{s}}\right)=L_{\text {vap }, 0} \cdot \sqrt{1-\left(\frac{T_{\mathrm{s}}}{T_{\text {crit }}}\right)^{2}} \tag{4} \end{equation*} and carrying out the integration, the resulting expression for the saturated vapour pressure is \begin{align*} p_{\mathrm{s}}= & p_{\text {atm }} \cdot \exp \left\{-\frac{L_{\text {vap }, 0} \cdot m_{\mathrm{A}}}{k_{\mathrm{B}}} \cdot\left[\frac{1}{T_{\mathrm{s}}} \sqrt{1-\left(\frac{T_{\mathrm{s}}}{T_{\text {crit }}}\right)^{2}}\right.\right. \\ & -\frac{1}{T_{\text {boil }}} \sqrt{1-\left(\frac{T_{\text {boil }}}{T_{\text {crit }}}\right)^{2}} \\ & \left.\left.-\frac{1}{T_{\text {crit }}}\left(\sin ^{-1}\left(\frac{T_{\mathrm{s}}}{T_{\text {crit }}}\right)-\sin ^{-1}\left(\frac{T_{\text {boil }}}{T_{\text {crit }}}\right)\right)\right]\right\} . \tag{5} \end{align*} Here, $L_{\mathrm{vap}, 0}$ is the latent heat of vaporization at absolute zero temperature, $p_{\text {atm }}=1$ bar and $T_{\text {boil }}$ and $T_{\text {crit }}$ are the boiling temperature at standard atmosphere (1 bar) and the critical temperature, respectively. Considering non-equilibrium effects within the Knudsen layer, the condensation flux reads [15] \begin{equation*} j^{-}=p_{\mathrm{Kn}} \sqrt{\frac{m_{\mathrm{A}}}{2 \pi \cdot k_{\mathrm{B}} T_{\mathrm{Kn}}}} \cdot \beta \cdot F^{-} \tag{6} \end{equation*} where $p_{\mathrm{Kn}}$ and $T_{\mathrm{Kn}}$ are the pressure and temperature in the vapour at the outer side of the Knudsen layer and $\beta$ and $F^{-}$are dimensionless functions that account for collisional effects in downstream flow. The function $\beta$ as well as $p_{\mathrm{Kn}}$ and $T_{\mathrm{Kn}}$ additionally require jump conditions due to the abrupt change in temperature and density across the Knudsen layer, $T_{\mathrm{Kn}} / T_{\mathrm{S}}$ and $\rho_{\mathrm{Kn}} / \rho_{\mathrm{s}}$, respectively. These are detailed within the appendix. Note that neglecting downstream collisional effects, i.e. $\beta=1$ and $F^{-}=1$, and disregarding the temperature jump across the Knudsen layer one arrives at the well-known Hertz-Knudsen formula. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9f4c77949db3cee9cebfg-04} \end{center} Figure 2. Evaporation coefficient as a function of Mach number. The maximum value of 0.82 is attained when vapour flow approaches the sonic state. As indicated in equation (1), the net mass transport considering condensation can be subsumed within the evaporation coefficient $\phi$ which, using equations (2), (6) and equations in the appendix, reads [4] \begin{equation*} \phi=\sqrt{2 \pi \gamma_{v}} \cdot M a_{\mathrm{Kn}}\left(T_{\mathrm{s}}\right) \cdot \frac{\rho_{\mathrm{Kn}}}{\rho_{\mathrm{s}}} \sqrt{\frac{T_{\mathrm{Kn}}}{T_{\mathrm{s}}}} \tag{7} \end{equation*} where $\gamma_{v}$ is the ratio of specific heats and $M a_{\mathrm{Kn}}\left(T_{\mathrm{S}}\right)$ is the flow Mach number at the outer boundary of the Knudsen layer as a function of the surface temperature $T_{\mathrm{s}}$. For monoatomic gases $\gamma_{v}$ is $5 / 3$. The Mach number is considered known in this formula and will be derived later. Equation (7) shows that $\phi$ is a function of $M a_{\mathrm{Kn}}\left(T_{\mathrm{s}}\right)$ alone, which is also reflected in figure 2. The evaporation coefficient approaches its maximum value of $\phi_{\max }=0.82$ when the vapour flow outside the Knudsen layer becomes sonic. Due to the rarefaction fan that develops upon passing the sonic point (see figure 1(b)), supersonic flow can be observed in front of the Knudsen layer with $M a_{v}\left(T_{\mathrm{s}}\right)>1$, whereas the flow at the outer boundary of the Knudsen layer is choked. Consequently, even under vacuum conditions or conditions of intense evaporation, $M a_{\mathrm{Kn}}\left(T_{\mathrm{s}}\right) \leqslant 1$ holds, hence preserving a maximum value of 0.82 for the evaporation coefficient $[2,4,13,16]$. This is consistent with values published in the literature. Anisimov and Rakhmatulina [17] studied the accuracy of the hydrodynamic solution of vapour expanding into a vacuum as compared to the kinetic solution. They obtained an evaporation coefficient of roughly 0.8 , once gas dynamic flow is established. Also Fischer [18] found that $\phi$ approaches 0.85 as the Knudsen number tends to 0.1 , i.e. when vapour motion is within the gas dynamic expansion regime. Sibold and Urbassek [19] determined a value of 0.84 using Monte Carlo simulations of the evaporation into a vacuum. In order to couple the Mach number to known quantities like the surface temperature, $T_{\mathrm{s}}$, flow states diagrams can be\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9f4c77949db3cee9cebfg-05} Figure 3. (left) Flow states diagram for pure titanium in a helium atmosphere and different external pressures $p_{\mathrm{a}}$. Curves calculated using equations (5) and (8) and values from table 1. (right) Temperatures $T_{\mathrm{s}, 0}$ at $M a_{\mathrm{Kn}}=0$ and $T_{\mathrm{s}, 1}$ at $M a_{\mathrm{Kn}}=1$ as function of $p_{\mathrm{a}}$ computed from the flow states diagram. For a given ambient pressure, the curves span the temperature range where the evaporation coefficient, $\phi$, increases from 0 to its maximum value of 0.82 . used [4]. These diagrams define the possible flow states of the vapour phase at given ambient conditions and temperatures $T_{\mathrm{s}}$. A flow states diagram for pure titanium vapour in a helium atmosphere at $T_{\mathrm{a}}=298 \mathrm{~K}$ is exemplarily shown in figure 3 , left. The allowed flow states for the vapour are thereby determined by the intersections of two sets of curves that are defined in terms of the pressure ratio $p_{\mathrm{s}} / p_{\mathrm{a}}$, where $p_{\mathrm{s}}$ is the pressure directly at the surface of the target and $p_{\mathrm{a}}$ that of the ambient atmosphere. The full curves represent $p_{\mathrm{s}} / p_{\mathrm{a}}$ based on fluid mechanic considerations [4]: \begin{align*} \frac{p_{\mathrm{s}}}{p_{\mathrm{a}}} & =\left[1+\gamma_{\mathrm{a}} \cdot M a_{\mathrm{Kn}}\left(T_{\mathrm{s}}\right) \cdot \frac{c_{\mathrm{Kn}}}{c_{\mathrm{a}}} \cdot\left[\frac{\gamma_{\mathrm{a}}+1}{4} \cdot M a_{\mathrm{Kn}}\left(T_{\mathrm{s}}\right)\right.\right. \\ & \left.\left.\cdot \frac{c_{\mathrm{Kn}}}{c_{\mathrm{a}}}+\sqrt{1+\left(\frac{\gamma_{\mathrm{a}}+1}{4} \cdot M a_{\mathrm{Kn}}\left(T_{\mathrm{s}}\right) \cdot \frac{c_{\mathrm{Kn}}}{c_{\mathrm{a}}}\right)^{2}}\right]\right] \\ & \times\left[\frac{\rho_{\mathrm{Kn}}}{\rho_{\mathrm{s}}} \cdot \frac{T_{\mathrm{Kn}}}{T_{\mathrm{s}}}\right]^{-1} \tag{8} \end{align*} where $\gamma_{\mathrm{a}}$ is the ratio of specific heats of the ambient gas and $c_{\mathrm{Kn}} / c_{\mathrm{a}}$ the ratio of the speeds of sound: \begin{equation*} \frac{c_{\mathrm{Kn}}}{c_{\mathrm{a}}}=\sqrt{\frac{m_{\mathrm{A}, \mathrm{a}} \cdot \gamma_{v} \cdot T_{\mathrm{Kn}}}{m_{\mathrm{A}, v} \cdot \gamma_{\mathrm{a}} \cdot T_{\mathrm{a}}}} \tag{9} \end{equation*} The dashed curves in figure 3, left, can be obtained from the ratio of the saturated vapour pressure from equation (5) to the ambient pressure, $p_{\mathrm{a}}$. For example, at an ambient atmosphere as specified in figure 3 and an external pressure of $p_{\mathrm{a}}=1 \mathrm{bar}$, evaporation would start at a surface temperature of $T_{\mathrm{s}}=3558 \mathrm{~K}$, which is the boiling point at standard atmosphere, and reach its maximum for temperatures $T_{\mathrm{S}} \geqslant 4230 \mathrm{~K}$. Between these two temperature values the Mach number is approximately a linear function of $T_{\mathrm{s}}$. Thus, to correlate $\phi$ from equation (7) with the surface temperature, it is sufficient to determine $T_{\mathrm{s}, 0}$ and $T_{\mathrm{s}, 1}$, where $M a_{\mathrm{Kn}}\left(T_{\mathrm{s}, 0}\right)=0$ and $M a_{\mathrm{Kn}}\left(T_{\mathrm{s}, 1}\right)=1$. Figure 3, right, shows the variation of $T_{\mathrm{s}, 0}$ and $T_{\mathrm{s}, 1}$ with ambient pressure $p_{\mathrm{a}}$. \subsection*{2.3. Recoil pressure} Due to the conservation of momentum, the expanding vapour generates a recoil pressure, $p_{\text {recoil }}$, onto the evaporating surface. In the state of thermodynamic equilibrium between the vapour and its condensed phase, the flux of evaporating particles matches those of condensing particles. For $\phi=0, p_{\text {recoil }}$ thus originates in equal measure from the recoil of leaving particles and from collisions of condensing particles with the surface $[1,6]$, giving the recoil pressure as $p_{\text {recoil }}=$ $0.5 p_{\mathrm{s}}+0.5 p_{\mathrm{Kn}}=p_{\mathrm{s}}$. Note that $p_{\mathrm{Kn}}=p_{\mathrm{s}}$ in this case, see equations in the appendix. For higher evaporation fluxes, i.e. $\phi>0$, the contribution of returning particles to the recoil is governed by the evaporation coefficient. The condensing vapour thereby not only originates from the outer side of the Knudsen layer where $p_{\text {Kn }}$ prevails but from the whole Knudsen layer. Assuming the pressure to be linear throughout the Knudsen layer region between the values $p_{\mathrm{s}}$ and $p_{\mathrm{Kn}}$, we derive the following formulation for the recoil pressure: \begin{align*} p_{\text {recoil }} & =\frac{1}{2} p_{\mathrm{s}}+\frac{1}{2} \cdot(1-\phi) \cdot\left(\frac{1}{2} p_{\mathrm{Kn}}+\frac{1}{2} p_{\mathrm{s}}\right) \\ & =\frac{1}{2} p_{\mathrm{s}} \cdot\left[1+\frac{1}{2} \cdot(1-\phi) \cdot\left(1+\frac{\rho_{\mathrm{Kn}}}{\rho_{\mathrm{s}}} \frac{T_{\mathrm{Kn}}}{T_{\mathrm{s}}}\right)\right] \tag{10} \end{align*} with $(1-\phi)$ being the fraction of returning particles. Evaporation into high vacuum and/or under powerful\\ irradiation hence results in a minimum recoil pressure of $p_{\text {recoil }}=0.56 p_{\mathrm{s}}$, which is comparable to the values used by other researchers [6, 20-22]. \section*{3. Numerical model} The evaporation model introduced in the preceding section is implemented in an existing code based on the LBM. The LBM employed is a two-dimensional (2D) single phase free surface method [23] that is capable of simulating hydrodynamics as well as thermodynamics, including wetting and capillary forces [24, 25], convective mass and heat transport and melting and solidification [26]. The specific enthalpy is modified by the energy deposited into the material by the beam within each computational time step. For the experiments conducted in this paper, an electron beam is considered as the energy source. Local energy absorption is accurately modelled as a function of target material, acceleration voltage, depth and local surface obliquity using appropriate depth-dose profiles [27]. The free surface between the liquid and the gas phase is implicitly tracked by a volume of fluid method where the fluid fraction of each surface cell is monitored by tracking the net mass exchange to neighbouring cells. When a cell is entirely filled or emptied, the state of this cell is changed accordingly thus inducing a movement of the free surface [23]. Fluid transport is driven by capillary forces and by the recoil due to evaporation. In this regard, it should be emphasized that Marangoni convection has not been taken into account in the numerical simulations presented herein. The numerical procedure for the evaporation is illustrated in the flow chart in figure 4 . The specific enthalpy, $h_{E}(x, t)$, is easily transferred into an equivalent temperature value, $T(x, t)$, by means of the specific heat capacity, $c_{p}$ [26]. Here, $x$ is the location of the cell within the numerical grid and $t$ is time. The temperature controlling the evaporation process is the surface temperature $T_{\mathrm{s}}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)$. Evaporation is performed directly at the free surface of the condensed phase, so that $x_{\mathrm{s}}$ comprises surface cells only. Other driving parameters are the physical properties of the sample material as well as those of the ambient gas, both of which are input values provided by the user. Note that multicomponent evaporation is not considered in the evaporation model, so that the sample material has effective physical properties. Provided that diffusive evaporation is negligible, the requirement for evaporation to take place is that the saturated vapour pressure exceeds the external pressure, i.e. $p_{\mathrm{s}}\left(T_{\mathrm{s}}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)\right)>p_{\mathrm{a}}$ and thus $M a_{v}\left(T_{\mathrm{s}}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)\right)>0$ or $T_{\mathrm{s}}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)>T_{\mathrm{s}, 0}$. If the latter condition is fulfilled, $p_{\mathrm{s}}$ and the net evaporation flux, $j^{\text {net }}$, are computed as per equations (5) and (1), respectively. Evaporation involves both the transfer of mass, $\Delta m_{\text {rvap }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)$, and energy, $\Delta E_{\text {rvap }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)$, from the condensed to the gas phase as well as recoil onto the evaporating surface generated by the expanding vapour, $\Delta p_{\text {recoil }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)$. These quantities can be calculated as $\Delta p_{\text {recoil }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)=p_{\text {recoil }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)-p_{\mathrm{a}}$ $\Delta m_{\text {vap }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)=j^{\text {net }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right) \cdot \Delta t \cdot \Delta x^{2}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9f4c77949db3cee9cebfg-06} \end{center} Figure 4. Flow chart of the numerical procedure for the evaporation from a free surface cell. \begin{align*} & \Delta E_{\text {vap }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)=\Delta m_{\text {vap }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right) \cdot\left[L_{\text {vap }}\left(T_{\mathrm{s}}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)\right)+L_{\text {melt }}\right. \\ & \left.\quad+c_{p, \mathrm{~s}} \cdot T_{\text {liquidus }}+c_{p, 1} \cdot\left(T_{\mathrm{s}}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)-T_{\text {liquidus }}\right)\right] \tag{13} \end{align*} with $\Delta x$ being the spatial resolution, $L_{\text {melt }}$ the heat of fusion, $c_{p, \mathrm{~s}}$ and $c_{p, 1}$ the specific heat capacity in the solid and the liquid state, respectively, and $T_{\text {liquidus }}$ being the liquidus temperature. Since the vapour phase is neglected in the free surface formulation used in our numerical model, the evaporated mass and energy is removed from the surface cells. Accordingly, the state variables of the lattice are updated applying equations (11) to (13). In the following, a subscript 'pre' denotes values before and 'post' values after the evaporation procedure: $p_{\mathrm{G}, \text { post }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)=p_{\mathrm{G}, \text { pre }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)+\Delta p_{\text {recoil }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)$ $m_{\text {post }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)=m_{\text {pre }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)-\Delta m_{\text {vap }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)$ $h_{\mathrm{E}, \text { post }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)=\frac{h_{\mathrm{E}, \text { pre }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right) \cdot m_{\text {pre }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)-\Delta E_{\text {vap }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)}{m_{\text {pre }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)-\Delta m_{\text {vap }}\left(\boldsymbol{x}_{\mathrm{s}}, t\right)}$. Thereby, the recoil pressure is treated as a modification of the local gas pressure, $p_{\mathrm{G}}[23]$, where $p_{\mathrm{G}, \text { pre }}$ includes a pressure term for the surface tension which counteracts the evaporation recoil pressure. \section*{4. Experimental verification} Experimental verification is given by ex situ measurements on samples processed by SEBM. SEBM is an additive \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9f4c77949db3cee9cebfg-07} \end{center} Figure 5. Schematic of the SEBM system showing the key components. manufacturing technology where parts are built in a layerwise manner by applying metal powder in layers of constant thickness. Figure 5 illustrates a schematic view of the SEBM system. The powder is loaded into hoppers, fed to the build area and then raked into a uniform layer. Each raked layer is preheated using the electron beam as the energy source and then selectively molten following a 2D cross section of a 3D CAD model with the electron beam. The major factors having an impact on the quality of the fabricated part are the beam power, $P$, and the scanning speed, $v$, of the electron beam. The adjustment of the beam power can be achieved by a change in beam current or acceleration voltage, respectively. Details of the SEBM process are described elsewhere [28,29]. For the experimental verification carried out within this section, we use a modified SEBM process on an Arcam EBM S12 system (Arcam AB, Mölndal, Sweden). Therefore, continuous single tracks are molten in solid samples of pure titanium and Ti-6Al-4V (grade 5 titanium alloy). The application of powder layers as well as the preheating of the sample is disabled, so that the experiments are conducted at room temperature. Helium is used as the processing gas, whereby the external pressure is set to a value of $p_{\mathrm{a}}=0.2 \mathrm{~Pa}$. The acceleration voltage of the electron beam is $60 \mathrm{kV}$. Numerical experiments are performed within a domain that only comprises a small section of the real sample where the electron beam passes through the 2D plane with a predefined scanning speed. This approach implies that the thermal field of each single track is not affected by its neighbouring track. In fact, the experiments are designed in a way that prevents such an overlap. Since simulations are carried out in 2D, the electron beam is deflected out-of-plane and is represented by a 2D Gaussian distribution with a width of $w=4 \sigma=400 \mu \mathrm{m}$, with $\sigma$ being the standard deviation. The sample material has effective physical properties that are listed in table 1.\\ Table 1. Physical properties of pure titanium and the titanium alloy Ti-6Al-4V as used for the numerical calculations. \begin{center} \begin{tabular}{lll} \hline Physical property & Pure Ti & Ti-6Al-4V \\ \hline $m_{\mathrm{A}}(\mathrm{u})$ & $47.9[30]$ & $46.77^{\mathrm{a}}[30]$ \\ density, liquid $\left(\mathrm{kg} \mathrm{m}^{-3}\right)$ & $4130[30]$ & $4122[36]$ \\ dyn. viscosity $\left(\mathrm{mPa} \mathrm{s}^{2}\right)$ & $3.3[31]$ & $4.76[37]$ \\ surface tension $\left(\mathrm{J} \mathrm{m}^{-2}\right)$ & $1.52[32]$ & $1.52[37]$ \\ $c_{p, \mathrm{~s}}$, mean $\left(\mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1}\right)$ & $605[33]$ & $670[38]$ \\ $c_{p, 1}\left(\mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\right)$ & $966[33]$ & $1126[38]$ \\ $T_{\text {solidus }}(\mathrm{K})$ & - & $1878[39]$ \\ $T_{\text {liquidus }}(\mathrm{K})$ & $1940[34]$ & $1928[39]$ \\ $T_{\text {boil }}(\mathrm{K})$ & $3558[34]$ & $3315[40]$ \\ $T_{\text {crit }}(\mathrm{K})$ & $7890[35]$ & $7890^{\mathrm{b}}[35]$ \\ $L_{\text {melt }}\left(\mathrm{kJ} \mathrm{kg}^{-1}\right)$ & $305[30]$ & $290[38]$ \\ $L_{\text {vap }, 0}\left(\mathrm{~kJ} \mathrm{~kg}^{-1}\right)$ & $9700[30]$ & $9700^{\mathrm{b}}[30]$ \\ \hline \end{tabular} \end{center} ${ }^{a}$ Average atomic mass. ${ }^{\mathrm{b}}$ Values from pure titanium. \subsection*{4.1. Melt pool geometry} Model validation is accomplished by comparing single tracks produced by SEBM in dense Ti-6Al-4V samples in terms of shape and dimensions with model predictions. The simulation results of the temporal evolution of the melt pool for a line energy of $E_{\mathrm{L}}=P / v=0.25 \mathrm{~kJ} \mathrm{~m}^{-1}$ at a beam power of $300 \mathrm{~W}$ are exemplarily shown in figure 6 . The electron beam initially heats up and then melts the material directly beneath it. In the irradiance regime typical of SEBM, there is severe local superheating of the melt. As the surface temperature exceeds approximately $2950 \mathrm{~K}$, the recoil of the expanding vapour becomes large enough (about $0.05 \mathrm{bar}$ ) to accelerate the melt from the centre of the beam interaction zone towards its periphery inducing deformation of the melt pool. The temperature and thus the flow velocity approach their maximum values of $3225 \mathrm{~K}$ and $1.3 \mathrm{~m} \mathrm{~s}^{-1}$, respectively, when the electron beam is about to pass through the 2D plane, figure $6(a)$, whereas the maximum melt pool depth is attained behind the beam at a distance of about $1 \sigma$, figure $6(b)$. The high flow velocity indicates that recoil pressure has to be considered under these conditions, which are common to SEBM. After the electron beam has traversed the plane, the surface temperature falls rapidly and the melt that was first expelled from the interaction zone fills the formed small cavity again, figure $6(c)$, and solidifies there. Figures $7(a)-(c)$ show the simulation results of the temporal evolution of the melt pool for the line energies 0.15 and $0.50 \mathrm{~kJ} \mathrm{~m}^{-1}$ at a beam power of $300 \mathrm{~W}$. Liquid melt is thereby represented by red areas, the heat affected zone by different shades of blue and the electron beam, if being within the 2D plane, by yellow areas. Temperatures during the trial peak at $3150 \mathrm{~K}$ for the track melted with the low $E_{\mathrm{L}}$ and $3250 \mathrm{~K}$ for that with the high $E_{\mathrm{L}}$, resulting in maximum recoil pressures of around 0.2 bar and 0.4 bar, respectively. The corresponding micrograph cross sections of the single track experiments are depicted in figure $7(d)$. The numerical model, even though $2 \mathrm{D}$, matches the experimental results remarkably well. Note that within the model hydro- as well as thermodynamics are not solved in the third dimension. That is, in the lateral direction melt flow is solely perpendicular to the\\ (a) centre of the beam \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9f4c77949db3cee9cebfg-08(2)} \end{center} (b) at $1 \times \sigma$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9f4c77949db3cee9cebfg-08(1)} \end{center} (c) at $1.5 \times \sigma$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9f4c77949db3cee9cebfg-08} \end{center} Figure 6. Simulated melt pool formation in a dense Ti-6Al-4V sample under the action of a $60 \mathrm{kV}$ electron beam of power $300 \mathrm{~W}$ and line energy $0.25 \mathrm{~kJ} \mathrm{~m}^{-1}$ at different beam positions, (a)-(c). Temperature plots are shown on the left and flow velocity on the right. The beam width is $4 \sigma=400 \mu \mathrm{m}$. Spatial resolution is $1 \mu \mathrm{m}$. direction of beam movement. Also, heat conduction out of the simulated plane is not accounted for, which is why for titanium and its alloys scanning speeds considerably below about 0.2 to $0.3 \mathrm{~m} \mathrm{~s}^{-1}$ may yield inaccurate predictions of the melt pool due to the thermal front preceding the electron beam. For higher scanning speeds, experimental and numerical results exhibit similar overall characteristics, not only with regard to the melt pool shape, but also the melt pool width and depth. The latter is thereby measured from the unprocessed surface where no protrusions exist at the melt pool periphery. The maximum attainable melt pool depth for beam powers of 120 and $300 \mathrm{~W}$ and different scanning speeds, as plotted in figure 8 , shows that numerical results are in good agreement with experimental data. \subsection*{4.2. Mass loss} The loss of mass due to evaporation is determined from the difference in mass before and after the trial. The samples are plates of pure titanium and Ti-6Al- $4 \mathrm{~V}$, respectively, with dimensions of about $40 \times 30 \mathrm{~mm}^{2}$ and a thickness of $5 \mathrm{~mm}$. The electron beam is deflected following a rectangular, closed contour with an edge length of $35 \mathrm{~mm} \times 25 \mathrm{~mm}$. This procedure is repeated a total of 200 to 500 times per sample and trial depending on process parameters. In order to prevent the plates from heating up beyond room temperature during the trial, the process is paused for $30 \mathrm{~s}$ after each contour. For the experiments at hand, beam powers of 150,300 and $450 \mathrm{~W}$ at a constant line energy of $E_{\mathrm{L}}=0.15 \mathrm{~kJ} \mathrm{~m}^{-1}$ are used. The scanning speeds are $1.0 \mathrm{~m} \mathrm{~s}^{-1}, 2.0 \mathrm{~m} \mathrm{~s}^{-1}$ and $3.0 \mathrm{~m} \mathrm{~s}^{-1}$, respectively. Sample masses are measured on an analytical balance with $0.1 \mathrm{mg}$ readability. In figure 9 simulation results are compared with experimental data. The mass loss was found to be a strong function of the beam width, $w$, obeying an exponential decay. This is in contrast to the melt pool geometry investigated in section 4.1 which, to a certain extent, is only weakly dependent on $w$. Since the beam width is difficult to access experimentally, the value of $w$ is varied in steps of $25 \mu \mathrm{m}$ within the range of 375-425 $\mu \mathrm{m}$. The numerical calculations show that for a constant beam width the mass loss increases exponentially with beam power. The measured mass loss, however, does not follow this trend, indicating that the electron beam widens with increasing beam power. Taking that as a premise, good agreement between numerical and experimental data is observed. By this means, the beam width would be slightly below $400 \mu \mathrm{m}$ for beam powers of $150 \mathrm{~W}$ and slightly above $400 \mu \mathrm{m}$ for $450 \mathrm{~W}$, which applies to both the experiments with pure titanium and Ti-6Al-4V. It is apparent from the results in figure 9 that total mass loss from the titanium alloy samples is approximately twice that from pure titanium under identical process conditions. The additional mass loss may be related to the aluminium which has a vapour pressure that, in the temperature regime of interest, is roughly one to two orders of magnitude higher than that of pure titanium. As noted above, multicomponent evaporation is currently not included in the evaporation model, requiring effective physical properties for the sample material, see table 1 . Since predicted mass losses are in accordance with experimental findings, these effective properties appear to accurately reproduce the behaviour of the titanium alloy. \section*{5. Simulation of processing maps for SEBM} The use of radiative energy sources for technical applications entails a process window that is well defined in terms of scanning speed $v$ (or pulse duration), beam power $P$ and line energy $E_{\mathrm{L}}$, respectively. This process window constitutes particular parameter sets within a processing map that are suited for producing sound parts. In this section, such processing maps are computed for an SEBM process. Thereby, instead of manufacturing parts by melting powder layer by layer, we simulate continuous single tracks obtained by selectively melting solid samples of Ti-6Al-4V. The energy source is a $60 \mathrm{kV}$ electron beam which has also been employed for experiments conducted in section 4 . In addition, processing maps for an electron beam with an acceleration voltage of $120 \mathrm{kV}$ are generated and compared with those obtained with the $60 \mathrm{kV}$ beam. The electron beam is deflected out of the simulated 2D plane. The intensity of the beam obeys a 2D Gaussian distribution with a constant width of $4 \sigma=400 \mu \mathrm{m}$ which is assumed to be independent of the beam power. Prior to melting the single tracks, the temperature of the sample material is set to an initial value of $800^{\circ} \mathrm{C}$. This substitutes for the preheating step which is typical for processing powder in SEBM. The processing gas $(\mathrm{He})$ is assumed to be at $800^{\circ} \mathrm{C}$ and at a pressure of $p_{\mathrm{a}}=0.2 \mathrm{~Pa}$. Factors limiting the SEBM process are the maximum melt pool depth to provide for a sufficient connection between two consecutive layers, strong melt pool dynamics due to the recoil of the expanding vapour and evaporative losses. These effects occur at opposite ends of the line energy spectrum $$ \boldsymbol{E}_{\mathrm{L}}=0.15 \mathrm{~kJ} / \mathrm{m}: P=300 \mathrm{~W}, v=2.0 \mathrm{~m} / \mathrm{s} \quad \boldsymbol{E}_{\mathrm{L}}=\mathbf{0 . 5 0} \mathbf{~ k J} / \mathbf{m}: P=300 \mathrm{~W}, v=0.6 \mathrm{~m} / \mathrm{s} $$ (a) centre of the beam\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9f4c77949db3cee9cebfg-09(3)} (b) at $1 \times \sigma$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9f4c77949db3cee9cebfg-09} (c) at $>2 \times \sigma$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9f4c77949db3cee9cebfg-09(1)} (d) micrographs\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9f4c77949db3cee9cebfg-09(2)} Figure 7. Continuous single tracks in dense Ti-6Al-4V samples melted by a $60 \mathrm{kV}$ electron beam with a power of $300 \mathrm{~W}$ at different line energies. (a) $-(c)$ Simulated temporal evolution of the melt pool with $\sigma=100 \mu \mathrm{m}$. Spatial resolution is $1 \mu \mathrm{m}$. (d) Micrograph cross sections of the experimental single tracks, whereby the molten area is indicated by a solid line and the computed envelope of the melt pool by a broken line. and thus span the aforementioned process window. The simulated processing maps for the $60 \mathrm{kV}$ electron beam are shown in figure 10, left. The melt pool depth, figure 10(a), increases with the line energy as expected. Generally, for a constant $E_{\mathrm{L}}$ and supposing the entire energy provided by the electron beam to be consumed for melting, the melt pool depth should be independent of the scanning speed hence leading to horizontal contour lines. However, owing to heat losses by thermal conduction into the bulk at very low scanning speeds and molten metal expulsion to the periphery of the melt pool due to evaporation at high scanning speeds (and high irradiance) the melt pool depth reaches its maximum somewhere in between, resulting in V-shaped contour lines. From the mass loss and recoil pressure contour plots in figures $10(b)$ and (c) it becomes apparent that a deep melt pool implicates considerable melt pool hydrodynamics and mass removal. These effects are most pronounced at higher scanning speeds. Melt pool oscillations induced by the recoil pressure lead to an unsteady melt pool surface. For instance, the 1 bar and 10 bar lines nearly coincide with a maximum velocity in the melt zone directly affected by the beam of approximately $10 \mathrm{~m} \mathrm{~s}^{-1}$ and $20 \mathrm{~m} \mathrm{~s}^{-1}$, respectively. The melt track, when solidified, exhibits characteristic corrugations that could not be balanced by surface tension, see also [41]. The dashed curve in figure $10(b)$ additionally illustrates the threshold above which maximum temperatures reached on the melt pool surface are in excess of the boiling temperature at standard atmosphere, $T_{\text {boil }}$. The evaporation of mass, on the other hand, is particularly important when processing alloys. Multicomponent evaporation may cause a local change in alloy composition, and eventually create gradients in the mechanical properties of the final part. The processing maps for the $120 \mathrm{kV}$ electron beam are depicted in figure 10, right. The main difference between the two acceleration voltages lies in the maximum depth of penetration. While for the $60 \mathrm{kV}$ beam most of the electron beam energy is dissipated within a distance of about $10 \mu \mathrm{m}$ from the target surface, it is about $30 \mu \mathrm{m}$ for the $120 \mathrm{kV}$ beam. This effectively increases the maximum melt pool depth by roughly $5-10 \%$, seen in the shift of the isolines to lower line \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9f4c77949db3cee9cebfg-10} \end{center} Figure 8. Maximum melt pool depth of continuous single tracks in dense Ti-6Al-4V samples for beam powers of 120 and $300 \mathrm{~W}$. energies in figure $10(d)$. The gain in melt pool depth is not considered significant, so that the lower bound of the process window can be defined irrespective of the electron beam's acceleration voltage. In contrast, the recoil pressure and the mass loss are severely affected by the acceleration voltage, since they are strong functions of the surface temperature. The contour lines of both the recoil pressure and the mass loss run into saturation at high scanning speeds. Consequently, there exists a line energy such that the recoil and the mass loss become largely independent of the scanning speed. This enables a reduction of the total process time without causing additional adverse effects due to evaporation. As the impact of the recoil pressure is not only connected with its peak value but also the duration of action which is not taken into account in figures $10(b)$ and $(e)$, the mass loss is more appropriate for defining the upper bound of the process window. The increase in acceleration voltage shifts the lines of constant mass loss to higher line energies by a value of about $0.05 \mathrm{~kJ} \mathrm{~m}^{-1}$. Due to more distinct volume heating in the case of the $120 \mathrm{kV}$ beam, the process window is thus considerably enlarged as compared to the $60 \mathrm{kV}$ beam. Hence, the $120 \mathrm{kV}$ beam can operate at higher $E_{\mathrm{L}}$ if porosity is an issue or at higher scanning speeds if total process time is of importance. For technical applications involving (partial) melting of the target it appears preferable to employ radiative energy sources with which bulk heating rather than surface heating can be achieved. This is most interesting for precise material processing, since thereby superheating of the target is less pronounced minimizing evaporative losses while preserving a certain melt pool depth. \section*{6. Conclusion} An evaporation model that accounts for the loss of mass and energy as well as the recoil pressure onto the melt surface has\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9f4c77949db3cee9cebfg-10(1)} Figure 9. Mass loss of pure titanium and Ti-6Al-4V samples due to evaporation for different beam powers at a constant line energy of $0.15 \mathrm{~kJ} \mathrm{~m}^{-1}$. Simulation results are plotted for different beam widths $w=4 \sigma$. been successfully implemented into a 2D lattice Boltzmann method. Numerical results were shown to compare very well with experimental measurements obtained by melting continuous single tracks by an electron beam. Finally, the model has been applied to create processing maps under conditions typical for selective electron beam melting (SEBM). The goal of this investigation has been to determine the impact of the electron beam's acceleration voltage on the attainable melt depth, the mass loss and the recoil due to evaporation. We conclude that due to a wider process window, an increase in acceleration voltage from 60 to $120 \mathrm{kV}$ for medium atomic number materials like titanium or its alloys is most promising.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9f4c77949db3cee9cebfg-11} Figure 10. Computed processing maps for single tracks in Ti-6Al-4V samples at a preheating temperature of $800^{\circ} \mathrm{C}$. The tracks are melted by an electron beam with an acceleration voltage of $60 \mathrm{kV}$ (left) and $120 \mathrm{kV}$ (right), respectively. The processing gas is He at a temperature of $800^{\circ} \mathrm{C}$ and a pressure of $0.2 \mathrm{~Pa}$. \section*{Acknowledgments} The authors gratefully acknowledge funding of the German Research Foundation (DFG) within the project KO 1984/9-1 and partial funding within the Collaborative Research Center 814 'Additive Manufacturing', project B2. \section*{Appendix. Knudsen layer jump conditions} The contact discontinuity at the direct interface between the condensed and the vapour phase can be modelled using macroscopic jump conditions for the temperature and the density, $T_{\mathrm{Kn}} / T_{\mathrm{S}}$ and $\rho_{\mathrm{Kn}} / \rho_{\mathrm{s}}$, respectively. In the following,\\ all functions are defined in terms of the dimensionless velocity $S_{\text {Kn }}[4,15]$ : \begin{equation*} S_{\mathrm{Kn}}=\sqrt{\frac{\gamma_{v}}{2}} \cdot M a_{\mathrm{Kn}}\left(T_{\mathrm{s}}\right) \tag{A1} \end{equation*} with $\gamma_{v}$ being the ratio of specific heats and $M a_{\mathrm{Kn}}\left(T_{\mathrm{s}}\right)$ being the flow Mach number of the vapour phase. For the Knudsen layer the following system of equations applies $[2-4,16]$ : \begin{equation*} \sqrt{\frac{T_{\mathrm{Kn}}}{T_{\mathrm{s}}}}=\sqrt{1+\pi\left(\frac{\gamma_{v}-1}{\gamma_{v}+1} \cdot \frac{S_{\mathrm{Kn}}}{2}\right)^{2}}-\sqrt{\pi} \cdot \frac{\gamma_{v}-1}{\gamma_{v}+1} \cdot \frac{S_{\mathrm{Kn}}}{2} \tag{A2} \end{equation*} $$ \begin{aligned} & \frac{\rho_{\mathrm{Kn}}}{\rho_{\mathrm{s}}}=\sqrt{\frac{T_{\mathrm{S}}}{T_{\mathrm{Kn}}}} \cdot\left[\frac{1}{2}\left(2 S_{\mathrm{Kn}}^{2}+1\right) \cdot \exp \left(S_{\mathrm{Kn}}^{2}\right)\right. \\ & \left.\cdot \operatorname{erfc}\left(S_{\mathrm{Kn}}\right)-\frac{S_{\mathrm{Kn}}}{\sqrt{\pi}}\right] \\ & +\frac{1}{2} \frac{T_{\mathrm{S}}}{T_{\mathrm{Kn}}} \cdot\left[1-\sqrt{\pi} \cdot S_{\mathrm{Kn}} \cdot \exp \left(S_{\mathrm{Kn}}^{2}\right) \cdot \operatorname{erfc}\left(S_{\mathrm{Kn}}\right)\right] \\ & \beta\left(S_{\mathrm{Kn}}\right)=\left[\left(2 S_{\mathrm{Kn}}^{2}+1\right)-\sqrt{\pi} \cdot S_{\mathrm{Kn}} \cdot \sqrt{\frac{T_{\mathrm{s}}}{T_{\mathrm{Kn}}}}\right] \\ & \cdot \exp \left(S_{\mathrm{Kn}}^{2}\right) \cdot \frac{\rho_{\mathrm{s}}}{\rho_{\mathrm{Kn}}} \sqrt{\frac{T_{\mathrm{s}}}{T_{\mathrm{Kn}}}} \\ & F^{-}\left(S_{\mathrm{Kn}}\right)=\exp \left(-S_{\mathrm{Kn}}^{2}\right)-\sqrt{\pi} \cdot S_{\mathrm{Kn}} \cdot \operatorname{erfc}\left(S_{\mathrm{Kn}}\right) \end{aligned} $$ where $\gamma_{v}$ is the ratio of specific heats which is $5 / 3$ for monoatomic gases and erfc the complementary error function. From the ideal gas law, the pressure in the vapour at the outer side of the Knudsen layer, $p_{\mathrm{Kn}}$, can now be expressed as \begin{equation*} p_{\mathrm{Kn}}=p_{\mathrm{s}} \cdot \frac{\rho_{\mathrm{Kn}}}{\rho_{\mathrm{s}}} \frac{T_{\mathrm{Kn}}}{T_{\mathrm{s}}} \tag{A6} \end{equation*} and the temperature $T_{\mathrm{Kn}}$ as \begin{equation*} T_{\mathrm{Kn}}=T_{\mathrm{s}} \cdot \frac{T_{\mathrm{Kn}}}{T_{\mathrm{s}}} \tag{A7} \end{equation*} \section*{References} [1] Hertz H 1882 Ueber die Verdunstung der Flüssigkeiten, insbesondere des Quecksilbers, im luftleeren Raume Ann. Phys. Chem. 17 177-93 [2] Anisimov S I 1968 Vaporization of metal absorbing laser radiation Sov. Phys.-JETP 27 182-3 [3] Ytrehus T 1975 Kinetic theory description and experimental results for vapor motion in arbitrary strong evaporation von Karman Institute for Fluid Dynamics Technical Note 112 [4] Knight C J 1979 Theoretical modeling of rapid surface vaporization with back pressure AIAA J. 17 519-23 [5] Mundra K and DebRoy T 1993 Calculation of weld metal composition change in high-power conduction mode carbon dioxide laser-welded stainless steel Metall. Trans. B 24 145-55 [6] Ki H, Mohanty P S and Mazumder J 2002 Modeling of laser keyhole welding: I. Mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free surface evolution Metall. Mater. Trans. A 33 1817-30\\ [7] Tan W, Bailey N S and Shin Y C 2013 Investigation of keyhole plume and molten pool based on a three-dimensional dynamic model with sharp interface formulation J. Phys. D: Appl. Phys. 46055501 [8] Zhang Z and Gogos G 2005 Effects of laser intensity and ambient conditions on the laser-induced plume Appl. Surf. Sci. 252 1057-64 [9] Aden M, Beyer E and Herziger G 1990 Laser-induced vaporisation of metal as a Riemann problem J. Phys. D: Appl. Phys. 23 655-61 [10] Zhang Z and Gogos G 2004 Theory of shock wave propagation during laser ablation Phys. Rev. B 69235403 [11] Zhang Z and Sheng B 2007 Thermal choke of the evaporation wave during laser ablation AIAA J. 45 3006-9 [12] Langmuir I 1913 The vapor pressure of metallic tungsten Phys. Rev. 2 329-42 [13] Tsai C-H and Olander D R 1986 Numerical modelling of heat and mass transport during rapid heating and vaporization of binary solids by absorbing radiation-application to $\mathrm{UO}_{2}$ J. Nucl. Mater. 137 279-87 [14] Yilbas B S 1997 Laser heating process and experimental validation Int. J. Heat Mass Transfer 40 1131-43 [15] Ytrehus T and Ostmo S 1996 Kinetic theory approach to interphase processes Int. J. Multiphase Flow 22 133-55 [16] Luikov A V, Perelman T L and Anisimov S I 1971 Evaporation of a solid into vacuum Int. J. Heat Mass Transfer 14 177-84 [17] Anisimov S I and Rakhmatulina A K 1973 The dynamics of the expansion of a vapor when evaporated into a vacuum Sov. Phys.-JETP 37 441-4 [18] Fischer J 1976 Distribution of pure vapor between two parallel plates under the influence of strong evaporation and condensation Phys. Fluids 19 1305-11 [19] Sibold D and Urbassek H M 1993 Monte Carlo study of Knudsen layers in evaporation from elemental and binary media Phys. Fluids A $5243-56$ [20] Batanov V A, Bunkin F V, Prokhorov A M and Fedorov V B 1973 Evaporation of metallic targets caused by intense optical radiation Sov. Phys.-JETP 36 311-22 [21] Mazhukin V I and Samokhin A A 1984 Kinetics of a phase transition during laser evaporation of a metal Sov. J. Quantum Electron. 14 1608-11 [22] Semak V and Matsunawa A 1997 The role of recoil pressure in energy balance during laser materials processing J. Phys. D: Appl. Phys. 30 2541-52 [23] Körner C, Thies M, Hofmann T, Thürey N and Rüde U 2005 Lattice Boltzmann model for free surface flow for modeling foaming J. Stat. Phys. 121 179-96 [24] Attar E and Körner C 2009 Lattice Boltzmann method for dynamic wetting problems $J$. Colloid Interface Sci. 335 84-93 [25] Körner C, Attar E and Heinl P 2011 Mesoscopic simulation of selective beam melting processes J. Mater. Process. Technol. 211 978-87 [26] Attar E and Körner C 2011 Lattice Boltzmann method for thermal free surface flows with liquid-solid phase transition Int. J. Heat Fluid Flow 32 156-63 [27] Klassen A, Bauereiß A and Körner C 2014 Modelling of electron beam absorption in complex geometries $J$. Phys. D: Appl. Phys. 47065307 [28] Heinl P, Rottmair A, Körner C and Singer R F 2007 Cellular titanium by selective electron beam melting $A d v$. Eng. Mater. $9360-4$ [29] Heinl P, Müller L, Körner C, Singer R F and Müller F A 2008 Cellular Ti-6Al-4V structures with interconnected macro porosity for bone implants fabricated by selective electron beam melting Acta Biomater. 4 1536-44 [30] Iida T and Guthrie R I L 1988 The Physical Properties of Liquid Metals (Oxford: Clarendon) [31] Ishikawa T, Paradis P-F, Okada J T and Watanabe Y 2012 Viscosity measurements of molten refractory metals using an electrostatic levitator Meas. Sci. Technol. 23025305 [32] Lu H M and Jiang Q 2005 Surface tension and its temperature coefficient for liquid metals J. Phys. Chem. B 109 15463-8 [33] Desai P D 1987 Thermodynamic properties of titanium Int. J. Thermophys. 8 781-94 [34] Brandes E A and Brook G B 1992 Smithells Metals Reference Book 7th edn (Oxford: Butterworth-Heinemann) p 14-2 [35] Ablesimov N E, Verkhoturov A D and Pyachin S A 1998 On the energy criterion for the erosion resistance of metals Powder Metall. Met. C 37 94-8 [36] Li J J Z, Johnson W L and Rhim W-K 2006 Thermal expansion of liquid Ti-6Al-4V measured by electrostatic levitation Appl. Phys. Lett. 89111913 [37] Wunderlich R K 2008 Surface tension and viscosity of industrial Ti-alloys measured by the oscillating drop method on board parabolic flights High Temp. Mater. Process. 27 401-12 [38] Boivineau M, Cagran C, Doytier D, Eyraud V, Nadal M-H, Wilthan B and Pottlacher G 2006 Thermophysical properties of solid and liquid Ti-6Al-4V (TA6V) alloy Int. J. Thermophys. 27 507-29 [39] Boyer R, Welsch G and Collings E W 1998 Materials Properties Handbook: Titanium Alloys (Materials Park, $\mathrm{OH}$ : ASM International) p 513 [40] Rai R, Burgardt P, Milewski J O, Lienert T J and DebRoy T 2009 Heat transfer and fluid flow during electron beam welding of $21 \mathrm{Cr}-6 \mathrm{Ni}-9 \mathrm{Mn}$ steel and Ti-6Al- $\mathrm{V}$ alloy J. Phys. D: Appl. Phys. 42025503 [41] Fabbro R 2010 Melt pool and keyhole behaviour analysis for deep penetration laser welding J. Phys. D: Appl. Phys. 43445501 \end{document} \documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[version=4]{mhchem} \usepackage{stmaryrd} \usepackage{hyperref} \hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,} \urlstyle{same} \usepackage{graphicx} \usepackage[export]{adjustbox} \graphicspath{ {./images/} } \title{Phase field simulation of powder bed-based additive manufacturing } \author{Liang-Xing Lu, N. Sridhar, Yong-Wei Zhang*\\ Institute of High Performance Computing, A*STAR, Singapore 138632, Singapore} \date{} %New command to display footnote whose markers will always be hidden \let\svthefootnote\thefootnote \newcommand\blfootnotetext[1]{% \let\thefootnote\relax\footnote{#1}% \addtocounter{footnote}{-1}% \let\thefootnote\svthefootnote% } %Overriding the \footnotetext command to hide the marker if its value is `0` \let\svfootnotetext\footnotetext \renewcommand\footnotetext[2][?]{% \if\relax#1\relax% \ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else% \if?#1\ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else\svfootnotetext[#1]{#2}\fi% \fi } \begin{document} \maketitle Full length article \section*{A R T I C L E I N F O} \section*{Article history:} Received 13 March 2017 Received in revised form 15 November 2017 Accepted 17 November 2017 Available online 1 December 2017 \section*{Keywords:} Additive manufacturing Phase field simulation Microstructure \begin{abstract} A B S T R A C $T$ Quality control in parts built layer-by-layer via Additive Manufacturing (AM) process is still a challenge since critical features, such as the control in porosity, residual stress and deformation, surface roughness and microstructure, are yet to be fully addressed. In this work, we develop a phase field model to simulate powder bed-based AM, focusing on the effects of two major process parameters, the beam power and scanning speed, on the melt pool size and shape, porosity and grain structure. The model reproduces many important phenomena observed experimentally and reveals scaling relations for the depth and length of melt pool, the porosity and the grain density on process parameters. We find critical power densities below which the grain density or the porosity increases rapidly and the grain structure is controlled by different mechanisms in different power density regimes which allows for the possibility of controlling the grain structure. The present work could serve as a useful reference for accurate control of defects and microstructure in AM build. \end{abstract} (C) 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. \section*{1. Introduction} Additive manufacturing (AM), also known as three-dimensional (3D) printing, refers to the process of building an object in a layerby-layer manner. Selective laser melting (SLM) and electron beam melting (EBM) are two commonly-used AM processes to create three-dimensional metal parts by fusing fine powder together [1-3]. In these AM processes, an electron or laser beam selectively scans a paved metal powder layer, resulting in the formation of a melt pool. Subsequent solidification of the melt pool transforms the porous metal powder into a dense layer. After completion of one layer, the whole powder bed is lowered and a new powder layer is spread on the surface of the just-solidified layer, and the scanningmelting-solidification process is repeated until the component is built. These metal powder bed-based additive manufacturing (MPBAM) technologies are currently being considered in the manufacturing of aerospace and medical orthopedic components. Clearly, component quality with MPBAM depends on many factors, such as packing and spreading of the metal powder, interaction of electron/laser beam with the powder, heat conduction in and between solid, melt pool and surrounding environment, solid to liquid phase transformation and re-solidification, fluid dynamics of the melt pool, and pre-heating of the powder bed, etc. [4-18]. As \footnotetext{\begin{itemize} \item Corresponding author. \end{itemize} E-mail address: \href{mailto:zhangyw@ihpc.a-star.edu.sg}{zhangyw@ihpc.a-star.edu.sg} (Y.-W. Zhang). } a result, control of the part quality is still a challenge. In particular, controls in porosity, residual stress and deformation, surface roughness, and microstructure are yet to be fully addressed. Various models and simulation methods have been developed to understand and control AM processes [7,10,16-21]: Packing of metal powder using the "rain" model or discrete element method [10,17]; simulation of residual stress with finite element algorithms based on homogenized approximation of the powder bed [16]; melt pool dynamics with either Navier-Stokes equation or lattice Boltzmann methods [7,10], and simulation of microstructure evolution using either cellular automaton method or phase field methods [19-21]. Clearly, there is a demand to develop an integrated computational platform coupling various phenomena or models together to understand and ultimately control and optimize the AM build process. As mentioned earlier, porosity and microstructure control is still largely not possible in current metal AM processes. Synchrotron tomography and three-dimensional reconstruction [22] show two dominant types of voids: process-induced voids with irregular crack-like geometry and gas-induced voids with rounded shape, with the former being caused by the insufficient fusion of powder, while the latter by overheating of powder. For gas-induced voids, there were several studies using fluid dynamic methods to model the melt flow and the trapping and freezing of gas bubbles in the melt pool $[7,23,24]$. However, for process-induced voids, we found only one reference [25] studying void formation during the melting and re-solidification of multilayers of the metal powder using\\ lattice Boltzmann method. Their simulation results were in qualitative agreement with experimental observations. In addition, a spatial Gaussian process regression model was developed to predict the porosity in metal-based AM process [26], and good agreement was achieved against experimental results. It is noted that these methods are unable to provide a physical understanding behind the metal AM process and there are few studies on the modelling and simulation for the formation of process-induced voids. Besides voids and porosity, microstructure is another important factor that strongly influences the mechanical properties of AMbuilt components. Existing experiments [1-3] show process parameters, such as beam power, scanning speed, hatch distance, and scan strategy greatly influence the grain size, aspect ratio, and grain texture. Often, the relationship between these process parameters and the component grain microstructure is very complex. Several studies were performed to understand the formation of microstructure in AM processes [27-31]. Zinoviev et al. [27]. coupled the Goldak heat source model with a cellular automata (CA) model to simulate columnar grain growth from the base plate. Botello et al. [28]. simulated the 2D grain structure of AA-2024 alloy by coupling a finite element model for the melt pool and a CA model for grain nucleation and growth. Both powder and melt pool dynamics were not explicitly considered in these studies. As opposed to their predictions, experimental observations show that the solidification process in powder bed AM is often dominated by epitaxial grain growth, and new grains are mainly introduced by partially melted powder. Considering this fact, it is necessary to explicitly consider powder in simulating the microstructure of AM components. Rai et al. $[29,30]$. developed a 2D model, which couples a powder scale lattice Boltzmann model with a CA model to simulate the microstructural evolution in IN718 alloy. They showed epitaxial columnar grain growth and new grain nucleation from partially melted powder. Recently, Panwisawas et al. [31]. employed a 3D framework to study the formation of grain structure from the melt pool using a fluid dynamics method. In this 3D work, a nucleation model was used to introduce new grains. Previous experimental observations [22] show that in the low to moderate power density regime, the contribution from convection in the fluid dynamics of the melt pool is insignificant and the resulting void formation is negligible. In this regime of MPBAM, mass transport via diffusion is the dominant mechanism in the melt pool dynamics and in consolidating the powder particles into the solidified part. Based on this understanding, the phase field method, which has been successfully applied to many microstructure evolution problems such as in dendritic solidification and grain growth [20,21], is an appropriate approach to simulate the metal AM process. In fact, there were several attempts in using phase field simulations for AM process. For example, Gong et al. [20]. and Sahoo et al. [21]. simulated the dendritic growth of Ti-6Al-4V alloy in electron beam-induced melt pool. Krivilyov et al. [32]. developed a phase field model to simulate the consolidation process of $\mathrm{Fe}$ powder. Clearly, in the diffusion-dominated regime, phase field method is capable of simulating melting, solidification, and grain growth and substantially reduces the complexity of the calculation algorithm and the use of computational resources. In the present work, a 3D phase field model is developed to simulate MPBAM process in the low to moderate power density regime. This new model captures melting and re-solidification and the grain structure formation under a unified framework. Instead of direct 3D simulations, large-scale 2D simulations are performed to study the effects of power density and scan speed on the formation of porosity and grain structure. These 2D simulations provide better visualization and intuitive comprehension on the details of MPBAM process than 3D simulations. These 2D simulations also reproduce many important features frequently observed in MPBAM in the low to moderate lower density regime, such as the balling effect, formation of process-induced pores, lack of fusion between layers, and solid state sintering between powder particles of the built components. The simulations also reveal scaling relations between the porosity and grain structure and the "power density", which is defined as the ratio of beam power to scanning velocity, and these scaling relations are consistent with existing experimental results. Although the current study focuses on MPBAM, the findings are expected to extend to other powder-based techniques that share similar mechanisms, such as direct energy deposition. \section*{2. Model} \subsection*{2.1. Phase and grain representations} Fig. 1 shows a schematic of the model. Four phases are included: the gas or vapor phase represented by $\eta^{v}$, the base metal phase represented by $\eta^{b}$, the solid phase represented by $\eta^{s}$ and the liquid phase represented by $\eta^{l}$. To characterize the grain structure, we also introduce a series of grain fields $\eta^{s i}$ in the solid phase, where each superscript $i$ represents one specific crystallographic orientation randomly picked from the orientation space. In order to retain mass conservation of the solid and liquid phases, we introduce a conserved phase field of $\rho$ to represent the density. Here, we define the phase and grain by using $\left(\left[\eta^{v}, \eta^{b}, \eta^{l}, \eta^{s}, \rho\right],\left[\eta^{s i}\right]\right)$. More specifically $\quad([1,0,0,0,0],[0,0 \ldots]), \quad\left(\left[0,1,0,0, \rho^{b}\right],[0,0 \ldots]\right) \quad$ and $\left(\left[0,0,1,0, \rho^{l}\right],[0,0 \ldots]\right)$ represent the vapor phase, the base metal and the liquid phase, respectively, the polycrystalline grains are represented by: $\quad\left(\left[0,0,0,1, \rho^{s}\right],[1,0,0, \ldots]\right)$ $\left(\left[0,0,0,1, \rho^{s}\right],[0,0, \ldots, 1,0,0 \ldots]\right)$. \subsection*{2.2. Phase field model} \section*{- Total free energy} In order to correctly simulate the AM process, the total free energy of the whole system $F$ must have a minimal value in the liquid, vapor and base metal phases when temperature is higher than melting point: $T>T_{m}$, and a minimal value in solid, vapor and base metal phases when temperature is lower than melting point $\left(T50 \mathrm{~J} / \mathrm{m}$. Fig. 3(f) shows the change in quasi-steady-state melt pool length $l_{\text {pool }}$ with the scanning speed and beam power. The length decreases with increase of scanning speed and the decrease of the beam power. Different from the scaling relation for pool depth, the scaling law is between $l_{\text {pool }} / P_{0}$ and power density $E_{v}$ as shown in Fig. 3(g). Besides the phase field simulations, we developed an analytical model to interpret the above simulation results for the melt pool size (Detailed derivations are given Section S6 of Supporting Information). We find that for relatively high scanning speed, we have: $d_{\text {pool }} \approx \frac{2 D \cdot E_{v}}{\sqrt{2 \pi} e^{1 / 2} K \Delta T}$ $l_{\text {pool }} \approx \frac{D \cdot P_{0} \cdot E_{v}}{\pi K^{2}(\Delta T)^{2}}$ where, $D$ and $K$ are the thermal diffusivity and thermal conductivity of the solid phase, $\Delta T$ is the difference between melting point and preheating temperature. The approximate linear scaling shown by the phase field results in Fig. 3(e) and (g) are consistent with the linear scaling relations derived above. We also note that the scaling law for the pool depth obtained in our simulations agrees well with experimental observations [35]. In the following sections, we show that considering the width and depth of the melt pool only is inadequate to fully understand the AM process. The length of the melt pool also plays an important role in the evolution of grain structure. \subsection*{3.3. Porosity} We carried out a series of simulations to investigate the relationship between porosity and process parameters. Fig. 4( $\left.\mathrm{a}_{13}\right)$ shows the porosity phase diagram from these simulations, and Fig. $4\left(a_{1}\right)-\left(a_{12}\right)$ show the void distribution together with grain structure at representative points in the phase space of power and scanning speed. The color in Fig. 4( $\left.\mathrm{a}_{13}\right)$ denotes the simulated porosity with lighter color corresponding to higher porosity. In Fig. 4( $\left.\mathrm{a}_{13}\right)$, the field space (the beam power and scanning speed) can be roughly divided into two regions, with the phase boundary represented by the dashed blue line. The phase in the lower-left region is free or nearly free of voids, while that in the upper-right region contains voids. In this region, farther the phase point is from the dashed line, higher is the porosity. As an extreme example, for the phase point at $P_{0}=40 \mathrm{~W}$ and $v=1200 \mathrm{~mm} / \mathrm{s}$ shown in Fig. $4\left(a_{4}\right)$, the porosity is $16 \%$. Fig. 4(b) shows the change of porosity with scanning speed and beam power. The porosity increases with increasing scanning speed and decreasing beam power. The scaling relation between porosity and $E_{v}$ is shown in Fig. 4(c). Note that besides our phase field simulation results, experimental results obtained from Ref. [33] are added in Fig. 4(b) and 4(c). It is seen that the phase field simulations agree well with the experimental data, indicating the experimental data also obeys the scaling relation. From Fig. 4(c), we see that there is a critical power density of $E_{v, \text { crit }} \approx 100 \mathrm{~J} / \mathrm{m}$, below which porosity increases rapidly. This critical power density obtained from Fig. 3(e) can be defined as the power density necessary for the melt pool depth to equal the layer thickness (with the porosity correction): $d_{\text {pool }}\left(E_{v}=E_{v, \text { crit }}\right)=\left(1+f_{0}\right) \cdot \delta$, where $f_{0}$ is the porosity of the powder bed before scanning, which is about $20 \%$ in the present work. For $\delta=30 \mu \mathrm{m}$, this relationship predicts a critical power density of $100 \mathrm{~J} / \mathrm{m}$, agreeing well with the phase field simulation results. To further verify this relationship, we performed additional simulations with a layer thickness of $60 \mu \mathrm{m}$ and predicted the critical power density as $230 \mathrm{~J} / \mathrm{m}$. The porosity values for $\delta=60 \mu \mathrm{m}$ are shown in Fig. 4(c) (in purple dots) and the critical power density is indeed around $230 \mathrm{~J} / \mathrm{m}$. \subsection*{3.4. Grain structure} As shown in Fig. 4(a), different grain structures were obtained in different phase regimes. Clearly, grains in the lower-left region are all columnar-like; while the grains in the upper-right region are\\ \includegraphics[max width=\textwidth, center]{2024_03_10_86b7739524e5a28e679dg-6} Fig. 3. Melt pool evolution predicted by the phase field model. a) Evolution of melt pool size and geometry with beam power of $80 \mathrm{~W}$ and scanning speed of $400 \mathrm{~mm} / \mathrm{s}$ for $\mathrm{A}_{1}$ and $A_{2}, 800 \mathrm{~mm} / \mathrm{s}$ for $B_{1}$ to $B_{4}$ and $1600 \mathrm{~mm} / \mathrm{s}$ for $C_{1}$ to $C_{7}$. Variation of melt pool length b) and depth c) with scanning distance, respectively. Beam power for b) and c) is set as $80 \mathrm{~W}$ and scanning speed as 400, 800 and $1600 \mathrm{~mm} / \mathrm{s}$ d) Variation of pool depth with scanning speed at different power values. e) Variation of pool depth with power density; f) Variation of pool length with scanning speed at different power values; and e) Variation of melt pool length over beam power with power density.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_86b7739524e5a28e679dg-7} Fig. 4. Evolution of porosity and microstructure with process parameters: $a_{1}$ ) - $a_{12}$ ) void distribution and grain structure under different power and scanning speed combinations; $a_{13}$ ) porosity map with lighter color corresponding to higher porosity; b) change of porosity with scanning speed at different values of beam power; and c) change of porosity with power density. The purple dot and line show the porosity simulated with $60 \mu \mathrm{m}$ layer thickness. Process parameters corresponding to the five purple circle dots from left to right are: $P_{0}=40 \mathrm{~W}, v=400 \mathrm{~mm} / \mathrm{s} ; P_{0}=160 \mathrm{~W}, v=1000 \mathrm{~mm} / \mathrm{s} ; P_{0}=80 \mathrm{~W}, v=400 \mathrm{~mm} / \mathrm{s} ; P_{0}=120 \mathrm{~W}, v=400 \mathrm{~mm} / \mathrm{s} ;$ and $P_{0}=160 \mathrm{~W}, v=400 \mathrm{~mm} / \mathrm{s}$, respectively.\\ mostly equiaxed. In the lower-left region, the depth of the melt pool is larger than the layer thickness so that powder particles fully melt. As a result, there are no new nuclei formed during the AM process. It is known that homo-epitaxial growth from pre-existing grains leads to the formation of columnar grain structure. In the upperright region, however, partially melted powder particles serve as nuclei for new orientations and thus interrupt the homo-epitaxial growth from the pre-existing grains. As the power density decreases, the number of partially melted powder particles increases, providing more nuclei and giving rise to a more equiaxed grain microstructure. In order to investigate the influence of process parameters on grain structure, we cut a region with $540 \mu \mathrm{m}$ height along the stacking direction (the $y$ axis) and $500 \mu \mathrm{m}$ width along the scanning direction (the $x$ axis) from each simulation and then calculate various quantities, such as the grain number $N_{g}$, the width of each grain along scanning direction $W_{g, i}$, the length of each grain $L_{g, i}$, the aspect ratio of each grain $R_{g, i}$, and the area size of each grain $A_{g, i}$. With these quantities, we calculate area averaged values, i.e., the averaged grain width: $W_{g}=\sum_{i} A_{g, i} W_{g, i} / \sum_{i} A_{g, i}$, the averaged grain length: $L_{g}=\sum_{i} A_{g, i} L_{g, i} / \sum_{i} A_{g, i}$ and averaged grain aspect ratio: $R_{g}=\sum_{i} A_{g, i} R_{g, i} / \sum_{i} A_{g, i}$ for each power-scanning speed combination and plot them in Fig. 5 and Fig. S5. Fig. 5(a) shows the change of grain density with scanning speed and beam power. Here, the grain density is defined as the grain number divided by the region area: $N_{v g}=N_{g} / 540 \mu \mathrm{m} / 500 \mu \mathrm{m}$. We see that the grain density increases with the increase of scanning speed and decrease of beam power. We also plot in Fig. 5(b) the relationship between $N_{v g}$ and $E_{v}$. It is seen that the grain density roughly obeys a scaling law. Interestingly, there is a critical value of $E_{v}(\sim 150 \mathrm{~J} / \mathrm{m})$ below which the grain density deceases rapidly with increasing $E_{v}$. This critical power density of $150 \mathrm{~J} / \mathrm{m}$ is larger than the one for porosity, which is near $100 \mathrm{~J} / \mathrm{m}$. This difference primarily arises from two sources: the wetting of melt pool on residual powder and the solid state sintering as described in Section 3.1. Examples are the grains labeled as A1 and A2 in Fig. 4( $\left.\mathrm{a}_{7}\right)$ and Fig. $4\left(a_{10}\right)$, where without any voids, new grains can still form. Besides the grain density, we also investigate the grain size influenced by process parameters. We find that the grain size is controlled by different mechanisms in different power density regimes, i.e., the partial melting induced nucleation in the lower power density regime, the competitive grain growth in the intermediate power density regime and the thermal gradient forced grain growth in the high power density regime (See detailed discussion in Section S7 of Supporting Information). We emphasize that the simulation results for grain structure and grain size agree well with many experimental observations. For example, previous experimental observations [11] often show zigzag morphology of GBs in AM components. This is also shown in our present simulations for the case of the round-like melt pool (the $40 \mathrm{~W}$ case). In addition, previous experiments show that although scanning strategy affects the grain structure, the most pronounced effect is from beam energy [11]. Our simulations show that in certain power density regime, the microstructure is dominated by long columnar grains. Since these columnar grains are epitaxially grown from pre-existing grains of the component, it is thus difficult to significantly change the microstructure by changing the scanning direction. However, in low power density regime, new grains are nucleated from partially melted powder, providing for the possibility of modulating the grain structure by controlling the motion of melt pool. As shown earlier, this modulation is sensitive to the curvature of the melt pool and is more pronounced in the case of rounded pool, which is typical in DED since it uses much slower scanning speed and larger beam spot. However, since the scanning speed in SLM and EBM is much faster than DED, this results in a smaller curvature of the solid-liquid interface. In this case, grain growth is mostly directional along the stacking direction, and thus insensitive to the motion of melt pool (the scanning direction). This finding also agrees well with grain structures obtained from experimental observations using SLM, EBM and DED [2]. Finally, we note that there are conflicting experimental observations about the grain size evolution. Kobryn et al. [12]. studied the microstructure and texture evolution of Ti-6Al-4V fabricated by direct laser melting, and found that the grain width decreases with increasing scan speed and increases with increasing power density. Han et al. [13]. also studied the microstructure of direct laser melted Ti-6Al$4 \mathrm{~V}$ alloy. However, they found that the grain size can be refined by decreasing the scanning speed and increasing laser power. Although these two works employ different machine systems and different process parameters, we find that the microstructure from Han et al. is more columnar-like than that from Kobryn et al. Based on the present work, we believe that their experiments are likely in different power density regimes: Kobryn's work is the regime where partial melting of powder and competitive grain growth dominates, while Han's work is in the regime where thermal gradient-driven grain growth dominates microstructural evolution.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_86b7739524e5a28e679dg-8} Fig. 5. Influence of process parameters on grain structure: a) change of grain density with scanning speed under different values of beam power, and b) change of grain density with power density. \section*{4. Conclusion} We have developed a phase field model to study the melt pool size and shape, porosity, and grain structure during powder bedbased additive manufacturing. With simulations, we find that both depth and length of melt pool increase with the increase of beam power density. The depth of the melt pool, the porosity and the grain density all follow a scaling relation with power density. However, the length of melt pool, grain size and aspect ratio only partially follow a scaling relation with power density. In addition, porosity is found to increase with the decrease of power density. When power density decreases to a critical value, porosity increases rapidly. Grain density increases with the decrease of power density. The critical power density for grain density is larger than the one for porosity. The grain structure is found to be controlled by different mechanisms in different power density regimes. In the low power density regime, partially melted powder contributes to formation of nuclei for new grains and interrupts homo-epitaxial grain growth. As a result, grain size in this regime slowly increases with the increase of power density and obeys a scaling relation. In the intermediate power density regime, columnar grain structure dominates and competitive grain growth controls grain size. The grain size in this regime increases rapidly with the increase of power density. In the high power density regime, the competition between columnar grains is suppressed by the high thermal gradient, and width of the grains decrease rapidly with the increase of power density, while the grain length only increases slightly. In the case of low power and low scanning speed, roundlike melt pool is able to promote the competition between columnar grains, resulting in the increase of both grain width and grain length. The present work reproduces many key experimental observations and reveals valuable insights into the relationship between process parameters and the melt pool size and shape, formation of porosity, and grain structure. \section*{Appendix A. Supplementary data} Supplementary data related to this article can be found at \href{https://doi.org/10.1016/j.actamat.2017.11.033}{https://doi.org/10.1016/j.actamat.2017.11.033}. \section*{References} [1] D. Herzog, V. Seyda, E. Wycisk, C. Emmelmann, Additive manufacturing of metals, Acta Mater 117 (2016) 371-392. [2] W.J. Sames, F.A. List, S. Pannala, R.R. Dehoff, S.S. Babu, The metallurgy and processing science of metal additive manufacturing, Int. Mat. Rev. 61 (5) (2016) 315-360. [3] W.E. Frazier, Metal additive manufacturing: a review, J. Mat. Eng. Perform. 23 (6) (2014) 1917-1928. [4] S. Das, Physical aspects of process control in selective laser sintering of metals, Adv. Eng. Mater 5 (2003) 701-711. [5] W. Devesse, D.D. Baere, P. Guillaume, Modeling of laser beam and powder flow interaction in laser cladding using ray-tracing, J. Laser Appl. 27 (2015) S29208. [6] W. Yan, J. Smith, W. Ge, F. Lin, W.K. Liu, Multiscale modeling of electron beam and substrate interaction: a new heat source model, Comput. Mech. 56 (2015) 265-276. [7] S.A. Khairallah, A.T. Anderson, A. Rubenchik, W.E. King, Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones, Acta Mater 108 (2016) 36-45. [8] T. Scharowsky, F. Osmanlic, R.F. Singer, C. Körner, Melt pool dynamics during selective electron beam melting, Appl. Phys. A 114 (2014) 1303-1307. [9] H. Nakamura, Y. Kawahito, K. Nishimoto, S. Katayama, Elucidation of melt flows and spatter formation mechanisms during high power laser welding of pure titanium, J. Laser Appl. 27 (2015) 032012. [10] C. Körner, E. Attar, P. Heinl, Mesoscopic simulation of selective beam melting process, J. Mat. Process. Technol. 211 (2011) 978-987. [11] L.L. Parimia, R.G. A, D. Clark, M.M. Attallaha, Microstructural and texture development in direct laser fabricated IN718, Mat. Charact. 89 (2014) 102-111. [12] P.A. Kobryn, S.L. Semiatin, Microstructure and texture evolution during solidification processing of Ti-6Al-4V, J. Mat. Process. Technol. 135 (2003) 330-339. [13] Y. Han, W. Lu, T. Jarvis, J. Shurvinton, X. Wu, Investigation on the microstructure of direct laser additive manufactured Ti6Al4V alloy, Mat. Res. 18 (2015) 24-28. [14] J. Yang, J. Han, H. Yu, J. Yin, M. Gao, Z. Wang, X. Zeng, Role of molten pool model on formability, microstructure and mechanical properties of selective laser melted Ti-6Al-4V alloy, Mat. Des. 110 (2016) 558-570. [15] J.P. Kruth, G. Levy, F. Klocke, T.H.C. Childs, Consolidation phenomena in laser and powder-bed based layered manufacturing, CIRP Ann. Manuf. Techn 56 (2) (2007) 730-759. [16] M. Megahed, H.-W. Mindt, N. N'Dri, H. Duan, O. Desmaison, Metal additivemanufacturing process and residual stress modeling, IMMI 5 (2016) 4. [17] S. Haeri, Y. Wang, O. Ghita, J. Sun, Discrete element simulation and experimental study of powder spreading process in additive manufacturing, Powder Technol. 306 (2017) 45-54. [18] M.J. Matthews, G. Guss, S.A. Khairallah, A.M. Rubenchik, P.J. Depond, W.E. King, Denudation of metal powder layers in laser powder bed fusion processes, Acta Mater 114 (2016) 33-42. [19] R. Chen, Q. Xu, B. Liu, Cellular automaton simulation of three-dimensional dendrite growth in $\mathrm{Al}-7 \mathrm{Si}-\mathrm{Mg}$ ternary aluminum alloys, Comput. Mat. Sci. 105 (2015) 90-100. [20] X. Gong, K. Chou, Phase-field modeling of microstructure evolution in electron beam additive manufacturing, JOM 67 (2015) 5. [21] S. Sahoo, K. Chou, Phase-field simulation of microstructure evolution of $\mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V}$ in electron beam additive manufacturing process, Add. Manuf. 9 (2016) 14-24. [22] G. Kasperovich, J. Haubrich, J. Gussone, G. Requena, Correlation between porosity and processing parameters in TiAl6V4, Mat. Des. 105 (2016) 160-170. [23] K. Chongbunwatana, Simulation of vapour keyhole and weld pool dynamics during laser beam welding, Prod. Eng. Res. Devel 8 (2014) 499-511. [24] J. Zhou, H.-L. Tsai, Porosity formation and prevention in pulsed laser welding, J. Heat. Transf. 129 (2007) 1014-1024. [25] A. Bauerei, T. Scharowsky, C. Körner, Defect generation and propagation mechanism during additive manufacturing by selective beam melting, J. Mat. Process. Technol. 214 (2014) 2522-2528. [26] G. Tapia, A.H. Elwany, H. Sang, Prediction of porosity in metal-based additive manufacturing usingspatial Gaussian process models, Add. Manuf. 12 (2016) 282-290. [27] A. Zinoviev, O. Zinovieva, V. Ploshikhia, V. Romanova, R. Balokhonov, Evolution of grain structure during laser additive manufacturing. Simulation by a cellular automata method, Mat. Des. 106 (2016) 321-329. [28] O. Lopez-Botello, U. Martinez-Hernandez, J. Ramírez, C. Pinna, K. Mumtaz, Two-dimensional simulation of grain structure growth within selective laser melted AA-2024, Mat. Des. 113 (2017) 369-376. [29] A. Rai, M. Markl, C. Körner, A coupled cellular automaton-lattice Boltzmann model for grain structure simulation during additive manufacturing, Comput. Mat. Sci. 124 (2016) 37-48. [30] A. Rai, H. Helmer, C. Körner, Simulation of grain structure evolution during powder bed based additive manufacturing, Add. Manuf. 13 (2017) 124-134. [31] C. Panwisawas, C. Qiu, M.J. Anderson, Y. Sovani, R.P. Turner, M.M. Attallah, J.W. Brooks, H.C. Basoalto, Mesoscale modelling of selective laser melting: thermal fluid dynamics and microstructural evolution, Comput. Mat. Sci. 126 (2017) 479-490 [32] M.D. Krivilyov, S.D. Mesarovic, D.P. Sekulic, Phase-field model of interface migration and powder consolidation in additive manufacturing of metals, J. Mat. Sci. 52 (8) (2017). [33] H. Gong, K. Rafi, T. Starr, B. Stucker, The effects of processing parameters on defect regularity in $\mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V}$ parts fabricated by selective laser melting and electron beam melting, Solid free. Fabr. Symp. (2013) 424-439. [34] M. Boivineau, C. Cagran, D. Doytier, V. Eyraud, M.-H. Nadal, B. Wilthan, G. Pottlacher, Thermophysical properties of solid and liquid Ti-6Al-4V (TA6V) alloy, Int. J. Thermophys. 27 (2006) 507-529. [35] C. Kusuma, The Effect of Laser Power and Scan Speed on Melt Pool Characteristics of Pure Titanium and Ti-6Al-4V Alloy for Selective Laser Melting, Wright State University, 2016 . \begin{itemize} \item \end{itemize} \end{document} \documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[version=4]{mhchem} \usepackage{stmaryrd} \usepackage{graphicx} \usepackage[export]{adjustbox} \graphicspath{ {./images/} } \usepackage{multirow} \usepackage{hyperref} \hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,} \urlstyle{same} \title{The Effects of Laser and Electron Beam Spot Size in Additive Manufacturing Processes } \author{EB-PBF $\mathrm{P}=670 \mathrm{~W} \quad \mathrm{~V}=3700 \mathrm{~mm} / \mathrm{s} \mathrm{L}_{0} / \mathrm{D}_{0}=20$} \date{} \begin{document} \maketitle Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy In Mechanical engineering Zachary Ryan Francis B.S. Mechanical Engineering, The Pennsylvania State University M.S. Mechanical Engineering, Carnegie Mellon University Carnegie Mellon University Pittsburgh, PA May 2017 Copyright (C) 2017, Zachary Francis \section*{Dedication} This dissertation is dedicated to: To my parents, John and Dorothy and my fiancé, Kelly \section*{Acknowledgements} The completion of this thesis was made possible through the support of many people known both academically and personally. I would like to thank my advisor, Dr. Jack Beuth, for advice and guidance throughout my pursuits at Carnegie Mellon University. I would also like to thank the other members of my committee, Dr. Fred Higgs, Dr. Jonathan Malen, and Dr. Tony Rollett. Their suggestions and input have shaped and improved the work in this dissertation. I would also like to acknowledge members of the staff in the department of Mechanical Engineering for their support. I am also grateful to the organizations providing financial support throughout my Ph.D. This research was funded by America Makes (The National Additive Manufacturing Innovation Institute), and Sandia National Laboratories. I would like to thank the members of Dr. Beuth's research group who have helped shape my work: Brian Fisher, Jason Fox, Joy Gockel, Colt Mongomery, Sneha Narra, and Luke Scime. They have all provided valuable input and helped overcome difficulties that were presented by the research. I would also like to extend a special thanks to Sneha Narra who helped plan and run countless experiments. Collaborators in various organizations have also helped me progress my research by providing important process insight. I must acknowledge collaborators Ted Reutzel of Penn State ARL, Scott Stecker of Sciaky Inc., and Bradley Jared of Sandia National Laboratories. They have helped organize and set up many experiments that helped build the findings of this thesis. I would like to thank my fiancé, Kelly, who has supported me throughout my time at Carnegie Mellon. Her loving support has made my pursuit of a Ph.D. much easier, and her great friendship has made my time in grad school much more enjoyable. Last, but not least, I would like to thank my parents, John and Dorothy. They have been supporting my academic endeavors for over 20 years, and have been an integral part to my success both inside and outside of the classroom. Without their guidance and encouragement, this work would not be possible. \begin{abstract} In this work, melt pool size in process mapped in power-velocity space for multiple processes and alloys. In the electron beam wire feed and laser powder feed processes, melt pool dimensions are then related to microstructure in the Ti-6Al-4V alloy. In the electron beam wire feed process, work by previous authors that related prior beta grain size to melt pool area is extended and a control scheme is suggested. In the laser powder feed process, in situ thermal imaging is used to monitor melt pool length. Real time melt pool length measurements are used in feedback control to manipulate the resulting microstructure. \end{abstract} In laser and electron beam direct metal additive manufacturing, characteristics of the individual melt pool and the resulting final parts are a product of a variety of process parameters. Laser or electron beam spot size is an important input parameter that can affect the size and shape of a melt pool, and has a direct influence on the formation of lack-of-fusion and keyholing porosity. In this work, models are developed to gain a better understanding of the effects of spot size across different alloys and processes. Models are validated through experiments that also span multiple processes and alloys. Methods to expand the usable processing space are demonstrated in the ProX 200 laser powder bed fusion process. In depth knowledge of process parameters can reduce the occurrence of porosity and flaws throughout processing space and allow for the increased use of non-standard parameter sets. Knowledge of the effects of spot size and other process parameters can enable an operator to expand the usable processing space while avoiding the formation of some types of flaws. Based on simulation and experimental results, regions where potential problems may occur are identified and process parameter based solutions are suggested. Methods to expand the usable processing\\ space are demonstrated in the ProX 200 laser powder bed fusion process. In depth knowledge of process parameters can reduce the occurrence of porosity and flaws throughout processing space and allow for the increased use of non-standard parameter sets. \section*{Table of Contents} Acknowledgements ..... IV\\ Abstract ..... VI\\ Table of Contents ..... VIII\\ Table of Figures ..... XIII\\ Nomenclature ..... XXI\\ Chapter 1: Introduction ..... 1\\ 1.1 Additive Manufacturing ..... 1\\ 1.2 Motivation ..... 3\\ 1.3 Literature Review ..... 4\\ 1.3.1 The Effects of Process Parameters ..... 4\\ 1.3.2 Process Monitoring and Control ..... 7\\ 1.3.3 Deposition Flaws ..... 8\\ 1.3.4 Microstructure ..... 9\\ 1.3.5 Modeling ..... 10\\ 1.4 Organization ..... 11\\ Chapter 2: Process Mapping and Microstructure Control of Ti-6Al-4V in Laser Powder Feed\\ and Electron Beam Wire Feed Processes ..... 13\\ 2.1 Overview ..... 13\\ 2.2 Methods ..... 14\\ 2.2.1 Process Mapping Approach ..... 14\\ 2.2.2 Finite Element Model ..... 15\\ 2.2.3 Experiment Design and Measurement ..... 18\\ 2.3 Results ..... 25\\ 2.3.1 Process Mapping the Sciaky Electron Beam Wire Feed Process ..... 26\\ 2.3.2 Process Mapping the LENS Laser Powder Stream Process ..... 29\\ 2.3.3 Microstructure Control in the Sciaky Electron Beam Wire Feed Process ..... 36\\ 2.3.4 Thermal Imaging and Microstructure Control in the LENS Process ..... 38\\ 2.4 Discussion ..... 40\\ Chapter 3: The Effects of Spot Size on Melt Pool Dimensions ..... 43\\ 3.1 Overview ..... 43\\ 3.2 Methods ..... 43\\ 3.2.1 Modeling ..... 43\\ 3.2.2 Experiments ..... 48\\ 3.2.3 Normalization ..... 50\\ 3.3 Results ..... 51\\ 3.3.1 Trends from Models ..... 52\\ 3.3.2 Single Bead Experiments ..... 57\\ 3.3.3 Spot Size Estimates ..... 65\\ 3.4 Discussion ..... 70\\ Chapter 4: The Effects of Spot Size on Porosity and Flaws ..... 73\\ 4.1 Overview ..... 73\\ 4.2 Methods ..... 73\\ 4.2.1 Identifying Keyholing Melt Pools ..... 73\\ 4.2.2 Variability and Porosity Measurement ..... 74\\ 4.2.3 Experiment Setup ..... 77\\ 4.3 Results ..... 79\\ 4.3.1 Depth and Width Variability in Keyhole Mode and Conduction Mode Melting ..... 79\\ 4.3.2 Spot Size Changes to Prevent Keyholing ..... 82\\ 4.3.3 Spot Size Changes to Reduce Bead-up ..... 85\\ 4.3.4 Spot Size Changes to Reduce Porosity ..... 89\\ 4.4 Discussion ..... 90\\ Chapter 5: The Effects of Spot Size on Ti-6Al-4V Deposition Microstructure ..... 93\\ 5.1 Overview ..... 93\\ 5.2 Methods ..... 93\\ 5.2.1 Modeling ..... 93\\ 5.2.2 Experiments and Microstructure Analysis ..... 97\\ 5.3 Results ..... 98\\ 5.3.1 Model Results ..... 98\\ 5.3.2 Single Bead Experiments ..... 102\\ 5.4 Discussion ..... 104\\ Chapter 6: Adjusting Spot Size to Expand Processing Space ..... 106\\ 6.1 Overview ..... 106\\ 6.2 Methods ..... 106\\ 6.2.1 Modeling ..... 106\\ 6.2.2 Experiment Design and Process Mapping ..... 107\\ 6.3 Results ..... 108\\ 6.3.1 Process Mapping ..... 108\\ 6.3.2 Spot Size Experiments ..... 111\\ 6.3.3 Expanding Processing Space ..... 114\\ 6.4 Discussion ..... 118\\ Chapter 7: Conclusions ..... 120\\ 7.1 Conclusions ..... 120\\ 7.2 Implications ..... 122\\ 7.3 Future Work ..... 124\\ References ..... 126\\ Appendix 1: Polishing and Etching Procedures ..... 145\\ Appendix 2: Melt Pool Width Measurements from LENS Ti-6Al-4V Experiments ..... 146\\ Appendix 3: Spot size effects on melt pool geometry - Experimental measurements compared with simulation results ..... 149 Appendix 5: Cross section changes at selected power-velocity combinations in the ProX 200 Appendix 6: Minimum spot sizes to avoid keyholing throughout power-velocity space in the ProX 200 process \section*{Table of Figures} Figure 1-1: Major direct metal additive manufacturing processes in power-velocity space .......... 2 Figure 2-1: Power-velocity process map for melt pool cross-sectional area for 316L stainless steel in the L-PBF process................................................................................................................... 15 Figure 2-2: 3D model used for finite element simulation in the ABAQUS software package .... 17 Figure 2-3: Key melt pool dimensions measured from finite element simulations..................... 17 Figure 2-4: LENS processed plate including single bead deposits and scaled powder feed rate . 19 Figure 2-5: Thermal imaging process control.......................................................................... 20 Figure 2-6: Sciaky electron beam wire feed process experiment plan ....................................... 21 Figure 2-7: Experiments plates deposited in the Sciaky process ............................................... 22 Figure 2-8: Key melt pool dimensions measured for a melt pool in from the Sciaky process ..... 23 Figure 2-9: Measurement of uncertainty in melt pool area........................................................ 24 Figure 2-10: Tracing of melt pool width for calculation of standard deviation........................... 25 Figure 2-11: Power-velocity process map of melt pool cross-sectional area in the Sciaky process Figure 2-12: Power-velocity process map of melt pool depth in the Sciaky process ................... 28 Figure 2-13: Power-velocity process map of melt pool width in the Sciaky process ................... 28 Figure 2-14: Power-velocity process map of melt pool cross-sectional area for the LENS process with no powder feed..................................................................................................................... 30 Figure 2-15: Power-velocity process map of melt pool cross-sectional area for the LENS process with scaled powder feed............................................................................................................... 31 Figure 2-16: Power-velocity process map of melt pool cross-sectional area for the LENS process with constant 3 gpm feed ................................................................................................................ 31 Figure 2-17: Power-velocity process map of melt pool cross-section area comparing different feed rate scenarios in the LENS process 32 Figure 2-18: Process maps of melt pool widths and depths in the LENS process for different material feed rate scenarios. 35 Figure 2-19: Relationship between prior beta grain width and effective melt pool width in electron beam wire feed processes... 37 Figure 2-20: Relationship between prior beta grain width and effective melt pool width for different deposition geometries in the Sciaky electron beam wire feed process .. 38 Figure 2-21: Trends for melt pool area, cooling rate, and prior beta grain size in the LENS laser powder feed process. 39 Figure 2-22: Prior beta grain width vs full melt pool length in the laser powder feed process .... 40 Figure 3-1: Flux distribution on the surface of a finite element model ...................................... 44 Figure 3-2: Melt pool area measurements for deformed no-added material melt pools............... 50 Figure 3-3: Example of identifying the normalized spot size based on width to depth ratio ....... 51 Figure 3-4: Normalized melt pool width vs. normalized spot size for different models .............. 53 Figure 3-5: Normalized melt pool depth vs. normalized spot size for different models .............. 54 Figure 3-6: Normalized melt pool cross-sectional area vs. normalized spot size for different models Figure 3-7: Width to depth ratio vs. normalized spot size for different models 56 Figure 3-8: EOS L-PBF, Ti-6Al-4V, 80W, $500 \mathrm{~mm} / \mathrm{s}$ experimental normalized width measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 2.5 ............................ 58 Figure 3-9: EOS L-PBF, Ti-6Al-4V, 80W, 500 mm/s experimental normalized depth measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 2.5 ............................ 58 Figure 3-10: EOS L-PBF, Ti-6Al-4V, 80W, $500 \mathrm{~mm} / \mathrm{s}$ experimental normalized area measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 2.5 59 Figure 3-11: Arcam S12 EB-PBF, Ti-6Al-4V, 670W, 1100 mm/s experimental normalized width measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 5 60 Figure 3-12: Arcam S12 EB-PBF, Ti-6Al-4V, 670W, 1100 mm/s experimental normalized depth measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 5 60 Figure 3-13: Arcam S12 EB-PBF, Ti-6Al-4V, 670W, $1100 \mathrm{~mm} / \mathrm{s}$ experimental normalized area measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 5 . 61 Figure 3-14: 3D Systems ProX 200 L-PBF, 17-4 PH stainless steel, 300 W, 1400 mm/s experimental normalized width measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 10 62 Figure 3-15: 3D Systems ProX 200 L-PBF, 17-4 PH stainless steel, 300 W, 1400 mm/s experimental normalized depth measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 10 62 Figure 3-16: 3D Systems ProX 200 L-PBF, 17-4 PH stainless steel, 300 W, 1400 mm/s experimental normalized area measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 10 63 Figure 3-17: Arcam S12 EB-PBF, IN 718, 670 W, 1300 mm/s experimental normalized width measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 20 ... 64 Figure 3-18: Arcam S12 EB-PBF, IN 718, 670 W, 1300 mm/s experimental normalized depth measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 20 .... 64 Figure 3-19: Arcam S12 EB-PBF, IN 718, 670 W, 1300 mm/s experimental normalized area measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 20 .... 65 Figure 3-20: Beam profile with key beam measurements labeled 66 Figure 3-21: Spot Size Estimates for the ProX 300 L-PBF process with best fit curves for typical laser behavior . 67 Figure 3-22: Spot Size Estimates for the ProX 200 L-PBF process with best fit curves for typical laser behavior .............................................................................................................................. 68 Figure 3-23: Spot Size Estimates for the EOS M 290 L-PBF process with best fit curves for typical laser behavior, and a curve based on spot size measurements................................................... 69 Figure 3-24: Spot Size Estimates for the Arcam S12 EB-PBF process with best fit curves ........ 70 Figure 4-1: Melt pool depth before (top) and after (bottom) tracing for variability analysis ....... 75 Figure 4-2: Bead-up (top) and smooth (bottom) melt pools as viewed from above, and from cross sections 76 Figure 4-3: Porosity optical image before (top) and after (bottom) selection of an intensity cutoff value from the intensity histogram (right). 77 Figure 4-4: Width and depth vs D/W ratio for single beads deposited in Ti-6Al-4V in the Arcam S12 EB-PBF process.................................................................................................................. 80 Figure 4-5: Standard deviations of width and depth vs D/W ratio for single beads deposited in Ti6Al-4V in the Arcam S12 EB-PBF process............................................................................... 81 Figure 4-6: Melt pool cross sections from increasing spot sizes transitioning from keyholing to non-keyholing melt pools 82 Figure 4-7: D/W ratio vs normalized spot size for all experimental Ti-6Al-4V data................... 83 Figure 4-8: D/W ratio vs normalized spot size for all experimental IN718 (left) and 316L stainless steel (right) data ........................................................................................................................ 84 Figure 4-9: D/W ratio vs normalized spot size for all experimental 17-4 PH (left) and 304 (right) data ................................................................................................................................................... 85 Figure 4-10: Width to full length (W/FL) versus normalized spot size ( $\left.\sigma / \mathrm{W}_{0}\right)$ for melt pools of different aspect ratios .................................................................................................................. 86 Figure 4-11: Observed bead-up and smooth melt pools deposited in 17-4 PH stainless steel in the ProX 200 L-PBF process ........................................................................................................... 87 Figure 4-12: Percent porosity measured at different magnifications for Ti-6Al-4V multi-layer pads deposited in the Arcam S12 machine at Carnegie Mellon......................................................... 89 Figure 5-1: Flux distribution on the surface of a finite element model ...................................... 95 Figure 5-2: Normalized cooling rate vs. normalized spot size for tophat and Gaussian beam distributions...................................................................................................................................... 99 Figure 5-3: Temperature and beam profile distributions for different normalized spot sizes .... 101 Figure 5-4: Experimental normalized prior beta grain width vs. normalized spot size for Ti-6Al$4 \mathrm{~V}$ 102 Figure 5-5: Relationships between prior beta grain width and effective melt pool width based on the original effective widths based on measurements, and spot size adjusted values based on finite element simulations 104 Figure 6-1: 316L experiments labeled good, keyholing, undermelting, and bead-up melt pools identified in melt pools throughout processing space (left), and finite element and experimental process map of melt pool areas with effective absorptivity values (right). 109 Figure 6-2: 17-4 experiments labeled good, keyholing, undermelting, and bead-up melt pools identified in melt pools throughout processing space (left), and finite element and experimental process map of melt pool areas with effective absorptivity values (right). 110 Figure 6-3: 304 experiments labeled good, keyholing, undermelting, and bead-up melt pools identified in melt pools throughout processing space (left), and finite element and experimental process map of melt pool areas with effective absorptivity values (right). 111 Figure 6-4: Labeled keyholing, "good", and undermelting melt pools from 316L experiments, and the points chosen for spot size adjustments 112 Figure 6-5: Cross section images of melt pools deposited at 300W, $400 \mathrm{~mm} / \mathrm{s}$, and various spot size values. 113 Figure 6-6: Cross section images of melt pools deposited at nominal and adjusted spot size values. Figure 6-7: Steps taken to determine an expanded processing space that avoid keyholing, undermelting, and bead-up melt pools 116 Figure 6-8: Processing space for 316L in the ProX 200 L-PBF process for nominal spot size (left), and variable spot size with original bead-up limit (right). 117 Figure 6-9: Expanded Processing space for 316L in the ProX 200 L-PBF process where increased spot size can eliminate keyholing and a portion of the bead-up region 118 Appendix Figure 1: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 2: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 3: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 4: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 5: Experimental and simulation normalized melt pool dimensions vs normalized spot size 153 Appendix Figure 6: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 7: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 8: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 9: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 10: Experimental and simulation normalized melt pool dimensions vs normalized spot size 158 Appendix Figure 11: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 12: Experimental and simulation normalized melt pool dimensions vs normalized spot size Appendix Figure 15: Melt pools deposited at nominal (left) and expanded (right) spot size at 300 W and $1400 \mathrm{~mm} / \mathrm{s}$ for 316L stainless steel in the ProX 200 L-PBF process 163 Appendix Figure 16: Melt pools deposited at nominal (left) and expanded (right) spot size at 300 W and $2400 \mathrm{~mm} / \mathrm{s}$ for 316L stainless steel in the ProX 200 L-PBF process Appendix Figure 17: Melt pools deposited at nominal (left) and expanded (right) spot size at 215 W and $400 \mathrm{~mm} / \mathrm{s}$ for 316L stainless steel in the ProX $200 \mathrm{~L}-\mathrm{PBF}$ process Appendix Figure 18: Melt pools deposited at nominal (left) and expanded (right) spot size at 130 W and $1400 \mathrm{~mm} / \mathrm{s}$ for 316L stainless steel in the ProX 200 L-PBF process 165 Appendix Figure 19: Focus offset settings (mm) in the ProX200 L-PBF process for 316L stainless steel to prevent keyhole mode melting in melt pools where it was identified at nominal settings Appendix Figure 20: Focus offset settings (mm) in the ProX200 L-PBF process for 17-4 stainless steel to prevent keyhole mode melting in melt pools where it was identified at nominal settings Appendix Figure 21: Focus offset settings (mm) in the ProX200 L-PBF process for 304 stainless steel to prevent keyhole mode melting in melt pools where it was identified at nominal settings \section*{Nomenclature} A - Melt pool cross sectional area $\mathrm{A}_{0}$ - Melt pool cross sectional area produced by a point heat source in simulations $\mathrm{C}_{\mathrm{p}}$ - specific heat D - Melt pool depth $\mathrm{D}_{0}$ - Melt pool depth produced by a point heat source in simulations EB-PBF - Electron beam powder bed fusion process EBWF - Electron beam wire feed process FL - Melt pool full length $\mathrm{k}$ - Thermal conductivity L - Melt pool length from the point of maximum depth (or latent heat of fusion) $\mathrm{L}_{0}$ - Melt pool length from the point of maximum depth produced by a point heat source in simulations L-PBF - Laser powder bed fusion process LPF - Laser powder feed process $\mathrm{n}$ - Operating parameter in Eagar-Tsai Model $\left(\mathrm{n}=\mathrm{qv} /\left(4 \pi \alpha^{2} \rho \mathrm{c}_{\mathrm{p}}\left(\mathrm{T}_{\text {melting }}-\mathrm{T}_{0}\right)\right)\right)$ q - Power input\\ $R$ - Distance from heat source $\left(R=\left(w^{2}+y^{2}+z^{2}\right)^{1 / 2}\right)$ $\mathrm{T}$ - Temperature $\mathrm{T}_{0}-$ Initial or background temperature $\mathrm{t}$ - Time $\mathrm{u}$ - Dimensionless distribution parameter in Eager-Tsai Model (u=(vo)/(2 $\alpha)$ ) v- Velocity $\mathrm{w}$ - Distance in $\mathrm{x}$-direction in a moving coordinate system ( $\mathrm{w}=\mathrm{x}-\mathrm{vt}$ ) W - Melt pool width $\mathrm{W}_{0}$ - Melt pool width produced by a point heat source in simulations $\mathrm{x}$ - Distance in $\mathrm{x}$-direction $\mathrm{y}$ - Distance in y-direction $\mathrm{z}$ - Distance in z-direction $\mathrm{z}_{0}$ - Offset of beam focal point from $\mathrm{z}=0$ at nominal settings $\alpha$ - Thermal diffusivity $\zeta$ - Dimensionless distance z\\ $\theta$ - Dimensionless temperature $\left(\theta=\left(T-T_{0}\right) /\left(T_{\text {melting- }}-T_{0}\right)\right)$ $\xi$ - Dimensionless distance in moving coordinate $(\xi=\mathrm{vw} /(2 \alpha))$ $\rho$ - Density $\sigma-$ Spot size $\sigma_{0}-$ Spot size at the beam focal point $\tau$ - Dimensionless time $\psi$-Dimensionless distance y \section*{Chapter 1: Introduction} \subsection*{1.1 Additive Manufacturing} Additive manufacturing (AM) is an automated manufacturing method that builds up parts by adding one layer at a time until completion. This method of manufacturing consists of processes ranging from desktop plastic 3D printers to industrial metal processes capable of producing final production parts. In most methods, the process begins with a computer aided design (CAD) model that is sliced into two dimensional layers before deposition paths and settings are generated. Deposition is accomplished by a few different methods which can affect the build rate, resolution, part quality, and more [1]. Work outlined in this thesis will focus on direct metal additive manufacturing processes (i.e. laser powder bed fusion, electron beam powder bed fusion, laser powder feed, and electron beam wire feed). Laser powder bed fusion (L-PBF) and electron beam powder bed fusion (EB-PBF) are similar process that spread thin layers of metal powder over each layer before using a laser or electron beam to melt and fuse material. Differences between the processes go beyond the heat source used to melt the powder. Electron beam powder bed fusion generally has higher deposition rates and scan speeds when compared to laser powder bed fusion, but has poorer surface finish and resolution [1] [2]. Additionally, electron beam powder bed fusion uses a high preheat before melting that helps reduce residual stress that may build up in parts deposited with laser powder bed fusion. The process also differs in alloys available for processing. Laser powder bed fusion equipment manufacturers allow for the use of a wide range of alloys including titanium alloys, steels, aluminum and more while electron beam powder bed fusion is only limited to a few alloys [3] [4]. Both processes are capable of generating final parts that require little to no post processing. Laser powder feed and electron beam wire feed processes generate near net shape parts and can have higher deposition rates when compared to the powder bed processes. Electron beam wire feed processes create a melt pool on the substrate using an electron beam, and wire stock to feed material into the melt pool. This process can create melt pools that can be over one inch in width and is primarily used to create larger near net shape parts [5]. The laser powder feed processes use a laser to create a melt pool on the substrate where inert gas blows powdered metal to add material [6]. This process creates near net shape parts on a smaller scale than the electron beam wire feed process and can also be used to repair existing parts [7] [8]. Both processes offer a wide range of alloys that can be used to produce parts [9] [10]. Power and velocity of the heat source are the most influential factors on individual melt pool size, and all four processes outlined above inhabit different regions when plotted in power-velocity space as shown in Figure 1-1. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-025} \end{center} Figure 1-1: Major direct metal additive manufacturing processes in power-velocity space Direct metal additive manufacturing has seen its earliest adoption in the aerospace and biomedical industries [2]. In the biomedical industry, this technology is especially useful because of the ability to create custom implants or braces for individual people and individual injuries. The aerospace industry's interest in additive manufacturing stems from the ability of the technology to manufacture more complex geometries that can help reduce weight, improve efficiency, and improve lead times [11]. Examples in industry have shown how additive manufacturing can combine multiple pieces into one part all while decreasing weight and increasing efficiency [12]. For these reasons, many other industries have shown interest in adopting the technology. \subsection*{1.2 Motivation} Increased use of direct metal additive manufacturing in industry and the desire to use it for final production parts has highlighted a need to better understand how process parameters can affect the final product. The most influential process parameters include power, velocity, laser/electron beam spot size, preheat, hatch spacing, and more. The multitude of parameters directly affects process outcomes like melt pool size, aspect ratio, resulting microstructure, and porosity among others. The effects of a process parameter on certain process outcomes is generally known; however, if a specific process outcome is desired, significant trial and error is currently required. Due to a lack of specific knowledge about the effects of many process parameters, part qualification can require a large amount of time and money [12] [13] [14]. The process parameters that have the biggest effect on deposition are the power and velocity of the heat source. Significant work in that area has shown how the two variables affect melt pool size. However, power and velocity alone can lead to unacceptable deposits in some regions of processing space. In these regions, spot size adjustments are needed to ensure consistent results\\ and the melt pool size must be balanced with hatch spacing and layer thickness, or material feed rate, to result in complete fusion between layers. Expanding the usable region of processing space can allow designers to use higher deposition rates, modified microstructure, improved surface finish, and more. Knowledge of how the different process parameters affect the resulting deposition can also be used to modify microstructure throughout a part. Since AM builds parts one melt pool at a time, microstructure can be tailored to the designer's needs in different regions of the design [15] [16]. This unique capability can only be realized if relations between process parameters, melt pools, and microstructure are well understood. \subsection*{1.3 Literature Review} \subsection*{1.3.1 The Effects of Process Parameters} Research into the effects of process parameters has been key to the development of additive manufacturing since its inception. Process parameters affect the melt pool geometry, microstructure, flaw formation and more. Process mapping is the method of plotting process outcomes in terms of process parameters and was originally used in additive manufacturing to show how thermal gradients, melt pool size, and residual stress is affected by parameters in the laser powder feed process [17] [18] [19] [20] [21] [22]. Process mapping has since been used to relate melt pool size to process variables in various alloys and processes [23] [24] [25] [26] [27] . In addition to melt pool dimensions, microstructure has been process mapped for its relationship to process parameters [28] [29] . The effects of process parameters has been analyzed outside of the realm of process mapping and has given insights to a number of other process outcomes. Porosity in AlSi10Mg parts was\\ analyzed for different hatch spacings, scan speeds, and scan strategies in the Realizer GmbH laser powder bed fusion process. It was found that smaller hatch spacing and lower scanning speed reduced porosity, and that a scanning strategy with a pre-sinter step produced parts with the greatest density [30]. Montgomery et al. found that typical powder layer thicknesses had a minimal effect on melt pool dimensions [25]. Process parameters were related to flaws in both the laser powder bed fusion and electron beam powder bed fusion processes for Ti-6Al-4V. Additionally, regions of processing space were labelled to show regions of appropriate, excessive, and insufficient energy input to avoid flaws [31]. In laser welding, Tzeng related process parameters to surface quality of the bead and found velocity, power, pulse duration, and power density to be the most influential factors [32]. Safdar et al. compared surface roughness values in experiments varying wall thickness, power, velocity, and spot size in Ti-6Al-4V with the Arcam electron beam powder bed fusion process [33]. Hann related enthalpy values to melt pool size and shape for laser welding [34]. Fatigue and fracture characteristics have also been analyzed in different regions of processing space [35]. \subsection*{1.3.1.1Effects of Spot Size} Beam spot size is a process parameter that has been identified as important to the size and shape of melt pools; however, minimal research has been done to methodically track its effects. Differences in single bead tracks for different power distributions has been analyzed and found that higher power density at the center of a Gaussian beam helped avoid insufficient melting at low powers when compared to a tophat and inverse Gaussian distributions [36] [37]. Roehling et al. investigated the effects of elliptical beam profiles and found elliptical shapes left rougher, discontinuous tracks with equiaxed grains when compared to a circular, Gaussian beam [38]. Other work in additive manufacturing identified some of the effects of changing spot size. Mudge\\ and Wald noted that spot size should be increased with power to increase deposition rate in the laser powder feed process, but that the change in process parameters would result in a coarser surface finish [39]. Miller et al. designed a laser powder bed fusion workstation with variable spot size to be able to increase deposition rate [40]. Bi et al. observed that a defocused beam decreases the melt pool surface temperature [41]. Increasing spot size was found to decrease the surface roughness of thin walls in thin wall structures in the electron beam powder bed fusion process [33]. The good processing window for IN 718 in the electron beam powder bed fusion process moves to a higher velocity region when the spot size is decreased. In the same process and material, the columnar grain structure was more consistent when a defocused beam was used [42]. In welding, research has been done to identify the effects of spot size on weld penetration depth, a smaller spot size yields a deeper weld [43] [44]. Spot size has also been shown to have an effect on the formation of potential flaws both in welding and additive manufacturing. In welding, keyholing porosity can be avoided by expanding the beam size [45] [46]. Norris et al. proposed that keyhole porosity can be avoided when the beam radius to keyhole depth ratio is greater than 0.15 [45]. In additive manufacturing, proposed normalized enthalpy thresholds to avoid keyhole took into consideration the beam power, velocity, and spot size [47]. Dinwiddie et al. was able to identify porosity or incomplete melting on the surface of newly melted layer in the electron beam powder bed fusion process and observed that a more diffuse beam had an increase in flaws in layers above an overhang [48]. Gong et al. measured increased porosity if spot size was either too large or too small, suggesting operators must find an optimum value to balance with other parameters [31]. \subsection*{1.3.2 Process Monitoring and Control} Process monitoring gives insights into the details of additive manufacturing processes and can help identify flaws when they occur. When monitoring is used in real time, control algorithms can be put in place to repair flaws or ensure desired outcomes are produced [49]. The laser powder feed process is a common process for real time monitoring due to its relatively low travel speeds. Early work in monitoring of the LENS process looked at temperatures within the melt pool to identify cooling rates that gave insight into the resulting microstructure [50]. Other work in the LENS laser powder feed process monitored the temperatures in the melt pool and modified power to maintain constant temperature to avoid additional oxidation [41]. Hu and Kovacevic used process monitoring in the laser powder feed process to control melt pool size to reduce variation and improve dimensional accuracy [51]. Monitoring has also been used to modify power to control layer height in addition to modifying melt pool temperature to follow defined paths [52] [53]. Although monitoring is generally easier in the laser powder feed process, work is continuing on monitoring different aspects of the other additive manufacturing processes. Melt pool monitoring in the laser powder bed fusion process has been used in feedback control to maintain consistent melt pool surface area [54] [55]. In the electron beam powder bed process, monitoring is taking place to detect porosity on the surface of parts to give insights on the effects of process parameters [48]. Mireles et al. used thermal imaging in the Arcam electron beam powder bed fusion process to identify pores in each layer before re-melting areas where a pore was identified [56]. Thermal imaging has also been used on a layer by layer basis to control process parameters to maintain consistent surface temperature as build height increases [57]. Layer by layer imaging has also been used to identify flaws in powder spreading that can result in flaws upon melting [55] [58] [59]. Process monitoring and feedback control has been used for many aspects of additive manufacturing and gives users greater confidence in the resulting part quality [60]. \subsection*{1.3.3 Deposition Flaws} Deposition flaws occur for a number of different reasons, but all have the ability to negatively impact the build quality and performance of additively manufactured parts. Two of the most common sources of flaws are porosity from lack of fusion and keyholing. Keyholing, often a desirable quality in welding due to an increased penetration depth, occurs when the beam energy density is high enough to vaporize material in the melt pool. Keyholing is more variable and can leave behind porosity, causing problems in additively manufactured parts. Significant research has been done in the welding community on the development of keyhole pores [43] [45] [61] [62] [63] [64]. Additionally, observations have been made noting increased variability when a keyholing melt pool is produced [45] [64] [65]. Detailed models of the keyholing process have been developed to gain a better understanding of the phenomenon [66] [67]. In additive manufacturing, King et al. proposed a method to avoid keyholing by proposing normalized enthalpy thresholds could signal when keyholing starts [47]. In addition to creating pores, vaporized material in keyhole melt pools can cause preferential loss of some alloying elements [43] [65] [68]. Porosity was analyzed across processing in both the EOS L-PBF and Arcam EB-PBF processes and showed how process parameters and resulting melt pools can influence the occurrence of different types of porosity [69] [70]. Lack of fusion flaws occur when the heat source does not sufficiently melt into the previous layer, or when the hatch spacing is too large. Previous work has identified methods to predict the occurrence of lack of fusion flaws based on melt pool dimensions [71]. Other work has observed\\ lack of fusion flaws as it related to various process parameters [30] [31]. Seifi et al. analyzed fracture toughness and fatigue crack growth in samples from the electron beam powder bed fusion process and found evidence of lack of fusion on the fracture surface [35]. Another major source of flaws in additively manufactured parts is related to fluid flow within the melt pools. Flow in weld pools not only influences variability in melt pool dimensions, but can also contribute to flaws that may occur [72]. Nemchinsky suggested thermocapillary instability arising from gradients in temperature and subsequently surface tension in melt pools could result in increased variability and flaws [73]. The bead-up phenomenon that is occasionally seen in additive manufacturing has been described as a result of Rayleigh instabilities in the melt pool where a liquid cylinder breaks up a continuous bead. The magnitude of these effects has been related to width to length ratio of the melt pool [74]. A width to length threshold has been suggested to avoid bead up in additive manufacturing [75]. In welding, Kou et al. found that the direction of fluid flow at the back of the melt pool can affect the development of porosity [76]. \subsection*{1.3.4 Microstructure} A strong understanding of the development of microstructure in additive manufacturing is critical for process parameter selection and the tailoring of mechanical properties throughout parts. . Kobryn identified the effects of power and velocity on grain size in Ti-6Al-4V [77] [28]. Other work process mapped cooling rates and thermal gradients. Information from thermal gradients and cooling rates was used to identify grain morphology that would develop in the deposition [78] [79] [80]. In more recent years, microstructure itself was related to melt pool area [81] [82] [83]. Accompanied with process maps for melt pool dimensions, this related microstructure to process parameters and allowed microstructure to be controlled directly from real time monitoring. Microstructure development has also been investigated in laser keyhole welding and insights to how microstructure forms in keyholing with additive manufacturing can be drawn [84]. Microstructure has been simulated and measured across many different additive manufacturing processes to add to the collective knowledge base. In the laser powder feed process, cooling rates were simulated and microstructure was analyzed [11] [85]. Kelly simulated the laser powder feed process and the development of Ti-6Al-4V microstructure to show how bands of colony alpha microstructure form do to heat cycles from following layers [86]. Lin et al. noted differences in grain structures between the laser powder bed fusion process and the electron beam powder bed fusion process [87]. Antonysamy measured Ti-6Al-4V prior beta grains in the laser powder bed and electron beam powder bed process and also produced tensile bars in the processes to compare to wrought properties [88]. Narra et al. demonstrated how to produce different regions in different areas of an additively manufactured part [89]. Murr et al. did tensile testing for the Arcam electron beam powder bed system and found properties similar to wrought material [90]. \subsection*{1.3.5 Modeling} Modelling the additive manufacturing process shares many similarities with models produced for welding. One of the most fundamental models for welding, is that of a simple moving point heat source [91]. The analytical model derived by Rosenthal can still give insights into the additive manufacturing process today. Christensen made improvements to the Rosenthal model by developing a dimensionless form [92]. Using superposition, Eagar and Tsai used these analytical models to create a model of a moving heat source with a Gaussian distribution [93]. A major limitation of these models, however, is the use of constant thermal properties. Early work in additive manufacturing improved on the understanding of processes and how process parameters may influence the melt pool and deposition [85] [94]. It was found that for a surface temperature of $2000 \mathrm{~K}$, less than $6 \%$ of the power is dissipated my mechanisms other than conduction. At 3080K, evaporation becomes a more important factor, but conduction still accounts for $80 \%$ of power dissipation [95]. With increasing computing power came more detailed models. Wang simulated a thin wall part to find a power program that would maintain a more consistent melt pool size as more layers were added [96]. Other multi-layer models were used to predict residual stress in the resulting part [97] [98]. Very complex models that take into account a large number of variables that include heat transfer, fluid flow, powder, and more have been developed to gain a better understanding of how the process works and how flaws may form [99] [100]. Microstructure modelling has also been insightful for the progress of additive manufacturing. In the laser powder feed process, Kelly modeled and identified how additional layers affected microstructure existing depositions [86]. Nie modeled microstructure evolution during solidification of IN 718. The model was used to produce results for various thermal gradientcooling rate combinations and compared to results from actual depositions with good agreement [101]. Zinoviev modeled 316 stainless steel microstructure development in the laser powder bed process [102]. The model yielded grain behaviors that are commonly seen in additive manufacturing. \subsection*{1.4 Organization} This thesis is organized into seven different chapters. The first chapter introduces additive manufacturing and the four primary direct metal additive manufacturing processes that are of primary interest. Motivation is given for the work before a literature review summarizes work\\ pertinent to this dissertation. The literature review covers effects of process parameters including spot size, monitoring and control, deposition flaws, microstructure, and modeling. The second chapter covers projects involving the process mapping and microstructure control of Ti-6Al-4V in the laser powder feed and electron beam wire feed processes. Finite element models are used to generate process maps for melt pool cross sectional area. Experiments are related to the process maps generated with finite element models via an effective absorptivity. In each process, methods to control microstructure via melt pool monitoring are proposed. Chapter three covers the effects of beam spot size on melt pool geometry in detail. Models based on the finite element method and the Rosenthal solution are used to systematically ascertain the effects of spot size. Normalization is used to plot melt pool dimensions to collapse a variety of results to simpler curves for each dimension. Experiments are shown to back up models results across multiple alloys, processes, and process parameters. Chapter four analyzes the effects of spot size on the occurrence of porosity in additively manufactured parts. Keyholing is identified in experimental melt pools and a method for avoiding the phenomena is presented. Guidance is also given on how to avoid lack of fusion flaws by balancing melt pool dimensions with hatch spacing and layer thickness. Experimental results of multi-layer deposits are presented. Chapter five extends work in previous chapters to identify if spot size has an effect on the resulting microstructure. Normalized cooling rates from simulations are presented and compared to both single layer and multi-layer experiments. The sixth chapter combines work done in this thesis to present a method to expand the available processing space. Methods for doing so are presented and used to improve usability of a laser powder bed fusion process for multiple alloys. Experiments are completed for both single layer and multi-layer deposits. Chapter seven summarizes the conclusions and contributions of this work. Recommendations for future work related to the subjects in this thesis are provided. \section*{Chapter 2: $\quad$ Process Mapping and Microstructure Control of Ti-} \section*{6Al-4V in Laser Powder Feed and Electron Beam Wire Feed} \section*{Processes} \subsection*{2.1 Overview} This chapter explores process mapping and microstructure control in the electron beam wire feed and laser powder feed processes. Knowledge about changes in melt pool geometry enables operators to correctly balance spot size, hatch spacing, and other parameters to build a part successfully. Operating outside of standard parameters can result in a preferred deposition rate, resolution, microstructure, or other outcomes. Previous work has been done outlining how optimal parameter sets can be found in processing space [103]. Methods to control microstructure for Ti-6Al-4V in these processes is also investigated. The focus of analysis in this work is centered on the size of prior beta grains. The alpha phase dominates most material properties (e.g. yield strength), but the alpha structure can be modified through post-\\ build heat treatment. Beta grains are an important factor for mechanical properties such as toughness [104] [105]. Additionally, the beta phase has an influence on the development of the alpha phase and therefore is important to measure in additive manufacturing [106] [107]. Relations are built in this chapter to relate melt pool dimensions to prior beta grain size for use with thermal imaging and feedback control systems. \subsection*{2.2 Methods} \subsection*{2.2.1 Process Mapping Approach} Process mapping is a method that allows a user to easily relate input parameters to desired process outcomes. There can be more than 100 process parameters for a particular additive manufacturing process, but a limited subset of those have a significant effect on the process outcomes. The process mapping approach isolates primary process variables and identifies how key process outcomes are affected. Plots are created that feature lines of constant melt pool dimensions, microstructure, susceptibility to flaw formation, or other key quantities. Figure 2-1 is an example of a process map showing lines of constant melt pool cross sectional area from finite element simulation data. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-038} \end{center} $=0.013 \mathrm{~mm}^{\wedge} 2$ \begin{itemize} \item $\mathrm{A}=0.0065 \mathrm{~mm}^{\wedge} 2$ \item $\mathrm{A}=0.0032 \mathrm{~mm}^{\wedge} 2$ \item $\mathrm{A}=0.0016 \mathrm{~mm}^{\wedge} 2$ \item $\mathrm{A}=0.0008 \mathrm{~mm}^{\wedge} 2$ \end{itemize} Figure 2-1: Power-velocity process map for melt pool cross-sectional area for 316L stainless steel in the L-PBF process To verify process maps, simple experiments that cover the range of processing space are completed and analyzed. In this case, melt pool cross-sectional areas can be measured and related to simulation data via an effective absorptivity. In some cases, different lines of constant melt pool area may have different effective absorptivities if keyholing melt pools are present. Melt pools in the keyholing regime can have an increased absorptivity due to internal reflections in the keyhole cavity [108]. \subsection*{2.2.2 Finite Element Model} Numerical models were developed in the ABAQUS software package to simulate a single deposition pass of the additive manufacturing processes used in this chapter. The models are similar in structure to the model of a moving heat source developed by Rosenthal [91]. The models used in this work are modified versions of those used by Fox [23]. Improvements on the Rosenthal model include temperature dependent properties, variable spot size, latent heat, and more. Temperature dependent properties for Ti-6Al-4V include thermal conductivity, specific heat, and density [109] [110]. Convection, radiation, fluid flow, powder effects and evaporation are neglected in these models as their influence has been shown to be minimal [95]. The sides of the model are given adiabatic boundary conditions and the base of the model is held at the prescribed preheat temperature. A symmetric boundary condition is used down the centerline of the melt pool. The model progresses by stepping a distributed flux heat source in the positive $\mathrm{X}$-direction in defined time steps to match the velocity prescribed by the user. The heat source travels through a fine mesh region to establish a well-defined steady state melt pool where cooling rate and melt pool dimensions can be measured. Biased elements are used to extend the substrate out far enough in all directions to prevent edge effects. For the electron beam wire feed process, added material is included to model the wire being fed into the melt pool. This is accomplished by initializing all elements before deactivating the elements representing added material. Added material elements are activated ahead of the applied flux in each time step until the end of the simulation. An example of the meshed substrate used to model the laser powder feed process is shown in Figure 2-2. A finite element melt pool is displayed in Figure 2-3 with some key dimensions labeled. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-040(1)} \end{center} Figure 2-2: 3D model used for finite element simulation in the ABAQUS software package \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-040} \end{center} Figure 2-3: Key melt pool dimensions measured from finite element simulations The ABAQUS software package models the moving heat source problem by solving the heat equation (Eq. 2-1). The heat equation balances energy stored in the material with energy leaving and energy being added. Eq. 2-1 $$ \frac{\partial}{\partial x}\left(k \frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(k \frac{\partial T}{\partial y}\right)+\frac{\partial}{\partial z}\left(k \frac{\partial T}{\partial z}\right)=\rho c_{p} \frac{\partial T}{\partial t} $$ When latent heat is considered, the equation becomes: Eq. 2-2 $$ \frac{\partial}{\partial x}\left(k \frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(k \frac{\partial T}{\partial y}\right)+\frac{\partial}{\partial z}\left(k \frac{\partial T}{\partial z}\right)=\rho c_{p} \frac{\partial T}{\partial t}+\rho L $$ ABAQUS uses a backward difference algorithm in the time domain for its simplicity and wellunderstood behavior. It is conditionally stable, but avoids oscillations that can be present in unconditionally stable methods, like the central difference method. ABAQUS uses a modified Newton-Raphson method to solve the resulting equation [111]. Key melt pool dimensions that can be gathered from simulation results include cross sectional area, width, depth, full length, length from maximum depth, and more. Completing a series of simulations throughout processing space can give insight to melt pool sizes and trends that can expected for different melt pool dimensions. Work presented in this chapter generally focuses on melt pool cross sectional area. \subsection*{2.2.3 Experiment Design and Measurement} Single bead process mapping experiments are deposited at power-velocity sets that form a grid throughout the available processing space. This design is able to give information about the different regions of processing space, and the flaws that may occur. In the LENS laser powder feed process, sixteen power-velocity combinations spanned 150-450 watts and 15-45 in/min. Three powder feed rate schemes were also used for single bead experiments in the LENS process. The nominal case for the process was given as $450 \mathrm{~W}, 25 \mathrm{in} / \mathrm{min}$, and 3 grams per minute (gpm) feed\\ rate. The first was the most simplistic, a no-added material case that compared directly to the simulations for the laser powder feed process. The second used the nominal powder feed rate of 3gpm throughout the entire processing space, and the third scaled powder feed rate from the nominal case with velocity. An image of a depositions from the LENS process with single bead experiments is shown in Figure 2-4. Single beads were deposited in straight lines 2.5 inches long to ensure steady state melt pool conditions have formed. Alternate geometries were also deposited at nominal parameters ( $450 \mathrm{~W}, 25 \mathrm{in} / \mathrm{min}, 3 \mathrm{gpm})$ for analysis of how melt pools and resulting microstructure differ for different geometries. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-042} \end{center} Figure 2-4: LENS processed plate including single bead deposits and scaled powder feed rate Thermal imaging was used to control melt pool length for microstructure control experiments in the laser powder stream process. The camera, provided by Stratonics, was a two wavelength imaging pyrometer with a temperature range of 1000 to 2000 Celsius, capturing four frames per second. Figure 2-5 shows the steps used to maintain a consistent melt pool length. The process of controlling melt pool length begins with process deposition at a prescribed set point. Thermal imaging gathers information about temperatures in and around the melt pool and a melt pool length measurement can be taken from this processed data. The length measurement is compared to a\\ desired value and power is controlled to achieve the specified value. In these experiments, a 10.5 inch single bead deposit was created. At each 3.5 inch interval, a different desired length was input to the controller. A proportional controller was used to change the melt pool length. At the time of these experiments, the integral and derivative portions of the controller had not yet been developed by Stratonics. At low specified lengths, some instability was seen in the control algorithm as is observed in the "Power control" plot in Figure 2-5. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-043} \end{center} Figure 2-5: Thermal imaging process control Process mapping experiments in the electron beam wire feed process were designed to extend the process map created by Fox to higher powers [23]. A nominal case for the Sciaky electron beam wire feed process was given as $10 \mathrm{~kW}, 30 \mathrm{in} / \mathrm{min}$, and $15 \mathrm{lbs} / \mathrm{hr}$. Experiments for process mapping ranged from $10-25 \mathrm{~kW}$ and 30-60 in/min. Feed rate was scaled with the anticipated melt\\ rate, which can be calculated with Eq. 2-3. Additionally, multi-layer experiments were completed at select points in processing space. The experiment plan with both single bead and multi-layer deposits in the electron beam wire feed process is shown in Figure 2-6. Eq. 2-3 $$ \text { Melt Rate }=A \times v $$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-044} \end{center} Figure 2-6: Sciaky electron beam wire feed process experiment plan Single layer beads were deposited across a $24 "$ x 12" x 1" Ti-6Al-4V plate. Single beads were deposited along a 22" stretch where process parameters were changed 11" into the deposit. This allowed for an increased number of melt pools to be deposited and with enough space to reach steady state melt pool dimensions. Single and multi-layer pads were built in either 21 " or 10 " blocks depending on the expected melt pool length. Multi-layer pads were created fifteen layers high, which was tall enough to reach steady state conditions in the $\mathrm{z}$ direction. A limitation of the machine required all deposits to be completed parallel to each other and in the same direction. Figure 2-7 shows three plates with single bead deposits, single layer pads, and multi-layer pads. The long pad on the left plate was stopped due to incorrect process parameters and built correctly on a later plate. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-045} \end{center} Figure 2-7: Experiments plates deposited in the Sciaky process Once experiments are completed, samples are prepared for analysis. Samples are crosssectioned, polished, and etched using Kroll's etchant. Procedures for polishing and etching can be found in Appendix 1. Samples are then imaged using an Alicona Infinite Focus optical microscope. Melt pool cross-sectional dimensions and average prior beta grain width can be measured. Prior beta grain size is measured using the intercept method [112]. Prior beta grains in these processes are columnar in nature so prior beta grain width is the dimension of focus in this study. A horizontal line is drawn perpendicular to the growth direction of columnar grains, and grains are counted then the total is divided by the length of the line. The process is repeated throughout the sample and all lines are averaged. Multi-layer pads were built to a height of $50 \mathrm{~mm}$ for the $10 \mathrm{~kW}, 30 \mathrm{in} / \mathrm{min}$ case, $40 \mathrm{~mm}$ for the $10 \mathrm{~kW}, 60 \mathrm{in} / \mathrm{min}$ case, and $15 \mathrm{~mm}$ for the $20 \mathrm{~kW}$, $60 \mathrm{in} / \mathrm{min}$ case. Prior beta grain width measurements in the $10 \mathrm{~kW}$ cases are measured at three height locations, $5 \mathrm{~mm}$ apart in the center\\ third of the deposit to determine if height is playing a role in prior beta grain width while avoiding any effects that may be caused by the edges of the deposit. The $20 \mathrm{~kW}$, $60 \mathrm{in} / \mathrm{min}$ case was built at a reduced height due to limited availability of added material and only measured at a single height. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-046} \end{center} Figure 2-8: Key melt pool dimensions measured for a melt pool in from the Sciaky process Figure 2-8 shows a melt pool cross section from the Sciaky process with key melt pool dimensions labeled. Cross-sectional width, depth and area are essential to the selection of process parameters like hatch spacing and material feed rate or layer thickness. Determination of melt pool boundaries can be difficult in some processes and alloys. In Ti-6Al-4V, this is because the beta transus temperature is much lower than the melting temperature causing significant microstructural transformations in the heat affected zone. To capture this uncertainty, the edge of prior beta grain growth can be used as an outer limit for the possible melt pool boundary. An inner limit for possible melt pool boundary can be formed by identifying the start of columnar growth in prior beta grains. A "Best Guess" measurement of the melt pool boundary is also taken. This boundary begins at where the straight edge of the substrate is interrupted by the melt pool. The boundary continues\\ through grains of similar size and shape to the other edge of the melt pool. Placement of these three boundaries are demonstrated in Figure 2-9.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-047} Figure 2-9: Measurement of uncertainty in melt pool area Since serial sectioning can be prohibitively time consuming especially when a high number of samples are required, variability in this study has only been found for melt pool width. Variability for melt pool width can be found by imaging the single bead melt track from above and tracing the edges of the melt pool as seen from above. Figure 2-10 shows a melt pool viewed from above before and after the extents of melt pool width are traced in red. The traced image is run through a MATLAB script that measures the distance between the two red lines at every pixel moving from left to right. From these measurements, average melt pool width and standard deviation can be calculated. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-048} \end{center} Figure 2-10: Tracing of melt pool width for calculation of standard deviation \subsection*{2.3 Results} This section presents Ti-6Al-4V process maps for cross-sectional melt pool dimensions in the Sciaky electron beam wire feed and LENS laser powder feed processes along with methods to control prior beta grain width. In the electron beam wire feed process, cross-sectional width, depth and area are process mapped with good agreement with finite element simulation results. Variations are observed between lines of constant melt pool depth and width. Trends in prior beta grain width follow those found in work by Gockel [81] for single bead deposits, and are compared with results from multi-layer pads. Process maps in the laser powder feed process again show good agreement between simulation and experimental results. Comparisons are made between different feed rate schemes, and effects of feed rate on geometry are explored. A method to control prior beta grain width with the use of thermal imaging is presented. \subsection*{2.3.1 Process Mapping the Sciaky Electron Beam Wire Feed Process} Direct metal additive manufacturing processes tend to have recommended parameter sets that the machine manufacturers suggest for producing successful parts; however, these do not take advantage of the full capacity of the technology. Process mapping of melt pool area gives insights into the parameters that can be used to modify resolution, deposition rate, or other process outcomes. Cross-sectional area process maps are displayed with lines of constant melt pool area that show where different melt pool sizes can be found in power-velocity processing space. Figure 2-11 displays the power-velocity process map generated for the Sciaky electron beam wire feed process. Data from finite element simulations is presented as solid lines. Experimental "Best guess" measurements are represented by circular data points and measurement uncertainty is displayed as dotted lines around each cross-sectional area value. To find locations of the desired melt pool area from experiments, measurements at deposited power-velocity combinations were piecewise linearly interpolated. An effective absorptivity of 0.89 minimized the $r^{2}$ value to 0.9493 when matching experimental results to finite element results for all cross-sectional areas. This effective absorptivity matches well with values used in the past for this process [23]. Agreement between finite element results and experimental measurements can be improved if adjustments are made to maintain a consistent aspect ratio between melt pool depth and width. Details on the adjustments are discussed in Chapter 6:. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-050} \end{center} Figure 2-11: Power-velocity process map of melt pool cross-sectional area in the Sciaky process Cross-sectional area is a useful melt pool dimension that provides valuable information about the melt pool, but melt pool width and depth can be more insightful when selecting parameters for a build. A process map of depth is shown in Figure 2-12 with uncertainty measured using the methods described in 2.2.3. Plotted depth values match cross-sectional area values used in Figure 2-11 if a semi-circular melt pool is assumed. Process mapped experimental points show a worse agreement with finite element results and an overall tighter grouping when compared to melt pool areas. This suggests that smaller changes in power are required to achieve a certain change in melt pool depth when compared to melt pool area. Melt pool width is process mapped in Figure 2-13 using cross-sectional measurements. Dotted lines represent measurement uncertainty (see Figure 2-9) and values plotted match depth and area values in Figure 2-11 and Figure 2-12 for and assumed semi-circular melt pool. As with melt pool depths, processed mapped melt pool widths do not match finite element results well. As opposed to depth, a greater change in power is needed to yield a certain change\\ in melt pool width. An explanation for differences in process map behavior is presented in Chapter 6:. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-051(1)} \end{center} Figure 2-12: Power-velocity process map of melt pool depth in the Sciaky process \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-051} \end{center} Figure 2-13: Power-velocity process map of melt pool width in the Sciaky process Melt pool width can be measured via two methods for single bead deposits. Table 1 displays average melt pool width and standard deviation as measured from above along with the maximum and minimum limits measured from cross sections. In this process, the standard deviation of melt pool width was relatively insignificant when compared to the average width measured showing a stable melt pool. Ranges for uncertainty are also larger than the windows created using average values measured from above with two standard deviations. Table 1: Melt pool width measurements in the Sciaky process \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{Melt Pool Width} \\ \hline \begin{tabular}{l} Power \\ (kW) \\ \end{tabular} & \begin{tabular}{l} Velocity \\ (in/min) \\ \end{tabular} & \begin{tabular}{l} "Best Guess" \\ Width from Cross \\ Section $(\mathrm{mm})$ \\ \end{tabular} & \begin{tabular}{l} Width Uncertainty \\ from Cross Section \\ $(\mathrm{mm})$ \\ \end{tabular} & \begin{tabular}{l} Average Width \\ from Above \\ $(\mathrm{mm})$ \\ \end{tabular} & \begin{tabular}{c} Standard \\ Deviation from \\ above $(\mathrm{mm})$ \\ \end{tabular} \\ \hline 10 & 30 & 13.7 & $12.9-15.0$ & 13.0 & 0.5 \\ \hline 10 & 45 & 11.5 & $10.2-12.7$ & 11.6 & 0.2 \\ \hline 10 & 60 & 10.6 & $9.3-11.6$ & 10.9 & 0.2 \\ \hline 15 & 30 & 16.0 & $14.9-17.8$ & 16.0 & 0.1 \\ \hline 15 & 45 & 13.0 & $12.0-15.1$ & 13.1 & 0.1 \\ \hline 15 & 60 & 11.3 & $10.8-13.6$ & 11.5 & 0.2 \\ \hline 20 & 30 & 19.4 & $18.2-20.7$ & 19.1 & 0.4 \\ \hline 20 & 45 & 16.3 & $15.0-17.4$ & 16.0 & 0.2 \\ \hline 20 & 60 & 14.3 & $13.2-15.1$ & 14.4 & 0.3 \\ \hline 25 & 30 & 21.2 & $19.6-22.5$ & 20.9 & 0.5 \\ \hline 25 & 45 & 17.4 & $15.8-18.7$ & 17.9 & 0.6 \\ \hline 25 & 60 & 16.1 & $14.1-16.6$ & 16.1 & 0.5 \\ \hline \end{tabular} \end{center} \subsection*{2.3.2 Process Mapping the LENS Laser Powder Stream Process} In the LENS laser powder feed process, a separate process map is generated for each powder feed scheme. The first scheme, which matches simulations most closely is the no added powder scheme. No powder added experiments and simulations give a more fundamental understanding of the melt pools being generated in the process because they involve fewer variables that affect\\ the resulting geometry. No added material experiments (Figure 2-14) match up very well with finite element results using and effective absorptivity of 0.31 minimizing $r^{2}$ to 0.9539 . Scaled feed experiments adjusted material feed rate with velocity based on the nominal case at $25 \mathrm{in} / \mathrm{min}$ and $3 \mathrm{gpm}$. This provided the melt pool with a consistent amount of fed material per unit distance. Results for scaled feed rate are shown in Figure 2-15 with good agreement between finite element simulations at an effective absorptivity of 0.36 and an $r^{2}$ value of 0.9523 . Constant 3 gpm feed rate experiments used 3 gpm powder feed throughout processing space and best matched finite element simulations with an effective absorptivity of 0.35 and an $\mathrm{r}^{2}$ value of 0.8307 . Regions of constant melt pool area for the $3 \mathrm{gpm}$ case drops at the low velocity case (15 in/min), signaling that a lower power is required to produce the melt pool area at low velocities. Again, uncertainty is measured as described in section 2.2.3 and interpolated to make the dotted lines windowing the "best guess" measurements. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-053} \end{center} Figure 2-14: Power-velocity process map of melt pool cross-sectional area for the LENS process with no powder feed. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-054(1)} \end{center} FEA: $\mathrm{A}=0.32 \mathrm{~mm} \mathrm{~mm}^{\wedge}$ FEA: $A=0.16 \mathrm{~mm}^{\wedge} 2$ FEA: $A=0.08 \mathrm{~mm}^{\wedge} 2$ Scaled $\mathrm{A}=0.32 \mathrm{~mm}^{\wedge} 2$ Scaled $\mathrm{A}=0.16 \mathrm{~mm} \mathrm{~mm}^{\wedge}$ Scaled $A=0.08 \mathrm{~mm}^{\wedge} 2$ Uncertainty Limit Figure 2-15: Power-velocity process map of melt pool cross-sectional area for the LENS process with scaled powder feed \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-054} \end{center} Figure 2-16: Power-velocity process map of melt pool cross-sectional area for the LENS process with constant $3 \mathrm{gpm}$ feed Comparison between the three different feed rate scenarios gives insights to the effects of powder feed rate. In all prescribed areas, the no-added material cases require more power to create\\ an equivalent area. This suggests that increased material feed increases the resulting melt pool area. The notion is supported when comparing the scaled feed rate and constant 3 gpm schemes. At the low velocity case, lower powers are needed by the $3 \mathrm{gpm}$ case to create an equivalent melt pool area when compared to the scaled feed scheme which used a feed rate of $1.8 \mathrm{gpm}$. At high velocity cases the opposite is true, the $3 \mathrm{gpm}$ case produces smaller melt pools than the scaled feed scheme which is providing above 3 gpm of powder. The "best guess" measurement of all three feed rate schemes are compared in Figure 2-17. Scaling the powder feed rate had a more consistent melt pool shape when compared to the constant $3 \mathrm{gpm}$ cases and had better agreement with both the finite element results and the no added material cases. While scaling powder feed rate with velocity proved better than no scaling, scaling feed rate with the expected melt rate (Melt rate $=$ $A \times v$ ) may provide a further improvement. This would scale material feed rate with the rate that material is melted. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-055} \end{center} Figure 2-17: Power-velocity process map of melt pool cross-section area comparing different feed rate scenarios in the LENS process. As with the Sciaky process, widths and depths have been process mapped for the LENS laser powder feed process. Figure 2-18 shows process maps of melt pool width on the left and melt pool depth on the right. From top to bottom, process maps show data for the constant 3 gpm feed rate, scaled feed rate, and no-added material. All values for constant width and depth match values used with melt pool area for an assumed semi-circular melt pool. Plotted points are found by linearly interpolating experimental "best guess" measurements and are bordered by dotted lines showing uncertainty from outer limit and inner limit boundaries for the melt pools. Melt pool widths best matched finite element results with effective absorptivities of 0.59 for constant 3gpm, 0.56 for scaled feed, and 0.58 for no added material. $\mathrm{R}^{2}$ values for the three cases are $0.8434,0.9542$, and 0.9311 respectively. These absorptivity values are significantly different than the values between 0.31 and 0.36 used in area measurements signaling that melt pool widths are larger than expected for the measured cross-sectional areas. In all cases, widths were too large to generate an experimental data set for the smallest constant width line of $0.45 \mathrm{~mm}$. Different powder feed rates appear to have little to no effect on melt pool width. Melt pool depth did not show consistent agreement with finite element results. The constant 3 gpm case, scaled feed rate case, and no added material case matched best with FEA results using effective absorptivities of $0.29,0.31$, and 0.21 respectively with $r^{2}$ values of the center width and depth cases $(\mathrm{W}=0.64 \mathrm{~mm}, \mathrm{D}=0.32 \mathrm{~mm})$ are $0.5846,0.7133$, and 0.7059 . Comparison between the constant 3 gpm and scaled feed cases (3 gpm has higher feed below $25 \mathrm{in} / \mathrm{min}$ and lower feed above) indicates that increasing feed rate increases melt pool depth. As material is added to the surface of the melt pool and the deposition grows taller, conduction pathways to draw heat away from the melt pool become restricted. This allows the molten material to remain longer and more powder to be added to the surface of the melt pool, increasing its measured depth. Another\\ phenomenon observed in melt pool depth process maps is comparatively poor alignment between experimental and finite element results in the constant $3 \mathrm{gpm}$ case due to the feed rate not being properly balanced with melt pool size to give consistent results. Differences in absorptivities used for melt pool area, width, and depth are again contributed to small spot sizes and near semi-circular melt pools from simulations. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-058(1)} \end{center} Melt Pool Depth\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-058} \begin{center} \begin{tabular}{lll} W=0.91 mm & FEA Results & $D=0.45 \mathrm{~mm}$ \\ W=0.64 mm & No Added Material & $D=0.32 \mathrm{~mm}$ \\ W=0.45 mm & Scaled Feed Rate & $D=0.23 \mathrm{~mm}$ \\ & Constant 3 gpm Feed & \\ \hline ......... Uncertainty Limit & & \\ \hline \end{tabular} \end{center} Figure 2-18: Process maps of melt pool widths and depths in the LENS process for different material feed rate scenarios Variability was again captured for melt pool width by measuring melt pool widths as viewed from above. Appendix 2 contains data comparing width measurements from above and those from cross sections. Standard deviations measured from above widths are typically below 5\% of the average melt pool width in all three feed rate schemes. This quantitatively backs up observations of smooth and consistent melt pools in single bead experiments from the laser powder feed process. \subsection*{2.3.3 Microstructure Control in the Sciaky Electron Beam Wire Feed Process} Where process mapping of the Sciaky electron beam wire feed process was an extension Soylemez and Fox, control of microstructure in the process will look to apply the same relationships developed by Gockel [81]. This section will focus on relationships between melt pool dimensions and Ti-6Al-4V prior beta grain size initially in single bead deposits throughout processing space, then in a single layer and multi-layer pad deposits of select parameter combinations. Knowledge of how melt pool dimensions impact microstructure can work hand in hand with melt pool monitoring to control microstructure throughout parts built with AM. Results and trends are compared to those found by Gockel and Narra [81] [89]. Average prior beta grain width measurements are plotted against effective melt pool width to compare to the relationship previously developed by Gockel. Effective melt pool width is the melt pool width calculated from area assuming a semicircular melt pool. Figure 2-19 compares single bead results from this work to single beads measured by Gockel for NASA's EBF3 electron beam wire feed process. Both sets of experimental results show average prior beta grain size changing linearly with effective width; however, work by Gockel shows larger grain sizes for melt pools of similar melt pool width. Primary reasons for the disparity between the two experiment sets are the use of different electron beam spot scanning strategies or microstructural differences in the\\ substrate. Error bars from this work show the uncertainty in effective width and the 95\% confidence interval for grain width. Error bars in work by Gockel show variation from multiple melt pools in average grain size and effective width. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-060} \end{center} Figure 2-19: Relationship between prior beta grain width and effective melt pool width in electron beam wire feed processes Experiments were also completed to identify if the trend observed in single bead deposits held up in bulk deposition geometries. Due to space constraints, only three power-velocity combinations were deposited and analyzed for single-layer and multi-layer pads. Figure 2-20 compares prior beta grain width measurements in single beads with those measured in pads. The error bars showing uncertainty in effective width for the pad deposits are based on single bead measurements at each respective power-velocity combination. Single layer pads saw a modest increase in prior beta grain width when compared to single bead results and appears to have a similar trend when compared to single beads. Prior beta grain width measurements similarly appears to follow the same trend, but with much higher grain widths. The consistency in trend and\\ increase in grain width for multi-layer deposits was similarly observed in the Arcam EB-PBF process by Narra et al [89]. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-061} \end{center} Figure 2-20: Relationship between prior beta grain width and effective melt pool width for different deposition geometries in the Sciaky electron beam wire feed process \subsection*{2.3.4 Thermal Imaging and Microstructure Control in the LENS Process} Relationships between effective melt pool width and prior beta grain width in the electron beam wire feed and EB-PBF processes by Gockel do not hold up in the laser powder feed region of processing space. This is primarily due to a mismatch between trends of cooling rate and melt pool area near the origin on a power-velocity process map. Figure 2-21 displays experimental and simulation results showing a mismatch of cooling rate and prior beta grain size with melt pool area. At low velocities, melt pool area trends toward a y-axis intercept where a finite melt pool size is preset at zero velocity. Cooling rate trends toward the origin where a cooling of zero is present at zero velocity. LENS Simulations \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-062(1)} \end{center} LENS Experimental \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-062} \end{center} -- Constant cooling rate - Constant area -- Constant prior beta grain size Figure 2-21: Trends for melt pool area, cooling rate, and prior beta grain size in the LENS laser powder feed process Due to the inability to apply the previously used prior beta grain width-effective melt pool width relationship, a relationship between melt pool full length, velocity, and prior beta grain width was developed. Aspects of melt pool geometry viewed from above are particularly useful as they can be used with thermal imaging to monitor the melt pool during deposition. For this reason, full melt pool length was a desirable geometry when relations between melt pool width and microstructure were shown to be insufficient. To test relationships between full length, velocity, and prior beta grain width, a thermal imaging feedback control system was set up by Stratonics at Penn State ARL on a LENS MR-7 machine. The system allowed a set full length to be controlled via changing laser power while at a fixed velocity. Experiments controlling melt pool length via thermal imaging were completed at $15 \mathrm{in} / \mathrm{min}, 30 \mathrm{in} / \mathrm{min}$, and $45 \mathrm{in} / \mathrm{min}$ and lengths of 1.27, 1.78, and $2.29 \mathrm{~mm}$. Figure 2-22 displays measured prior beta grain widths against full melt pool length for different lines of constant velocity. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-063} \end{center} Figure 2-22: Prior beta grain width vs full melt pool length in the laser powder feed process Error bars represent the $95 \%$ confidence interval for prior beta grain width. Unlike relationships used for the electron beam wire feed process, the relationships between melt pool geometry and microstructure in the laser powder feed process are also dependent on travel velocity. However, since velocity is a primary process parameter, prior beta grain size in Ti-6Al-4V can be indirectly controlled by directly controlling melt pool full length. This method and relationship has the potential to enable location specific microstructure control throughout actual parts. \subsection*{2.4 Discussion} Key melt pool dimensions have been process mapped in the electron beam wire feed and laser powder feed process. In the electron beam wire feed process, experimental cross-sectional area measurements matched finite element results with an effective absorptivity of 0.89 . When comparisons were made between cross-sectional area, width, and depth, there was a discrepancy between how sensitive the different dimensions were to power and velocity. Melt pool depth showed a greater sensitivity to the process parameters than area and melt pool width showed a\\ lesser sensitivity. These differences in sensitivity are due to the use of a consistent spot size, the details of which are discussed later in Chapter 3:. Process mapping in the laser powder feed process compared cross section dimensions in three different powder feed rate schemes. Experimental process maps of area matched no-added material finite element results well with effective absorptivities of 0.31 for no-added material, 0.36 for a scaled feed rate, and 0.35 for a constant $3 \mathrm{gpm}$ feed rate. Increasing the powder feed rate was found to cause an increase in cross-sectional area. When process maps of depth and width were compared with area, similar differences in sensitivity to power and velocity were again observed. There were also significant differences in the effective absorptivities found for depth, width, and area showing that experimental melt pools are consistently shallower than the semi-circular melt pools created in simulations. Again, this can be contributed to spot size and is discussed in the following chapters. There were also larger variations in effective absorptivity across the different feed rate schemes for melt pool depth than melt pool width. This signals that feed rate has a significant effect on depth and has little effect on width. Microstructure was analyzed in single bead and multi-layer deposits in the electron beam wire feed process and relations between melt pool geometry and prior beta grain width suggested by Gockel were verified. Measurements from single beads showed a linear relationship between prior beta grain width and effective melt pool width. The trend was generally parallel to results by Gockel, but shifted to lower grain sizes. The difference is likely due to differing substrate microstructure or other differences between the Sciaky process used in this work and NASA's EBF3 process used by Gockel. Measurements from single layer and multi-layer pads at three different power-velocity combinations showed similar trends at higher prior beta grain widths. In the laser powder feed process trends found in the electron wire feed process were found to be non-applicable. New relationships between prior beta grain width, full melt pool length, and velocity were developed. Single bead deposits were generated by controlling laser power to maintain a desired full length at a specified velocity. Prior beta grain measurements formed different linear relationships between microstructure and full melt pool length for different velocities. The relationships developed were successfully used to guide a feedback control systems with the use of thermal imaging. \section*{Chapter 3: The Effects of Spot Size on Melt Pool Dimensions} \subsection*{3.1 Overview} Spot size can play an important role in the development of melt pool geometry, the effects of which directly affect the quality of a part built using additive manufacturing. This chapter outlines how key melt pool dimensions change with increasing spot size independent of melt pool size, process, and alloy. Simulations are developed based on both analytical and finite element models for tophat and Gaussian beam profiles to understand melt pool behavior with different beam sizes. Experiments from various processes, alloys, and melt pool shapes show good agreement with simulation results to validate the models. Experiments can additionally be used to estimate spot sizes in different processes. The methods to estimate spot size are discussed and experimental results are fit to characteristic curves. Experimental estimates are also compared to beam measurements from the EOS M 290 process. Estimates of spot size can be used to guide focus changes to reliably predict melt pool geometry in additive manufacturing processes. \subsection*{3.2 Methods} \subsection*{3.2.1 Modeling} Work in this chapter is a product of both finite element based and analytical based models. Finite element simulations used in spot size analysis are based on those used in Chapter 2:, and simulate top hat or Gaussian flux distributions. Analytically based models are evolutions of the Rosenthal model of a moving point heat source [91]. The Eagar-Tsai model simulates a moving heat source with a Gaussian heat source and is a modification of the Rosenthal model [93]. Another model was created to simulate a top hat heat source by using the principle of superposition with\\ the original Rosenthal model. These models were used to identify how melt pool geometry changes with increasing spot size. \subsection*{3.2.1.1 Finite Element Models} The finite element model used in this section was a slight modification on the model used for the laser powder feed process. The model simulates a distributed moving heat source on a large substrate that is long enough to reach steady state melt pool size and wide and deep enough to avoid edge effects and a symmetry boundary condition down the center of the melt pool. The heat flux is distributed across elements on the surface to make a semi-circular shape. The number of elements with applied heat flux is determined by stepping through elements in the X-direction and rounding to the nearest element in the Y-direction to create the correct shape. Two different flux distributions within the spot size were simulated. One model uses a tophat distribution where all flux values are set equal, and a second approximates a Gaussian distribution. The spot size value used from Gaussian distribution simulations follows the D86 width measurement technique commonly used to find laser beam diameter [113]. The distribution of the heat flux for a typical model is shown in Figure 3-1. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-067} \end{center} Figure 3-1: Flux distribution on the surface of a finite element model The Gaussian heat source model extended the Gaussian profile out to two standard deviations, and amplitude is adjusted to provide the full power input. Since the Gaussian profile is fit onto a set of square elements, the smallest spot sizes used (4 element radius) had the largest percent error between the discrete and true distribution (25\%). Other spot sizes simulated were multiples of 4 elements through the radius and have significantly decreased error in respect to modelling a Gaussian beam profile. Simulations of spot size span multiple processes and alloys. In all cases, the finite element models use temperature dependent thermal properties. \subsection*{3.2.1.2 Rosenthal and Eagar-Tsai Models} In addition to finite element models, simpler models for tophat and Gaussian beam distributions were used to identify effects of increasing spot size. The models do not include temperature dependent properties or latent heat, but a solution can be found in a matter of seconds compared to hours or days. The first model, simulating a tophat distribution, is based off the moving heat source model developed by Rosenthal [91] shown in Eq. 3-1. Eq. 3-1 $$ T-T_{0}=\frac{q}{2 \pi k R} e^{-\frac{v(w+R)}{2 \alpha}} $$ Where $T$ is the temperature of the location of interest, $T_{0}$ is the preheat temperature, $q$ is the input power, $v$ is the travel velocity, $k$ and $\alpha$ are thermal properties, and $w$ and $R$ specify the location. The equation gives the temperature at a specified location relative to a point heat source. To create a tophat heat source, multiple Rosenthal models are organized into a circular shape with 100 instances across the diameter. The principle of superposition is used to sum the solutions for\\ a specified point in space. Melt pool boundaries are found by using the Newton-Raphson method and maximum width, depth, and area is found using the golden-section search method. The Eagar-Tsai model was developed based on the Rosenthal model and simulates a moving heat source with a Gaussian distribution. Where the original Rosenthal model can be solved analytically, the derived Eagar-Tsai model in Eq. 3-2 must be solved numerically [93]. Eq. 3-2 $$ \theta=\frac{n}{\sqrt{2 \pi}} \int_{0}^{\frac{v^{2} t}{2 \alpha}} \frac{\tau^{-\frac{1}{2}}}{\tau+u^{2}} e^{-\frac{\xi^{2}+\psi^{2}+2 \xi \tau+\tau^{2}}{2 \tau+2 u^{2}}-\frac{\zeta^{2}}{2 \tau}} d \tau $$ Dimensionless temperature is represented by $\theta$, and $\xi, \psi$, and $\zeta$ represent dimensionless distance in $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$. Dimensionless time is represented by $\tau . u$ is a dimensionless heat source distribution parameter and $n$ is an operating parameter that includes power, velocity, and thermal properties. The integral was solved numerically with the trapezoid method, and melt pool boundaries and maximum geometry values were found via the Newton-Raphson and goldensection search methods as with the tophat distribution model. \subsection*{3.2.1.3 Model Settings used in Spot Size Simulations} Simulations were run for various processes, alloys, and process parameter settings. Table 2 shows the model settings used to generate results from simulations where spot size was varied. The provided $\mathrm{L}_{0} / \mathrm{D}_{0}$ value is the melt pool length to depth ratio found at a point heat source, the $T_{\text {prop }}$ value is the temperature at which thermal properties are used for the Rosenthal and EagerTsai models. $\mathrm{T}_{\text {prop }}$ is left blank for finite element simulations since temperature dependent properties were used. Table 2: Model settings used for simulations of spot size increases \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline $\mathbf{L}_{0} / \mathbf{D}_{0}$ & Process & Alloy & Model & \begin{tabular}{l} Power \\ (W) \\ \end{tabular} & \begin{tabular}{l} Velocity \\ $(\mathrm{mm} / \mathrm{s})$ \\ \end{tabular} & \begin{tabular}{c} Background \\ Temp (K) \\ \end{tabular} & \begin{tabular}{l} $\mathbf{T}_{\text {prop }}$ \\ $(\mathbf{K})$ \\ \end{tabular} \\ \hline 1.25 & \begin{tabular}{l} Laser powder bed \\ fusion (L-PBF) \\ \end{tabular} & AlSi10Mg & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 100 & 845 & 308 & 500 \\ \hline 1.25 & \begin{tabular}{l} Laser powder feed \\ (LPF) \\ \end{tabular} & \begin{tabular}{c} $17-4 \mathrm{PH}$ \\ stainless steel \\ \end{tabular} & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 85 & 30 & 308 & 1000 \\ \hline 1.25 & \begin{tabular}{l} Laser powder feed \\ (LPF) \\ \end{tabular} & \begin{tabular}{c} $17-4 \mathrm{PH}$ \\ stainless steel \\ \end{tabular} & \begin{tabular}{c} Finite \\ Element \\ \end{tabular} & 87.5 & 30 & 293 & \\ \hline 1.25 & \begin{tabular}{l} Laser powder bed \\ fusion (L-PBF) \\ \end{tabular} & AlSi10Mg & \begin{tabular}{c} Finite \\ Element \\ \end{tabular} & 50 & 660 & 308 & \\ \hline 2.5 & \begin{tabular}{l} Laser powder bed \\ fusion (L-PBF) \\ \end{tabular} & Ti-6Al-4V & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 60 & 910 & 308 & 1800 \\ \hline 2.5 & \begin{tabular}{l} Laser powder feed \\ (LPF) \\ \end{tabular} & \begin{tabular}{l} 316L stainless \\ steel \\ \end{tabular} & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 470 & 50 & 308 & 1000 \\ \hline 2.5 & \begin{tabular}{l} Laser powder feed \\ (LPF) \\ \end{tabular} & \begin{tabular}{l} 316L stainless \\ steel \\ \end{tabular} & \begin{tabular}{c} Finite \\ Element \\ \end{tabular} & 400 & 35 & 293 & \\ \hline 2.5 & \begin{tabular}{l} Laser powder bed \\ fusion (L-PBF) \\ \end{tabular} & Ti-6Al-4V & \begin{tabular}{c} Finite \\ Element \\ \end{tabular} & 40 & 525 & 308 & \\ \hline 5 & \begin{tabular}{l} Laser powder bed \\ fusion (L-PBF) \\ \end{tabular} & $\mathrm{CoCr}$ & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 100 & 1075 & 308 & 950 \\ \hline 5 & \begin{tabular}{l} Electron beam wire \\ feed (EBWF) \\ \end{tabular} & IN 625 & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 3000 & 21.2 & 293 & 1027 \\ \hline 5 & \begin{tabular}{l} Electron beam wire \\ feed (EBWF) \\ \end{tabular} & Ti-6Al-4V & \begin{tabular}{c} Finite \\ Element \\ \end{tabular} & 3880 & 21.2 & 293 & \\ \hline 5 & \begin{tabular}{l} Laser powder bed \\ fusion (L-PBF) \\ \end{tabular} & $\mathrm{CoCr}$ & \begin{tabular}{c} Finite \\ Element \\ \end{tabular} & 95 & 476 & 308 & \\ \hline 10 & \begin{tabular}{l} Electron beam powder \\ bed fusion (EB-PBF) \\ \end{tabular} & $\mathrm{CoCr}$ & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 500 & 450 & 1073 & 1175 \\ \hline 10 & \begin{tabular}{l} Electron beam wire \\ feed (EBWF) \\ \end{tabular} & Ti-6Al-4V & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 20000 & 18.2 & 293 & 935 \\ \hline 10 & \begin{tabular}{l} Electron beam wire \\ feed (EBWF) \\ \end{tabular} & Ti-6Al-4V & \begin{tabular}{c} Finite \\ Element \\ \end{tabular} & 20000 & 17.3 & 293 & \\ \hline 10 & \begin{tabular}{l} Electron beam powder \\ bed fusion (EB-PBF) \\ \end{tabular} & Ti-6Al-4V & \begin{tabular}{l} Finite \\ Element \\ \end{tabular} & 600 & 265 & 1073 & \\ \hline 20 & \begin{tabular}{l} Electron beam wire \\ feed (EBWF) \\ \end{tabular} & IN 625 & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 25000 & 33.9 & 293 & 850 \\ \hline 20 & \begin{tabular}{l} Electron beam powder \\ bed fusion (EB-PBF) \\ \end{tabular} & Ti-6Al-4V & \begin{tabular}{l} Rosenthal/ \\ Eagar-Tsai \\ \end{tabular} & 1500 & 1375 & 1073 & 1800 \\ \hline 20 & \begin{tabular}{l} Electron beam powder \\ bed fusion (EB-PBF) \\ \end{tabular} & Ti-6Al-4V & \begin{tabular}{c} Finite \\ Element \\ \end{tabular} & 1430 & 423 & 1073 & \\ \hline 20 & \begin{tabular}{l} Electron beam wire \\ feed (EBWF) \\ \end{tabular} & Ti-6Al-4V & \begin{tabular}{c} Finite \\ Element \\ \end{tabular} & 32000 & 42.3 & 293 & \\ \hline \end{tabular} \end{center} \subsection*{3.2.2 Experiments} Experiments were completed in five different processes and five different alloys shown in Table 3. In all cases, specific power-velocity combinations were chosen for single bead deposits, and spot size was varied incrementing from a focused to defocused beam. Measurements of melt pool cross section width, depth, and area are used to compare against models. Since trends are the most important aspect in this chapter, only the "best guess" measurements will be used as defined in section 2.2.3. Table 3: Spot size experiment processes, alloys, and process parameters \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline Process & Alloy(s) & Power & Velocity & \begin{tabular}{c} Focus Setting \\ Range \\ \end{tabular} & \begin{tabular}{l} Expected \\ Lo/Do \\ \end{tabular} \\ \hline \multirow{2}{*}{}\begin{tabular}{c} Sciaky Electron \\ Beam Wire Feed \\ \end{tabular} & \multirow{2}{*}{Ti-6Al-4V} & $10 \mathrm{~kW}$ & $19.0 \mathrm{~mm} / \mathrm{s}$ & 0.12 to 0.27 in & 15 \\ \hline & & $25 \mathrm{~kW}$ & $12.7 \mathrm{~mm} / \mathrm{s}$ & 0.25 to 0.60 in & 20 \\ \hline \multirow{6}{*}{}\begin{tabular}{c} Arcam S12 EB- \\ PBF \\ \end{tabular} & \multirow{3}{*}{Ti-6Al-4V} & $670 \mathrm{~W}$ & $270 \mathrm{~mm} / \mathrm{s}$ & -20 to $38 \mathrm{~mA}$ & 5 \\ \hline & & $670 \mathrm{~W}$ & $1100 \mathrm{~mm} / \mathrm{s}$ & 0 to $26 \mathrm{~mA}$ & 10 \\ \hline & & $670 \mathrm{~W}$ & $3700 \mathrm{~mm} / \mathrm{s}$ & 0 to $21 \mathrm{~mA}$ & 20 \\ \hline & \multirow{3}{*}{IN718} & $670 \mathrm{~W}$ & $90 \mathrm{~mm} / \mathrm{s}$ & 10 to $60 \mathrm{~mA}$ & 5 \\ \hline & & $670 \mathrm{~W}$ & $400 \mathrm{~mm} / \mathrm{s}$ & -8 to $52 \mathrm{~mA}$ & 10 \\ \hline & & $670 \mathrm{~W}$ & $1300 \mathrm{~mm} / \mathrm{s}$ & 0 to $38 \mathrm{~mA}$ & 20 \\ \hline \multirow{4}{*}{}\begin{tabular}{l} 3D Systems ProX \\ 200 L-PBF \\ \end{tabular} & \multirow{4}{*}{}\begin{tabular}{c} Stainless Steel (304, \\ 316L, 17-4 PH) \\ \end{tabular} & $300 \mathrm{~W}$ & $500 \mathrm{~mm} / \mathrm{s}$ & 0 to $22 \mathrm{~mm}$ & 5 \\ \hline & & $215 \mathrm{~W}$ & $750 \mathrm{~mm} / \mathrm{s}$ & 0 to $15 \mathrm{~mm}$ & 5 \\ \hline & & $130 \mathrm{~W}$ & $1400 \mathrm{~mm} / \mathrm{s}$ & 0 to $5.5 \mathrm{~mm}$ & 5 \\ \hline & & $300 \mathrm{~W}$ & $2400 \mathrm{~mm} / \mathrm{s}$ & 0 to $8 \mathrm{~mm}$ & 10 \\ \hline \multirow{3}{*}{}\begin{tabular}{l} 3D Systems ProX \\ 300 L-PBF \\ \end{tabular} & \multirow{3}{*}{}\begin{tabular}{c} Stainless Steel (304, \\ 316L, 17-4 PH) \\ \end{tabular} & $400 \mathrm{~W}$ & $600 \mathrm{~mm} / \mathrm{s}$ & 0 to $6.5 \mathrm{~mm}$ & 5 \\ \hline & & 205 W & $1200 \mathrm{~mm} / \mathrm{s}$ & 0 to $21 \mathrm{~mm}$ & 5 \\ \hline & & $400 \mathrm{~W}$ & $3000 \mathrm{~mm} / \mathrm{s}$ & 0 to $11 \mathrm{~mm}$ & 10 \\ \hline \multirow{7}{*}{EOS M 290 L-PBF} & \multirow{7}{*}{Ti-6Al-4V} & $80 \mathrm{~W}$ & $500 \mathrm{~mm} / \mathrm{s}$ & 0 to $14 \mathrm{~mm}$ & 2.5 \\ \hline & & $370 \mathrm{~W}$ & $450 \mathrm{~mm} / \mathrm{s}$ & 0 to $28.5 \mathrm{~mm}$ & 5 \\ \hline & & $270 \mathrm{~W}$ & $580 \mathrm{~mm} / \mathrm{s}$ & 0 to $19 \mathrm{~mm}$ & 5 \\ \hline & & $170 \mathrm{~W}$ & $910 \mathrm{~mm} / \mathrm{s}$ & 0 to $11.5 \mathrm{~mm}$ & 5 \\ \hline & & $370 \mathrm{~W}$ & $1900 \mathrm{~mm} / \mathrm{s}$ & 0 to $18 \mathrm{~mm}$ & 7.5 \\ \hline & & $330 \mathrm{~W}$ & $2150 \mathrm{~mm} / \mathrm{s}$ & 0 to $15.5 \mathrm{~mm}$ & 7.5 \\ \hline & & $270 \mathrm{~W}$ & $2550 \mathrm{~mm} / \mathrm{s}$ & 0 to $13 \mathrm{~mm}$ & 7.5 \\ \hline \end{tabular} \end{center} Experiments in the Sciaky electron beam wire feed process held individual process parameters power, velocity, and deposition rate constant. Values under "Focus Setting Range" represent the actual spot size created by scanning a focused electron beam into concentric circles. To modify the spot size, the concentric circles are expanded or contracted. A problem encountered at large spot sizes and small melt pool depths is that the fed wire can become a limiting factor if it starts contacting the base of the substrate at the bottom of the melt pool. At small spot sizes, keyhole mode melting was present which is a phenomenon not modeled in this work. Keyholing melt pools are therefore not included in the analysis of spot size effects on geometry, but are discussed in Chapter 4:. Experiments in the electron beam and laser powder bed fusion processes were all completed without a powder layer to remove an additional variable that may have an influence on the results. In the Arcam EB-PBF process, spot size can be adjusted by changing the focus offset parameter that changes the current in the focusing coils for the electron beam. Spot size was also affected by the power in this process, so all experiments were completed at the same power, $670 \mathrm{~W}$. In the 3D systems ProX 200 and 300 L-PBF machines, a defocus parameter can be used to change the spot size. The parameter changes the focus plane of the laser and is changed in units of millimeters. The EOS M 290 machine does not have any spot size adjustments available to general users, but for single bead experiments, spot size can be increased by dropping the build plate. Therefore, "Focus setting range" refer to how far the build plate had been dropped to deposit the layer. While spot sizes are not an available parameter on the EOS M 290, it was an available parameter on older models. Cross-sectional dimensions for no-added melt pools in the powder bed processes commonly distorts from the original shape due to fluid flow and surface forces. The melt pool area viewed\\ from the cross section can also be increased or decreased by the bead up phenomenon [74]. In these cases the melt pool dimension measurement neglects the surplus or dearth of material present in the cross section. Figure 3-2 shows how melt pools with these conditions are measured in this work. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-073} \end{center} Figure 3-2: Melt pool area measurements for deformed no-added material melt pools \subsection*{3.2.3 Normalization} In order to compare changes in dimensions across different melt pool sizes and alloys, melt pool dimensions (W, D, A, etc.) were normalized by their value at a point heat source $\left(\mathrm{W}_{0}, \mathrm{D}_{0}, \mathrm{~A}_{0}\right.$, etc.). Spot size $(\sigma)$ is normalized by the respective melt pool width at a point heat source. After normalization, geometry changes grouped together by melt pool aspect ratio, which can be represented by the length to depth ratio $\left(\mathrm{L}_{0} / \mathrm{D}_{0}\right)$. Length in this case is measured from the point of maximum depth. For experiments, point source values are based on values from models, or if model results are unavailable, they can be determined from the melt pool cross section deposited with the smallest spot size that does not cause keyhole mode melting. In the case of an unknown spot size, the depth to width ratio (D/W) of the melt pool cross section can be used to place experimental points on the normalized spot size $\left(\sigma / \mathrm{W}_{0}\right)$ axis (Figure 3-3). This method can also be used in conjunction with the point source melt pool width to back out estimates for actual spot sizes in the process. Estimated spot size values from the EOS M 290 experiments are compared against measured values in section 3.3.3. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-074} \end{center} Figure 3-3: Example of identifying the normalized spot size based on width to depth ratio \subsection*{3.3 Results} The focus of this chapter is on the relationships between certain melt pool dimensions and spot size. Trends in cross sectional width, depth, and area are developed for finite element and Rosenthal based models. Experimental measurements are compared against model results to verify the identified trends for different melt pool geometries. Backed-out spot size estimates based on experimental measurements and developed trends are compared to measurements in the EOS M290 and Sciaky processes. Additionally, estimated spot sizes are presented for the Arcam and 3D Systems processes. \subsection*{3.3.1 Trends from Models} Simulations were completed for particular power-velocity combinations for selected processes and alloys to develop trends for how melt pool dimensions change with increasing spot size. Trends for normalized melt pool width from finite element and Rosenthal based models for tophat and Gaussian beam distributions are shown in Figure 3-4. Melt pool width (W) is normalized by the point source melt pool width $\left(\mathrm{W}_{0}\right)$. Spot size $(\sigma)$ is also normalized by the point source melt pool width to create the normalized spot size parameter used throughout this section. For all models and $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios, melt pool width increases with increasing spot size before collapsing as material stops being melted. Different $\mathrm{L}_{0} / \mathrm{D}_{0}$ lines follow a similar initial trends before lower $\mathrm{L}_{0} / \mathrm{D}_{0}$ values break off from trends followed by higher length to depth ratios. Results from tophat models show a greater increase in melt pool width and a longer shared trend between different $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios. In general, the models show that width in melt pools of different alloys and processes follow the same trends with increasing spot size. Differences between lines of the same $\mathrm{L}_{0} / \mathrm{D}_{0}$ label are primarily due to slight differences between the actual $\mathrm{L}_{0} / \mathrm{D}_{0}$ values of the process parameters used in the models. Normalized Width vs. Normalized Spot Size\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-076} \begin{center} \begin{tabular}{|c|c|c|c|} \hline $\mathrm{L}_{0} / \mathrm{D}_{0}=2.5$ & $L_{0} / D_{0}=5$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=10$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=20$ \\ \hline $\longrightarrow$ L-PBF Ti-6Al-4V & L-PBF CoCr & EB-PBF CoCr & - EBWF IN625 \\ \hline — LPF 316L SS & — EBWF IN 625 & — EBWF Ti-6Al-4V & - EB-PBF Ti-6Al-4V \\ \hline $\longrightarrow$ LPF 316L SS & $\multimap$ EBWF Ti-6Al-4V & $\longrightarrow$ EBWF Ti-6Al-4V & $\multimap$ EB-PBF Ti-6Al-4V \\ \hline $\rightarrow$ L-PBF Ti-6Al-4V & $\multimap$ L-PBF CoCr & $\multimap$ EB-PBF Ti-6Al-4V & $\multimap$ EBWF Ti-6AI-4V \\ \hline \end{tabular} \end{center} Figure 3-4: Normalized melt pool width vs. normalized spot size for different models Melt pool depth is normalized by the point source depth $\left(\mathrm{D}_{0}\right)$ and plotted against normalized spot size in Figure 3-5. In all models and $\mathrm{L}_{0} / \mathrm{D}_{0}$ cases, normalized melt pool depth decreases continuously with increasing spot size. For normalized depth, tophat and Gaussian beam profiles give very similar results. As with normalized width results, melt pools with smaller $\mathrm{L}_{0} / \mathrm{D}_{0}$ values have a faster dropping normalized depth and larger $\mathrm{L}_{0} / \mathrm{D}_{0}$ values all follow a similar trend before separation. It should also be noted that in expanded spot sizes, the location of maximum depth and width occur at different locations in the melt pool. The point of maximum width occurred ahead\\ of the point of maximum depth regardless of alloy, process, and $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio. The difference in location can be attributed to how the heat is applied to the two different areas. The width of the melt pool is influenced by the width of the beam inputting heat into the system. Maximum depth is an evolution of the maximum temperature found at the surface, which is located at the back of the beam spot where materials has been heated by the passing heat source. The maximum heat applied to the material in the direction of melt pool width occurs ahead of the point of maximum temperature, thus developing the maximum width ahead of the maximum depth. Normalized Depth vs. Normalized Spot Size\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-077} \begin{center} \begin{tabular}{|c|c|c|c|} \hline $\mathrm{L}_{0} / \mathrm{D}_{0}=2.5$ & $L_{0} / D_{0}=5$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=10$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=20$ \\ \hline — L-PBF Ti-6AI-4V & L-PBF CoCr & EB-PBF CoCr & — EBWF IN625 \\ \hline — LPF 316L SS & — EBWF IN 625 & EBWF Ti-6Al-4V & - EB-PBF Ti-6Al-4V \\ \hline $\hookrightarrow$ LPF 316L SS & $\multimap$ EBWF Ti-6AI-4V & $\multimap$ EBWF Ti-6Al-4V & $\multimap$ EB-PBF Ti-6Al-4V \\ \hline $\rightarrow$ L-PBF Ti-6Al-4V & $\multimap$ L-PBF CoCr & $\multimap$ EB-PBF Ti-6Al-4V & $\multimap$ EBWF Ti-6Al-4V \\ \hline \end{tabular} \end{center} Figure 3-5: Normalized melt pool depth vs. normalized spot size for different models Cross-sectional area is a combination of both melt pool width and depth. Since melt pool width and depth have differing trends with increasing spot size, normalized melt pool area exhibits a more mild response to normalized spot size (Figure 3-6). Melt pools with small $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios are relatively unaffected by increasing spot size before dropping. Melt pools with large $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios show an increase in melt pool area before decreasing, larger $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios have a greater increases in area. As seen in normalized width plots, a tophat heat source results in larger potential increases in area when compared to a Gaussian profile. Normalized Area vs. Normalized Spot Size\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-078} \begin{center} \begin{tabular}{c|c|c|c|} \hline $\mathrm{L}_{0} / \mathrm{D}_{0}=2.5$ & \multicolumn{1}{|c}{$\mathrm{L}_{0} / \mathrm{D}_{0}=5$} & $\mathrm{~L}_{0} / \mathrm{D}_{0}=10$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=20$ \\ \hline $-\mathrm{L}-\mathrm{PBF}$ Ti-6Al-4V & - L-PBF CoCr & - EB-PBF CoCr & - EBWF IN625 \\ - LPF 316L SS & - EBWF IN 625 & - EBWF Ti-6Al-4V & - EB-PBF Ti-6Al-4V \\ $\rightarrow$ LPF 316L SS & $\rightarrow$ EBWF Ti-6Al-4V & $\longrightarrow$ EBWF Ti-6Al-4V & $\rightarrow$ EB-PBF Ti-6Al-4V \\ $\rightarrow$ L-PBF Ti-6Al-4V & $\rightarrow$ L-PBF CoCr & $\longrightarrow$ EB-PBF Ti-6Al-4V & $\longrightarrow$ EBWF Ti-6Al-4V \\ \hline \end{tabular} \end{center} Figure 3-6: Normalized melt pool cross-sectional area vs. normalized spot size for different models Depth to width ratios observed in model results are presented in Figure 3-7. Increases in width and decreases in depth combine to cause quick decreases in the depth to width ratios. All curves follow the same general trend until each $\mathrm{L}_{0} / \mathrm{D}_{0}$ lines approaches insufficient power density to melt. Since the y-axis in these plots does not require knowledge of a point source dimension, they can be very useful to determine a normalized spot size for experimental points when beam sized are unknown. These plots have been key to relating experimental and simulation results. \section*{Depth to Width Ratio vs. Normalized Spot Size} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-079} \end{center} \begin{center} \begin{tabular}{|c|c|c|c|} \hline $\mathrm{L}_{0} / \mathrm{D}_{0}=2.5$ & $L_{0} / D_{0}=5$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=10$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=20$ \\ \hline L-PBF Ti-6Al-4V & L-PBF CoCr & EB-PBF CoCr & — EBWF IN625 \\ \hline — LPF 316L SS & — EBWF IN 625 & - EBWF Ti-6Al-4V & — EB-PBF Ti-6Al-4V \\ \hline $\hookrightarrow$ LPF 316L SS & $\multimap$ EBWF Ti-6Al-4V & $\multimap$ EBWF Ti-6Al-4V & $\rightarrow$ EB-PBF Ti-6Al-4V \\ \hline $\rightarrow$ L-PBF Ti-6Al-4V & $\rightarrow$ L-PBF CoCr & $\multimap$ EB-PBF Ti-6AI-4V & $\multimap$ EBWF Ti-6Al-4V \\ \hline \end{tabular} \end{center} Figure 3-7: Width to depth ratio vs. normalized spot size for different models \subsection*{3.3.2 Single Bead Experiments} Single bead experiments were deposited to verify the trends observed in simulations. In this section, all experiments are compared for the tophat and Gaussian beam profiles modeled in finite element simulations. This section will display experiments from $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios of 2.5, 5, 10, and 20. Additional experiment sets are plotted in Appendix 3. Error bars in this section show the uncertainty in point source dimensions $\left(\mathrm{W}_{0}, \mathrm{D}_{0}\right.$, and $\left.\mathrm{A}_{0}\right)$ that are used to normalize experimental width, depth, and area measurements. Experiments from the EOS Ti-6Al-4V, $80 \mathrm{~W}, 500 \mathrm{~mm} / \mathrm{s}$, and expected $2.5 \mathrm{~L}_{0} / \mathrm{D}_{0}$ case were measured and normalized based on a $\mathrm{W}_{0}$ value of $113 \mu \mathrm{m}$. Spot sizes for these experiments are based on measurements taken at $40 \mathrm{~W}$ in the EOS M 290 machine at CMU [114] [115]. The normalized experimental measurements are compared against finite element results in Figure 3-8, Figure 3-9, and Figure 3-10. Across the three measured melt pool dimensions, experiments match poorly with trends created from an assumed tophat beam distribution. Better agreement is seen between experimental measurements and simulation results from an assumed Gaussian beam profile. While there is some mismatch in the normalized depth and width experiments and simulation results, experimental results for normalized area closely matched simulation results. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-081} \end{center} $\longrightarrow$ LPF 316L SS Normalized Width, Gaussian Beam Profile $\longrightarrow$ L-PBF Ti-6Al-4V \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-081(1)} \end{center} \begin{itemize} \item Experimental \end{itemize} Figure 3-8: EOS L-PBF, Ti-6Al-4V, 80W, $500 \mathrm{~mm} / \mathrm{s}$ experimental normalized width measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 2.5 \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-081(2)} \end{center} Figure 3-9: EOS L-PBF, Ti-6Al-4V, 80W, $500 \mathrm{~mm} / \mathrm{s}$ experimental normalized depth measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 2.5 \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-082(1)} \end{center} $\longrightarrow$ LPF 316L SS \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-082} \end{center} $\longrightarrow$ L-PBF Ti-6AI-4V \begin{itemize} \item Experimental \end{itemize} Figure 3-10: EOS L-PBF, Ti-6Al-4V, 80W, $500 \mathrm{~mm} / \mathrm{s}$ experimental normalized area measurements compared with finite element results for an $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 2.5 Experiments from the Arcam S12 EB-PBF Ti-6Al-4V 670W, $1100 \mathrm{~mm} / \mathrm{s}$ case had a projected $\mathrm{L}_{0} / \mathrm{D}_{0}$ and were measured and normalized based on a $\mathrm{W}_{0}$ value of $835 \mu \mathrm{m}$. Experimental spot size values in these plots are based on trends created from backed out spot sizes from six experiment sets in the process. The backed out values and best fit is discussed in section 3.3.3. Comparison between normalized experimental and finite element results for width, depth, and area are presented in Figure 3-11, Figure 3-12, and Figure 3-13. In the plots for normalized melt pool width, experimental measurements follow similar trends to those observed in simulations. For normalized melt pool width and depth, experimental measurements agree well with simulation results from both an assumed tophat and Gaussian beam intensity profile. In the case of melt pool area, good agreement is again observed for both a tophat and Gaussian beam profile, but agreement with a Gaussian profile is slightly improved. In general, trends from finite element simulations do a very good job of describing changes in melt pool dimensions for this experiment set. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-083} \end{center} $$ \begin{aligned} & \longrightarrow \text { EBWF Ti-6AI-4V } \\ & \longrightarrow \text { L-PBF CoCr } \end{aligned} $$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-083(1)} \end{center} \begin{itemize} \item Experimental \end{itemize} Figure 3-11: Arcam S12 EB-PBF, Ti-6Al-4V, 670W, $1100 \mathrm{~mm} / \mathrm{s}$ experimental normalized width measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 5\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-083(2)} \begin{itemize} \item Experimental \end{itemize} Figure 3-12: Arcam S12 EB-PBF, Ti-6Al-4V, 670W, $1100 \mathrm{~mm} / \mathrm{s}$ experimental normalized depth measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 5\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-084} $\rightarrow$ EBWF Ti-6Al-4V $\hookrightarrow$ L-PBF CoCr \begin{itemize} \item Experimental \end{itemize} Figure 3-13: Arcam S12 EB-PBF, Ti-6Al-4V, 670W, $1100 \mathrm{~mm} / \mathrm{s}$ experimental normalized area measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 5 Experiments from the 3D Systems ProX 200 L-PBF process performed at $300 \mathrm{~W}$ and 1400 $\mathrm{mm} / \mathrm{s}$ with an expected $\mathrm{L}_{0} / \mathrm{D}_{0}$ of 10 , were measured and normalized based on a $\mathrm{W}_{0}$ value of $71 \mu \mathrm{m}$. Experimental spot size values in these plots are based on trends created from backed-out spot sizes from twelve experiment sets in the process. The backed-out values and best fit are discussed in section 3.3.3. Comparison between normalized experimental and finite element results for width, depth, and area are presented in Figure 3-14, Figure 3-15, and Figure 3-16. For normalized width, experimental results are a poor match with simulation results based on a tophat beam profile. However, good agreement is observed between experiments and simulations results using a Gaussian beam profile. For normalized melt pool depth, good agreement is seen between experimental measurements and simulation results for both a tophat and Gaussian beam distribution. Normalized melt pool area again shows improved agreement between experiments and Gaussian simulation results when compared to tophat simulation results. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-085} \end{center} $\longrightarrow$ EBWF Ti-6AI-4V \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-085(1)} \end{center} $\longrightarrow$ EB-PBF Ti-6AI-4V \begin{itemize} \item Experimental \end{itemize} Figure 3-14: 3D Systems ProX 200 L-PBF, 17-4 PH stainless steel, $300 \mathrm{~W}, 1400 \mathrm{~mm} / \mathrm{s}$ experimental normalized width measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 10\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-085(2)} $\longrightarrow$ EB-PBF Ti-6AI-4V \begin{itemize} \item Experimental \end{itemize} Figure 3-15: 3D Systems ProX 200 L-PBF, 17-4 PH stainless steel, 300 W, 1400 mm/s experimental normalized depth measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 10 \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-086} \end{center} Figure 3-16: 3D Systems ProX 200 L-PBF, 17-4 PH stainless steel, 300 W, 1400 mm/s experimental normalized area measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 10 Experiments from the Arcam S12 EB-PBF process in IN 718 at $670 \mathrm{~W}, 1300 \mathrm{~mm} / \mathrm{s}$, and expected $\mathrm{L}_{0} / \mathrm{D}_{0}$ of 20, were measured and normalized based on a $\mathrm{W}_{0}$ value of $390 \mu \mathrm{m}$. Comparison between normalized experimental and finite element results for width, depth, and area are presented in Figure 3-17, Figure 3-18, and Figure 3-19. For normalized melt pool width experimental measurements agree with simulation results except at high normalized spot sizes. Experimental results fell below the simulation curve for an assumed tophat distribution, and above the curve for a Gaussian distribution. For normalized melt pool depth, experimental measurements fell slightly below the curves for tophat and Gaussian distributions. Slightly better agreement was found for the tophat distribution. Experimental measurements of normalized melt pool area matched simulation data from an assumed Gaussian distribution. Uneven agreement of experiments with tophat and Gaussian distributions suggests the beam profile in the Arcam process is neither tophat nor Gaussian, but a combination of the two. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-087(1)} \end{center} Normalized Width, Gaussian Beam Profile $\longrightarrow$ EB-PBF Ti-6AI-4V \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-087(3)} \end{center} $\longrightarrow$ EBWF Ti-6AI-4V \begin{itemize} \item Experimental \end{itemize} Figure 3-17: Arcam S12 EB-PBF, IN 718, $670 \mathrm{~W}, 1300 \mathrm{~mm} / \mathrm{s}$ experimental normalized width measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 20 Normalized Depth, Tophat Beam Profile \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-087(2)} \end{center} $\longrightarrow$ EB-PBF Ti-6Al-4V \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-087} \end{center} $\longrightarrow$ EBWF Ti-6Al-4V \begin{itemize} \item Experimental \end{itemize} Figure 3-18: Arcam S12 EB-PBF, IN 718, $670 \mathrm{~W}, 1300 \mathrm{~mm} / \mathrm{s}$ experimental normalized depth measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 20\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-088} $\longrightarrow$ EB-PBF Ti-6Al-4V $\longrightarrow$ EBWF Ti-6AI-4V \begin{itemize} \item Experimental \end{itemize} Figure 3-19: Arcam S12 EB-PBF, IN 718, 670 W, $1300 \mathrm{~mm} / \mathrm{s}$ experimental normalized area measurements compared with finite element results for an $L_{0} / D_{0}$ ratio of 20 \subsection*{3.3.3 Spot Size Estimates} Measurements of spot size are key to knowing how certain melt pools will change when defocus parameters are adjusted. Backing out estimates of spot size from experiments can be very useful for machines where the spot size values are unknown. This section will present estimates from experiments for different machines and compare estimates with actual measurements of spot size in the EOS M 290 machine, and the ProX 200 machine. Estimated spot size values from multiple power-velocity combinations and alloys can be fit to curves describing lasers and electron beams that are off-focus. The first step to estimate spot size based on experimental measurements is to identify a normalized spot size associated with the depth to width ratio of a melt pool as described in section 3.2.3. Normalized spot size values $\left(\sigma / \mathrm{W}_{0}\right)$ can be translated to estimated spot sizes by simply\\ multiplying by the point source width $\left(\mathrm{W}_{0}\right)$. Point source width values were ascertained from simulations created by the author of this thesis and others [23] [116]. Characteristic curves can be fit to the spot size data to describe how the beam size changes with the defocus parameter. For lasers, Eq. 3-3 is used. Eq. 3-3 $$ \sigma(z)=\sigma_{0} \sqrt{1+\left(\frac{z-z_{0}}{z_{r}}\right)^{2}} $$ Where $\sigma$ is the spot size at a defined offset, $z$. The minimum beam spot size, or waist, is represented by $\sigma_{0}$, the Rayleigh length by $z_{r}$, and $z_{0}$ represents the $z$ location where the minimum spot size is present. Figure 3-20 shows the physical meaning of the variables discussed. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-089} \end{center} Figure 3-20: Beam profile with key beam measurements labeled Estimated beam spot sizes for the ProX 300 L-PBF process are shown in Figure 3-21 along with best fit curves. Estimated spot sizes for an assumed tophat beam profile closely match estimated values for an assumed Gaussian beam profile. The best fit curve created for a tophat beam profile matched experimental results with an $\mathrm{r}^{2}$ value of 0.936 with $\sigma_{0}, z_{r}$, and $z_{0}$ values of\\ $121 \mu \mathrm{m}, 4.03 \mathrm{~mm}$, and $-1.4 \mathrm{~mm}$ respectively. For an assumed Gaussian beam profile, the best fit curve matched experimental data with an $\mathrm{r}^{2}$ value of 0.945 , and fitted $\sigma_{0}, z_{r}$, and $z_{0}$ values of 101 $\mu \mathrm{m}, 3.25 \mathrm{~mm}$, and $-1.6 \mathrm{~mm}$. Both best fit curves match the data very well and can likely be used to guide defocus adjustments for future experiments and builds. In general, an assumed Gaussian profile estimated smaller spot sizes at small offsets and larger spot sizes at large offsets when compared to the assumed tophat beam profile. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-090} \end{center} Figure 3-21: Spot Size Estimates for the ProX 300 L-PBF process with best fit curves for typical laser behavior Estimated beam spot sizes for the ProX 200 L-PBF process are shown in Figure 3-22 along with best fit curves. The best fit curve created for a tophat beam profile matched experimental results with an $\mathrm{r}^{2}$ value of 0.974 with $\sigma_{0}, z_{r}$, and $z_{0}$ values of $3 \mu \mathrm{m}, 0.12 \mathrm{~mm}$, and $-1.62 \mathrm{~mm}$ respectively. For an assumed Gaussian beam profile, the best fit curve matched experimental data with an $\mathrm{r}^{2}$ value of 0.977 , and fitted $\sigma_{0}, \mathrm{z}_{\mathrm{r}}$, and $z_{0}$ values of $3 \mu \mathrm{m}, 0.11 \mathrm{~mm}$, and $-1.12 \mathrm{~mm}$. The values guiding the best fit curves suggest unrealistically low values for the waist ( $\sigma_{0}$ ) of the beam;\\ however, these curves are likely still useful for guiding defocus changes in future experiments and builds. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-091} \end{center} Figure 3-22: Spot Size Estimates for the ProX 200 L-PBF process with best fit curves for typical laser behavior In the EOS M 290 process, spot size estimates and best fit curves are also compared against curves developed from actual measurements. A series of measurements were taken in the machine at Carnegie Mellon using Primes FocusMonitor equipment at $40 \mathrm{~W}$ and $200 \mathrm{~W}$ to find the Rayleigh length, beam radius, and z offset [114] [115]. Figure 3-23 shows experimental estimates and their best fit lines alongside a curve created from average values from the 200 and $40 \mathrm{~W}$ beam measurements. Very good agreement was observed between estimated experimental spot size values, and those based on measurements. Table 4 shows values from measurements, and curve fittings for the process. Additional information on the beam measurements is provided in Appendix 4. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-092} \end{center} Figure 3-23: Spot Size Estimates for the EOS M 290 L-PBF process with best fit curves for typical laser behavior, and a curve based on spot size measurements Table 4: Beam curve information from measurements and fitted curves for the EOS M 290 L-PBF process \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \cline { 2 - 6 } \multicolumn{1}{c|}{} & $\sigma_{0}(\mu \mathrm{m})$ & $\mathbf{z}_{\mathbf{r}}(\mathrm{mm})$ & $\mathrm{z}_{0}(\mathrm{~mm})$ & \begin{tabular}{c} Tophat \\ profile $\mathbf{r}^{2}$ \\ \end{tabular} & \begin{tabular}{c} Gaussian \\ profile $\mathbf{r}^{2}$ \\ \end{tabular} \\ \hline 200 W Measurements & 104.726 & 5.778 & -1.48 & 0.842 & 0.822 \\ \hline 40 W Measurements & 83.216 & 4.794 & -0.37 & 0.905 & 0.965 \\ \hline Fitted Tophat & 96 & 5.71 & -1.16 & 0.923 & \\ \hline Fitted Gaussian & 69 & 4.25 & -1.86 & & 0.969 \\ \hline \end{tabular} \end{center} Spot sizes in the Arcam S12 EB-PBF process were similarly estimated for different focus offset values. Figure 3-24 displays estimated values from experimental data along with best fit curves. The profile for electron beams also follows the same general profile in the z-direction as lasers. Current in the focusing coils is expected to change the spot size parabolically with changes to focus offset current [117] [118], however observations made to settings in the Arcam software appears to follow the trends produced by lasers. It is unknown whether the focus offset current that is set in the software is modified before changes are made in the process. The best fit curve created for\\ a tophat beam profile matched experimental results with an $\mathrm{r}^{2}$ value of 0.9674 with $\sigma_{0}, z_{r}$, and $z_{0}$ values of $513 \mu \mathrm{m}, 11.3 \mathrm{~mm}$, and $3.0 \mathrm{~mm}$ respectively. For an assumed Gaussian beam profile, the best fit curve matched experimental data with an $\mathrm{r}^{2}$ value of 0.9535 , and fitted $\sigma_{0}$, $\mathrm{z}_{r}$, and $z_{0}$ values of $302.2 \mu \mathrm{m}, 6.66 \mathrm{~mm}$, and $2.1 \mathrm{~mm}$. The minimum spot size in the process is expected to be around $300 \mu \mathrm{m}$ [119], which is in good agreement with the assumed Gaussian profile. While the minimum spot size of the assumed Gaussian profile is in better agreement with the cited value, the tophat distribution appears to fit the data better. The beam profile likely falls between that of a tophat and Gaussian beam in this process. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-093} \end{center} Figure 3-24: Spot Size Estimates for the Arcam S12 EB-PBF process with best fit curves \subsection*{3.4 Discussion} The effects of laser and electron beam spot size across different melt pool sizes, alloys, and processes has been simulated and verified by experiments. Changing melt pool width, depth, and area were normalized by their point source values ( $\mathrm{W}_{0}, \mathrm{D}_{0}$, and $\mathrm{A}_{0}$ ) from simulations to remove variations in melt pool size. Spot size was also normalized by point source width. After\\ normalization, changes in melt pool dimensions with spot size grouped together by the $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio, or aspect ratio. Normalized melt pool width increased for all cases before dropping. Larger $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios had larger increases in width and withstood larger spot sizes before melting ceased. Normalized depth exhibited continuous decreases for any increases in spot size. For both normalized widths and depths, melt pool appear to follow similar changes before smaller $\mathrm{L}_{0} / \mathrm{D}_{0}$ melt pools dropped off from the trend. Normalized melt pool areas displayed distinctly different behavior between large and small $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios. Trends for small aspect ratios had small decreases in normalized area across low normalized spot sizes before larger decreases at higher spot sizes. Larger $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios had increases in normalized area at low and moderate spot sizes before dropping at higher normalized spot sizes. The behavior of normalized melt pool dimensions was also dependent on the assumed beam profile. Tophat and Gaussian beam profiles both followed similar trends with increasing spot sizes, but a Gaussian profile had smaller increases in width and area. Experimental results showed agreement with simulations across various $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios, alloys, and processes, but typically had better agreement with curves generated from a Gaussian beam profile. Spot size values were also estimated based on experimental results and fit to characteristic curves. Depth to width ratios were measured for all spot size experiments and used to identify normalized spot sizes for each individual case. Normalized spot sizes are multiplied by simulation point source width to give an estimated spot size. Completed over a range of experimental points, estimated spot sizes give an idea of how spot size increases with offset parameters. In the EOS M 290 process, experimental estimates were compared with curves generated from beam measurements and saw very good agreement with an $r^{2}$ value of 0.965 for an assumed Gaussian\\ beam profile. Estimated spot sizes can be used to guide offset changes for future experiments and builds. \section*{Chapter 4: $\quad$ The Effects of Spot Size on Porosity and Flaws} \subsection*{4.1 Overview} In this chapter, the influence of spot size on melt pool morphological characteristics such as keyholing, variability, and porosity is analyzed. Variability in melt pool width and depth measurements is studied to find how keyhole mode melting influences single bead deposits. Keyholing is found to have little effect on the standard deviation of melt pool width, but a significant effect on standard deviation of melt pool depth. A depth to width ratio of 0.5 is used to identify keyholing and develop a normalized spot size threshold to avoid keyholing for multiple alloys. Insights into the effects of spot size on geometry and the presence of keyhole mode melting is used to design multi-layer pad experiments based on a large range of single bead melt pool areas. Porosity is measured in the multi-layer samples and compared to the nominal case. \subsection*{4.2 Methods} \subsection*{4.2.1 Identifying Keyholing Melt Pools} Melting in additive manufacturing or welding processes occurs in one of two ways, conduction mode melting and keyhole mode melting. In conduction mode melting, the melt pool is created by heat conducting down from the surface to develop the melt pool. In keyhole mode melting, the beam raises the temperature high enough to vaporize significant amount of material. This can result in deep and narrow melt pools that are desirable in some welding applications, but is more variable and can leave behind porosity [45] [66]. In additive manufacturing, conduction mode melting is desired to avoid the porosity associated with keyhole mode melting and achieve more consistent results. To identify melt pools that were deposited with keyhole mode melting, the depth to width ratio (D/W) is used. Melt pools with a depth to width ratio greater than 0.5 were deemed "keyholing" melt pools, as a semi-circular melt pool is the deepest that can be formed via only conduction mode melting [120]. While work by other authors has suggested identifying keyholing by using normalized enthalpy thresholds [47] [120], this research looks to identify thresholds based on relationships between the spot size and melt pool dimensions developed in Chapter 3:. Depth to width ratio trends can be compared for finite element simulations and experimental measurements to identify locations where experiments deviate from the predicted trends, and where the ratio exceeds 0.5 . From this information, a normalized spot size can be suggested to avoid keyhole mode melting for different alloys. \subsection*{4.2.2 Variability and Porosity Measurement} To identify the presence of any additional variability in keyhole or conduction mode melt pools, variability in melt pool width and depth is analyzed. Melt pool width can be easily traced after imaging melt pools from above. A script in MATLAB was developed by Fox to measure the distances between two regions manually painted red on an image [23]. Melt pool widths traced in red can be measured for both melt pool dimensions and standard deviation. To acquire enough measurements for variability in melt pool depth, single bead melt pools need to be serial sectioned, or sectioned down the center of the bead. In this work, a series of melt pools were sectioned down the center of the bead with a wire EDM to measure depth variability using a similar MATLAB script as described above for width measurement. An additional component to the script included a best fit linear trend along the bottom of the melt pool to compensate for changing depths resulting from a misaligned cut. The traced melt pool was also\\ cut off at the top surface of the melt pool to eliminate variability from the surface of the melt pool in a potential uneven cut. Melt pool depths were traced over a distance of $20 \mathrm{~mm}$. Figure 4-1 shows a portion of a sectioned melt pool before and after being traced. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-098} \end{center} Figure 4-1: Melt pool depth before (top) and after (bottom) tracing for variability analysis Analysis of bead-up melt pools could be completed by simply observing the surface of the single bead deposits. Bead up melt pools occur when instabilities in the melt pool begin breaking the liquid metal into individual droplets and is characterized by melt pools with inconsistent amounts of material in cross sections. Figure 4-2 shows two melt pools viewed from above and from cross sections. The top melt pool shows the inconsistent characteristics associated with beadup melt pools while the bottom image shows a smooth melt pool with no bead-up issues present. Bead-up phenomenon can occur in long and narrow melt pools and can be a major source of porosity. Previous work by Yadroitsev et al. identified a width to full length ratio (W/FL) as a threshold for bead-up melt pools in additive manufacturing [75]. To quantify the effects of spot size on the occurrence of the bead-up phenomenon, width to full length ratio was plotted against normalized spot size for different $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios. Observations from experimental melt pools can be used to verify the suggested cutoff values.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-099} Figure 4-2: Bead-up (top) and smooth (bottom) melt pools as viewed from above, and from cross sections Porosity measurements are completed on multi-layer pad experiments via optical images to analyze compare different parameter sets on how much porosity is present in the resulting deposit. Polished sections of a multi-layer deposit were imaged at three different magnifications, 2.5X, 10X, and 50X to be able to identify porosity of different size scales. Porosity measurements were gathered through the use of a MATLAB script developed by Luke Scime [121]. The code converts microscope images to a grayscale image, a brightness intensity histogram is displayed for the user to choose a cutoff intensity for identifying pores. The image is then converted to a binary black and white image based on the input cutoff value and porosity is calculated. Figure 4-3 shows the generated grayscale image with intensity histogram, and the resulting black and white image from a selected intensity cutoff value of 50 .\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-100} Figure 4-3: Porosity optical image before (top) and after (bottom) selection of an intensity cutoff value from the intensity histogram (right) \subsection*{4.2.3 Experiment Setup} Experiments for this work consisted of both single bead experiments to analyze specific keyholing melt pools and variability, and multi-layer pads experiments to analyze porosity at different process parameter settings. This work made use of the same single bead experiments used in Chapter 3:, and some additional experiments designed to look more specifically at keyholing. Experiments involved particular power-velocity sets at chosen $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios where spot size was varied for different single bead deposits. These single bead deposits transitioned from keyhole mode melting at small spot sizes to conduction mode melting at larger spot sizes. Based on these experiments, relationships could be drawn between melt pool depth, width, spot size, and the occurrence of keyholing. Variability in melt pool depth was analyzed in a series of single beads at one power-velocity combination and multiple spot sizes. The chosen power-velocity combination was selected because of its relatively large size, making sectioning easier, and the occurrence of both significant keyhole and conduction mode melting across the spot size settings. Multi-layer experiments were completed to analyze porosity in multi-layer pads build with a variety of process parameters. The experiments seek to identify porosity at different melt pool areas and compare nominal settings against settings with altered spot size and balanced hatch spacing and layer thickness. The multi-layer pads were deposited in the Arcam S12 EB-PBF process at a layer thickness of $70 \mu \mathrm{m}$ in Ti-6Al-4V. Powder used for the build was gas atomized Ti-6Al-4V powder supplied by Arcam. The powder had been used in multiple previous builds and therefore may not have the same characteristics as virgin powder provided by Arcam. Table 5 outlines the settings used for each multi-layer pad deposited for these experiments. In general, the scan speed of the electron beam increases with increasing speed function [89], and increasing focus offset expands the beam. Settings to produce desired areas, and assistance with hatch spacing determination were provided by Sneha Narra [122]. \section*{Table 5: Multi-layer pad experiment plan to analyze porosity} \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline Experiment \# & \begin{tabular}{c} Speed \\ Function \\ \end{tabular} & \begin{tabular}{c} Nominal Area \\ Multiple \\ \end{tabular} & \begin{tabular}{c} Focus Offset \\ $(\mathbf{m A})$ \\ \end{tabular} & \begin{tabular}{c} Hatch \\ Spacing $(\boldsymbol{\mu m})$ \\ \end{tabular} \\ \hline 1 & 36 & $1 X$ & 19 & 200 \\ 2 & 72 & $0.5 X$ & 19 & 200 \\ 3 & 20 & $2 X$ & 19 & 1150 \\ 4 & 36 & $1 X$ & 10 & 362 \\ 5 & 72 & $0.5 X$ & 5 & 153 \\ 6 & 72 & $0.5 X$ & 0 & 220 \\ 7 & 152 & $0.25 X$ & 0 & 133 \\ 8 & 10 & $4 X$ & 28 & 1100 \\ 9 & 20 & $2 X$ & 25 & 290 \\ \hline \end{tabular} \end{center} Experiment one was deposited at the nominal settings for speed, focus offset, and hatch spacing in Ti-6Al-4V in the Arcam S12 machine at Carnegie Mellon. Experiments two and three used settings at larger and smaller cross-sectional areas with modified hatch spacing, but without\\ modified focus offset. Experiment four used the nominal area setting with a decreased focus offset and increased hatch spacing intended to improve deposition rate while balancing melt pool width and hatch spacing to avoid introducing lack of fusion porosity. Experiments five and six were deposited at power and velocity settings designed to result in half the nominal area, and decreased focus offset and hatch spacing values to reduce porosity. Experiment seven used power and velocity settings to produce an area one quarter of the nominal size. Focus offset and hatch spacing were reduced to maintain low porosity. Experiment eight was designed for a melt pool four times larger than nominal with an increase in hatch spacing and focus offset to deposit successfully. Experiment nine used settings for an area twice that of nominal with increased focus offset and hatch spacing values to improve deposition quality. \subsection*{4.3 Results} \subsection*{4.3.1 Depth and Width Variability in Keyhole Mode and Conduction Mode Melting} Many in the welding community have shown that keyhole mode welding can introduce increased variability in melt pool dimensions [45] [64] [65]. An investigation of additive manufacturing melt pools at different spot sizes was used to determine how variability in melt pool dimensions change at different magnitudes of keyholing. Figure 4-4 shows how melt pool depth and width change as a melt pool transitions into keyhole mode melting. Experiments were completed in the Arcam S12 EB-PBF process at a power of $670 \mathrm{~W}$, and velocity of $265 \mathrm{~mm} / \mathrm{s}$. Depth to width values over 0.5 are considered keyholing melt pools, and larger values indicate more severe keyholing. Melt pool widths showed less change as depth to width ratio increased into\\ the keyhole mode melting range, but melt pool depths steadily increased. This suggests that increases in depth to width ratio in keyholing melt pools is primarily due to depth increases. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-103} \end{center} Figure 4-4: Width and depth vs D/W ratio for single beads deposited in Ti-6Al-4V in the Arcam S12 EB-PBF process Similar to the plot above, standard deviations measured for the melt pools have been plotted against depth to width ratio for the 670 W, 265 mm/s EB-PBF experiments in Figure 4-5. Standard deviations for melt pool width taken from above view images suggest that the mechanisms that drive keyhole mode melting have little effect on the variability of the width of the melt pool. Standard deviations for width are consistently between 12 and $17 \mu \mathrm{m}$ with no significant trend with respect to depth to width ratio. Standard deviations for melt pool depth were gathered from sections down the length of the melt pool. In conduction mode melting, standard deviations for depth typically fell below those found for melt pool width. In keyholing melt pools above depth to width ratios above 0.5 , standard deviations increase significantly with increasing depth to width ratio. This signals that in more severe keyhole melt pools, the variability in the melt pool also\\ become more severe, which reinforces the notion that keyhole mode melting is undesirable in additive manufacturing. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-104} \end{center} Figure 4-5: Standard deviations of width and depth vs D/W ratio for single beads deposited in Ti$6 \mathrm{Al}-4 \mathrm{~V}$ in the Arcam S12 EB-PBF process Although the data presented in this section is limited to data from one power-velocity combination, the observed trends give insight to how melt pool depth and width changes in conduction and keyhole mode melting scenarios. Keyholing has little effect on the width of melt pools, but can dramatically increase melt pool depth. While keyhole mode melting may be desirable in some welding applications, the variability in depth and large depth to width aspect ratios make keyhole mode melting unwanted when compared to more consistent melt pools deposited in conduction mode melting. \subsection*{4.3.2 Spot Size Changes to Prevent Keyholing} Key to depositing successfully throughout processing space while avoiding keyhole mode melting is the ability to eliminate the occurrence of keyholing through process variable modification. Figure 4-6 displays Ti-6Al-4V melt pools produced in the Arcam S12 EB-PBF process at Carnegie Mellon at $670 \mathrm{~W}, 265 \mathrm{~m} / \mathrm{s}$, and different focus offset values. At narrow beam sizes, keyholing melt pools are produced. As spot sizes are increased, keyholing becomes less severe, and melt pools are created via conduction mode melting. Knowledge of the melt pool and spot size can be used to avoid keyhole mode melting and the adverse effects that come with it. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-105} \end{center} Figure 4-6: Melt pool cross sections from increasing spot sizes transitioning from keyholing to nonkeyholing melt pools To get an understanding of how spot size can be used to avoid the keyholing phenomenon, depth to width ratio is plotted against normalized spot size. Figure 4-7 shows depth to width values for all Ti-6Al-4V experiments from the Arcam S12 EB-PBF and EOS M 290 L-PBF processes along with the FEA line for an assumed Gaussian profile at a $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 5 . To avoid keyholing by the $\mathrm{D} / \mathrm{W}$ threshold of 0.5 used in this work, a corresponding normalized spot size $\left(\sigma / \mathrm{W}_{0}\right)$ value of 1 is necessary to ensure keyhole mode melting is avoided in Ti-6Al-4V. This means that spot sizes must be kept above the estimate point source width of a melt pool to avoid keyholing. There is also a second threshold of interest that may signal reduced variability in melt pools. At a depth\\ to width ratio near 0.3 , all experimental measurements begin good agreement not only with the finite element curve for depth to width, but also with other experiments. This depth to width threshold corresponds to a normalized spot size of 1.25. These two thresholds suggest that maintaining normalized spot sizes above 1 can help avoid keyhole mode melting, and normalized spot sizes above 1.25 produce more predictable melt pool sizes in Ti-6Al-4V. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-106} \end{center} Figure 4-7: D/W ratio vs normalized spot size for all experimental Ti-6Al-4V data A Similar analysis can be completed to find normalized spot size thresholds to avoid keyholing in other alloys. Figure 4-8 displays experimental data for both Inconel 718, and 316L stainless steel along with finite element data. IN718 experiments were completed only in the Arcam S12 EB-PBF process, while 316L stainless steel experiments were completed in the 3D Systems ProX 200 and ProX 300 L-PBF processes. The number of experiments completed in IN718 is much more limited than those for Ti-6Al-4V presented earlier, but a similar threshold value for keyholing can be found. A threshold for keyholing is found at a normalized spot size value of 0.9 , just below\\ the value found for Ti-6Al-4V. The keyholing threshold for normalized spot size in 316L stainless steel was similarly found to be 0.9. Both IN718, and 316L stainless steel thresholds were based off fewer experiments when compared to Ti-6Al-4V, and therefore a threshold for reduced variability in melt pool results could not be determined. Inconel 718 \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-107(1)} \end{center} 316L Stainless Steel \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-107} \end{center} $\rightarrow-$ Gaussian FEA Figure 4-8: D/W ratio vs normalized spot size for all experimental IN718 (left) and 316L stainless steel (right) data Keyholing thresholds can also be found for 17-4 PH stainless steel, and 304 stainless steel based on experiments from the ProX 200 and ProX 300 L-PBF experiments. Figure 4-9 shows experimental D/W data for 17-4 PH and 304 stainless steel compared against a finite element curve $\left(\mathrm{L}_{0} / \mathrm{D}_{0}=5\right)$. For 17-4 PH stainless steel, a threshold for keyholing based on experimental measurements is determined to be 0.9 , which falls in line with values attained for IN718 and 316L stainless steel. A normalized spot size threshold to avoid keyholing for 304 stainless steel based on experimental data is determined to be 0.9. As with IN718 and 316L stainless steel, there is not enough experimental data to determine a second threshold for reduced variability. 17-4 PH Stainless Steel \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-108(1)} \end{center} \begin{itemize} \item Experimental Measurements\\ 304 Stainless Steel \end{itemize} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-108} \end{center} $\rightarrow$ Gaussian FEA Figure 4-9: D/W ratio vs normalized spot size for all experimental 17-4 PH (left) and 304 (right) data Plotting depth to width ratio for all experiments against normalized spot size has enabled thresholds to be developed based on spot size and melt pool size to be able to avoid keyhole mode melting. Across five different alloys, thresholds to avoid keyholing were found to be very similar. A conservative threshold to avoid keyholing across all five alloys studied in this section is a normalized spot size of 1 . This means that to avoid keyholing, the spot size must be kept above the point source width from simulations, or estimated from experiments. A second threshold was observed in Ti-6Al-4V experiments for reduced variability, but such a threshold could not be determined in other alloys. \subsection*{4.3.3 Spot Size Changes to Reduce Bead-up} In addition to keyhole mode melting, bead-up melt pools can introduce porosity into additive manufacturing deposits due to the inconsistent surface of the melt pools. Yadroitsev et al. suggested a minimum width to full length ratios to avoid instability depending on the angle the\\ melt pool creates with the substrate. At an angle of 180 degrees, where the melt pool is contacting the substrate at one point, the W/FL threshold is found to be 0.26 , and for a free cylinder with no contact to a substrate, the threshold is 0.32 . These two numbers will be used as indicators for potential instability and the onset of bead-up. Width to Full Length Ratio vs. Normalized Spot Size\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-109} \begin{center} \begin{tabular}{|c|c|c|c|} \hline $\mathrm{L}_{0} / \mathrm{D}_{0}=2.5$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=5$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=10$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=20$ \\ \hline - L-PBF Ti-6Al-4V & - L-PBF CoCr & - EB-PBF CoCr & - EBWF IN625 \\ \hline — LPF 316L SS & — EBWF IN 625 & — EBWF Ti-6Al-4V & — EB-PBF Ti-6Al-4V \\ \hline $\rightarrow$ LPF 316L SS & $\multimap$ EBWF Ti-6Al-4V & $\hookrightarrow$ EBWF Ti-6Al-4V & $\rightarrow$ EB-PBF Ti-6Al-4V \\ \hline $\rightarrow$ L-PBF Ti-6Al-4V & $\rightarrow$ L-PBF CoCr & $\multimap$ EB-PBF Ti-6Al-4V & $\multimap$ EBWF Ti-6Al-4V \\ \hline \end{tabular} \end{center} Figure 4-10: Width to full length (W/FL) versus normalized spot size $\left(\sigma / W_{0}\right)$ for melt pools of different aspect ratios Figure 4-10 shows trends in width to full length ratio with increasing spot size for different $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios. Shorter melt pools at smaller L0/D0 melt pools do not enter the bead-up region regardless of the spot size, however L0/D0 values above five require increased spot size to increase the width to full length ratio and avoid bead-up melt pools. For an assumed tophat beam\\ distribution, W/FL continually increases at an increasing slope. With a Gaussian beam distribution, W/FL ratio continually increases with normalized spot size, but the changes become less significant at larger spot sizes. More important than the behavior of the width to full length ratio is the value of the normalized spot size where $\mathrm{L}_{0} / \mathrm{D}_{0}$ lines cross the bead-up thresholds. For this, similar values can be obtained for both tophat and Gaussian beam distributions. Melt pools from a series of spot size experiments deposited in the 3D Systems ProX 200 LPBF process in 17-4 stainless steel are presented in Figure 4-11. Width to full length values can be found based on normalized spot size, $\mathrm{L}_{0} / \mathrm{D}_{0}$ values, and the presented Gaussian simulation data. As spot size is increased, width to full length ratio increases, and severity of bead-up decreases. For the case presented below, a bead-up threshold exists between a W/FL ratio of 0.26 and 0.32 . The average of the two values (0.29) is used as a threshold for this case with a W/FL uncertainty of 0.03 . \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-110} \end{center} Figure 4-11: Observed bead-up and smooth melt pools deposited in 17-4 PH stainless steel in the ProX 200 L-PBF process Observations similar to those presented above were completed in melt pool tracks across different alloys and processes to verify thresholds proposed by Yadroitsev when spot size is increased. Melt pools can be plotted in W/FL versus $\sigma / \mathrm{W}_{0}$ space for the associated $\mathrm{L}_{0} / \mathrm{D}_{0}$ values to determine the bead-up threshold for different power-velocity combinations. Table 6 shows W/FL thresholds observed from various spot size experiments. The threshold presented is the average W/FL value between the last bead-up melt pool, and the first smooth melt pool. Uncertainty in the measurement is simply the difference between those average values and the W/FL value of the last bead-up melt pool. \section*{Table 6: Experimental bead-up identification and measurement} \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline Process & Alloy & \begin{tabular}{c} Power \\ (W) \\ \end{tabular} & \begin{tabular}{c} Velocity \\ (mm/s) \\ \end{tabular} & \begin{tabular}{c} W/FL \\ threshold \\ \end{tabular} & \begin{tabular}{c} W/FL \\ Uncertainty \\ \end{tabular} \\ \hline Arcam S12 & Ti-6Al-4V & 670 & 1100 & 0.3 & 0.01 \\ Arcam S12 & Ti-6Al-4V & 670 & 550 & 0.275 & 0.005 \\ EOS M 290 & Ti-6Al-4V & 370 & 1900 & 0.265 & 0.005 \\ EOS M 290 & Ti-6AI-4V & 330 & 2150 & 0.28 & 0.01 \\ ProX 200 & SS 316L & 300 & 2400 & 0.29 & 0.03 \\ ProX 200 & SS 17-4 PH & 300 & 2400 & 0.29 & 0.03 \\ ProX 200 & SS 304 & 300 & 2400 & 0.29 & 0.03 \\ \hline \end{tabular} \end{center} Strong agreement is observed between proposed bead-up thresholds and those observed for no-added material Ti-6Al-4V and stainless steel single bead deposits. Although good agreement is observed between Ti-6Al-4V and stainless steel deposits, bead-up was not observed in Inconel 718 deposits where it was expected due to a low width to full length ratio. With a layer of added powder, bead-up may occur in the Inconel deposits, but further work is required to explain the discrepancy between alloys. A conservative W/FL threshold to avoid bead-up melt pools is suggested as 0.32 based on the largest cutoff observed with uncertainty. \subsection*{4.3.4 Spot Size Changes to Reduce Porosity} Based on previous information gathered about the effects of spot size on geometry and onset of keyholing, multi-layer pads were built in the Arcam S12 EB-PBF process. The power and velocity settings were based on different desired melt pool areas. Spot size was adjusted to give preferable melt pool shape, and hatch spacing was adjusted to ensure complete melting. Figure 4-12 displays percent porosity measured in each sample at different magnifications, and displays some key experiment settings. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-112} \end{center} Figure 4-12: Percent porosity measured at different magnifications for Ti-6Al-4V multi-layer pads deposited in the Arcam S12 machine at Carnegie Mellon Experiments two, three, and eighth all had significant porosity of 15, 28, and 14 percent respectively. These would not be acceptable for use with the process parameters used, but may be suitable with adjustments to spot size or hatch spacing. Experiment nine, at a melt pool area of $2 \mathrm{X}$ resulted in similar porosity as the nominal settings in experiment one. Porosity in these\\ experiments could likely be reduced by changing process parameters, as porosity at the nominal power-velocity settings was decreased in experiment four by decreasing spot size and increasing hatch spacing. A larger hatch spacing was able to be used because the smaller spot size gave better penetration into the substrate than the nominal focus settings. This simple decrease in spot size enabled a deposition rate 81 percent higher than standard settings at the same power and velocity. The two lowest porosity samples in experiments five and six were produced at the $0.5 \mathrm{X}$ powervelocity settings. During the design of these experiments, the complete profile of spot size versus focus offset was unknown, and thus the two experiments were deposited at very similar spot sizes. A narrow spot size compared to nominal settings gave the $0.5 \mathrm{X}$ melt pools additional penetration into the substrate, and a smaller hatch spacing in experiment five resulted in reduced porosity. Experiment seven, with $0.25 \mathrm{X}$ power and velocity, also had significantly reduced porosity when compared to the nominal condition with decreased spot size and hatch spacing. With correct adjustments to spot size, hatch spacing and layer thickness can be adjusted to create successful deposits. Adjustments made in experiments in this section allowed for successful deposition with melt pools that were one quarter to double the area of the nominal case. This wide range of available melt pool sizes can allow an operator to take advantage of qualities deposited at different melt pool sizes or in different regions of processing space. \subsection*{4.4 Discussion} Keyhole mode melting can be avoided in additive manufacturing melt pools by increasing spot size. Variability in single bead melt pools was analyzed for both melt pool widths and depths. Depth to width ratio was used as an indicator of the presence and severity of keyhole mode melting, and both depth and width were plotted against this ratio. A depth to width ratio greater that 0.5\\ was considered a keyholing melt pool. As a depth to width ratio increased, changes in width became less sensitive to increasing severity of keyhole mode melting. Melt pool depth, however, steadily changed with increasing D/W ratio signaling that depth is primarily responsible for increases in melt pool area in keyhole mode melting. Standard deviations were calculated in melt pool widths as measured from above, and melt pool depths from sections down the length of the melt pool. Standard deviations in melt pool width were unaffected by keyhole mode melting and increasing severity of the phenomenon. Standard deviations in melt pool depth saw a jump in melt pool with $\mathrm{D} / \mathrm{W}$ ratios greater than 0.5 and increasing variability with increasing keyhole severity. Methods to identify keyholing based on depth to width ratio were explored and used to determine a normalized spot size $\left(\sigma / \mathrm{W}_{0}\right)$ threshold to avoid keyhole mode melting in Ti-6Al-4V, IN718, 316L stainless steel, 17-4 PH stainless steel, and 304 stainless steel. Normalized spot size thresholds for the different alloys were found to be 1.0 for Ti-6Al-4V, and 0.9 for all other alloys analyzed. Since all values were very close, a conservative estimate for all alloys analyzed is to follow the value of 1.0 to avoid keyhole mode melting in the alloys presented. While the alloys in this study all gave very similar results, analogous studies would need to be performed to confirm thresholds for different alloys. In addition to keyholing, spot size can be used to avoid the formation of bead-up melt pools. Melt pool width to full length (W/FL) ratio has been established as an important indicator for the development of bead-up melt pools by previous authors [74]. Trends for W/FL against normalized spot size are developed based on simulations, and experiments are used to verify thresholds to avoid bead-up suggested by Yadroitsev [75]. Good agreement is observed between experimental and proposed thresholds suggesting spot size can be used to methodically avoid bead-up melt pools\\ in additive manufacturing. A conservative threshold is considered to be a W/FL ratio of 0.32 , but the value may need to be modified when a powder layer is present. Knowledge of keyholing thresholds and geometrical changes due to spot size changes was used to design multi-layer pad experiments for a range of melt pool sizes. By modifying focus offset and hatch spacing, porosity at nominal power-velocity settings was able to be decreased while increasing deposition rate by 81 percent. Lower porosities were also achieved for process parameters at areas 0.5 , and 0.25 times the nominal case. Similar porosity values were found for parameters yielding an area twice that of the nominal case. By including spot size in process parameter adjustments, high quality depositions can be created by avoiding keyhole and lack of fusion porosity. \section*{Chapter 5: The Effects of Spot Size on Ti-6Al-4V Deposition} \section*{Microstructure} \subsection*{5.1 Overview} The microstructure in an additively manufactured part is a key factor determining the part's mechanical properties. Models used in previous chapters are used to gain insights into how spot size affects cooling rates, which play an important role in the development of microstructure. Differences between tophat and Gaussian beam profiles are explored, and differences in results between the two cases are explained. Prior beta grain measurements from various Ti-6Al-4V experiments show no correlation with changing spot sizes. The absence of a trend with spot size requires an amendment to the findings by Gockel [81] that suggest a direct relationship between spot size and effective melt pool width. \subsection*{5.2 Methods} \subsection*{5.2.1 Modeling} Work in this chapter makes use of the finite element, Rosenthal, and Eagar-Tsai models used in Chapter 3:. Much of this section reiterates the details of those models; information on the methods used that are specific to this chapter begins in section 5.2.1.3. Work in this chapter is a product of both finite element based and analytical based models. Finite element simulations used in spot size analysis are based on those used in Chapter 2:, and simulate top hat or Gaussian flux distributions. Analytically based models are evolutions of the Rosenthal model of a moving point heat source [91]. The Eagar-Tsai model simulates a moving heat source with a Gaussian heat source and is a modification of the Rosenthal model [93]. Another\\ model was created to simulate a top hat heat source by using the principle of superposition with the original Rosenthal model. These models were used to identify how melt pool geometry changes with increasing spot size. \subsection*{5.2.1.1 Finite Element Models} The finite element model used in this section was a slight modification on the model used for the laser powder feed process. The model simulates a distributed moving heat source on a large substrate that is long enough to reach steady state melt pool size and wide and deep enough to avoid edge effects and a symmetry boundary condition down the center of the melt pool. The heat flux is distributed across elements on the surface to make a semi-circular shape. The number of elements with applied heat flux is determined by stepping through elements in the X-direction and rounding to the nearest element in the Y-direction to create the correct shape. Two different flux distributions within the spot size were simulated. One model uses a tophat distribution where all flux values are set equal, and a second approximates a Gaussian distribution. The spot size value used from Gaussian distribution simulations follows the D86 width measurement technique commonly used to find laser beam diameter [113]. The distribution of the heat flux for a typical model is shown in Figure 3-1. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-118} \end{center} Figure 5-1: Flux distribution on the surface of a finite element model The Gaussian heat source model extended the Gaussian profile out to two standard deviations, and amplitude is adjusted to provide the full power input. Since the Gaussian profile is fit onto a set of square elements, the smallest spot sizes used (4 element radius) had the largest percent error between the discrete and true distribution (25\%). Other spot sizes simulated were multiples of 4 elements through the radius and have significantly decreased error in respect to modelling a Gaussian beam profile. Simulations of spot size span multiple processes and alloys. In all cases, the finite element models use temperature dependent thermal properties. \subsection*{5.2.1.2 Rosenthal and Eagar-Tsai Models} In addition to finite element models, simpler models for tophat and Gaussian beam distributions were used to identify effects of increasing spot size. The models do not include temperature dependent properties or latent heat, but a solution can be found in a matter of seconds compared to hours or days. The first model, simulating a tophat distribution, is based off the moving heat source model developed by Rosenthal [91] shown in Eq. 3-1. \section*{Eq. 5-1} $$ T-T_{0}=\frac{q}{2 \pi k R} e^{-\frac{v(w+R)}{2 \alpha}} $$ Where $T$ is the temperature of the location of interest, $T_{0}$ is the preheat temperature, $q$ is the input power, $v$ is the travel velocity, $k$ and $\alpha$ are thermal properties, and $w$ and $R$ specify the location. The equation gives the temperature at a specified location relative to a point heat source. To create a tophat heat source, multiple Rosenthal models are organized into a circular shape with 100 instances across the diameter. The principle of superposition is used to sum the solutions for a specified point in space. Melt pool boundaries are found by using the Newton-Raphson method and maximum width, depth, and area is found using the golden-section search method. The Eagar-Tsai model was developed based on the Rosenthal model and simulates a moving heat source with a Gaussian distribution. Where the original Rosenthal model can be solved analytically, the derived Eagar-Tsai model in Eq. 3-2 must be solved numerically [93]. Eq. 5-2 $$ \theta=\frac{n}{\sqrt{2 \pi}} \int_{0}^{\frac{v^{2} t}{2 \alpha}} \frac{\tau^{-\frac{1}{2}}}{\tau+u^{2}} e^{-\frac{\xi^{2}+\psi^{2}+2 \xi \tau+\tau^{2}}{2 \tau+2 u^{2}}-\frac{\zeta^{2}}{2 \tau}} d \tau $$ Dimensionless temperature is represented by $\theta$, and $\xi$, $\psi$, and $\zeta$ represent dimensionless distance in $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$. Dimensionless time is represented by $\tau . u$ is a dimensionless heat source distribution parameter and $n$ is an operating parameter that includes power, velocity, and thermal properties. The integral was solved numerically with the trapezoid method, and melt pool boundaries and maximum geometry values were found via the Newton-Raphson and goldensection search methods as with the tophat distribution model. \subsection*{5.2.1.3 Modeling Cooling Rate} Simulation results for cooling rates have been determined from the different types of models described above using two different methods. In finite element simulations, a MATLAB script developed by Brian Fisher [123] measures the distance between the liquidus and solidus temperatures to generate a thermal gradient at the tail of the melt pool. The gradient is then multiplied by the heat source travel velocity to give a cooling rate for the steady state melt pools. In the Rosenthal based models used in this section, the absence of latent heat makes calculation of cooling rate easier. The gradient at the tail of the melt pool is multiplied by velocity to give the cooling rate for the simulation. Important to this work are the trends in cooling rates, thus the specific values are inconsequential. \subsection*{5.2.2 Experiments and Microstructure Analysis} Experimental data used in this section was gathered from those used for geometry analysis in Chapter 3:. The Ti-6Al-4V single bead experiments are deposited at select power-velocity combinations in the Arcam S12 EB-PBF, EOS M 290 L-PBF, and Sciaky electron beam wire feed processes. Once experiments were completed, samples are prepared for analysis. Samples are crosssectioned, polished, and etched using Kroll's etchant. Procedures for polishing and etching can be found in Appendix 1. Samples are then imaged using an Alicona Infinite Focus optical microscope. Melt pool cross-sectional dimensions and average prior beta grain width can be measured. Prior beta grain size is measured using the intercept method [112]. Prior beta grains in these processes are columnar in nature so prior beta grain width is the dimension of focus in this study. A horizontal\\ line is drawn perpendicular to the growth direction of columnar grains, and grains are counted then the total is divided by the length of the line. Work in this chapter will use normalized spot size values identified in Chapter 3:, but will focus on the microstructure of the depositions as opposed to the melt pool geometry. Melt pool geometries were previously normalized by their point source simulation values. Similarly, grain width is to be normalized; however, a point source grain size cannot be gleaned from simulations. Grain widths are therefore normalized by values found at small, non-keyholing melt pools, and may be based on two to three melt pools to reduce the influence of a single melt pool. \subsection*{5.3 Results} \subsection*{5.3.1 Model Results} Models of a moving heat source were used to identify trends in cooling rates and give insight as to how prior beta grain widths may change with increasing spot size. Figure 5-2 displays trends for normalized cooling rates $\left(\mathrm{CR} / \mathrm{CR}_{0}\right)$ in melt pools of different $\mathrm{L}_{0} / \mathrm{D}_{0}$ values. Similar to melt pool dimensions in earlier chapters, cooling rate is normalized by the point source value of cooling rate $\left(\mathrm{CR}_{0}\right)$. Trends are presented for both tophat and Gaussian beam profiles, as well as Rosenthalbased and finite element models. With a tophat beam distribution, cooling rates remain fairly constant with increasing spot size before sharply increasing at high normalized spot sizes. Melt pools with higher L0/D0 ratios have smoother increases in normalized cooling rate. This is in contrast to the behavior of normalized cooling rates for a Gaussian beam profile. With a Gaussian beam profile normalized cooling rates increase similar to with a tophat distribution before leveling out and decreasing at large spot sizes. Larger potential increases in cooling rate are observed in melt pools with larger $\mathrm{L}_{0} / \mathrm{D}_{0}$ values. There is also a discrepancy\\ between the trends observed in the Eagar-Tsai model, and the Gaussian distribution finite element model. Normalized cooling rates from the Gaussian finite element model only display slight leveling in some chosen curves, and has higher peaks than those observed by the Eagar-Tsai model. The differences between the two model results can be attributed to approximations made in generating the Gaussian heat flux distribution in the finite element models. The interface between elements with surface flux, and elements without surface flux, at the edge of the simulated beam lead to artificially higher gradients at the tail of the melt pool at large spot sizes. With a beam profile simulated to further extents, the differences between the two models would be reduced. \section*{Normalized Cooling Rate vs. Normalized Spot Size} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-122} \end{center} \begin{center} \begin{tabular}{|c|c|c|c|} \hline $\sigma / W_{0}$ & & & $\sigma / W_{0}$ \\ \hline $\mathrm{L}_{0} / \mathrm{D}_{0}=2.5$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=5$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=10$ & $\mathrm{~L}_{0} / \mathrm{D}_{0}=20$ \\ \hline $\longrightarrow$ L-PBF Ti-6Al-4V & - L-PBF CoCr & - EB-PBF CoCr & - EBWF IN625 \\ \hline — LPF 316L SS & — EBWF IN 625 & — EBWF Ti-6Al-4V & — EB-PBF Ti-6Al-4V \\ \hline $\rightarrow$ LPF 316L SS & $\hookrightarrow$ EBWF Ti-6Al-4V & $\multimap$ EBWF Ti-6Al-4V & $\rightarrow$ EB-PBF Ti-6Al-4V \\ \hline $\multimap$ L-PBF Ti-6Al-4V & $\multimap$ L-PBF CoCr & $\multimap$ EB-PBF Ti-6Al-4V & $\multimap$ EBWF Ti-6Al-4V \\ \hline \end{tabular} \end{center} Figure 5-2: Normalized cooling rate vs. normalized spot size for tophat and Gaussian beam distributions Differences between the two trends in cooling rate between tophat and Gaussian beam profiles is attributed to the temperature profiles created in the melt pools. Figure 5-3 compares the beam and temperature distributions down the centerline of the melt pool generated from the Rosenthal superposition tophat profile and Eagar-Tsai Gaussian profile models over various normalized spot sizes. The curves were created for a simulation of IN625 in the electron beam wire feed process at $3 \mathrm{~kW}$ and $21 \mathrm{~mm} / \mathrm{s}$ with a $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio of 5 . With a tophat beam profile, the maximum temperature occurs at the back edge of the beam before dropping sharply as the material cools. As the beam is expanded, the peak temperature develops closer to the melting temperature. This in turn brings the steep drop in temperature at the back of the beam spot closer to the melting temperature, raising the gradients at the melting point and similarly the cooling rates. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-124} \end{center} Figure 5-3: Temperature and beam profile distributions for different normalized spot sizes With a Gaussian beam profile, the peak temperature also occurs toward the back of the beam spot; however, energy is still being input into the melt pool behind the peak temperature. This offsets some of the heat being conducted away and gives a smoother temperature profile compared to the tophat distribution. As spot size is increased, the melting point occurs at a location with\\ steeper gradients on the melt pool cooling curve. As the spot size continues to increase, the melt point approaches the rounded peak of the temperature curve and begins decreasing. \subsection*{5.3.2 Single Bead Experiments} Data from single bead experiments was gathered from experiments in the Arcam S12 EB-PBF, EOS M 290 L-PBF, and Sciaky electron beam wire feed processes. Prior beta grains from each experiment set were measured to get average grain sizes in the melt pools at different spot sizes. Measurements were normalized based on prior beta grain widths in relatively small, non-keyholing melt pools and plotted against normalized spot size. Figure 5-4 shows normalized grain width $\left(\mathrm{GW} / \mathrm{GW}_{0}\right)$ versus normalized spot size data from all experimental measurements. The data does not form a discernable trend suggesting spot size has little to no effect on prior beta grain width in Ti-6Al-4V. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-125} \end{center} Figure 5-4: Experimental normalized prior beta grain width vs. normalized spot size for Ti-6Al-4V The lack of correlation between prior beta grain width and spot size also means that there cannot be a relationship solely between grain size and melt pool dimensions, as the spot size does\\ not change the melt pool dimensions. This suggests a corollary needs to be added to the findings by Gockel [81] that prior beta grain width scales with the square root of melt pool area. At large spot sizes, wide and shallow melt pools can have significantly reduced melt pool areas. An adjusted relationship between melt pool area and prior beta grain width should read as follows: Prior beta grain width in Ti-6Al-4V scales with the square root of area for consistent cross sectional shape. By considering the relationship for a consistent cross sectional shape, differences in area due to spot size no longer has influence over the trend. An additional benefit of using the relationship with consistent melt pool shape is the ability to directly use the measured melt pool width, rather than calculate effective melt pool width based on cross-sectional area measurements. In light of the information presented in this chapter, relationships between melt pool dimensions and prior beta grain width in the Sciaky electron beam wire feed process from section 2.3.3 can be modified. Figure 5-5 shows the relationship between average prior beta grain width and effective melt pool width for both the original effective width values based on area measurements and adjusted effective width values that account for the effects of spot size on melt pool area. Adjusted values were ascertained through the fitted finite element process map for crosssectional area associated with the process. The two groups of data still give very similar results, but a steeper slope is observed in the adjusted values. Larger differences would be expected between the two trends if more extreme melt pool shapes were present in the experiments. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-127} \end{center} Figure 5-5: Relationships between prior beta grain width and effective melt pool width based on the original effective widths based on measurements, and spot size adjusted values based on finite element simulations. \subsection*{5.4 Discussion} In addition to melt pool dimensions in previous chapters, the effects of spot size on cooling rate has been simulated. Trends between normalized cooling rates and normalized spot size show that cooling rate is generally not correlated with spot size for small and moderate spot sizes, while there is a strong, positive, correlation at large spot sizes. Simulations also identified significant differences in cooling rate at large spot sizes between beam distribution assumptions. Sharp decreases in applied heat at the edge of a tophat beam result in increasingly steep gradients and increasing cooling rates while the smoother shape of a Gaussian beam results in smaller increases in cooling rates, and even decreases in cooling rate for small $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratios. Based on the results of cooling rate trends from simulations, grain size is expected to decrease with increasing tail cooling rate at large spot sizes. Contrary to expectations, Ti-6Al-4V single bead experiments from multiple processes at various normalized spot sizes had no dependence\\ upon spot size. This observation requires that the notion that grain width scales with melt pool area only holds true if the shape of the melt pool remains constant. It is important to note that these experimental measurements are for single bead results only, and the observed trends may not hold for multi-layer deposits. More work is required in the future to confirm or qualify the experimental findings in this chapter. \section*{Chapter 6: Adjusting Spot Size to Expand Processing Space} \subsection*{6.1 Overview} Previous chapters have shown various ways that spot size influences different aspects of additive manufacturing deposits. Work presented here presents how those findings can be implemented to expand the usable processing space in additive manufacturing processes. Three stainless steels are process mapped in the ProX 200 L-PBF process at the nominal spot size. Issues are noted with the melt pools created throughout processing space, and expanded spot size experiments are completed for 316L stainless steel. Expanded spot size experiments make use of findings in Chapter 4: to eliminate keyholing at target power-velocity combinations. New melt pool measurements are used to create a modified process map with an increased usable processing space. A method is proposed to systematically increase the "good" processing space by avoiding keyholing, and preventing the occurrence of bead-up melt pools in some regions. \subsection*{6.2 Methods} \subsection*{6.2.1 Modeling} Finite element process maps in this section are based on a series of two dimensional simulations completed using the Abaqus software package. The model is made up of a single plane and a point heat source that travels node by node along the y-axis. The model is radially symmetric about the y-axis, thus the model is simulating a heat source moving axially down the center of a cylinder. Simulating a simple heat source traversing a flat substrate of material is the goal of the model, so energy input on each step is doubled to compensate for energy lost to half of the modeled cylinder. As with finite element models used in previous sections, the two-dimensional model has a section of fine mesh where the melt pool will develop and be measured before a biased mesh\\ creates a large enough substrate to simulate a semi-infinite domain. The model is long enough to allow melt pools to reach a steady state. Temperature dependent thermophysical properties are used for 316L, 17-4, and 304 stainless steel used in this chapter [124] [125] [126]. Melt pool dimensions measured from the simulations includes melt pool width, depth, crosssectional area, and length values. The two dimensional models require less computing time when compared to the three dimensional models due to simplifications in the model geometry. A drawback of the model is the inability to model heat source distributions that are not a point heat source. The two dimensional model is therefore used as a basic model to create process maps, or to quickly ascertain point source and $\mathrm{L}_{0} / \mathrm{D}_{0}$ values that can be used for spot size adjustments. \subsection*{6.2.2 Experiment Design and Process Mapping} Experiments took place in the 3D Systems ProX 200 L-PBF process for process mapping and spot size analysis purposes. For process mapping experiments, points for single bead experiments were chosen throughout the capable power and velocity in a grid pattern. Selected powers and velocities consisted of 45, 130, 215, and 300 watts for power, and 400, 900, 1400, 1900, 2400, 2900, and $3400 \mathrm{~mm} / \mathrm{s}$ for velocity. All points were deposited at the nominal focus offset setting of zero, which results in a maximally focused beam with an estimated spot size of $30 \mu \mathrm{m}$ from section 3.3.3. To generate a process map with lines of constant melt pool area, values measured from melt pools are piecewise linearly interpolated to find locations of a prescribed area in power-velocity space. The experimental process map can then be related to finite element results through an effective absorptivity. Effective absorptivity is found by dividing the power required to produce a certain melt pool area in finite element simulations by the power required in experiments to produce the\\ same area. Melt pool dimensions are measured after sectioning, polishing, and etching experimental deposits. Measurements of melt pool area were taken in such a way that a surplus or dearth of material was ignored, in the same fashion as outlined in section 3.2.2. Polishing and etching procedures for the stainless steel alloys are provided in Appendix 1. Included in this chapter are experiments designed to eliminate keyholing at power-velocity combinations previously used for process mapping experiments. Seven points in processing space that had been classified as keyholing melt pools from 316L stainless steel process mapping experiments were selected to develop a new process map that is not influenced by the increased melt pool areas produced by keyholing. At each power-velocity combination, findings in Chapter 4: were used to guide selection of new focus offset values. A new process map could then be created using the newly deposited single beads at larger spot sizes. \subsection*{6.3 Results} \subsection*{6.3.1 Process Mapping} Process maps of cross-sectional area were developed for 316L, 17-4, and 304 stainless steels in the 3D Systems ProX 200 process. In addition, specific experimental points were identified as keyholing, undermelting, bead-up, or good melt pools. Keyholing melt pools were identified as melt pools with a depth to width ratio greater than 0.5 , and undermelting melt pools were identified as melt pools width a depth less than the nominal layer thickness that would lead to lack-of-fusion porosity. Bead-up melt pools were labeled as such based on above view observations of the single bead deposits. "Good" melt pools were the remaining melt pools that had not been labeled as having geometrical problems. Figure 6-1 shows the labeled points, and area process map for 316L stainless steel. Keyholing melt pools dominated the high power, low velocity region of processing\\ space at the nominal focus settings, and undermelting dominated the low power, high velocity region. Bead-up melt pools occurred in the high power, high velocity region of processing space and coincided with many keyholing and undermelting melt pools. A very small region is left to be categorized as "good" points, which severely limits the range of settings that can be used to produce successful parts. The influence of keyholing and undermelting can also be seen in the process map. While experimental measurements match up very well with finite element results, it only does so when different effective absorptivities are used for each line of constant area. Melt pools at smaller areas were effected by comparatively larger normalized spot sizes that worked to reduce the melt pool area in experiments, and resulted in lower effective absorptivities. Conversely, larger melt pools with small normalized spot sizes had increased melt pool areas due to the keyholing phenomenon, and therefore larger effective absorptivities. The significant differences in effective absorptivity, and small "good" processing space are remedied in section 6.3.3.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-132} Figure 6-1: 316L experiments labeled good, keyholing, undermelting, and bead-up melt pools identified in melt pools throughout processing space (left), and finite element and experimental process map of melt pool areas with effective absorptivity values (right). Process mapping and regions of keyholing and undermelting melt pools are also explored for the 17-4 PH stainless steel alloy. Figure 6-2 displays categorized melt pools in power-velocity processing space along with a melt pool area process map for the alloy. Unlike 316L stainless steel, experiments throughout power-velocity processing space are dominated by keyholing and undermelting melt pools. It is important to note, however, that there were no melt pools that required both a keyholing and undermelting label. This suggests that there would be a small region of "good" melt pools along the interface of the two regions. The process map displays similar behavior as the 316L process map, where small melt pools in the undermelting region had significantly smaller effective absorptivities than those in the keyholing region. Even with differences in effective absorptivities, the process map can be used to find different geometries throughout the capable process space.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-133} Figure 6-2: 17-4 experiments labeled good, keyholing, undermelting, and bead-up melt pools identified in melt pools throughout processing space (left), and finite element and experimental process map of melt pool areas with effective absorptivity values (right). Process mapping and melt pool labeling was also completed for the 304 stainless steel alloy in Figure 6-3. As with the previous two alloys, keyholing melt pools dominate the high power, low velocity region of power-velocity space, and undermelting dominates the low power, high velocity\\ region. One "good" point signals a small region of ideal processing space between the three larger regions of keyholing, undermelting, and bead-up. The melt pool area process map also resembles those from the other two stainless steel alloys. Small melt pools with shallow depth to width ratios have decreased absorptivities while large melt pools exhibit keyholing, which further increases the melt pool area.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-134} Figure 6-3: 304 experiments labeled good, keyholing, undermelting, and bead-up melt pools identified in melt pools throughout processing space (left), and finite element and experimental process map of melt pool areas with effective absorptivity values (right). Similar results across the stainless steel alloys highlight a common problem. There is a very small region of processing space that is ideal for use in the ProX 200 L-PBF process at standard spot sizes. Additionally, the changing effective absorptivities and melt pool shapes makes identification of desired process parameters more difficult. Solutions to these identified problems are explored in section 6.3.3. \subsection*{6.3.2 Spot Size Experiments} Spot size experiments were completed in the process not only to verify models and trends developed in Chapter 3:, but also to make adjustments to the process maps presented in section 6.3.1. This section will discuss results from experiments directed at eliminating specific keyholing melt pools labeled throughout 316L stainless steel power-velocity space. Figure 6-4 shows the labeled points from the process mapping experiments with nominal focus along with the points chosen for spot size adjustments. The chosen points are primarily in the keyholing region and have been chosen in such a way that a coarse process map can be formed from the resulting data. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-135} \end{center} Figure 6-4: Labeled keyholing, "good", and undermelting melt pools from 316L experiments, and the points chosen for spot size adjustments At each point chosen for adjusted spot size experiments, a specific spot size was chosen based on simulation point source widths and the keyholing threshold established in Chapter 4:. Point source width values in these experiments were based on simulation values and the effective absorptivity of 0.36 from the $1600 \mu \mathrm{m}^{2}$ constant area line used in the process map. This constant area line was chosen as it was the largest non-keyholing area line used in the process map. Figure 6-5 shows melt pools deposited at $300 \mathrm{~W}, 400 \mathrm{~mm} / \mathrm{s}$, and various spot sizes including the nominal\\ case at a focus offset of $0 \mathrm{~mm}$ and estimated spot size of $30 \mu \mathrm{m}$ from section 3.3.3. For this powervelocity combination, the melt pool produced with an estimated spot size of $165 \mu \mathrm{m}$ would be the case chosen as a more ideal melt pool for an updated process map. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-136} \end{center} Figure 6-5: Cross section images of melt pools deposited at $300 \mathrm{~W}, 400 \mathrm{~mm} / \mathrm{s}$, and various spot size values. Spot size adjustments for the other selected power velocity combinations were also successful at preventing keyhole mode melting. Figure 6-6 shows results from two other selected powervelocity combinations; one case at $215 \mathrm{~W}$ and $1400 \mathrm{~mm} / \mathrm{s}$, and the other at $130 \mathrm{~W}$ and $400 \mathrm{~mm} / \mathrm{s}$. In both cases, the spot size adjustments intended to eliminate keyholing and give a smooth, arcing melt pool were successful in doing so. The findings of Chapter 4: were also successful in eliminating keyholing in melt pools at the other power-velocity combinations chosen for spot size adjustments in this chapter. Images of the other selected melt pools at the original and adjusted spot size settings are available in Appendix 5.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-137} Figure 6-6: Cross section images of melt pools deposited at nominal and adjusted spot size values. \subsection*{6.3.3 Expanding Processing Space} Using information presented in this thesis, the usable processing space can be increased through the intelligent control of spot size. Figure 6-7 outlines a method that can be implemented to increase the usable processing space. Step one begins with a process map generated from experimental measurements at a constant, nominal, spot size. Point source simulation data is fit to the measurements with different absorptivities for each constant area line. The limits of the usable processing space are bound by keyholing at high power and low velocity, undermelting at low power and high velocity, and bead-up at high power and high velocity. In step two, an effective absorptivity is selected from the largest non-keyholing melt pools, or from melt pools near the normalized spot size threshold for keyholing. Chapter 4: identifies a normalized spot size $\left(\sigma / \mathrm{W}_{0}\right)$ value of one as a threshold to avoid keyholing in multiple alloys. Step three involves the creation of a new process map created using point source simulation data spread throughout processing space using the effective absorptivity identified in step two for\\ all melt pool areas. Additionally, a specific spot size is assigned to each constant area line based on the normalized spot size requirements to avoid keyholing based on the identified normalized spot size threshold. Melt pool dimensions in this process map can be used to guide spot size changes for purposes beyond keyhole avoidance if it is desired. Step four shows the identification of the usable processing space with the newly developed process map and spot sizes aimed at eliminating keyhole mode melting. The undermelting region remains constant in this case since no changes in layer thickness have been implemented. The limit for bead-up melt pools is based on a width to full length ratio calculated from point source simulations. Details on the threshold for bead-up melt pools are discussed in Chapter 4:. Step five, the final step, makes use of the relationships between normalized spot size, and width to full length ratio to further expand processing space. The new bead-up line is determined by increasing spot size of a certain melt pool area until the depth is equal to the layer thickness. The normalized spot size of the associated changes can be used to determine the maximum $\mathrm{L}_{0} / \mathrm{D}_{0}$ ratio that can be used while still remaining below the bead-up threshold for W/FL. It is important to note that the usable processing space gained between steps four and five will require additional spot size increases to avoid bead-up melt pools. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-139} \end{center} 1: Process map created from experiments at nominal spot size. Small processing space identified due to keyholing, undermelting, and bead-up \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-139(3)} \end{center} 2: Effective absorptivity identified for largest non-keyholing area based on simulation data and\\ 3: New process map developed effective absorptivity and spot size adjustments \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-139(1)} \end{center} 4: Expanded processing space identified for new process map with beadup limit \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-139(2)} \end{center} 5: Processing space further expanded to account for mitigation of bead-up via spot size increases Figure 6-7: Steps taken to determine an expanded processing space that avoid keyholing, undermelting, and bead-up melt pools The steps outlined above have been implemented for 316L stainless steel in the ProX $200 \mathrm{~L}-$ PBF process. Figure 6-8 shows plots that refer to steps one and four. On the left, the original process map created with nominal absorptivity and varying absorptivities to fit experimental and simulation data. A very narrow region of usable processing space is observed around the green, $1600 \mu \mathrm{m}^{2}$ area measurements. On the right, a new area process map was developed based on expanded spot size experiments discussed in section 6.3.2. The area lines at high powers and low velocities have been modified as\\ a result of the spot size changes. Details on the spot size changes suggested for 316L, and the other stainless steel alloys are available in Appendix 6. In the adjusted plot, the $13000 \mu \mathrm{m}^{2}$ line could no longer be created with the experiment set, and $6450 \mu \mathrm{m}^{2}$ and $3200 \mu \mathrm{m}^{2}$ have shifted to higher power regions with lower effective absorptivities. The new process map also has much more consistent effective absorptivities throughout processing space. The outlier is the $800 \mu \mathrm{m}^{2}$ case where the minimum spot size results in a higher normalized spot size and decreased melt pool areas. The "good" processing space is now only bound by the W/FL threshold for bead-up, and the minimum depth required to melt through the layer thickness. In this plot, W/FL is based on point source values from simulations. The only spot size requirements for this initial change in "good" processing space is to set the normalized spot size to a value of one. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-140} \end{center} Figure 6-8: Processing space for 316L in the ProX $200 \mathrm{~L}-\mathrm{PBF}$ process for nominal spot size (left), and variable spot size with original bead-up limit (right) Where Figure 6-8 showed how spot size increases processing space when it is used to eliminate keyholing, it does not show how spot size can be used to further expand processing space by preventing the occurrence of bead-up melt pools. Figure 6-9 shows power-velocity space with a "good" processing space that has been expanded even further by increasing spot size to eliminate\\ bead-up in some melt pools. It is important to note that the necessary spot size may be different for each power-velocity point in the specified processing space, and will still need to be balanced with hatch spacing and the fixed layer thickness to deposit successfully. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-141} \end{center} Figure 6-9: Expanded Processing space for 316L in the ProX $200 \mathrm{~L}-\mathrm{PBF}$ process where increased spot size can eliminate keyholing and a portion of the bead-up region \subsection*{6.4 Discussion} This chapter discusses the application of the findings earlier in the thesis that enable a user to expand the "good" processing space through specific spot size adjustments. Process maps were developed for three stainless steel alloys in the 3D Systems ProX 200 L-PBF process. The results showed a very small range where keyholing melt pools were not present and the melt pools were deep enough to melt through the layer thickness. Additionally, fitted simulation results required different effective absorptivity values for each line of constant area. Differences in effective absorptivity were due to increases in melt pool area in keyholing melt pools, and decreased area in small melt pools with larger normalized spot sizes. For 316L stainless steel, a selection of keyholing points were chosen for expanded focus experiments where specific spot sizes were\\ chosen to eliminate keyholing based on the normalized spot size threshold suggested in Chapter 4:. In different L-PBF processes, the "good" processing window would differ based on the nominal spot size. For example, the EOS M 290 process would have a larger window at nominal parameters due to a larger spot size, but would be shifted to higher powers and lower velocities. The suggested changes in spot size were successful in eliminating keyhole mode melting, and the new melt pool areas could be used to form an updated process map. Methods to expand processing space with increased spot size are presented, and the 316L experiments are used as a case study. An original process map was adjusted to account for spot size increases that eliminated keyholing melt pools, and more consistent effective absorptivities were observed. New limits on the usable processing space were also formed to account for the ability mitigate the presence beadup melt pools by further increasing spot size. In general, the proposed method sets up guidelines for maximizing the "good" processing space through spot size modification. \section*{Chapter 7: $\quad$ Conclusions} \subsection*{7.1 Conclusions} Additive manufacturing processes have the capability to transform the manufacturing industry by providing increased flexibility in part geometry and complexity. To take full advantage of the capabilities of AM, operators need to be able to produce parts throughout processing space while avoiding porosity and flaw formation. Work in this thesis analyzes the effects of three different process parameters, power, velocity, and spot size, on melt pool geometry. Ti-6Al-4V is process mapped in power-velocity space for the electron beam wire feed and laser powder feed processes. Relationships are also drawn between melt pool geometry and resulting prior beta grain width in the two processes. The process maps and microstructure relationships give insights into where melt pool sizes and Ti-6Al-4V beta grain sizes can be found throughout processing space. Beam spot size has also been identified as having a major influence on melt pool geometry. Melt pool dimensions were normalized by dimensions generated by point heat source simulations, and spot size was normalized by the point heat source melt pool width. It was found that when normalized melt pool dimensions are plotted against normalized spot size, changes in melt pool dimensions grouped together based on the point source length to depth aspect ratio. These normalizations were used to describe how different melt pool dimensions changed with increasing spot size and compare against experimental measurements. It was also shown that experimental melt pool dimensions can be used to estimate how spot size changes with a focusing parameter in additive manufacturing processes; this is useful as direct-diameter measurements can often be challenging to perform. The influence of spot size on the formation of keyhole mode melting and bead-up melt pools was determined; both of these melt pool morphologies can be a major source of porosity and flaws in additively manufactured parts. Increases in spot size have been shown to eliminate the presence of keyholing, and a normalized spot size threshold is proposed to prevent keyholing in five alloys. Width to full length ratio has been identified by previous authors as an indicator of bead-up melt pools. Changes in the ratio with normalized spot size have been presented and a suggested threshold to avoid bead-up melt pools is verified. Analysis of the effects of spot size on Ti-6Al-4V beta microstructure is also presented in this thesis. Normalized cooling rates are plotted against normalized spot sizes for different length to width ratios, and beam energy distributions. Contrary to expectations, experimental measurements for prior beta grain width did not have a relationship with spot size. This suggests that relationships developed between melt pool geometry and prior beta grain width in Ti-6Al-4V will only hold true for consistent melt pool shapes. The information presented is combined to suggest a robust method for increasing the usable processing space by expanding the limits for the onset of keyholing and bead-up melt pools. The method is applied to 316L stainless steel in the 3D Systems ProX 200 L-PBF process, and is able to drastically increase the usable processing space by avoiding keyholing and bead-up. In addition to expanding processing space, the method results in more consistent effective absorptivities that relate simulation results to experimental measurements. The proposed method to expand processing space can be used to reliably produce parts using a larger range of a process's capabilities. \subsection*{7.2 Implications} Where previous work has named the general effects of spot size on melt pool geometry, flaws, and microstructure, this research found detailed relationships between spot size and various process outcomes. Some of the important implications of this research is presented below. \begin{itemize} \item Expansion of the Ti-6Al-4V electron beam wire feed process map, and verification of geometry-microstructure relationships. This work enables machine operators greater knowledge of how melt pool dimensions change throughout processing space, which allows for faster development of parameters and shorter qualification times. Relationships developed by Gockel [81] were verified at higher powers and the developed body of knowledge allows for easier development of location specific microstructure in the electron beam wire feed process. Monitoring melt pool width opens up real time indirect control of microstructure for the electron beam wire feed process. \item Process mapping Ti-6Al-4V in the LENS laser powder feed process and development of relationships between geometry and microstructure. Similar to the work in the electron beam wire feed process, this work gives insights into the geometry produced by powervelocity combinations throughout processing space. Relationships between melt pool full length, velocity, and prior beta grain width aide in the development of location specific microstructure. Monitoring melt pool full length and velocity opens up real time indirect control of microstructure for the laser powder feed process. \item Development of relationships between beam spot size and the resulting melt pool dimensions across any alloy and process Relationships between spot size and melt pool dimensions helps in the designing of process parameters when normalized spot size is not\\ consistent. Modification of spot size can be used to create melt pools of preferable melt pool geometry that can increase build rate or decrease porosity. \item Identification of methods to prevent keyhole mode melting through spot size increases. Increases to beam spot size have been shown to be capable of eliminating keyhole mode melting. Normalized spot size thresholds have been proposed to reliably avoid keyholing melt pools in five different alloys. These findings give guidelines to avoid keyholing that can introduce variability and porosity into an additively manufactured part. \item Identification of methods to prevent bead-up melt pools through spot size increases. Similar to keyholing, findings showed that bead-up melt pools can be avoiding through increases in spot size. Width to full length thresholds (for bead-up) are verified, and changes in the ratio with normalized spot size are presented. The findings related to bead-up melt pools allow an operator to methodically avoid lack-of-fusion issues associated with bead up meltpools. \item Identifying effects of spot size on Ti-6Al-4V prior beta grain width. Simulation cooling rates and experimental prior beta grain widths were compared against normalized spot size. While cooling rates had large increases at large spot sizes, no relation was observed between prior beta grain width and spot size. This suggests that when relationships between Ti-6Al-4V microstructure and melt pool geometry are being used, the trends only hold true for consistent cross-sectional aspect ratios. \item Expansion of usable processing space through spot size modification. Findings from this dissertation are combined to develop a method for significantly expanding the usable processing space. Spot size is modified according to thresholds for keyholing and bead-up melt pools to expand the usable processing space, and the method is demonstrated for 316L\\ stainless steel in the ProX200 L-PBF process. This method can be used to expand the usable processing space with minimal porosity in the part. This allows operators to take advantage of build rate, microstructural, or other qualities present in different regions of processing space. \end{itemize} \subsection*{7.3 Future Work} A primary theme of this dissertation is the relation of process parameters to melt pool geometry and other process outcomes. Detailed knowledge of the effects of process parameters help to prevent the formation of porosity, and can be used to tailor microstructure or other preferable outcomes. While this research makes significant progress in understanding the effects of power, velocity, and spot size, there is still room for more progress. Suggested areas for future work are listed below. \begin{itemize} \item Effects of other process parameters. While the effects of some primary process parameters have been explored in this work, the effects of other important variables (material feed rate, hatch spacing, etc.) on melt pool geometry, microstructure, etc. have not been thoroughly explored. \item Effects in different deposition geometries. Results presented for process maps and spot size effects in this dissertation were based on models and experiments in steady state melt pools in bulk material. Analysis determining if these trends hold for other deposition geometries should be completed before the findings are applied in regions of parts with different geometries. \item Verification in multi-layer depositions. Verification of many findings in this research was limited to single track depositions with no added material. Further analysis is required to\\ determine if the findings are affected by added material either in the form of a powder layer, or fed material. \item Thresholds in other alloys. Thresholds found for keyholing and bead-up melt pools likely vary based on the alloy system being used. While many of the alloys used in this research yielded similar results, material properties do have an influence on the thresholds found for different materials. \end{itemize} \section*{References} [1] I. Gibson, D. Rosen and B. Stucker, Additive Manufacturing Technologies, Second ed., Springer, 2015. [2] Wohlers Associates, "Wohlers Report 2013," Fort Collins, 2013. [3] Arcam AB, "Metal Powders," [Online]. Available: \href{http://www.arcam.com/technology/products/metal-powders/}{http://www.arcam.com/technology/products/metal-powders/}. [Accessed 12 Frebruary 2016]. [4] EOS GmbH, "Materials for Metal Manufacturing," [Online]. Available: \href{http://www.eos.info/material-m}{http://www.eos.info/material-m}. [Accessed 12 February 2016]. [5] K. M. Taminger and R. A. Hafley, "Electron Beam Freeform Fabrication for Cost Effective Near-Net Shape Manufacturing," in NATO/RTOAVT-139 Specialist' Meeting on Cost Effective Manufacture vie Net Shape Processing, Amsterdam, Netherlands, 2006. [6] C. Atwood, M. Griffith, L. Harwell, E. Schlienger, M. Ensz, J. Smugeresky, T. Romero, D. Greene and D. Reckaway, "Laser Engineered Net Shaping (LENS): A Tool for Direct Fabrication of Metal Parts," Sandia National Laboratories, Albuquerque, NM, 1998. [7] R. Grylls, "Laser Engineered Net Shapes," Advanced Materials \& Processes, vol. 161, no. 1, pp. 45-46, 2003.\\ Performance Tooling Combining High Speed Milling and Laser Cladding," in 23rd Annual Congress on Applications of Lasers and Electro-Optics, 2004. [9] Sciaky Inc., "ELECTRON BEAM ADDITIVE MANUFACTURING (EBAM ${ }^{\mathrm{TM}}$ )," [Online]. Available: \href{http://www.sciaky.com/additive-manufacturing/wire-am-vs-powderam}{http://www.sciaky.com/additive-manufacturing/wire-am-vs-powderam}. [Accessed 12 February 2016]. [10] Optomec, "LENS Materials," [Online]. Available: \href{http://www.optomec.com/3d-printedmetals/lens-materials/}{http://www.optomec.com/3d-printedmetals/lens-materials/}. [Accessed 12 February 2016]. [11] F. G. Arcella and F. H. Froes, "Producing Titanium Aerospace Components from Powder Using Laser Forming," JOM, pp. 28-30, May 2000. [12] L. Robinson and J. Scott, "Layers of Complexity: Making the Promises Possible for Additive Manufacturing of Metals," JOM, vol. 66, no. 11, pp. 2194-2207, 2014. [13] M. Seifi, A. Salem, J. Beuth, O. Harrysson and J. Lewandowski, "Overview of Materials Qualification Needs for Metal Additive Manufacturing," JOM, vol. 68, no. 3, pp. 747-764, 2016. [14] J. Beuth, J. Lewandowski, O. Harrysson, B. Stucker and N. Klingbeil, "Rapid Qualification Methods for Powder Bed Direct Metal AM Processes," in Solid Freeform Fabrication Symposium, Austin, TX, 2014. [15] S. Tammas-Williams and I. Todd, "Design for Additive Manufacturing with Site-Specific Properties in Metals and Alloys," Scripta Materialia, 2016. [16] K. P. Cooper and S. G. Lambrakos, "Thermal Modeling of Direct Digital Melt-Deposition Processes," Journal of Materials Engineering and Performance, vol. 20, no. 1, pp. 48-56, 2010. [17] J. Beuth and N. Klingbeil, "The Role of Process Variables in Laser-Based Direct Metal Solid Freeform Fabrication," JOM, pp. 36-39, 2001. [18] N. W. Klingbeil, J. W. Zinn and J. L. Beuth, "Measurement of Residual Stresses in Parts Created by Shape Deposition Manufacturing," in Solid Freeform Fabrication Symposium, Austin, TX, 1997. [19] N. W. Klingbeil, J. L. Beuth, R. K. Chin and C. H. Amon, "Residual Stress-Induced Warping in Direct Metal Solid Freeform Fabrication," International Journal of Mechanical Sciences, vol. 44, pp. 57-77, 2002. [20] N. W. Klingbeil, J. L. Beuth, R. K. Chin and C. H. Amon, "Measurement and Modeling of Residual Stress-Induced Warping in Direct Metal Deposition Processes," in Solid Freeform Fabrication Symposium, Austin, TX, 1998. [21] A. Vasinonta, J. Beuth and M. Griffith, "Process Maps for Predicting Residual Stress and Melt Pool Size in the Laser-Based Fabrication of Thin-Walled Structures," Journal of Manufacturing Science and Engineering, vol. 129, no. 1, pp. 101-109, 2007. [22] A. Vasinonta, J. Beuth and M. Griffith, "A Process Map for Consistent Build Conditions in the Solid Freeform Fabrication of Thin-Walled Structures," ASME Journal of Manufacturing Science and Engineering, vol. 123, pp. 615-622, 2001. [23] J. Fox, "Transient Melt Pool Response in Additive Manufacturing of Ti-6Al-4V (Doctoral dissertation)," Carnegie Mellon University, Pittsburgh, PA, 2015. [24] E. Soylemez, J. Beuth and K. Taminger, "Controlling Melt Pool Dimensions Over a Wide Range of Material Deposition Rates in Electron Beam Additive Manufacturing," in Solid Freeform Fabrication Symposium, Austin, TX, 2010. [25] C. Montgomery, J. Beuth, L. Sheridan and N. Klingbeil, "Process Mapping of Inconel 625 in Laser Powder Bed Additive Manufacturing," SFF Symposium Proceedings, pp. 11951204, August 2015. [26] A. Birnbaum, P. Aggarangsi and J. Beuth, "Process Scaling and Transient Melt Pool Size Control in Laser-Based Additive Manufacturing Processes," in Solid Freeform Fabrication Conference, Austin, TX, 2003. [27] J. Beuth, J. Fox, J. Gockel, C. Montgomery, R. Yang, H. Qiao, E. Soylemez, P. Reeseewatt, A. Anvari, S. Narra and N. Klingbeil, "Process Mapping for Qualification Across Multiple Direct Metal Additive Manufacturing Processes," in Solid Freeform Fabrication Symposium, Austin, TX, 2013.\\ Processing of Ti-6Al-4V," Journal of Materials Processing Technology, vol. 13, pp. 330339, 2003. [29] P. Kobryn, E. Moore and S. Semiatin, "The Effect of Laser Power and Traverse Speed on Microstructure, Porosity and Build Height in Laser Deposited Ti-6Al-4V," Scripta Materialia, vol. 43, pp. 299-305, 2000. [30] N. Aboulkhair, N. Everitt, I. Ashcroft and C. Tuck, "Reduscing Porosity in AlSi10Mg Parts Processed by Selectove Laser Melting," Additive Manufacturing, vol. 1, no. 4, pp. 77-86, 2014. [31] H. Gong, K. Rafi, H. Gu, T. Starr and B. Stucker, "Analysis of Defect Generation in Ti6Al-4V Parts Made Using Powder Bed Fusion Additive Manufacturing Processes," Additive Manufacturing, vol. 1, no. 4, pp. 87-98, 2014. [32] Y.-F. Tzeng, "Effects of Operating Parameter on Surface Quality for the Pulsed Laser Welding of Zinc-Coated Steel," Journal of Materials Processing Technology, vol. 100, pp. 163-170, 2000. [33] A. Safdar, H. Z. He, L.-Y. Wei, A. Snis and L. E. Chavez de Paz, "Effect of process parameters settings and thickness on surface roughness of EBM produced Ti-6Al-4V," Rapid Prototyping Journal, vol. 18, no. 5, pp. 401-408, 2012.\\ $[34]$ D. B. Hann, J. Iammi and J. Folkes, "A simple methodology for predicting laserweld properties from material and laser parameters," Journal of Physics D: Applied Physics, 2011. [35] M. Seifi, D. Christiansen, J. Beuth, O. Harrysson and J. Lewandowski, "Process Mapping, Fracture and Fatigue Behavior of Ti-6Al-4V Produced by EBM Additive Manufacturing," in Ti-2015: The 13th World Conference on Titanium, San Diego, CA, 2015. [36] A. Okunkova, P. Peretyagin, Y. Vladimirov, M. Volosova, R. Torrecillas and S. V. Federov, "Laser-Beam Modulation to Improve Effiviency of Selective Laser Melting for Metal Powders," in Proc. SPIE, Laser Sources and Applications II, Brussels, Belgium, 2014. [37] P. Y. Peretyagin, I. V. Zhirnov, Y. G. Vladimirov, T. V. Tarasova and A. A. Okun'kova, "Track Geometry in Selective Laser Melting," Russian Engineering Research, vol. 35, no. 6, pp. 473-476, 2015. [38] T. T. Roehling, S. S. Q. Wu, S. A. Khairallah, J. D. Roehling, S. S. Soezeri, M. F. Crumb and M. J. Matthews, "Modulating Laser Intensity Profile Ellipticity for Microstructural Control During Metal Additive Manufacturing," Acta Materialia, pp. ISSN 1359-6454, 2017. [39] R. P. Mudge and R. N. Wald, "Laser Engineered Net Shaping Advances Additive Manufacturing and Repair," Welding Journal, pp. 44-48, January 2007.\\ $[40]$ D. Miller, C. Deckard and J. Williams, "Variable beam size SLS workstation and enhanced SLS model," Rapid Prototyping Journal, vol. 3, no. 1, pp. 4-11, 1997. [41] G. Bi, C. N. Sun and A. Gasser, "Study on Influential Factors for Process Monitoring and Control in Laser Aided Additive Manufactring," Journal of Materials Processing Technology, vol. 213, pp. 463-468, 2013. [42] H. E. Helmer, C. Körner and R. F. Singer, "Additive manufacturing of nickel-based superalloy Inconel 718 by selective electron beam melting: Processing window and microstructure," Journal of Materials Research, vol. 29, no. 17, pp. 1987-1996, September 2014. [43] C. A. Walsh, "Laser Welding - Literature Review," Materials Science and Metallurgy Department, University of Cambridge, 2002. [44] G. Verhaeghe, P. Hilton and TWI Ltd, "The effect of spot size and laser beam quality on welding," International Congress on Applications of Lasers \& Electro-Optics, 2005. [45] J. T. Norris, C. V. Robino, D. A. Hirschfeld and M. J. Perricone, "Effects of Laser Parameters on Porosity Formation: Investigating Millimeter Scale Continuous Wave Nd: YAG Laser Welds," Welding Journal, pp. 198-203, October 2011. [46] J. Zhou and H.-L. Tsai, "Porosity Formation and Prevention in Pulsed Laser Welding," Journal of Heat Transfer, vol. 129, no. 8, pp. 1014-1024, August 2007. [47] W. E. King, H. D. Barth, V. M. Castillo, G. F. Gallegos, J. W. Gibbs, D. E. Hahn, C. Kamath and A. M. Rubenchik, "Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing," Journal of Materials Processing Technology, vol. 214, no. 12, pp. 2915-2925, December 2014. [48] R. Dinwiddie, R. Dehoff, P. Lloyd, L. Lowe and J. Ulrich, "Thermographic In-Situ Process Monitoring of the Electon Beam Melting Technology used in Additive Manufacturing," in Proceedings of SPIE, San Francisco, CA, 2013. [49] M. L. Griffith, W. H. Hofmeister, G. A. Knorovsky, D. O. MacCallum, E. M. Schlienger and J. E. Smugersky, "Direct Laser Additive Fabrication System with Image Feedback Control". United States Patent 6,459,951 B1, 1 Oct. 2002. [50] W. Hofmeister and M. Griffith, "Solidification in Direct Metal Deposition by LENS Processing," JOM, vol. 53, no. 9, pp. 30-34, 2001. [51] D. Hu and R. Kovacevic, "Sensing, Modelling and Control for Laser-Based Additive Manufacturing," International Journal of Machine Tools and Manufacture, vol. 43, no. 1, pp. 51-60, 2003. [52] L. Song and J. Mazumder, "Feedback Control of Melt Pool Termperature During Laser Cladding Process," IEEE Transactions on Control Systems Technology, vol. 19, no. 6, pp. 1349-1356, 2011. [53] L. Song, V. Bagavath-Singh, B. Dutta and J. Mazumder, "Control of Melt Pool Temperature and Deposition Height During Direct Metal Deposition Process," International Journal of Advanced Manufacturing Technology, vol. 58, no. 1, pp. 247-256, 2012. [54] T. Craeghs, F. Bechmann, S. Berumen and J.-P. Kruth, "Feedback Control of Layerwise Laser Melting using Optical Sensors," Physics Procedia, vol. 5, pp. 505-514, 2010. [55] T. Craeghs, S. Clijsters, E. Yasa and J.-P. Kruth, "Online Quality Control of Selective Laser Melting," in Solid Freeform Fabrication, Austin, TX, 2011. [56] J. Mireles, S. Ridwan, P. Morton, A. Hinojos and R. Wicker, "Analysis and Correction of Defects within Parts Fabricated using Powder Bed Fusion Technology," Surface Topography: Metrology and Properties, vol. 3, no. 3, 2015. [57] B. Fisher, "Thermal Imaging and Feedback Control of Ti64 EBM (Internal Report)," Carnegie Mellon University, Pittsburgh, PA, 2016. [58] J. Jacobsmuhlen, S. Kleszczynski, G. Witt and D. Merhof, "Detection of Elevated Regions in Surface Images from Laser Beam Melting Processes," in IECON, Yokohama, 2015. [59] L. Scime, "Anomaly Detection and Classification in a Laser Powder Bed Additive Manufacturing Process using a Trained Computer Vision Algorithm (Internal Report)," Carnegie Mellon University, Pittsburgh, PA, 2017. [60] G. Tapia and A. Elwany, "A Review on Process Monitoring and Control in Metal-Based Additive Mnaufacturing," Journal of Manufacturing Science and Engineering, vol. 136, pp. 060801-1 - 060801-10, 2014. [61] E. Akman, A. Demir, T. Canel and T. Sinmazcelik, "Laser Welding of Ti6Al4V titanium alloys," Journal of Materials Processing Technology, vol. 209, no. 8, pp. 3705-3713, April 2009. [62] J. D. Madison and L. K. Aagesen, "Quantitative characterization of porosity in laser welds of stainless steel," Scripta Materialia, vol. 67, no. 9, pp. 783-786, November 2012. [63] R. Rai, J. W. Elmer, T. A. Palmer and T. DebRoy, "Heat transfer and fluid flow during keyhole mode laser welding of tantalum, Ti-6Al-4V, 304L stainless steel and vanadium," Journal of Physics D: Applied Physics, vol. 40, no. 18, pp. 5753-5766, August 2007. [64] P. S. Wei and T. C. Chao, "The Effects of Entrainment on Pore Shape in Keyhole Mode Welding," Journal of Heat Transfer, vol. 137, August 2015. [65] M. Pastor, H. Zhao, R. P. Martukanitz and T. Debroy, "Porosity, Underfill and Magnesium Loss during Contiunous Wave Nd:YAG Laser Welding of Thin Plates of Aluminum Alloys 5182 and 5754," Welding Research Supplement, pp. 207s-216s, 1999. [66] W. Tan and Y. Shin, "Analysis of Multi-Phase Interaction and Its Effects on Keyhole Dynamics with a Multi-Physics Numerical Model," Journal of Physics D: Applied Physics, vol. 47, 2014. [67] W. Tan, N. Bailey and Y. Shin, "Investigation of Keyhole Plume and Molten Pool Based on a Three-Dimensional Dynamic Model with Sharp Interface Formulation," Journal of Physics D: Applied Physics, vol. 46, 2013. [68] F. Verhaeghe, T. Craeghs, J. Heulens and L. Pandelaers, "A pragmatic model for selective laser melting with evaporation," Acta Materialia, vol. 57, no. 20, pp. 6006-6012, December 2009. [69] R. Cunningham, S. Narra, C. Montgomery, J. Beuth and A. Rollett, "Synchrotron-Based Xray Microtomography Characterization of the Effect of Processing Variables on Porosity Formation in Laser Powder-Bed Fusion Additive Manufacturing of Ti-6Al-4V," JOM, Vols. DOI: 10.1007/s11837-016-2234-, 2017. [70] R. Cunningham, S. Narra, T. Ozturk, J. Beuth and A. Rollet, "Evaluating the Effect of Processing Parameters on Porosity in Electron Beam Melted Ti-6Al-4V via Synchrotron X-ray Microtomography," JOM, vol. 68, no. 3, pp. 765-771, 2016. [71] M. Tang, P. C. Pistorius and J. L. Beuth, "Prediction of Lack-of-Fusion Porosity for Powder Bed Fusion," Additive Manufacturing, vol. 14, pp. 39-48, 2017. [72] K. C. Mills, B. J. Keene, R. F. Brooks and A. Shirali, "Marangoni Effects in Welding," Philosophical Transactions of the Royal Society A, vol. 356, no. 1739, pp. 911-925, 1998. [73] V. A. Nemchinsky, "The Role of Thermocapillary Instability in Heat Transfer in a Liquid Metal Pool," International Journal of Heat and Mass Transfer, vol. 40, no. 4, pp. 881-891, 1997. [74] U. Gratzke, P. D. Kapadia, J. Dowden, J. Kroos and G. Simon, "Theoretical Approach to the Humping Phenomenon in Welding Processes," Journal of Physics D: Applied Physics, vol. 25, no. 11, pp. 1640-1647, 1992. [75] I. Yadroitsev, A. Gusarov, I. Yadroitsava and I. Smurov, "Single Track Formation in Selective Laser Melting of Metal Powders," Journal of Materials Processing Technology, vol. 210, pp. 1624-1631, 2010. [76] S. Kou and Y. H. Wang, "Weld Pool Convection and Its Effect," Welding Research Supplement, pp. 63s-70s, March 1986. [77] P. A. Kobryn and S. L. Semiatin, "The Laser Additive Manufacture of Ti-6Al-4V," JOM, pp. 40-42, 2001. [78] S. Bontha and N. Klingbeil, "Thermal Process Maps for Controlling Mictostructure in Laser-Based Solid Freeform Fabrication," in Solid Freeform Fabrication Symposium, Austin, TX, 2003. [79] S. Bontha, C. Brown, D. Gaddam, N. W. Klingbeil, P. A. Kobryn, H. L. Fraser and J. W. Sears, "Effects of Process Variables and Size Scale on Solidification Microstructure in Laser-Based Solid Freeform Fabrication of Ti-6Al-4V," in Solid Freeform Fabrication Symposium, Austin, TX, 2004. [80] S. Bontha, N. Klingbeil, P. Kobryn and H. L. Fraser, "Effects of Process Variables and Size Scale on Solidification Microstructure in Beam-Based Fabrication of Bulky 3D Structures," Materials Science and Engineering, vol. 513, pp. 311-318, 2009. [81] J. Gockel, Integrated Control of Solidification Microstructure and Melt Pool Dimensions in Additive Manufacturing of Ti-6Al-4V (Doctoral dissertation), PhD Thesis: Carnegie Mellon University, 2014. [82] J. Gockel, J. Fox, J. Beuth and R. Hafley, "Integrated Melt Pool and Microstructure Control for Ti-6Al-4V Thin Wall Additive Manufacturing," Materials Science and Technology, vol. 31, no. 8, pp. 912-916, 2015. [83] J. Gockel, J. Beuth and K. Taminger, "Integrated Control of Solidification Microstructure and Melt Pool Dimension in Electron Beam Wire Feed Additive Manufacturing of Ti-6Al4V," Additive Manufacturing, vol. 1, pp. 119-126, 2014. [84] W. Tan and Y. Shin, "Multi-Scale Modeling of Solidification and Microstructure Developement in Laser Keyhole Welding Process for Austenitic Stainless Steel," Computational Materials Science, vol. 98, pp. 446-458, 2015. [85] R. C. Dykhuizen and D. Dobranich, "Cooling Rates in the LENS Process," Sandia National Laboratories, Albuquerque, NM, 1998. [86] S. M. Kelly, "Thermal and Microstructure Modeling of Metal Deposition Processes with Application to Ti-6Al-4V," Virginia Polytechnic Institute and State University, PhD Thesis, 2004. [87] J. Lin, Y. Lv, Y. Liu, Z. Sun, K. Wang, Z. Li, W. Yixiong and B. Xu, "Microstructural Evolutionand Mechanical Property of Ti-6Al-4V Wall Deposited by Continuous Plasma Arc Additive Manufacturing Without Post Heat Treatment," Journal of the Mechanical Behavior of Biomedical Materials, vol. 69, pp. 19-29, 2017. [88] A. A. Antonysamy, "Microstructure, Texture, and Mechanical Property Evolution during Additive Manufacturing of Ti6Al4V Alloy for Aerospace Applications," University of Manchester, PhD Thesis, 2012. [89] S. P. Narra, R. Cunningham, D. Christiansen, J. Beuth and A. D. Rollett, "Toward Enabling Spatial Control of Ti-6Al-4V Solidification Microstructure in the Electron Beam Melting Process," in SFF Symposium, Austin, TX, 2015. [90] L. E. Murr, E. V. Esquivel, S. A. Quinones, S. M. Gaytan, M. I. Lopez, E. Y. Martinez, F. Medina, D. H. Hernandez, E. Martinez, J. L. Martinez, S. W. Stafford, D. K. Brown, T. Hoppe, W. Meyers, U. Lindhe and R. B. Wicker, "Microstructures and Mechanical Properties of Electron Beam-Rapid Manufactured Ti-6Al-4V Biomedical Prototypes Compared to Wrought Ti-6Al-4V," Materials Characterization, vol. 60, pp. 96-105, 2009. [91] D. Rosenthal, "The Theory of Moving Sources of Heat and Its Application to Metal Treatments," Transactions of the A.S.M.E., pp. 849-866, 1946. [92] N. Christensen , V. Davies and K. Gjermundsen, "The Distribution of Temperature in Arc Welding," British Welding Journal, vol. 12, no. 2, pp. 54-75, 1965. [93] T. W. Eagar and N. S. Tsai, "Temperature Fields Produced by Traveling Distributed Heat Sources," Welding Research Supplement, pp. 346-355, 1983. [94] R. C. Dykhuizen and D. Dobranich, "Analytical Thermal Models for the LENS Process," Sandia National Laboratories, Albuquerque, NM, 1998. [95] D. Dobranich and R. C. Dykhuizen, "Scoping Thermal Calculations of the LENS Process," Sandia National Laboratories, Albuquerque, NM, 1998. [96] L. Wang, S. Felicelli, Y. Gooroochurn, P. T. Want and M. F. Horstemeyer, "Optimization of the LENS Process for Steady Molten Pool Size," Materials Sciance and Engineering, vol. 474, pp. 148-156, 2008. [97] P. Michaleris, "Modeling Metal Deposition in Heat Transfer Analyses of Additive Manufacturing Processes," Finitie Elements in Analysis and Design, vol. 86, pp. 51-60, 2014. [98] E. Denlinger, J. Heigel, P. Michaleris and T. Palmer, "Effect of Inter-Layer Dwell Time on Distortion and Residual Stress in Additive Manifacturing of Titanium and Nickel Alloys," Journal of Materials Processing Technology, vol. 215, pp. 123-131, 2015. [99] W. E. King, A. T. Anderson, R. M. Ferencz, N. E. Hodge, C. Kamath, S. A. Khairallah and A. M. Rubenchik, "Laser Powder Bed Fusion Additive Manufacturing of Mateal; Physica, Computational, and Materials Challenges," Applied Physics Reviews, vol. 2, no. 4, 2015. [100] S. Khairallah, A. Anderson, A. Rubenchik and W. King, "Laser Powder-Bed Fusion Additive Manufacturing: Physics of Complex Melt Flow and Formation Mechanisms of Pores, Splatter, and Denudation Zones," Acta Materialia, vol. 108, pp. 36-45, 2016. [101] P. Nie, O. A. Ojo and Z. Li, "Numerical Modeling of Microstructure Evolution During Laser Additive Manufacturing of a Nickel-Based Superalloy," Acta Materialia, vol. 77, pp. 85-95, 2014. [102] A. Zinoviev, O. Zinovieva, V. Ploshikhin, V. Romanova and R. Balokhonov, "Evolution of Grain Structure During Laser Additive Manufacturing. Simulation by a Cellular Automata Method," Materials and Design, vol. 106, pp. 321-329, 2016. [103] D. Clymer, J. Beuth and J. Cagan, "Additive Manufacturing Process Design," in Solid Freeform Fabrication Symposium, Austin, TX, 2016. [104] M. Donachie, Titanium: A Technical Guide, ASM International, 2007. [105] P. W. Early and S. J. Burns, "Improved Toughness From Prior Beta Grains in Ti-6Al-4V," Scripta Metallurgica, vol. 11, pp. 867-869, 1977. [106] R. Filip, K. Kubiak, W. Ziaja and J. Sieniawski, "The Effect of Microstructure on the Mechanical Properties of Two-Phase Titanium Alloys," Journal of Materials Processing Technology, vol. 133, no. 1-2, pp. 84-89, 2003. [107] C. Leyens and M. Peters, Titanium and Titanium Alloys: Fundamentals and Applications, Beerfelden, Germany: Wiley-VCH Verlag GmbH \& Co. KGaA, 2005. [108] Y. Arata and I. Miyamoto, "Laser Welding," Technocrat, vol. 11, no. 5, pp. 33-42, 1978. [109] M. Boivineau, C. Cagran, D. Doytier, V. Eyraud, M. Nadal, B. Wilthan and G. Pottlacher, "Thermophysical Properties of Solid and Liquid Ti-6Al-4V (TA6V) Alloy," International Journal of Thermophysics, vol. 27, no. 2, pp. 507-529, 2006. [110] J. Li, L. Johnson and W. Rhim, "Thermal Expansion of Liquid Ti-6Al-4V Measure by Electrostatic Levitation," Applied Physics Letters, vol. 89, 2006. [111] Dassault Systems, Abaqus Theory Guide: 2.11.1 Uncoupled heat transfer analysis, Simulia - Abaqus 6.14, 2014. [112] ASTM Standard E112-13, "Standard Test Methods for Determining Average Grain Size," ASTM International, West Conshocken, PA, 2013. [113] D. Wright, "Beamwidths of a Diffracted Laser using Four Proposed Methods," Optical and Quantum Electronics, vol. 24, pp. S1129-S1135, 1992. [114] S. Goodrich, SI1866\_11AUG16\_200w.foc, Pittsburgh, PA: EOS GmbH, 2016. [115] S. Goodrigh, SI1866\_11AUG16\_40w.foc, Pittsburgh, PA: EOS GmbH, 2016. [116] S. Narra, "Melt pool area of select power- velocity combinations in IN718 and Ti-6Al-4V," Carnegie mellon University. Internal Report, Pittsburgh, PA, 2017. [117] R. Egerton, "Chapter 2: Electron Optics," in Physical Principles of Electron Microscopy: An Introduction to TEM, SEM, and AEM, Springer, 2005, pp. 27-55. [118] D. Weill, J. Rice, M. Shaffer and J. Donovan, "Chapter Four: The Electron Beam and Electron Optics," in Electron Beam MicroAnalysis Theory and Application, Eugene, OR, University of Oregon Center for Advanced Materials Characterization in Oregon (CAMCOR), 2013, pp. 4-1 to 4-30. [119] Neue Materialien Furth GMBH, "Selective Electron Beam Melting (SEBM) of Metals," [Online]. Available: \href{http://www.nmfgmbh.de}{http://www.nmfgmbh.de}. [Accessed 9 September 2015]. [120] J. W. Elmer, W. H. Giedt and T. W. Eagar, "The Transition from Shallow to Deep Penetration during Electron Beam Welding," Welding Research, pp. 167-s - 176-s, 1990. [121] L. Scime, "Bulk Porosity," MATLAB Script, Carnegie Mellon, 2016. [122] S. Narra, "Melt pool areas and settings in the Arcam S12 process," Internal Report Carnegie Mellon University, Pittsburgh, PA, 2016. [123] B. Fisher, "Determination of cooling rate from finite element simulations," Internal MATLAB Script. Carnegie Mellon University, Pittsburgh, PA, 2017. [124] J. R. Chukkan, M. Vasudevan, S. Muthukumaran, R. R. Kumar and N. Chandrasekhar, "Simulation of Laser Butt Welding of AISI 316L Stainless Steel Sheet Using Various Heat Sources and Experimental Validation," Journal of Materials Processing Technology, vol. 219, pp. 48-59, 2015. [125] Y. S. Touloukian and C. Y. Ho, "Thermophysical Properties of Selected Aerospace Materials, Part II. Thermophysical Properties of Seven Materials," CINDAS-Purdue University, West Lafayette, IN, 1977. [126] R. H. Bogaard, P. D. Desai, H. H. Li and C. Y. Ho, "Thermophysical Properties of Stainless Steels," Thermochimica Acta, vol. 218, pp. 373-393, 1993. [127] J. W. Elmer, W. H. Giedt and T. W. Eagar, "The Transition from Shallow to Deep Penetration during Electron Beam Welding," Welding Research, pp. 167-s to 176-s, 1990. \section*{Appendix 1: Polishing and Etching Procedures} \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{Ti-6Al-4V Polishing and Etching} \\ \hline \multirow{5}{*}{\includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-168(1)} } & Surface & Abrasive/Size & Load (Ibs) & \begin{tabular}{c} Base Speed \\ $($ rpm) and \\ direction \\ \end{tabular} & \begin{tabular}{c} Time \\ (min:sec) \\ \end{tabular} \\ \hline & Carbimet Disks & 320 Grit SiC water cooled & 6 & $240-300>>$ & Until Plane \\ \hline & UltraPol Cloth & \begin{tabular}{c} $9 \mu \mathrm{m}$ MetaDi Diamond \\ Suspension \\ \end{tabular} & 6 & $120-150><$ & 10:00 \\ \hline & Microcloth & \begin{tabular}{c} $0.05 \mu \mathrm{m}$ Activated \\ MasterMet Colloidal Silica \\ \end{tabular} & 6 & $120-150><$ & 10:00 \\ \hline & \begin{tabular}{l} >> denotes com \\ $><$ denotes cont \\ \end{tabular} & \begin{tabular}{l} limentary motion between \\ a motion \\ \end{tabular} & secimen ho & r and platen & \\ \hline \multirow{6}{*}{\includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-168(3)} } & \multicolumn{2}{|c|}{Kroll's Etchant} & & & \\ \hline & Chemical & Amount & & & \\ \hline & Distilled Water & $92 \mathrm{ml}$ & & & \\ \hline & $\mathrm{HNO}_{3}$ & $6 \mathrm{ml}$ & & & \\ \hline & $\mathrm{HF}$ & $2 \mathrm{ml}$ & & & \\ \hline & Procedure: & \multicolumn{4}{|c|}{Swab or submerge samples for $15-30$ seconds} \\ \hline \end{tabular} \end{center} \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{Stainless Steel Polishing and Etching} \\ \hline \multirow{6}{*}{\includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-168} } & Surface & Abrasive/Size & Load (Ibs) & \begin{tabular}{l} Base Speed \\ $(r p m)$ and \\ direction \\ \end{tabular} & \begin{tabular}{l} Time \\ (min:sec) \\ \end{tabular} \\ \hline & Carbimet Disks & 320 Grit SiC water cooled & 6 & $300 \gg$ & Until Plane \\ \hline & UltraPol Cloth & \begin{tabular}{l} $9 \mu \mathrm{m}$ MetaDi Diamond \\ Suspension \\ \end{tabular} & 6 & $150><$ & 5:00 \\ \hline & TriDent & \begin{tabular}{l} $3 \mu \mathrm{m}$ MetaDi Diamond \\ Suspension \\ \end{tabular} & 6 & $150>>$ & 3:00 \\ \hline & MicroCloth & \begin{tabular}{c} $0.05 \mu \mathrm{m}$ Activated \\ MasterMet Colloidal Silica \\ \end{tabular} & 6 & $150><$ & 2:00 \\ \hline & \multicolumn{5}{|c|}{}\begin{tabular}{l} >> denotes complimentary motion between specimen holder and platen \\ $><$ denotes contra motion \\ \end{tabular} \\ \hline \multirow{5}{*}{\includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-168(2)} } & \multicolumn{2}{|c|}{Oxalic Acid Etchant} & & & \\ \hline & Chemical & Amount & & & \\ \hline & Distilled Water & $10 \%$ wt. & & & \\ \hline & Oxalic Acid & $90 \%$ wt. & & & \\ \hline & Procedure: & Electroetch samples at $1 \mathrm{Af}$ & r $90-120 \mathrm{~s}$ & & \\ \hline \end{tabular} \end{center} \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{IN 718 Polishing and Etching} \\ \hline \multirow{6}{*}{\includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-169} } & Surface & Abrasive/Size & Load (Ibs) & \begin{tabular}{c} Base Speed \\ $(r p m)$ and \\ direction \\ \end{tabular} & \begin{tabular}{c} Time \\ (min:sec) \\ \end{tabular} \\ \hline & Carbimet Disks & 240 Grit SiC water cooled & 6 & $300>>$ & Until Plane \\ \hline & Apex Hercules S & \begin{tabular}{c} $9 \mu \mathrm{m}$ MetaDi Diamond \\ Suspension \\ \end{tabular} & 6 & $150><$ & 5:00 \\ \hline & TriDent & \begin{tabular}{l} $3 \mu \mathrm{m}$ MetaDi Diamond \\ Suspension \\ \end{tabular} & 6 & $150>>$ & 5:00 \\ \hline & ChemoMet & \begin{tabular}{c} $0.05 \mu \mathrm{m}$ Activated \\ MasterMet Colloidal Silica \\ \end{tabular} & 6 & $150><$ & 2:00 \\ \hline & \multicolumn{5}{|c|}{}\begin{tabular}{l} >> denotes complimentary motion between specimen holder and platen \\ >< denotes contra motion \\ \end{tabular} \\ \hline \multirow{6}{*}{سِ} & \multicolumn{2}{|c|}{Waterless Kallings Etchant} & & & \\ \hline & Chemical & Amount & & & \\ \hline & Ethanol & $50 \mathrm{ml}$ & & & \\ \hline & $\mathrm{HCL}$ & $50 \mathrm{ml}$ & & & \\ \hline & Copper Chloride & $2.5 \mathrm{~g}$ & & & \\ \hline & Procedure: & \multicolumn{4}{|c|}{Swab or submerge samples for $15-30$ seconds} \\ \hline \end{tabular} \end{center} \section*{Appendix 2: Melt Pool Width Measurements from LENS Ti-6AI-4V} \section*{Experiments} \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{Laser Powder Feed Process Melt Pool Width (Constant 3 gpm Feed Rate)} \\ \hline \begin{tabular}{c} Power \\ (W) \\ \end{tabular} & \begin{tabular}{c} Velocity \\ (in/min) \\ \end{tabular} & \begin{tabular}{c} Best Guess" \\ Width from \\ Cross Section \\ (mm) \\ \end{tabular} & \begin{tabular}{c} Width \\ Uncertainty \\ from Cross \\ Section (mm) \\ \end{tabular} & \begin{tabular}{c} Average Width \\ from Above \\ (mm) \\ \end{tabular} & \begin{tabular}{c} Standard \\ Deviation \\ from above \\ (mm) \\ \end{tabular} \\ \hline 450 & 15 & 1.85 & $1.67-2.05$ & 1.98 & 0.08 \\ \hline 450 & 25 & 1.63 & $1.47-1.85$ & 1.72 & 0.06 \\ \hline 450 & 35 & 1.49 & $1.29-1.67$ & 1.57 & 0.05 \\ \hline 450 & 45 & 1.38 & $1.24-1.63$ & 1.44 & 0.07 \\ \hline 350 & 15 & 1.48 & $1.32-1.57$ & 1.45 & 0.07 \\ \hline 350 & 25 & 1.31 & $1.20-1.52$ & 1.34 & 0.05 \\ \hline 350 & 35 & 1.24 & $1.07-1.38$ & 1.22 & 0.04 \\ \hline 350 & 45 & 1.12 & $0.98-1.25$ & 1.13 & 0.04 \\ \hline 250 & 15 & 1.14 & $1.13-1.31$ & 1.12 & 0.08 \\ \hline 250 & 25 & 1.03 & $0.97-1.11$ & 1.01 & 0.04 \\ \hline 250 & 35 & 0.95 & $0.87-1.06$ & 0.94 & 0.04 \\ \hline 250 & 45 & 0.91 & $0.85-1.01$ & 0.86 & 0.03 \\ \hline \end{tabular} \end{center} \begin{center} \begin{tabular}{|l|l|l|l|l|l|} \hline 150 & 15 & 0.68 & $0.66-0.76$ & 0.66 & 0.05 \\ \hline 150 & 25 & 0.66 & $0.64-0.80$ & 0.61 & 0.03 \\ \hline 150 & 35 & 0.59 & $0.53-0.61$ & 0.54 & 0.03 \\ \hline 150 & 45 & 0.51 & $0.48-0.57$ & 0.47 & 0.02 \\ \hline \end{tabular} \end{center} \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{Laser Powder Feed Process Melt Pool Width (Scaled Feed Rate)} \\ \hline \begin{tabular}{c} Power \\ (W) \\ \end{tabular} & \begin{tabular}{c} Velocity \\ (in/min) \\ \end{tabular} & \begin{tabular}{c} West Guess" \\ Width from \\ (mm) \\ \end{tabular} & \begin{tabular}{c} Width \\ Uncertainty \\ from Cross \\ Section (mm) \\ \end{tabular} & \begin{tabular}{c} Average Width \\ from Above \\ (mm) \\ \end{tabular} & \begin{tabular}{c} Standard \\ Deviation \\ from above \\ (mm) \\ \end{tabular} \\ \hline 450 & 15 & 1.87 & $1.79-2.03$ & 1.82 & 0.05 \\ \hline 450 & 25 & 1.61 & $1.49-1.79$ & 1.60 & 0.03 \\ \hline 450 & 35 & 1.43 & $1.32-1.54$ & 1.46 & 0.03 \\ \hline 450 & 45 & 1.30 & $1.20-1.47$ & 1.36 & 0.04 \\ \hline 350 & 15 & 1.53 & $1.42-1.72$ & 1.50 & 0.05 \\ \hline 350 & 25 & 1.33 & $1.24-1.52$ & 1.36 & 0.03 \\ \hline 350 & 35 & 1.19 & $1.06-1.31$ & 1.23 & 0.05 \\ \hline 350 & 45 & 1.15 & $1.11-1.30$ & 1.13 & 0.03 \\ \hline 250 & 15 & 1.14 & $1.05-1.29$ & 1.10 & 0.03 \\ \hline 250 & 25 & 1.02 & $0.94-1.10$ & 1.00 & 0.03 \\ \hline 250 & 35 & 0.92 & $0.82-1.01$ & 0.90 & 0.02 \\ \hline 250 & 45 & 0.86 & $0.79-0.96$ & 0.86 & 0.02 \\ \hline 150 & 15 & 0.67 & $0.66-0.73$ & 0.63 & 0.02 \\ \hline 150 & 25 & 0.62 & $0.62-0.75$ & 0.58 & 0.02 \\ \hline 150 & 35 & 0.54 & $0.49-0.61$ & 0.53 & 0.02 \\ \hline 150 & 45 & 0.51 & $0.46-0.60$ & 0.50 & 0.02 \\ \hline \end{tabular} \end{center} \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{Laser Powder Feed Process Melt Pool Width (No Added Material)} \\ \hline \begin{tabular}{c} Power \\ (W) \\ \end{tabular} & \begin{tabular}{c} Velocity \\ (in/min) \\ \end{tabular} & \begin{tabular}{c} Best Guess" \\ Width from \\ Cross Section \\ (mm) \\ \end{tabular} & \begin{tabular}{c} Uncertainty \\ from Cross \\ Section (mm) \\ \end{tabular} & \begin{tabular}{c} Average Width \\ from Above \\ (mm) \\ \end{tabular} & \begin{tabular}{c} Standard \\ Deviation \\ from above \\ (mm) \\ \end{tabular} \\ \hline 450 & 15 & 1.77 & $1.65-1.98$ & 1.88 & 0.06 \\ \hline 450 & 25 & 1.56 & $1.49-1.76$ & 1.62 & 0.05 \\ \hline 450 & 35 & 1.44 & $1.31-1.59$ & 1.45 & 0.08 \\ \hline 450 & 45 & 1.33 & $1.21-1.45$ & 1.34 & 0.12 \\ \hline 350 & 15 & 1.49 & $1.35-1.67$ & 1.50 & 0.05 \\ \hline 350 & 25 & 1.33 & $1.23-1.49$ & 1.35 & 0.03 \\ \hline 350 & 35 & 1.22 & $1.13-1.33$ & 1.26 & 0.06 \\ \hline 350 & 45 & 1.15 & $1.03-1.29$ & 1.16 & 0.07 \\ \hline \end{tabular} \end{center} \begin{center} \begin{tabular}{|l|l|l|l|l|l|} \hline 250 & 15 & 1.13 & $1.00-1.24$ & 1.16 & 0.02 \\ \hline 250 & 25 & 1.01 & $0.96-1.13$ & 0.99 & 0.03 \\ \hline 250 & 35 & 0.92 & $0.84-1.04$ & 0.93 & 0.06 \\ \hline 250 & 45 & 0.87 & $0.80-0.97$ & 0.89 & 0.07 \\ \hline 150 & 15 & 0.71 & $0.59-0.84$ & 0.69 & 0.02 \\ \hline 150 & 25 & 0.67 & $0.44-0.72$ & 0.66 & 0.03 \\ \hline 150 & 35 & 0.62 & $0.42-0.79$ & 0.55 & 0.04 \\ \hline 150 & 45 & 0.57 & $0.41-0.71$ & 0.52 & 0.04 \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-172} \end{center} \begin{itemize} \item Experimental \end{itemize} Appendix Figure 1: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} \section*{L-PBF Ti-6Al-4V P=370 W V=450 mm/s L $\mathrm{L}_{0} / \mathrm{D}_{0}=5$} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-173} \end{center} $\rightarrow$ L-PBF CoCr \begin{itemize} \item Experimental \end{itemize} Appendix Figure 2: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} L-PBF Ti-6Al-4V P=270 W V=580 mm $/ \mathrm{s} \mathrm{L}_{0} / \mathrm{D}_{0}=5$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-174} $$ \begin{aligned} & \longrightarrow \text { EBWF Ti-6Al-4V } \\ & \longrightarrow \text { L-PBF CoCr } \\ & \text { - Experimental } \end{aligned} $$ Appendix Figure 3: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} \section*{L-PBF Ti-6Al-4V P=170 W V=910 mm $/ \mathrm{s}_{0} / \mathrm{D}_{0}=5$} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-175(2)} \end{center} \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-175}\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-175(1)} $\rightarrow$ L-PBF CoCr \begin{itemize} \item Experimental \end{itemize} Appendix Figure 4: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} L-PBF Ti-6Al-4V P=370 W V=1900 mm $/ \mathrm{s}_{0} / D_{0}=7.5$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-176} $\hookrightarrow$ L-PBF CoCr \begin{itemize} \item Experimental \end{itemize} Appendix Figure 5: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} L-PBF Ti-6Al-4V P=330 W V=2150 mm $/ \mathrm{s}_{0} / D_{0}=7.5$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-177} $\longrightarrow$ EBWF Ti-6Al-4V $\rightarrow$ L-PBF CoCr \begin{itemize} \item Experimental \end{itemize} Appendix Figure 6: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-178} \end{center} $\longrightarrow$ EBWF Ti-6Al-4V $\rightarrow$ L-PBF CoCr \begin{itemize} \item Experimental \end{itemize} Appendix Figure 7: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-179} \end{center} $\longrightarrow$ EBWF Ti-6Al-4V $\longrightarrow$ EB-PBF Ti-6Al-4V \begin{itemize} \item Experimental \end{itemize} Appendix Figure 8: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} \section*{EB-PBF IN718 P=670 W V $=400 \mathrm{~mm} / \mathrm{s} \mathrm{L}_{0} / \mathrm{D}_{0}=10$} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-180} \end{center} $\longrightarrow$ EBWF Ti-6Al-4V $\rightarrow$ EB-PBF Ti-6Al-4V \begin{itemize} \item Experimental \end{itemize} Appendix Figure 9: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} Electron Beam Wire Feed $P=10 \mathrm{~kW} V=45 \mathrm{in} / \mathrm{min} L_{0} / D_{0}=15$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-181(2)} \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-181}\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-181(1)} $\rightarrow$ EB-PBF Ti-6Al-4V $\sigma / \mathrm{W}_{0}$ $\rightarrow$ EBWF Ti-6Al-4V \begin{itemize} \item Experimental \end{itemize} Appendix Figure 10: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions} Electron Beam Wire Feed $P=25 \mathrm{~kW} V=30 \mathrm{in} / \mathrm{min} \mathrm{L}_{0} / \mathrm{D}_{0}=20$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_401e5513c4e18c8ab9e1g-182} $\rightarrow$ EB-PBF Ti-6Al-4V $\longrightarrow$ EBWF Ti-6Al-4V \begin{itemize} \item Experimental \end{itemize} Appendix Figure 11: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Normalized Melt Pool Dimensions } \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-183} \end{center} $\rightarrow$ EB-PBF Ti-6Al-4V $\rightarrow$ EBWF Ti-6Al-4V \begin{itemize} \item Experimental \end{itemize} Appendix Figure 12: Experimental and simulation normalized melt pool dimensions vs normalized spot size \section*{Appendix 4: Laser beam measurements in the EOS M 290 process} Laser measurements were taken by Sean Goodrich using Primes FocusMonitor equipment that uses a rotating pinhole to direct segments of the beam to a detector. The D86 laser measurement method is used to provide the beam diameter. \section*{Measurements at $40 \mathrm{~W}$ :} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-184} \end{center} Appendix Figure 13: Beam Measurements taken in the EOS M 290 process at $40 \mathrm{~W}$ Focus Radius: $41.608 \mu \mathrm{m}$ Focus radius X: $42.874 \mu \mathrm{m}$ Focus Radius Y: $40.299 \mu \mathrm{m}$ $\mathrm{K}: 0.952$ Kx: 0.917 Ky: 0.990 M2: 1.05 M2x: 1.09 M2y: 1.01 Position Z: $0.34 \mathrm{~mm}$ Position Z(X): $0.34 \mathrm{~mm}$ Position Z(Y): $0.342 \mathrm{~mm}$ Rayleigh Length: $4.794 \mathrm{~mm}$ Rayleigh Length X: $4.905 \mathrm{~mm}$ Rayleigh Length $Y: 4.68 \mathrm{~mm}$ Beam Parameter: $0.4 \mathrm{~mm} * \mathrm{mrad}$ Beam Parameter X: $0.4 \mathrm{~mm} * \mathrm{mrad}$ Beam Parameter Y: $0.3 \mathrm{~mm} * \mathrm{mrad}$ Focus Symmetry (rx/ry): 1.06 Astigmatic difference: -0.00 \section*{Measurements at $200 \mathrm{~W}$ :} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-185} \end{center} $\mu \mathrm{m}$ \section*{Appendix Figure 14: Beam Measurements taken in the EOS M 290 process at $200 \mathrm{~W}$} Focus Radius: $52.363 \mu \mathrm{m}$ Focus radius X: $55.445 \mu \mathrm{m}$ Focus Radius Y: $49.067 \mu \mathrm{m}$ K: 0.724 Kx: 0.701 Ky: 0.756 M2: 1.38 M2x: 1.43 M2y: 1.32 Position Z: $1.59 \mathrm{~mm}$ Position Z(X): $1.63 \mathrm{~mm}$ Position Z(Y): $1.56 \mathrm{~mm}$ Rayleigh Length: $5.778 \mathrm{~mm}$ Rayleigh Length X: $6.266 \mathrm{~mm}$ Rayleigh Length Y: $5.29 \mathrm{~mm}$ Beam Parameter: $0.5 \mathrm{~mm} * \mathrm{mrad}$ Beam Parameter X: $0.5 \mathrm{~mm} * \mathrm{mrad}$ Beam Parameter Y: $0.5 \mathrm{~mm} * \mathrm{mrad}$ Focus Symmetry (rx/ry): 1.13 Astigmatic difference: 0.02 \section*{Appendix 5: Cross section changes at selected power-velocity} \section*{combinations in the ProX 200 Process} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-186} \end{center} Appendix Figure 15: Melt pools deposited at nominal (left) and expanded (right) spot size at $300 \mathrm{~W}$ and $1400 \mathrm{~mm} / \mathrm{s}$ for 316L stainless steel in the ProX $200 \mathrm{~L}-\mathrm{PBF}$ process \section*{Power $=\mathbf{3 0 0} \mathrm{W} \quad$ Velocity $=2400 \mathrm{~mm} / \mathrm{s}$} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-187(1)} \end{center} Appendix Figure 16: Melt pools deposited at nominal (left) and expanded (right) spot size at $300 \mathrm{~W}$ and $2400 \mathrm{~mm} / \mathrm{s}$ for 316L stainless steel in the ProX $200 \mathrm{~L}-\mathrm{PBF}$ process \section*{Power $=215 \mathrm{~W} \quad$ Velocity $=400 \mathrm{~mm} / \mathrm{s}$} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-187} \end{center} Appendix Figure 17: Melt pools deposited at nominal (left) and expanded (right) spot size at $215 \mathrm{~W}$ and $400 \mathrm{~mm} / \mathrm{s}$ for 316L stainless steel in the ProX $200 \mathrm{~L}-\mathrm{PBF}$ process \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-188} \end{center} Appendix Figure 18: Melt pools deposited at nominal (left) and expanded (right) spot size at $130 \mathrm{~W}$ and $1400 \mathrm{~mm} / \mathrm{s}$ for 316L stainless steel in the ProX $200 \mathrm{~L}-\mathrm{PBF}$ process \section*{Appendix 6: Minimum spot sizes to avoid keyholing throughout} power-velocity space in the ProX 200 process \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-189} \end{center} Appendix Figure 19: Focus offset settings (mm) in the ProX200 L-PBF process for 316L stainless steel to prevent keyhole mode melting in melt pools where it was identified at nominal settings \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-190(1)} \end{center} $\bullet$ Good $\cdot$ Keyholing $\bullet$ Undermelting $\square$ Bead-up Appendix Figure 20: Focus offset settings (mm) in the ProX200 L-PBF process for 17-4 stainless steel to prevent keyhole mode melting in melt pools where it was identified at nominal settings \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_401e5513c4e18c8ab9e1g-190} \end{center} Appendix Figure 21: Focus offset settings (mm) in the ProX200 L-PBF process for 304 stainless steel to prevent keyhole mode melting in melt pools where it was identified at nominal settings \end{document} \documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[version=4]{mhchem} \usepackage{stmaryrd} \usepackage{hyperref} \hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,} \urlstyle{same} \usepackage{graphicx} \usepackage[export]{adjustbox} \graphicspath{ {./images/} } \title{Macroscopic simulation and experimental measurement of melt pool characteristics in selective electron beam melting of Ti-6Al-4V } \author{Daniel Riedlbauer ${ }^{1} \cdot$ Thorsten Scharowsky $^{2} \cdot$ Robert F. Singer $^{2} \cdot$ Paul Steinmann $^{1}$.\\ Carolin Körner ${ }^{2} \cdot$ Julia Mergheim ${ }^{1}$} \date{} %New command to display footnote whose markers will always be hidden \let\svthefootnote\thefootnote \newcommand\blfootnotetext[1]{% \let\thefootnote\relax\footnote{#1}% \addtocounter{footnote}{-1}% \let\thefootnote\svthefootnote% } %Overriding the \footnotetext command to hide the marker if its value is `0` \let\svfootnotetext\footnotetext \renewcommand\footnotetext[2][?]{% \if\relax#1\relax% \ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else% \if?#1\ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else\svfootnotetext[#1]{#2}\fi% \fi } \begin{document} \maketitle Received: 28 August 2015 / Accepted: 22 April 2016 / Published online: 12 May 2016 (C) The Author(s) 2016. This article is published with open access at \href{http://Springerlink.com}{Springerlink.com} \begin{abstract} Selective electron beam melting of Ti-6Al-4V is a promising additive manufacturing process to produce complex parts layer-by-layer additively. The quality and dimensional accuracy of the produced parts depend on various process parameters and their interactions. In the present contribution, the lifetime, width and depth of the pools of molten powder material are analyzed for different beam powers, scan speeds and line energies in experiments and simulations. In the experiments, thin-walled structures are built with an ARCAM AB A2 selective electron beam melting machine and for the simulations a thermal finite element simulation tool is used, which is developed by the authors to simulate the temperature distribution in the selective electron beam melting process. The experimental and numerical results are compared and a good agreement is observed. The lifetime of the melt pool increases linearly with the line energy, whereby the melt pool dimensions show a nonlinear relation with the line energy. \end{abstract} Keywords Additive manufacturing $\cdot$ Selective electron beam melting $\cdot$ Ti-6Al-4V $\cdot$ Heat transfer simulation $\cdot$ Melt pool characteristics \footnotetext{$\boxtimes$ Daniel Riedlbauer \href{mailto:daniel.riedlbauer@ltm.uni-erlangen.de}{daniel.riedlbauer@ltm.uni-erlangen.de} 1 Chair of Applied Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Egerlandstraße 5, 91058 Erlangen, Germany 2 Chair of Metals Science and Technology, Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstraße 5, 91058 Erlangen, Germany } \section*{1 Introduction} The titanium aluminium vanadium alloy $\mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V}$ is a commonly used engineering material in the automotive, aerospace and medical industry [20], well suited for light weight construction due to its low density and good mechanical properties. In the last few years, Ti-6Al-4V also became more important for the additive manufacturing of geometrically complex parts by the selective electron beam melting process (SEBM) [17]. The SEBM process is just one among many additive manufacturing processes [6] and is subject to extensive research to exploit the potentials of the electron beam, such as extremely high scan speeds and the high energy density. Major issues are the power consumption and efficiency of the electron beam [5], the evaporation of alloying elements [19], the choice of suited process parameters [19] and the search for new materials [10, 13-15, 26, 28, 29]. In the SEBM process of metal powders, the size and lifetime of the melt pool have a significant influence on the dimensional accuracy of the produced part [1], especially for thin-walled structures [25]. However, due to the extremely high temperatures of several thousand Kelvin and experimental challenges as X-rays, vacuum and metallization, the measurement of temperatures and melt pool characteristics is very difficult during the SEBM process. Therefore, it is helpful to model and simulate the SEBM process to investigate the evolution of temperatures and the dimensions and lifetime of the melt pool. The insights gained from the simulations can be used to further improve the predictability of the melting process and to optimize the parameters of the SEBM process, e.g. beam power and scan speed. For the simulation of the SEBM process, various modelling approaches exist. In [2, 23, 24], the Lattice - Boltzman \begin{itemize} \item Method (LBM) is used to simulate the temperature in a Ti-6Al-4V powder bed on a mesoscopic scale resolving particular powder particles. However, the simulation of single powder particles on small time and length scales is computationally intensive and thus not suited for the simulation of the complete SEBM process. For this purpose, the finite element method (FEM) seems to be more appropriate since it considers the powder material as a continuum. This method is applied in $[11,18,30]$ to simulate the mechanical stresses and warpage of the re-solidified Ti-6Al-4V material in the SEBM process. The simulation of the temperature distribution with FEM in the SEBM process is conducted in [32,33] to analyze the preheating of the metallic powder material and to study the impact of scan speed and beam power on the temperature distribution and the part quality. In [9], the temperature distribution in the SEBM process is simulated with FEM and the influence of different scan strategies on the homogeneity of the temperature distribution is analyzed. \end{itemize} In the present contribution, the temperature distribution in the SEBM of Ti-6Al-4V is simulated with FEM for different scan parameters to investigate the melt pool width, depth and life time. Analogous experiments are performed and the experimental and numerical results are compared. \section*{2 Experimental setup} \subsection*{2.1 Selective electron beam melting process} The SEBM process is a powder bed-based additive manufacturing process using an electron beam as heat source for melting metal powders. The process takes place in a vacuum chamber to achieve a high quality electron beam and to guarantee protection of powder material from the atmosphere. For this contribution, experimental work is done using an ARCAM AB A2 machine, which is schematically shown in Fig. 1. A high speed camera Photron Fastcam SA3 with an Infinity K2 DistaMax Long-Distance Microscope objective and a Cavitar Cavilux HF laser with a wavelength of $810 \mathrm{~nm}$ $\pm 10 \mathrm{~nm}$ for illumination are installed on top of the vacuum chamber for process observation. The building process starts with preheating the steel start plate to the building temperature of $730^{\circ} \mathrm{C}$. Afterwards, the four steps of the build process are repeated until completion of the parts. The four-process steps are powder application by a rake, preheating of the applied layer, selective melting according to part geometry and lowering of the build table. During the process, a small helium pressure of $2.0 \times 10^{-6}$ bar is maintained in the vacuum chamber to increase the stability of the process. After finalizing the build process, the powder is removed from the parts by shot peening with the same powder which is used for the process. Nearly $100 \%$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-2} \end{center} Fig. 1 Schematic view of the electron beam melting equipment of the powder is reused for the next build process [16]. In the present research, an Ti-6Al-4V powder with a composition following DIN 17851 and a mean particle diameter $d_{0,50}$ of $69 \mu \mathrm{m}$ is used. The powder exhibits a particle size distribution between a minimum particle size of $33 \mu \mathrm{m}$ and a maximum size of $118 \mu \mathrm{m}$. For each layer, the build platform is lowered by the nominal layer thickness $d_{\text {nominal }}$ equal t $50 \mu \mathrm{m}$. Remark 1 Due to the consolidation of the powder, the effective powder layer thickness $d_{\text {effective }}$ is larger than 50 $\mu m$ and depends on the experimentally determined relative powder density $\rho_{\text {rel }}=58.3 \%$ as $d_{\text {effective }}=\frac{d_{\text {nominal }}}{\rho_{\text {rel }}}=\frac{50 \mu \mathrm{m}}{0.583}=86 \mu \mathrm{m}$. Since the consolidation of the powder is not modelled a constant effective powder layer thickness $d_{\text {effective }}$ of $86 \mu m$ is assumed in the simulations. In the experiments, the electron beam describes a single straight line in each layer resulting in a wall after several layers. Two building processes are performed and for each parameter combination in Table 1 a wall with a height of 3 $\mathrm{mm}$ and thus 60 powder layers is built. A parameter combination is investigated by varying the electron beam power $P_{\mathrm{b}}$, the scan speed $v_{\mathrm{b}}$ and the energy input or line energy $E_{\mathrm{l}}$, which is defined as $E_{1}:=P_{\mathrm{b}} / v_{\mathrm{b}}$. The parameter combinations in Table 1 are chosen since the quality of the so produced parts is sufficiently high. Table 1 Parameter combinations for experiments \begin{center} \begin{tabular}{lll} \hline $P_{\mathrm{b}}[\mathrm{W}]$ & $v_{\mathrm{b}}\left[\frac{\mathrm{m}}{\mathrm{s}}\right]$ & $E_{\mathrm{l}}\left[\frac{\mathrm{J}}{\mathrm{mm}}\right]$ \\ \hline 160 & 1.6 & 0.1 \\ 240 & 0.8 & 0.3 \\ 320 & 1.6 & 0.2 \\ 480 & 1.6 & 0.3 \\ 640 & 1.6 & 0.4 \\ 720 & 2.4 & 0.3 \\ 800 & 4.0 & 0.2 \\ 1120 & 5.6 & 0.2 \\ 1600 & 8.0 & 0.2 \\ \hline \end{tabular} \end{center} \section*{3 Simulation} \subsection*{3.1 Thermal model} For the simulation of the dimensions and lifetime of the melt pool, the temperature distribution during the SEBM process for Ti-6Al-4V is required. It is simulated from a macroscopic point of view, i.e. the powder material is not modelled as single particles, but as a continuum with homogenized material properties. The same approach of a continuum body is used for the molten and the re-solidified material. In order to compute the unknown temperature $\vartheta$, the transient heat transfer equation $\dot{\vartheta} \rho(\vartheta) c(\vartheta)=-\operatorname{div} \boldsymbol{q}+f$ is solved. The quantity $\dot{\vartheta}$ represents the derivative of $\vartheta$ with respect to time $t$. The density $\rho$ and the heat capacity $c$ are functions of the temperature $\vartheta$ and make (3) highly nonlinear. Equation (3) describes how the temperature changes due to heat fluxes $\boldsymbol{q}$ and heat sources $f$ and captures heat transfer by conduction, convection and radiation. In the building chamber in the SEBM process, high vacuum is assumed and therefore heat convection is neglected. The heat flux generated by heat conduction $\boldsymbol{q}_{\mathrm{c}}$ is characterized by Fourier's law $\boldsymbol{q}_{\mathrm{c}}=-\boldsymbol{K}(\vartheta) \cdot \nabla \vartheta$ Isotropic material behaviour is assumed and the temperature dependent conductivity tensor $\boldsymbol{K}$ is described by $\boldsymbol{K}(\vartheta)=K(\vartheta) \boldsymbol{I}$. The heat flux $\boldsymbol{q}_{\mathrm{r}}$ induced by radiation is captured by $\boldsymbol{q}_{\mathrm{r}}=\epsilon \sigma\left[\vartheta^{4}-\vartheta_{0}{ }^{4}\right] \boldsymbol{n}$. with the environment temperature $\vartheta_{0}$. The quantity $\sigma$ is the Stefan-Boltzmann constant, $\epsilon$ is the emissivity of the material and $\boldsymbol{n}$ is the normal vector on the surface of the radiating material. The power input of the electron beam is taken into account by the volumetric heat source term $f$ in equation (3). Similar to the electron beam in the real process, the heat source $f$ moves along the surface of the currently processed powder layer to melt the powder material. The distribution of $f$ is modelled by the electron beam model developed in [22]. The basis of the electron beam model is a set of semi-empirical equations and theoretical considerations. Absorption, penetration depth, electron backscattering and transmission are incorporated in the model, which is applied in [22] for Lattice Boltzmann simulations of the temperature distribution in the SEBM process and is validated against experiments in [22]. In order to solve (3), appropriate initial and boundary conditions for the unknown temperature have to be added. The different phases of Ti-6Al-4V in the SEBM process are considered in the thermal model by temperature and phase-dependent material parameters. \subsection*{3.2 Discretisation and implementation of the thermal model} In order to numerically solve the heat transfer (3) for the unknown temperature $\vartheta$, it has to be discretized in time and space. For the discretization, the method of Rothe is adopted and thus (3) is discretized first in time and then in space. The temporal discretization is performed with an implicit Runge-Kutta method [12]. For the spatial discretization of Eq. 3, an adaptive FE method with a very fine FE mesh in the vicinity of the electron beam is used to capture extreme temperature gradients in the vicinity of the electron beam. In contrast, the mesh in the remaining simulation space is as coarse as possible to minimize computing time. The mesh refinement in the beam vicinity is exemplarily shown in Fig. 8. In the simulation, the position of the electron beam is known at any time step and, therefore, the mesh can be refined in these areas without the use of error estimators. The discretized version of Eq. 3 is implemented with the finite element library deal.II [4]. The library is focussed on the efficient numerical solution of partial differential equations with a large number of degrees of freedom. \subsection*{3.3 Material parameters and setup} In agreement with the experiments, Ti-6Al-4V metal powder is used for the simulations. The different phases of Ti-6Al-4V are considered in the thermal model by the phase and temperature dependency of the material parameters. The melting and solidification temperatures $\theta_{\mathrm{m}}$ and $\theta_{\mathrm{s}}$ are 1674 and $1615{ }^{\circ} \mathrm{C}$, respectively [8]. The density $\rho$ is assumed to be different for each material phase, but constant in temperature, compare Table $2[3,27]$. The heat capacity $c$ is prescribed as a nonlinear function of temperature $\vartheta$ and is shown in Fig. 2, left. Its peak in the region of $\theta_{\mathrm{m}}$ represents the effect of latent heat [7, 21]. Table 2 Density $\rho$ of the different material phases for the simulation of the SEBM process for Ti-6Al-4V \begin{center} \begin{tabular}{ll} \hline Material phase & $\rho\left[\mathrm{kg} / \mathrm{m}^{3}\right]$ \\ \hline Powder & 2564 \\ Melt & 3800 \\ Solid & 4420 \\ \hline \end{tabular} \end{center} The temperature dependency of the heat conductivity $K$ is illustrated in Fig. 2, right. For all phases, the conductivity $K$ increases linearly in temperature [7]. Similar as in the experiments, the electron beam describes a straight path on top of the current powder layer for different combinations of $P_{\mathrm{b}}$ and $v_{\mathrm{b}}$ (Table 3). In the simulations, more parameter combinations are investigated than in the experiments. The additional combinations are highlighted in gray in Table 3. The simulation space and the boundary conditions are depicted in Fig. 3. The dimensions of the cuboidal simulation space are $30 \times 3.6 \times 4 \mathrm{~mm}$ and at the beginning of a simulation the whole space represents powder material. The temperature at all boundaries of the simulation space but the one on top is held constant at $800{ }^{\circ} \mathrm{C}$, which is the value measured in\\ \includegraphics[max width=\textwidth, center]{2024_03_10_96b190af052f10fc4811g-4(1)} Fig. 2 Heat capacity and conductivity of the material phases\\ Table 3 Parameter combinations for simulations \begin{center} \begin{tabular}{ccc} \hline $P_{\mathrm{b}}[\mathrm{W}]$ & $v_{\mathrm{b}}\left[\frac{\mathrm{m}}{\mathrm{s}}\right]$ & $E_{1}\left[\frac{\mathrm{J}}{\mathrm{mm}}\right]$ \\ \hline 160 & 1.6 & 0.1 \\ 240 & 0.8 & 0.3 \\ 240 & 2.4 & 0.1 \\ 320 & 0.8 & 0.4 \\ 320 & 0.2 & 1.6 \\ 4.0 & 0.1 & 400 \\ 480 & 1.6 & 0.3 \\ 640 & 1.6 & 0.4 \\ 720 & 2.4 & 0.3 \\ 800 & 4.0 & 0.2 \\ 960 & 0.4 & 2.4 \\ 1120 & 5.6 & 0.2 \\ 1200 & 4.0 & 0.3 \\ \hline 1280 & 0.2 & 6.4 \\ \hline 1600 & 8.0 & 0.2 \\ \hline \end{tabular} \end{center} experiments. At the top boundary, heat can be exchanged with the environment by radiation. Assuming that the powder bed is preheated homogeneously, the initial temperature is set to $800{ }^{\circ} \mathrm{C}$ everywhere in the simulation space. The diameter of the beam spot is equal to $400 \mu \mathrm{m}$, similar as in the experiments. The time step sizenteration ranges from 4 to $20 \mu s$ during the scanning process and is adaptively increased up to $50 \mathrm{~ms}$ during the deposition of the next powder layer. In the simulations $25,000-190,000$ trilinear hexahedral finite elements are used for the spatial discretization. As indicated in Fig. 8, the mesh at the current beam position is always very fine to obtain accurate results and further refinement of the finite element mesh did not change the results for the temperature distribution significantly. The electron beam describes its path on the actual layer of material. Afterwards, the material cools down for $2.5 \mathrm{~s}$, then the next powder layer is deposited by a rake and after a time period of $2.5 \mathrm{~s}$ the beam starts to describe its path on top of the added layer. As depicted in Fig. 4, the deposition \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-4} \end{center} Fig. 3 Simulation space with boundary conditions and melt pool width $d_{\mathrm{w}}$ and depth $d_{\mathrm{d}}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-5} \end{center} Fig. 4 Deposition of a new powder layer in the SEBM simulation by adding new finite elements of the new powder layer is realized by sequentially adding single lines of finite elements on top of the simulation space. The blue finite elements in Fig. 4 represent powder material, and the white elements characterize solidified material in the previous layer. \section*{4 Determination of melt pool quantities} \subsection*{4.1 Lifetime of the melt pool} In the experiments, the melt pool lifetime is measured by the evaluation of high speed camera images. Pictures of the melting process are taken with a frame rate of $10,000 \mathrm{fps}$ for a building area of about $0.4 \times 2.8 \mathrm{~mm}$. The state of the material in the region of the beam path is analyzed by observing reflections on the surface of the current powder layer. As illustrated on the left hand side in Fig. 5, moving reflections indicate a liquid state and thus the existence of a molten pool. Solidification is completed if the reflections do not change anymore. The time from the passing of the electron beam until the standstill of the reflections is defined as the life time of the melt pool [31]. On the top in Fig. 5 ,images of the simulation are shown, which correspond to the experimental results at the bottom. The red zone characterizes the melt pool and the finite-element mesh is suppressed in this zone. In the last image, the material is completely solidified. The melt pool lifetime $t_{1}$ is measured at point $\mathrm{S}$ (Fig. 3) in the center of the straight beam path and it is ensured that $t_{1}$ is computed in a stationary state of the melt pool. \subsection*{4.2 Width and depth of the melt pool} The melt pool width $d_{\mathrm{w}}$ itself can hardly be measured experimentally during the SEBM process. Therefore, it is approximated by the wall thickness of the built part after the \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-5(2)} \end{center} Fig. 5 Measurement and simulation of the lifetime of the melt pool for a melt line with $v_{\mathrm{b}}=5.6 \mathrm{~m} / \mathrm{s}$ and $P_{\mathrm{b}}=1120 \mathrm{~W}$ material is cooled down. A built wall is exemplarily shown in Fig. 6a. The wall thickness is determined by using a Scanco Medical micro-computed tomograph (X-ray acceleration voltage $80 \mathrm{kV}$; initial current $133 \mu \mathrm{A}$; integration time $300 \mathrm{~ms}$; voxel size $10 \mu \mathrm{m}$ ). The measuring equipment is calibrated using a Ti-6Al-4V sheet with a known thickness of 1.1 $\mathrm{mm}$. The walls are scanned perpendicular to the building direction which is exemplarily shown in Fig. 7a. The thickness of the wall $d_{\mathrm{w}}$ is measured 50 times for each image and a mean wall thickness $d_{\mathrm{w}, \mathrm{m}}$ is computed for\\ \includegraphics[max width=\textwidth, center]{2024_03_10_96b190af052f10fc4811g-5(1)} Fig. 6 Wall (built with $v_{\mathrm{b}}=5.6 \mathrm{~m} / \mathrm{s}$ and $P_{\mathrm{b}}=1120 \mathrm{~W}$ ) (a) optical micrograph, (b) SEM image, (c) micro section\\ \includegraphics[max width=\textwidth, center]{2024_03_10_96b190af052f10fc4811g-6} Fig. 7 (a) Measurement of the wall thickness for a built wall in a CT image (b) melt pool width and depth in the simulation each layer. The mean wall thickness $\bar{d}_{\mathrm{w}, \mathrm{m}}$ is then derived as the arithmetic mean of $d_{\mathrm{w}, \mathrm{m}}$ for 60 layers. The wall thickness is only an approximation for the melt pool width $d_{\mathrm{w}}$ as three uncertainties arise: shrinkage during solidification, thermal contraction during cooling to room temperature and powder particles sticking to the wall due to incomplete melting. Solidification and cooling from building temperature to room temperature lead to shrinkage. Due to incomplete melting of powder particles, they can stick to the wall on both sides (Fig. 6) and increase the measured wall thickness up to several tens of micrometers. In Fig. 6c, a micro section of a wall is shown and powder particles sticking to the wall can be observed. Due to phase changes in Ti-6Al-4V during cooling, the melt pool depth cannot be derived from changes in the solidification morphology as in other materials. Therefore, the depth of the melt pool is only computed in the simulations. The simulated width and depth of the melt pool are indicated by $d_{\mathrm{w}}$ and $d_{\mathrm{d}}$ in Fig. 7b, respectively. Both quantities depend on the computed temperature distribution evaluated at the integration points and are not necessarily multiples of the finite element dimensions. Since the melt pool width and depth in a certain point are not constant over time, they are computed at point $\mathrm{S}$ (Fig. 3) for all time steps and only their maximum values are considered. \section*{5 Results and discussion} \subsection*{5.1 Lifetime of the melt pool} Experiments and simulations are performed for different combinations of electron beam power $P_{\mathrm{b}}$ and scan speed $v_{\mathrm{b}}$ (Tables 1 and 3). The simulated temperature distribution, which is the basis for computing the melt pool width $d_{\mathrm{w}}$, depth $d_{\mathrm{d}}$ and lifetime $t_{1}$, is shown in Fig. 8 for one parameter combination. The colors represent the temperature distribution in ${ }^{\circ} \mathrm{C}$. Light blue finite elements characterize powder material and dark red areas molten material. The solidified material of the currently treated layer is represented by the elements in the light red areas along the beam path. Dark blue elements \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-6(2)} \end{center} Fig. 8 Simulation of the SEBM process and adaptive mesh refinement in the vicinity of the beam for $P_{\mathrm{b}}=800 \mathrm{~W}$ and $v_{\mathrm{b}}=4 \mathrm{~m} / \mathrm{s}$ indicate solidified material of previously processed layers. In the upper image, the very fine finite element mesh in the area of the path is suppressed for reasons of recognizability. In the simulations, the maximum temperature is always located at the current position of the beam. It is about 2370 ${ }^{\circ} \mathrm{C}$ for the first layer and about $2310{ }^{\circ} \mathrm{C}$ for further layers, as heat can spread faster when at least one layer of highlyconductive solidified material is below the currently treated powder layer. The results for the simulated and experimental lifetimes $t_{1}$ for different line energies $E_{1}$ and a constant scan speed $v_{\mathrm{b}}$ of $1.6 \mathrm{~m} / \mathrm{s}$ are depicted in Fig. 9 . \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-6(1)} \end{center} Fig. 9 Comparison of the experimental and simulated melt pool lifetime $t_{1}$ for different line energies $E_{1}$ and constant scan speed $v_{\mathrm{b}}$ of 1.6 $\mathrm{m} / \mathrm{s}$. The solid line is a guide for the eye to indicate the linear relation of $t_{1}$ and $E_{1}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-7(1)} \end{center} Fig. 10 Comparison of the experimental and simulated melt pool lifetime $t_{1}$ for different scan speeds $v_{\mathrm{b}}$ The error bars define the range of the standard deviation of the measured values. A good agreement between the experimental and simulated values for $t_{1}$ is observed. Figure 9 illustrates that for higher line energies $E_{1}$ the lifetime $t_{1}$ becomes larger, since more energy is induced into the material and mainly conducted into the molten material due to its comparatively high heat conductivity. Hence, a longer time span is required for solidification. The observed relation between the line energy $E_{1}$ and the melt pool lifetime $t_{1}$ is approximately linear in the simulations and experiments. The effect of the scan speed $v_{\mathrm{b}}$ on the melt pool lifetime $t_{1}$ is shown in Fig. 10. The life time of the melt pool $t_{1}$ is plotted as a function of the scan speed $v_{\mathrm{b}}$ for different line energies $E_{1}$. The simulated and measured melt pool lifetimes coincide well for the investigated parameter combinations. When the line energy $E_{1}$ is kept constant and the scan speed $v_{\mathrm{b}}$ is increased, the lifetime of the melt pool remains nearly constant. This tendency is found in the experiments and the simulations. Due to the good agreement between experiments and simulations the developed simulation tool seems to be able to predict the lifetime of the melt pool in the SEBM process of Ti-6Al-4V properly. \subsection*{5.2 Width of the melt pool} The measured wall thickness $d_{\mathrm{w}, \mathrm{m}}$ is shown in Fig. 11 over the height of the wall for one parameter combination. The thickness $d_{\mathrm{w}, \mathrm{m}}$ increases only slightly over the wall height. In the simulations, the computed melt pool width $d_{\mathrm{w}}$ also grows only marginally over the wall height. Therefore, \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-7(2)} \end{center} Fig. 11 Wall thickness over build height in experiments for $P_{\mathrm{b}}=1120$ $\mathrm{W}$ and $v_{\mathrm{b}}=5.6 \mathrm{~m} / \mathrm{s}$ $d_{\mathrm{w}}$ is only calculated (and averaged to $\bar{d}_{\mathrm{w}, \mathrm{m}}$ ) for the second, third and fourth layer to save computing time. The melt pool width of the first layer is not considered, since it is very different from the following layers. The experimental wall thickness and the simulated melt pool width are investigated for the parameter sets in the Tables 1 and 3, respectively, and the results are illustrated in Fig. 12. The error bars characterize the range of the standard deviation of the measured wall thicknesses, which is with about $200 \mu \mathrm{m}$ for every parameter combination quite high due to powder particles sticking on both sides of the wall. Due to the same reason the experimental melt pool widths are higher than the simulated ones. Another reason for the deviations might be that the dynamics of the melt pool [31] can \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-7} \end{center} Fig. 12 Comparison of the experimental and simulated melt pool width for different scan speeds $v_{\mathrm{b}}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_96b190af052f10fc4811g-8} \end{center} Fig. 13 Dependency of the melt pool depth $d_{\mathrm{d}}$ on the scan speed $v_{\mathrm{b}}$ and the line energy $E_{1}$ not be captured by the thermal simulation. Therefore, the flow of the melt, which increases the dimensions of the melt pool, is not considered in the simulation. The sets with line energy $E_{1}$ of $0.2 \mathrm{~J} / \mathrm{mm}$ show similar melt pool widths for experiments ( 414 to $475 \mu \mathrm{m}$ ) and simulations (344 to $352 \mu \mathrm{m}$ ), respectively. This was expected, since a similar amount of energy is induced into the material due to the same line energy. A similar melt pool width is also observed for the simulations with a line energy of $0.1,0.3$, and $0.4 \mathrm{~J} / \mathrm{mm}$, respectively. The simulations show further that the melt pool width increases nonlinearly with the line energy. The influence of the line energy on the melt pool width decreases for higher line energies. In summary, the experimental results coincide well with the computed melt pool widths in the simulations. \subsection*{5.3 Depth of the melt pool} The effect of the scan speed on the melt pool depth is simulated and depicted in Fig. 13. The melt pool depth $d_{\mathrm{d}}$ is nearly constant for a constant line energy $E_{1}$. It increases for higher line energies $E_{1}$ and varies from about $100 \mu \mathrm{m}$ to almost $200 \mu \mathrm{m}$. This is reasonable since the volume of molten material depends on the amount of energy induced into the material. Therefore, not only the melt pool width $d_{\mathrm{w}}$ but also the depth $d_{\mathrm{d}}$ increases for a higher line energy $E_{1}$. In comparison to the melt pool width $d_{\mathrm{w}}$ the depth $d_{\mathrm{d}}$ enlarges more significantly for greater $E_{1}$. This is also reasonable, since the heat conductivity of solid material is much higher than the one of powder and heat is mainly dissipated by the solidified material below the melt pool. \section*{6 Conclusion} In the present contribution, the SEBM process of Ti-6Al-4V was investigated. The lifetime and width of the melt pool in the process were simulated with FEM and compared with experimental measurements. Experimental and numerical results for the lifetime of the melt pool coincide well for all investigated parameter combinations. The lifetimes increase for higher line energies and stay constant for higher scan speeds when the line energy is kept constant. The width of the melt pool was approximated by the thickness of the wall built in the SEBM process. The wall thickness and the simulated melt pool width turned out to be nearly constant over the height of the wall and a good agreement between both was observed. The simulations showed that the influence of the line energy on the melt pool width reduces for higher line energies. The melt pool depth was only determined in simulations for various parameter combinations. It is almost constant when the line energy is constant. For higher line energies, the melt pool depth increased. The developed simulation tool will be used for further investigations of the SEBM process. For instance, the temperature history in the material during the process will be simulated for different scan paths, since it has a major influence on the mechanical properties of the produced part. Furthermore, the spatial homogeneity of the temperature distributions for various scan paths will be compared, as more homogeneous distributions are supposed to lead to less defective parts. Acknowledgments The authors thank the German Research Foundation (DFG) for funding the Collaborative Research Centre 814, sub-projects $\mathrm{C} 3$ and B2. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http:// \href{http://creativecommons.org/licenses/by/4.0/}{creativecommons.org/licenses/by/4.0/}), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \section*{References} \begin{enumerate} \item Aggarangsi P, Beuth JL, Gill DD (2004) Transient changes in melt pool size in laser additive manufacturing processes. In: Solid freeform fabrication proceedings, pp 163-1747 \item Ammer R, Rüde U, Markl M, Jüchter V, Körner C (2014) Validation experiments for LBM simulations of electron beam melting. Int J Modern Phys C 25(12):1441,009 \item ASM: Titanium ti-6al-4v (grade 5) annealed (2014). \href{http://asm}{http://asm}. \href{http://matweb.com/search/SpecificMaterial.asp?bassnum=MTP641}{matweb.com/search/SpecificMaterial.asp?bassnum=MTP641}. \end{enumerate} Technical datasheet for Ti-6Al-4V from ASM Aerospace Specifications Metals Inc. \begin{enumerate} \setcounter{enumi}{3} \item Bangerth W, Hartmann R, Kanschat G (2007) deal.II - a generalpurpose object-oriented finite element library. ACM Trans Math Softw (TOMS) 33(4):24 \item Baumers M, Tuck C, Hague R, Ashcroft I, Wildman R (2010) A comparative study of metallic additive manufacturing power consumption. In: Proceedings of the 2010 solid freeform fabrication symposium \item Bikas H, Stavropoulos P, Chryssolouris G (2015) Additive manufacturing methods and modelling approaches: a critical review. Int J Adv Manuf Technol:1-17 \item Boivineau M, Cagran C, Doytier D, Eyraud V, Nadal MH, Wilthan B, Pottlacher G (2006) Thermophysical properties of solid and liquid Ti-6Al-4V alloy. Int J Thermophys 27(2):507-529 \item Carpenter: Titanium alloy Ti-6Al-4V (2014). \href{http://cartech.ides}{http://cartech.ides}. com. Technical datasheet for Ti-6Al-4V from Carpenter \item Chen YX, Wang XJ, Chen SB (2014) The effect of electron beam energy density on temperature field for electron beam melting. Adv Mater Res 900:631-638 \item Cormier D, Harrysson O, West H (2004) Characterization of H13 steel produced via electron beam melting. Rapid Prototyp J 10(1):35-41 \item Denlinger ER, Heigel JC, Michaleris P (2014) Residual stress and distortion modeling of electron beam direct manufacturing Ti-6Al$4 \mathrm{~V}$. In: Proceedings of the institution of mechanical engineers, part b: journal of engineering manufacture p 0954405414539494 \item Ellsiepen P. (1999) Zeit- und ortsadaptive Verfahren angewandt auf Mehrphasenprobleme poröser Medien. Inst. für Mechanik (Bauwesen), Ph.D. thesis \item Frigola P, Harrysson O, Horn T, Ramirez D, Murr L (2014) Fabricating copper components with electron beam melting. Adv Mater Process 172(7):20-24 \item Gaytan S, Murr L, Martinez E, Martinez J, Machado B, Ramirez D, Medina F, Collins S, Wicker R (2010) Comparison of microstructures and mechanical properties for solid and mesh cobalt-base alloy prototypes fabricated by electron beam melting. Metallurg Mater Trans A 41(12):3216-3227 \item Harrysson O, Cormier D, Marcellin-Little D, Jajal K (2003) Direct fabrication of metal orthopedic implants using electron beam melting technology. In: Solid freeform fabrication symposium proceedings, pp 439-446 \item Heinl P, Müller L, Körner C, Singer RF, Müller FA (2008) Cellular Ti-6Al-4V structures with interconnected macro porosity for bone implants fabricated by selective electron beam melting. Acta Biomaterialia 4(5):1536-1544 \item Heinl P, Rottmair A, Körner C, Singer RF (2007) Cellular titanium by selective electron beam melting. Adv Eng Mater 9(5):360-364 \item Jamshidinia M, Kong F, Kovacevic R (2013) The coupled CFDFEM model of electron beam melting. ASME District F - Early Career Tech Conf Proc 12:163-171 \item Juechter V, Scharowsky T, Singer R, Körner C (2014) Processing window and evaporation phenomena for $\mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V}$ produced by selective electron beam melting. Acta Materialia 76:252258 \item Karunakaran K, Bernard A, Suryakumar S, Dembinski L, Taillandier G (2012) Rapid manufacturing of metallic objects. Rapid Prototyp J 18(4):264-280 \item Kaschnitz E, Reiter P, McClure J (2002) Thermophysical properties of solid and liquid $90 \mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V}$ in the temperature range from 1400 to $2300 \mathrm{~K}$ measured by millisecond and microsecond pulse-heating techniques. Int J Thermophys 23(1):267-275 \item Klassen A, Bauereiß A, Körner C (2014) Modelling of electron beam absorption in complex geometries. J Phys D: Appl Phys 47(6):065,307 \item Körner C, Attar E, Heinl P (2011) Mesoscopic simulation of selective beam melting processes. J Mater Process Technol 211(6):978987 \item Markl M, Ammer R, Rüde U, Körner C (2014) Improving hatching strategies for powder bed based additive manufacturing with an electron beam by 3D simulations. CoRR arXiv:1403.3251 \item Murr L, Gaytan S, Medina F, Martinez E, Martinez J, Hernandez D, Machado B, Ramirez D, Wicker R (2010) Characterization of Ti-6Al-4V open cellular foams fabricated by additive manufacturing using electron beam melting. Mater Sci Eng A 527(7):1861-1868 \item Murr L, Martinez E, Gaytan S, Ramirez D, Machado B, Shindo P, Martinez J, Medina F, Wooten J, Ciscel D et al (2011) Microstructural architecture, microstructures, and mechanical properties for a nickel-base superalloy fabricated by electron beam melting. Metallurg Mater Trans A 42(11):3491-3508 \item Rai R, Burgardt P, Milewski J, Lienert T, DebRoy T (2009) Heat transfer and fluid flow during electron beam welding of $21 \mathrm{Cr}-6 \mathrm{Ni}-9 \mathrm{Mn}$ steel and Ti-6Al-4V alloy. J Phys D: Appl Phys 42(2):025,503 \item Ramirez D, Murr L, Li S, Tian Y, Martinez E, Martinez J, Machado B, Gaytan S, Medina F, Wicker R (2011) Open-cellular copper structures fabricated by additive manufacturing using electron beam melting. Mater Sci Eng A 528(16):5379-5386 \item Ramirez D, Murr L, Martinez E, Hernandez D, Martinez J, Machado B, Medina F, Frigola P, Wicker R (2011) Novel precipitate-microstructural architecture developed in the fabrication of solid copper components by additive manufacturing using electron beam melting. Acta Mater 59(10):4088-4099 \item Riedlbauer D, Steinmann P, Mergheim J (2014) Thermomechanical finite element simulations of selective electron beam melting processes: performance considerations. Comput Mech 54(1):109122 \item Scharowsky T, Osmanlic F, Singer R, Körner C (2014) Melt pool dynamics during selective electron beam melting. Appl Phys A 114(4):1303-1307 \item Shen N, Chou Y (2012) Numerical thermal analysis in electron beam additive manufacturing with preheating effects. In: Proceedings of the 23rd solid freeform fabrication symposium, pp 774-784 \item Zäh MF, Lutzmann S (2010) Modelling and simulation of electron beam melting. Product Eng 4(1):15-23 \end{enumerate} \end{document} \documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[version=4]{mhchem} \usepackage{stmaryrd} \usepackage{hyperref} \hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,} \urlstyle{same} \usepackage{graphicx} \usepackage[export]{adjustbox} \graphicspath{ {./images/} } \usepackage{bbold} \usepackage{multirow} \title{Assessing printability maps in additive manufacturing of metal alloys } \author{Luke Johnson ${ }^{\text {a, }}{ }^{*}$, Mohamad Mahmoudi ${ }^{b}$, Bing Zhang ${ }^{b}$, Raiyan Seede a, Xueqin Huang a,\\ Janine T. Maier ${ }^{c}$, Hans J. Maier ${ }^{\text {d }}$, Ibrahim Karaman ${ }^{\text {a }}$, Alaa Elwany ${ }^{\text {b }}$,\\ Raymundo Arróyave ${ }^{\mathrm{a}, \mathrm{b}}$\\ a Department of Materials Science and Engineering, Texas A\&M University, College Station, TX, USA\\ ${ }^{\mathrm{b}}$ Department of Industrial and Systems Engineering, Texas A\&M University, College Station, TX, USA\\ ' Institute of Product and Process Innovation, Leuphana University of Lüneburg, Lüneburg, Germany\\ ${ }^{\mathrm{d}}$ Institut für Werkstoffkunde (Materials Science), Leibniz Universität Hannover, Garbsen, Germany} \date{} %New command to display footnote whose markers will always be hidden \let\svthefootnote\thefootnote \newcommand\blfootnotetext[1]{% \let\thefootnote\relax\footnote{#1}% \addtocounter{footnote}{-1}% \let\thefootnote\svthefootnote% } %Overriding the \footnotetext command to hide the marker if its value is `0` \let\svfootnotetext\footnotetext \renewcommand\footnotetext[2][?]{% \if\relax#1\relax% \ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else% \if?#1\ifnum\value{footnote}=0\blfootnotetext{#2}\else\svfootnotetext{#2}\fi% \else\svfootnotetext[#1]{#2}\fi% \fi } \begin{document} \maketitle Full length article \section*{A R T I C L E I N F O} \section*{Article history:} Received 15 January 2019 Received in revised form 1 July 2019 Accepted 2 July 2019 Available online 5 July 2019 \section*{Keywords:} Printability Additive manufacturing High entropy alloys $\mathrm{NiNb}$ Selective laser melting \begin{abstract} A B S T R A C $T$ We propose a methodology for predicting the printability of an alloy, subject to laser powder bed fusion additive manufacturing. Regions in the process space associated with keyhole formation, balling, and lack of fusion are assumed to be strong functions of the geometry of the melt pool, which in turn is calculated for various combinations of laser power and scan speed via a Finite Element thermal model that incorporates a novel vaporization-based transition from surface to volumetric heating upon keyhole formation. Process maps established from the Finite Element simulations agree with experiments for a $\mathrm{Ni}-5 \mathrm{wt} . \% \mathrm{Nb}$ alloy and an equiatomic CoCrFeMnNi High Entropy Alloy and suggest a strong effect of chemistry on alloy printability. The printability maps resulting from the use of the simpler Eagar-Tsai model, on the other hand, are found to be in disagreement with experiments due to the oversimplification of this approach. Uncertainties in the printability maps were quantified via Monte Carlo sampling of a multivariate Gaussian Processes surrogate model trained on simulation outputs. The printability maps generated with the proposed method can be used in the selection-and potentially the design-of alloys best suited for Additive Manufacturing. \end{abstract} [. 2019 Published by Elsevier Ltd on behalf of Acta Materialia Inc. \section*{1. Introduction} Despite known unique capabilities of metal-based Additive Manufacturing (AM) and the advances it has undergone over the past two decades, significant gaps are yet to be bridged in order to bring it to full maturity. A major roadblock is the high degree of variability in metal AM-fabricated parts, which poses serious challenges related to the qualification and certification $(\mathrm{Q} \& \mathrm{C})$ of critical AM components [1]. Challenges to $\mathrm{Q} \& \mathrm{C}$ efforts are only compounded by the fact that metal AM has focused only on a handful of major alloy classes, with the bulk of the focus on titanium [2-4] (mostly Ti-6Al-4V), nickel [5-7] (IN625, IN718), stainless steels $[8,9]$ and other alloying systems that were not initially designed to be manufactured using AM technologies such as shape memory alloys [10-13]. \footnotetext{\begin{itemize} \item Corresponding author. Texas A\&M University, Department of Materials Science and Engineering, 3003 TAMU, College Station, TX, 77843-3003, USA. \end{itemize} E-mail address: \href{mailto:lukejohnson@tamu.edu}{lukejohnson@tamu.edu} (L. Johnson). } High variability in the quality and performance of metal AM parts can be attributed to the use of different processing schemes, energy source, raw materials, etc. Even when considering a single AM technology-such as laser powder bed fusion (L-PBF)-variability from the use of different machines, intrinsic variability in processing conditions, variance in local thermal histories, part geometry, and form of feedstock can have a significant impact [14,15]. The early stages of research on metal AM focused on identifying machine-specific process conditions capable of yielding AM parts from conventional alloy feedstock with properties comparable to their as-cast or wrought counterparts [16-19]. More recently, and motivated by the challenges associated with variability, the underlying paradigm for metal AM is shifting towards one that emphasizes control: it is no longer necessary to merely match the properties of conventional alloys, but rather to satisfy properties that enable $\mathrm{Q} \& \mathrm{C}$ of critical AM components for a specific application. As such, the processing routes (AM parameters, pre-or postprocessing) selected must ensure that part performance is met on a repeatable basis. In order to gain a better grasp of the ultimate causes for\\ variability in AM, research efforts have been spent on developing strategies for improved process monitoring and control [20]. In-situ monitoring approaches have already achieved a considerable degree of sophistication [21] and these approaches have moved beyond real-time measurement of melt pool dynamics [22] to monitoring the transfer of energy to the material [23]. In-situ monitoring has also begun to be used as a way to assess the quality of AM builds [24,25]. Considerable challenges persist in this approach as some aspects of the thermal history associated with the solidification process (such as cooling rates, thermal gradients, etc.) are still exceedingly difficult to measure, although progress has been made in AM processes at moderate solidification rates [26]. A closed-loop control system capable of adjusting process conditions upon detection the onset of defect formation in real time remains highly challenging. However, some efforts have attempted to use lower resolution, lower temperature imaging techniques $[20,21,27]$ as a strategy to monitor the AM process. These techniques are useful in controlling longer range physical phenomena like residual stress, but the time and length scales of the thermal gradients they capture are too slow and large to provide adequate data for controlling extremely fast phenomena like melt pool instabilities. In addition to visual imaging, acoustic signal analysis has shown some potential for detecting keyhole and crack formation $[21,28]$. Further development of monitoring technologies will eventually lead to a better control of the AM process, particularly in light of the considerable sensitivity of most metal AM feedstock to variations in AM process conditions. An admittedly less developed, but arguably more promising path forward from the materials perspective is to design alloys that are less sensitive to variations in AM processing conditions in the first place. Looking at the problem from this materials-centric viewpoint inevitably leads to the consideration of materialsinherent "printability" and the subsequent question of how to define such a metric. In this paper, we propose a printability metric defined as the (hyper)volume in process parameter space for a laser powder bed fusion (L-PBF) metal AM process. Specifically we attempt to identify regions in the laser power vs scan speed space associated with builds that are free of major defects, limiting our analysis to single tracks. We proceed to define this feasibility region in terms of the geometry of the melt pool in a way that is alloy agnostic by first carrying out predictions of melt pool dimensions using finite element methods within the COMSOL Multiphysics ${ }^{\circledR}$ heat transfer module. The thermal model includes phase-dependent thermophysical properties which are used to approximate heat and mass transport phenomena such as melting, solidification, vaporization, and keyhole formation. By combining best estimates of thermophysical properties with the high-fidelity thermal models we predict the printability map of two alloys: a Ni-5wt.\%Nb (NiNb) alloy as a binary proxy for IN718 as well as a prototypical equiatomic CoCrFeMnNi high entroy alloy (HEA). The predicted printability maps are compared to an exhaustive exploration of the process space via experiments. The impact of using simplified thermal models as well as the effect of uncertainty in the thermo-physical properties are also examined. \section*{2. On the printability of metal alloys} The notion that different alloy chemistries are more/less suitable to processing via AM should not be surprising as historically this has been the case with other processing technologies/materials combinations. The influence of alloy composition on the quality of AM parts was illustrated early on by Childs et al. [29], who investigated the effect of process parameters on the build quality of stainless and tool steels printed with L-PBF techniques. Their results suggest that even small changes in the composition of the printed material can result in significant changes to the region in the process parameter space corresponding to successful prints. In agreement with this early work, Tomus et al. [30] recently investigated the suceptibility of Hastelloy alloys to hot-cracking and found that minor modifications to the $\mathrm{C}$ and Si content of the alloy reduced the tendency for hot-cracking. Harrison et al. [31] followed a different approach and modified a baseline Hastelloy formulation to increase solid solution strengthening and thus provide higher resistance to cracking. Martin et al. [32] successfully printed otherwise unprintable aluminum alloys by doping the powder feedstock with tailored inoculants to control the solidification. In a simplified manner, one could consider two different types of factors that control the degree to which a given alloy can be printed: intrinsic features of the alloy itself, such as solidification range, presence of competing secondary solid phases, etc. can affect the microstructural morphology or texture of the printed material, while extrinsic factors such as process conditions affect the overall consistency of the fabricated part. AM research has primarily focused on finding useful combinations of these extrinsic factors such as laser power and speed [33], or linear energy density which is the ratio of these two parameters [10]. Both intrinsic/extrinsic factors are affected not only by the local processing conditions but by the alloy's thermodynamic and thermo-physical characteristics. Feasible regions in the alloy-process space can be identified in terms of their printability, which could be considered to be a global indicator for the resistance of an alloy-process combination to the formation of microscopic/macroscopic defects that compromise the integrity of the print. Questions remain as to how to properly quantify the printability of an alloy-process combination although there are some recent efforts in this direction. Mukerjee et al. [34], for example, identified different dimensionless parameters that were used to estimate the susceptibility of an alloy-process combination to thermally-induced part distortion, composition heterogeneity due to differential evaporation, as well as incomplete inter-layer fusion and the resulting porosity due to incomplete penetration of the melt pool into the previous layers. These printability indicators were constructed from a combination of materials properties (such as melting, boiling points, thermal diffusivities, heat capacities, etc.), process conditions (such as linear energy density) as well as characteristics of the melt pool (width, depth, volume, area) and thus provide a way to evaluate the impact of process conditions on specific alloy formulations. Using their printability criteria, Mukherjee et al. [34] investigated some of the most common metal alloys used in AM (IN718, SS316, Ti64) and found some correlation between their printability indicators and the presence of different kinds of issues such as thermal distortion, porosity or lack of composition control (due to differential evaporation) for three different processing conditions. This approach is useful for evaluating printability on a point-bypoint basis, but it does not characterize the holistic printability of the alloy across all combinations of laser powers and scan speeds. As such it cannot take issues such as process variability into account. In a related (earlier) work, Juechter et al. [35] investigated the processing space for Selective Electron Beam Melting (SEBM) with the goal of identifying combinations of scanning speed and linear energy density that resulted in minimal porosity and reduced composition changes due to differential evaporation. Through a combination of in-situ thermal monitoring and post-fabrication characterization, Scime and Beuth [25] have recently developed a method for mapping melt pool defects to laser powers and scan speeds, and related the incidence of such defects to major characteristics of the melt pool geometry. The quality of the solidified structure during AM ultimately\\ depends on the characteristics of the melt pool and it is thus reasonable to expect that criteria based on melt pool geometry can be used to establish thresholds for the onset of melt-pool related defects such as lack-of-fusion, balling, and keyhole formation [34,36], which are some of the most dominant defect modes in LPBF [37]. Lack-of-fusion occurs when the incident energy is insufficient to melt the substrate to a significant depth, which can result in large and/or very sharp voids within the as-built part. Balling is a periodic oscillation in the size and shape of a solidified track caused by capillary-driven instabilities of the melt pool and this oscillation leads to surface variations that can affect powder spreading during processing of the subsequent layer and that can lead to void formation. Keyholing is the formation of a depression in the surface of the melt pool due to recoil pressure from intense vaporization directly under the laser. The criteria for the onset of balling can be constructed from criteria used in welding and laser processing [38]. The lack-of-fusion threshold can be determined by comparing the melt pool depth and the powder layer thickness [34], while the onset of keyhole formation can be accounted for by considering the aspect ratio of the melt pool-further discussion of the criteria is described in 3.3. Process parameter combinations that lie beyond established threshold values for the above criteria are eliminated from the feasible process space and the remaining region is regarded as the printable region or printability map. The size and shape of this remaining region/volume can be used as a criteria for the design of an alloy suitable for AM. In this context, a large predicted successful build region is an indication that some alloy of interest is insensitive to variations in process parameters. This approach can potentially be quite significant as it implies the possibility of establishing a given alloy's printability map both before the onset of an experimental campaign and during each costly synthesis and characterization iteration. Beyond size-based design metrics of the printable region, selecting process conditions at points furthest from the boundaries of this printable area (i.e. robust design) provides maximum protection from inherent variability in machine processing conditions [39-42]. Instead of eliminating or reducing variability, the design parameters of interest are guided to a region where the variability has less of an impact on the successful outcome of the build. Variability in machine parameters such as laser power and scan speed can be directly incorporated via constant-valued offsets to the boundaries based on the predicted or measured uncertainties. Incorporation of uncertainty in thermo-physical properties is accomplished through the use of surrogate model-based uncertainty quantification $[15,43]$. In this work, we explore the use of melt pool geometry-based criteria constructed by combining high-fidelity thermal models with best-estimates for the values of thermo-physical properties of two different alloy systems. A Ni-5wt.\%Nb binary alloy is selected as it can be considered to be a proxy for IN718, particularly with regards to the segregation of $\mathrm{Nb}$ into interdendritic regions. Due to the small amounts of $\mathrm{Nb}$ it is to be expected that the thermophysical properties of this alloy are relatively close to those of $\mathrm{Ni}$ and thus it is expected that the uncertainty in the values of these properties would be small. On the other hand, the CoCrFeMnNi high entropy alloy was chosen since it is very likely that HEAs, due to their phase stability characteristics-i.e. reduced competition of secondary solid phases upon solidification and significantly reduced diffusion kinetics-could become a very important feedstock for metal AM. \section*{3. Methodology} The general workflow for predicting printability (Fig. 1) starts with thermal model-based calculations of temperature profiles and subsequent melt pool dimensions for laser powers and speeds that span the process space. Gaussian Process response surfaces are then constructed for each of the three major melt pool dimensions and subsequently used to calculate ratios $L / W, W / D, D / t$ throughout the entire design space $-L, W$ and $D$ correspond to the length, width and depth of the melt pool while $t$ corresponds to the powder bed layer thickness. Regions of process space with $D / t<1.5, L / W>2.3$ and $W / D<1.5$ are labeled as regions susceptible to lack of fusion, balling, or keyhole formation, respectively. These threshold values are based on geometrical considerations and empirically determined values from literature $[17,36,44]$. Any area of the process space that is not labeled with a specific defect is considered to be a feasible combination of print parameters. Details of each step in this workflow are presented in subsequent sections. \subsection*{3.1. Thermal model} There is a plethora of approaches to modeling laser interactions with matter, from high-fidelity powder-scale methods [45-47] requiring thousands of simulation hours on a super-computing cluster to semi-analytical based models [48] that take minutes to run on a laptop. Finite element based methods are somewhere in between these two extremes with varying degrees of computational efficiency and fidelity based on the physical assumptions of the particular model. Selecting which approach to use depends on the physical phenomena being studied, required accuracy, access to computational resources, and the desired frequency of feedback/ iteration between computational and experimental methods. The method for assessing printability presented in this study \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_03a3ec6f9e764fa92ed6g-03} \end{center} Fig. 1. A general workflow for the printability framework described in this paper. Processing parameters and phase-dependent material properties such as specific heat $\left(C_{p}\right)$, density $(\rho)$, and thermal conductivity $(k)$ are provided to the thermal model. Melt pool dimensions calculated from the thermal model $(L, W, D)$ and user prescribed powder layer thickness $(t)$ are then used in the determination of defect formation using the ratios seen in the orange, purple, and green arrows. Any process parameters that do not belong to a defect are considered to be in a region of good quality.\\ requires $O(10)$ simulations that are accurate throughout process space while maintaining relatively low computational cost such that the method could feasibly be introduced into an iterative optimization/design scheme. An Eagar-Tsai model [48] can be used to rapidly conduct many simulations throughout the entire process space, but its many simplifications-including the neglect of phase transformation effects as well as the use of temperatureindependent properties [48]-limit the predictive accuracy to narrow ranges of the process parameter space, although there are certainly improvements over this effective but simplified model that can account for some of its deficiencies [49]. A powder-scale model including fluid flow would be the most physically accurate, but the computational time per simulation renders the approach unable to sample the entire process space in a reasonable time. With this in mind, a conduction based finite-element thermal model was developed with the Comsol Multiphysics ${ }^{\mathbb{R}}$ heat transfer module. The general form of the heat transfer equation below describes the transient evolution of temperature $(T)$ within a material domain as it is subject to some thermal $\operatorname{load}(\mathrm{s})(Q)$. $\rho C_{p} \frac{\partial T}{\partial t}+\nabla(-k \nabla T)=Q$ The rate of temperature evolution within the domain is governed by the thermo-physical properties of the material, namely density $(\rho)$, specific heat $\left(C_{p}\right)$, and conductivity $(k)$. In this model, we modify and expand the model to account for additional physical phenomena such as energy contributions from phase transformations and temperature/phase-dependent thermo-physical properties. A coordinate transformation is also applied to the transient term: $\frac{\partial T}{\partial t}=\frac{\partial T}{\partial x} \frac{\partial x}{\partial t}+\frac{\partial T}{\partial y} \frac{\partial y}{\partial t}+\frac{\partial T}{\partial z} \frac{\partial z}{\partial t}=\nabla T \vec{v}$ This transformation shifts the reference frame from a Lagrangian reference frame fixed on the material substrate to an Eulerian reference frame fixed to the laser heat source moving at a constant scan speed $\vec{v}$. The elimination of the transient term in the heat transfer equation comes at the expense of introducing nonlinearity in the form of an advective term: $\rho C_{p} \nabla T \vec{v}+\nabla(-k \nabla T)=Q$\\ Equation (3) represents the steady-state form of the equation which can be solved an order of magnitude faster, even with a very fine $2 \mu \mathrm{m}$ mesh in and around the melt pool. This fine mesh significantly reduces mesh size effects and convergence issues associated with the nonlinear nature of problem. A schematic of the Finite Element domain and a representative melt pool can be seen in Fig. 2. Boundary effect testing showed that a domain size of $6 \mathrm{~mm} \times 1.5 \mathrm{~mm} \times 1.5 \mathrm{~mm}$ was sufficient for all laser power and scan speed combinations. Boundary conditions for this model consist of mirror plane symmetry on boundary 3 and Dirichlet conditions on boundaries 1 , 2,4 , and 5 with a fixed temperature of $T_{0}=298 \mathrm{~K}$. The surface (boundary 6) contains all of the heat transfer phenomena that contribute to the source term $(Q)$ in Equation (3). $Q=q_{\text {rad }}+q_{c o n v}+q_{v a p}+q_{\text {beam }}$ $q_{\text {rad }}=\varepsilon \sigma_{B}\left(T_{a m b}^{4}-T^{4}\right)$ $q_{c o n v}=h\left(T_{a m b}-T\right)$ $q_{v a p}=L_{v} \sum_{i=1}^{n} X_{i} 44.331 p_{i}(T) \sqrt{\frac{M W_{i}}{T}}$ $q_{\text {beam }}=a(T) P\left[\frac{1}{2 \pi \sigma^{2}} \exp \left(-\frac{\left(r-r_{0}\right)^{2}}{2 \sigma^{2}}\right)\right]$ Equations (5)-(8) describe surface radiation, natural surface convection, vaporization, and deposited beam power, respectively. The radiation and convection terms are of the form typically implemented in finite element modeling of L-PBF. The evaporative energy loss $q_{v a p}$ and beam deposition $q_{\text {beam }}$ include modifications that account for mass transport and energy transport within the vapor phase, respectively. Equation (7) is a Bolten-Block/Eagar model [50] that has been slightly modified to include temperature dependent partial pressure relationships calculated using equations described in Ref. [51]. Equation (8) includes a phasedependent absorptivity term that allows for the incorporation of keyhole formation without the need to consider more computationally expensive fluid dynamics. Details of the parameters contained within these equations are included in the next section. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_03a3ec6f9e764fa92ed6g-04} \end{center} Fig. 2. Schematic showing the Finite Element model's a) domain size, meshing technique, boundary conditions and b) isotherms from a representative melt pool simulation with the laser traveling in the positive $\mathrm{x}$-direction. \subsection*{3.2. Model parameters} The parameters in Equations (3)-(8) can be generally categorized into temperature/phase-dependent and non-temperature/ phase-dependent properties. Physical parameters considered to be constant within each simulation are: Stefan-Boltzmann constant $\left(\sigma_{B}\right)$, ambient temperature $\left(T_{a m b}=298 \mathrm{~K}\right)$, molecular weights of each element $\left(M W_{i}\right)$, and emissivity $(\varepsilon=0.7)$. We note that the value for emissivity is based on an average of many alloys and is not a parameter of interest since the radiative contribution to the energy balance at the surface is orders of magnitude smaller than that of vaporization. Laser process parameters such as laser power $(P)$, scan speed $(\vec{v})$, standard deviation $(\sigma)$, and centerpoint $\left(r_{0}\right)$ are also considered to be constant during each simulation. $\sigma$ is calculated as $1 / 4$ of the beam diameter as is common throughout the literature. The set of temperature-dependent properties consists of: density $(\rho)$, specific heat $\left(C_{p}\right)$, thermal conductivity $(k)$, absorptivity $(a)$ and partial pressure of each element $\left(p_{i}\right)$. Phase-dependent values for all of these properties can be found in Table 1. The natural convection coefficient $(h)$ in Equation (6) is calculated within Comsol through a Nusselt number correlation based on the shape and orientation of the specified surface. These effective convection coefficients are stored in a lookup table within COMSOL for a number of common geometries and orientations. In this case, the geometry is a flat plate and the orientation is horizontal with the heat flux being normal to the surface and flow is assumed to be laminar. The convective contribution to heat flux in the melt pool is at least 3 orders of magnitude less than that of radiation and vaporization, but their contributions quickly equalize outside of the melt pool. Convection was included in the interest of completeness, but has a relatively small influence on the melt pool predictions. \subsection*{3.2.1. Phase transitions} Smooth transitions between the phase-dependent thermophysical property values $\left(\rho, C_{p}, k, \alpha\right)$ in Table 1 are realized by averaging the properties of each phase based on their respective fractions during the transformation. Latent heats of fusion and vaporization ( $L_{m}$ and $L_{v}$, respectively) are included in the model through addition of an equivalent heat capacity during their respective transformations. Details of this effective property approach were explained in a previous publication [52]. \subsection*{3.2.2. Property calculations} Due to a lack of experimental thermo-physical property data, values for the Ni-5wt.\%Nb alloy in Table 1 were calculated using a weighted average of $\mathrm{Ni}$ and $\mathrm{Nb}$ elemental properties found in Ref. [53]. A weighted average is sufficiently accurate in this case due to the dilute nature of this single-phase solid-solution alloy. The values of the thermo-physical properties of the HEA are taken directly from the literature sources cited in Table 1. For both alloys, vapor phase conductivity and absorptivity values are selected to approximate the transmission and subsequent reflection of the laser within the vapor void present during keyhole-mode melt pools. We note that in the case of HEA we also employed rules of mixtures to estimate the thermo-physical properties. While in the case of dilute alloys this approximation is well grounded, we acknowledge that in the case of concentrated alloys the rule of mixtures assumption may not be warranted, particularly in the case of thermal conductivity, which tends to be suppressed due to increased phonon scattering. The impact of uncertainty in these properties is considered below but a better approach would be to construct predictive models, perhaps through machine learning methods, of composition-dependent properties. Ongoing work by the present authors seeks to address this issue. \subsection*{3.2.3. Variable absorptivity} Absorptivity values for all phases are chosen based on a recent study from Lawrence Livermore National Lab that shows experimental evidence for low effective absorptivity of the solid/liquid phases and high effective absorptivity upon vaporization and keyhole formation [23]. Conductivity of the vapor phase in the vertical z-direction was increased by an order of magnitude to approximate the transmission of electromagnetic laser energy through the vapor phase. The combined increases in absorptivity and conductivity lead to a more realistic representation of lasermatter interaction at the point of incidence over a wide range of laser powers and scan speeds. Laser penetration of the vapor phase allows the system to transition seamlessly between surface and volumetric heating conditions without any changes to the laser source term which eliminates the need to select between the two approaches a priori. Low energy densities do not form a significant amount of vapor, so the laser does not penetrate the substrate and the simulation converges to a conduction-mode melt pool. Conversely, process parameters with high energy density lead to simulations with a stable region of vapor and the laser energy is transferred deeper into the substrate via the enhanced vapor conductivity. Table 1 Phase-dependent thermo-physical properties used in the thermal modeling of the Ni-5wt.\%Nb and the CoCrFeMnNi HEA studied in this work. For the Ni-5wt.\%Nb alloy, property values for each phase are calculated using a weighted average of the pure elemental properties of each constituent. HEA properties directly taken from literature as cited. \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|} \hline \multirow[t]{2}{*}{Phase (i)} & \multicolumn{2}{|l|}{Solid $(S)$} & \multicolumn{2}{|l|}{Liquid $(L)$} & & Vapor (V) \\ \hline & $\mathrm{NiNb}$ & HEA & $\mathrm{NiNb}$ & HEA & $\mathrm{NiNb}$ & HEA \\ \hline $\rho_{i}\left[\mathrm{~kg} / \mathrm{m}^{3}\right]$ & $8900[\mathrm{M}]$ & $7700[54]$ & $8450[53]$ & $7400[53]$ & $\rho(T)[50]$ & $\rho(T)[50]$ \\ \hline $C_{p}^{i}[\mathrm{~J} / \mathrm{kgK}]$ & $550[53]$ & $600[53]$ & $650[53]$ & $650[55]$ & $C_{p}(T)[55]$ & $C_{p}(T)[55]$ \\ \hline $\alpha_{i}$ [unitless] & $0.3[23]$ & $0.3[23]$ & $0.3[23]$ & $0.3[23]$ & $0.6[23]$ & $0.6[23]$ \\ \hline $k_{i}[\mathrm{~W} / \mathrm{mK}]$ & $85[53]$ & $20[53]$ & $120[53]$ & $40[53]$ & $5[55]$ & $5[55]$ \\ \hline $k_{i z}[\mathrm{~W} / \mathrm{mK}]$ & & & & & $1000[\mathrm{~A}]$ & $1000[\mathrm{~A}]$ \\ \hline \multirow[t]{2}{*}{Transform. $(t)$} & & \multicolumn{2}{|l|}{Solid $\leftrightarrow$ Liquid $(m)$} & & \multicolumn{2}{|l|}{Liquid $\leftrightarrow$ Vapor $(v)$} \\ \hline & & $\mathrm{NiNb}$ & HEA & & $\mathrm{NiNb}$ & HEA \\ \hline $T_{t}[\mathrm{~K}]$ & & $1703[\mathrm{M}]$ & $1644[54]$ & & 3209 [55] & 3086 [54] \\ \hline $\Delta T_{t}[\mathrm{~K}]$ & & $50[53]$ & 100 [53] & & $200[\mathrm{~A}]$ & $500[\mathrm{~A}]$ \\ \hline $L_{t}[\mathrm{~kJ} / \mathrm{kg}]$ & & 290 [55] & $232[55]$ & & 7100 [55] & 4961 [54] \\ \hline \end{tabular} \end{center} [M] value taken from powder supplier Material Safety Datasheet. [A] Artificially enhanced as described in Section 3.2.3. This vapor/keyhole based laser absorption model is in direct contrast with current absorption methods common in AM literature that focus primarily on powder layer effects. Volumetric heat sources are typically used to represent the penetration and absorption of laser energy within the thin layer of powder above the substrate. While this laser-powder interaction is valid prior to melt pool formation, it fails to represent the primary incidence of the laser upon molten metal once the melt pool has formed during normal operations $[23,56]$. As such, the powder layer and the effective material properties associated with it are not directly modeled. \subsection*{3.3. Printability predictions} Results of the fully developed thermal model must be extended, analyzed and post-processed in order to predict various defect prone regions of the process parameter space. Any portion of the process space that is not part of a defect prone region is defined as printable. This section describes the steps necessary to predict those regions and the uncertainty bounds on their boundaries. \subsection*{3.3.1. Response surface modeling} The Matlab®based OODace Toolbox [57] was used to calibrate three Gaussian Process (GP) models to melt pool length, width, and depth predictions from a grid of 30 thermal model simulations that spanned the full ranges of laser power and speed available on a 3D Systems®ProX DMP 200 L-PBF system. The resulting GP response surfaces can be used as computationally inexpensive surrogates [43] for calculating critical ratios $(L / W, W / D, D / t)$ of melt pool dimensions and powder layer thickness. Since GP predictions are inexpensive, these calculations can be performed on a much finer grid of laser powers and scan speeds which results in more refined definitions of the boundaries between each print region in the process space. \subsection*{3.3.2. Printabllity criteria} Regions of the process space are defined through comparisons of critical ratio response surface values to the threshold criteria $(L / W<2.3, W / D<1.5, D / t>1.5)$, which are derived from empirical observations, physical principles, and pure geometrical considerations. The threshold value $L / W<2.3$ is related to melt pool "balling" or "humping"; a phenomenon that is widely considered to be the result of Plateau-Rayleigh instabilities in the molten metal $[17,44]$. Although there is no agreed upon value for the $L / W$ ratio threshold in the literature, values typically range between $22$ would be a reasonable approximation for a half-circle melt pool in conduction mode laser processing with isotropic material parameters and heat flow. In practice, the presence of other heat transfer modes such as radiation, convection, and vaporization dissipate heat at the surface which results in a decrease in depth of conduction mode cross sections. As such, a keyhole threshold of $W / D>1.5$ is a better predictor. In comparison, the lack of fusion criteria $(D / t>1.5)$ is quite simple. If the depth of the melt pool $D$ does not exceed the prescribed powder layer thickness $t$, the melt pool will not fully fuse to the substrate. We note that recently, Letenneur and collaborators [58] carried out an investigation of criteria based on melt-pool dimensions and the onset of defects-specifically lack of fusion and balling-for a number of alloys and, by combining models and experiments found criteria that are in agreement with those put forward here, although their assumed onset of balling was less conservative than our proposed threshold. Similarly, work by Scime and Beuth [25] put forward similar criteria for the onset of defects arising from the geometric characteristics of the melt pool. These criteria are meant to be approximate guidelines for the comparison of alloy printability and optimization of their compositions/processing. As such, the threshold values are subject to change according the risk tolerance of the process designer. In addition to changing the threshold values, some assessment of potential risks can be incorporated through the propagation of uncertainty in the parameters of the thermal model. \subsection*{3.3.3. Uncertainty propagation} The effect of material property uncertainty on the location of successful print region boundaries is calculated via surrogate model based uncertainty propagation [43]. A Gaussian Processbased surrogate model is calibrated to the melt pool dimension results from a set of 300 Latin-Hypercube samples over the 6 critical material parameters $\left(K_{S}, K_{L}, K_{V}, K_{V} z, \alpha_{S / l}, \alpha_{V}\right)$. Conductivities and absorptivities were chosen as the parameters of interest due to their significant influence on the results and the relatively high degree of uncertainty in their values. Of the three primary thermophysical properties $\left(C_{p}, \rho, k\right)$, conductivity values are much more difficult to measure/calculate [59], especially in the liquid and vapor phases due to the high temperatures and the confounding effects of natural convection during the measurement process [60]. Additionally, the liquid conductivity is often artificially elevated in AM thermal modeling to approximate the effect of convection. Once the surrogate model has been calibrated to the thermal model, all material parameters are fixed except one, which is subjected to 10,000 Monte Carlo sampling steps. Input distributions for each parameter were defined as normal distributions centered within the user-defined upper and lower bounds assigned to the LHS search space. Parameters for these input distributions can be seen in Table 2. Although the user-defined nature of these distributions introduces some bias, this could be eliminated on future studies through techniques such as Bayesian calibration. 95\% confidence intervals of the resultant distributions for melt pool dimensions and their ratios are then used to find confidence intervals for the print-region boundaries. \subsection*{3.4. Experimental} The materials used to manufacture L-PBF specimens were gas atomized equiatomic CoCrFeMnNi powder and $\mathrm{Ni}-5 \mathrm{wt}$.\%Nb powder provided by Nanoval GmbH \& Co. KG. Single tracks were printed using a 3D Systems ProX DMP 200 Laser Type (fiber laser with a Gausian profile, $\lambda=1070 \mathrm{~nm}$, and beam size $=100 \mu \mathrm{m}$ ). CoCrFeMnNi single tracks were printed on an arc melted $\mathrm{CoCr}-$ FeMnNi base plate. The tracks were $15 \mathrm{~mm}$ in length with $1.5 \mathrm{~mm}$ spacing between each track. The Ni-5wt.\%Nb alloy was subject to two separate experiments with the only difference being the substrate material. The first experiment (Exp1 in Figs. 3 and 6), consisted of printing the Ni-5wt.\%Nb alloy on a pure nickel substrate. Table 2 Mean $\mu$ and standard deviation $\sigma$ values for the input parameter distributions used in the Monte Carlo based uncertainty propagation described in Section 3.3.3 \begin{center} \begin{tabular}{lll} \hline Parameter & $\mu$ & $\sigma$ \\ \hline $K_{S}[W / m K]$ & 80 & 8 \\ $K_{L}[W / m K]$ & 150 & 20 \\ $K_{V}[W / m K]$ & 12 & 3 \\ $K_{L z}[W / m K]$ & 1.0 & 0.25 \\ $K_{V z}[W / m K]$ & 1500 & 175 \\ $a_{s / l}$ & 0.32 & 0.035 \\ $a_{V}$ & 0.7 & 0.04 \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_03a3ec6f9e764fa92ed6g-07} \end{center} Fig. 3. Printability maps that predict melt pool morphology regions for a Ni-5wt.\%Nb alloy. Predicted regions are as follows: good quality (blue,G), keyholing (green,KEY), balling (purple, BALL), and Lack of Fusion (orange,LOF). Experimentally observed morphologies throughout the process parameters space are indicated by markers of different shapes following the same color scheme as the predicted regions. Hollow and filled markers indicate if the data is from Exp1 or Exp2, respectively. Four representative melt pool cross sections from each region can be seen on the right. Eagar-Tsai predictions are essentially uninformative in this case due to constant material properties and the neglect of phase transformation effects. The second experiment (Exp2 in Figs. 3 and 6) was printed on a base plate of $\mathrm{Ni}-5 \mathrm{wt} . \% \mathrm{Nb}$ that was itself printed and subsequently homogenized $1100{ }^{\circ} \mathrm{C}$ for $1 \mathrm{~h}$, then air cooled) in order to erase its AM microstructure so that the single track melt pools would be easier to see. These tracks were $10 \mathrm{~mm}$ in length with $1 \mathrm{~mm}$ spacing between tracks. Cross sections of the single tracks were wire cut using wire electrical discharge machining (EDM). The specimens were polished down to $0.25 \mu \mathrm{m}$, then vibratory polished in colloidal silica. A mixture of $10 \mathrm{~mL} \mathrm{H} 2 \mathrm{O}, 1 \mathrm{~mL} \mathrm{HNO} 3,5 \mathrm{~mL} \mathrm{HCl}$, and $1 \mathrm{~g} \mathrm{FeCl} 3$ was used to etch HEA single tracks for metallographic investigation. Kalling's Solution No. 2 (5 g CuCl2, $100 \mathrm{~mL} \mathrm{HCl}$, and $100 \mathrm{~mL}$ ethanol) was used to etch the Ni-5wt.\%Nb single tracks. Optical Microscopy was carried out using a Keyence VH-X digital microscope equipped with a VH-Z100 wide range zoom lens. Width and depth measurements were conducted using the VH-X microscope software. Three cross sections were cut and measured from each track. The displayed width and depth values are averaged from these three measurements. \section*{4. Results and discussion} In additive manufacturing, as with other manufacturing techniques, it is of utmost importance to develop an understanding of the feasible conditions for processing the material. This section presents and discusses printability predictions from the above methodology for $\mathrm{Ni}-5 \mathrm{wt}$.\%Nb and CoCrFeMnNi HEA, and compares the resultant maps against systematic experimental investigation of the process parameter space for those alloys carried out as part of this work. It is important to emphasize that the experimental investigation of the process parameter space was not used in any way to fit the material properties or model parameters used in the computational methodology or the subsequent construction of the predicted printability maps. Maps labeled Finite Element in the figures presented below are constructed through the application of the printability criteria to melt pool dimension predictions from the Finite Element model developed herein. The same criteria were applied to Eagar-Tsai melt pool dimension predictions for comparison. Cross sectional images of representative melt pool morphologies from each process parameter region, identified by the criteria above, are also shown in these figures beside each set of maps. The observed morphologies of every experimental track are indicated by markers of different color and shape. After a comparison of the predictions and experiments for each alloy, boundary uncertainty plots, determined according to the methodology discussed in 3.3.3, for key parameters of the Finite Element model are analyzed. Comparisons of the boundary widths in each plot indicate the relative importance of each thermophysical parameter and identify potential sources of improvement in the Finite Element model and its assumptions. \subsection*{4.1. Printability maps for $\mathrm{Ni}-5 \mathrm{wt}$ \% Nb alloy} Fig. 3 shows the predicted printability map for the Ni-5wt.\%Nb alloy in comparison with experiments. The top printability map was determined using FE-based predictions of the geometric characteristics of the melt pool under different processing conditions. Different regions are labeled after the dominant type of defect (or their absence) to be expected based on the criteria described above. At low powers and (generally) at high velocities it is evident that the dominant defect is lack-of-fusion (light brown/ orange). At relatively low scan speeds and high power the predicted dominant defect is keyholing (green). On the other hand, in the high scan speed-high power region of the process space the dominant defect is balling (magenta) due to capillary-based instabilities of the melt pool. The so-called printable region (blue) in power-scan speed space thus results from the subtraction of these three defect-prone regions from the power-scan speed space. As is evident from the figure, there is overall an acceptable level of agreement between the predicted and the actual measured printability maps for the Ni-5wt.\%Nb alloy investigated in this work, with the majority of the experimental points falling within the correct predicted region. However, there are a few exceptions near the keyhole and balling boundaries. There is a clear delineation between the experimentally observed keyhole and good quality melt pool results, but the slope of the predicted border is too horizontal. Two experimentally observed balling conditions are also mis-classified as printable by the Finite Element model. These misclassifications near the keyhole and balling borders are likely due to the lack of free-surface fluid-flow modeling which can more accurately predict laser penetration, viscosity, and surface tension effects that are important during keyholing and balling phenomena. Beyond comparisons between models and overall experimental results for the $\mathrm{Ni}-5 \mathrm{wt} . \% \mathrm{Nb}$ printability map, we note that there are also minor disagreements between the two sets of experimental observations near the keyhole and balling boundaries in the $\mathrm{Ni}$ $5 \mathrm{wt}$.\%Nb map. The most obvious discrepancy is an observation of a good single track in the Exp1 dataset (hollow markers, Fig. 3) at a higher laser power and similar scan speed $(P=200 \mathrm{~W}, \mathrm{v}=1275$ $\mathrm{mm} / \mathrm{s}$ ) than two single tracks with balling morphologies $(\mathrm{P}=178 \mathrm{~W}, \mathrm{v}=1154 \mathrm{~mm} / \mathrm{s}$ and $\mathrm{P}=178 \mathrm{~W}, \mathrm{v}=1515 \mathrm{~mm} / \mathrm{s})$ in the Exp2 dataset (solid markers, Fig. 3). This shift in the onset of balling\\ to lower laser powers and scan speeds in Exp2 can be attributed to the slight differences in the experimental conditions due to the differences in powder handling and substrate material. Exp1 single tracks were deposited on a pure Ni substrate whereas Exp2 tracks were deposited on a Ni-5wt.\%Nb substrate. In contrast to the Finite Element thermal model, the Eagar-Tsai model possesses almost no predictive capability with these printability criteria. It drastically overestimates the size of the lack-offusion region and fails to identify the keyhole and balling regions entirely. The uninformative nature of this Eagar-Tsai-based printability map is due to two key simplifying assumptions with the model itself: i) constant thermo-physical properties and ii)surfaceonly energy deposition for all processing conditions. These assumptions render the model unable to capture phase change phenomena and the transition to laser penetration during keyholing, respetively. The result is an inability to predict the drastic changes in melt pool aspect ratios that are so critical to melt pool stability and the printability criteria used herein. This also makes it difficult to calibrate the Eagar-Tsai model to both depth and width over the entire parameter space; an issue which can be seen in the predicted-actual plots in Fig. 4. Further examination of the performance of the Eagar-Tsai (ET) and Finite Element thermal models relative to experiments can be observed in Fig. 4, which shows that the ET model over-predicts the melt pool width and under-predicts the melt pool depth for this set of material parameters. Since the model assumes constant thermophysical properties $\left(\rho, C_{p}, k\right)$, changes to any one of them will uniformly affect the melt pool dimensions and calibrating for the width will ultimately shift the depth predictions further astray. Changing multiple thermo-physical properties at once offers more flexibility, but the effect is still limited. In contrast, the Finite Element model has phase-dependent thermo-physical properties and includes additional heat transfer considerations like the transition from surface to volumetric heating, described in the\\ \includegraphics[max width=\textwidth, center]{2024_03_10_03a3ec6f9e764fa92ed6g-08} Fig. 4. Diagnostic plots showing the predictive accuracy of the Finite Element and Eagar-Tsai models for both melt pool width and depth for the Ni-5wt.\%Nb alloy. The Finite Element model has much better agreement with the depth as would be expected with the improved laser source term. The Eagar-Tsai model over-predicts width and under-predicts depth. methodology section. This allows for more accurate predictions over a wider range of the process parameter space and results in better width predictions and very good agreement with depth measurements, also seen in Fig. 4. While the results presented so far suggest a very good agreement between the predicted printability regions and the independent experimentally determined melt pool geometry maps, further verification of the proposed framework can be provided by comparing these results with those of Scime and Beuth [25]. The motivation for Scime and Beuth was to develop a framework for the identification of melt pool signatures indicative of flaw formation in L-PBF processed Inconel 718. They used in-situ thermal monitoring combined with post-fabrication characterization to establish relationships (via machine learning) between process conditions and melt pool characteristics. Remarkably, they settled on exactly the same characteristics (balling, lack-of-fusion, keyhole formation) as the ones used in the present work-and arrived at independently-to construct the predicted printability maps. By comparing Figs. 3 and 5, it is seen that the agreement between the predicted Ni-5wt.\%Nb printability map and the printability map determined by Scime and Beuth [25] is extremely good, showing the same topology and even presenting a reasonable quantitative agreement with regards to the actual position of the feasible, keyholing, lackof-fusion and balling regions. This agreement with experimental results from a different research group and L-PBF system (EOS M290) highlights the generalizability of the computational methodology herein. Ideally, an experimental methodology like the one described in Ref. [25] could be combined with the computational methods of this framework to create a single synergistic workflow for iterative optimization of printability. Experimental process characterization for an existing alloy would inform this computational framework which would then be used to search for promising alloy modifications to test in the next iteration of the design process. \subsection*{4.1.1. Boundary uncertainties for $\mathrm{Ni}-5 \mathrm{wt}$ \% $\mathrm{Nb}$ map} The additional physics included in the Finite Element model comes at the price of increased number of parameters. In order to establish which of these parameters have the most effect on the predicted printability maps, we propagate uncertainty from key thermo-physical properties to the print region boundaries of the\\ \includegraphics[max width=\textwidth, center]{2024_03_10_03a3ec6f9e764fa92ed6g-08(1)} ADDED BY CURRENT AUTHORS Printable Region Fig. 5. Experimentally determined melt pool morphology map for an Inconel718 alloy (reproduced with permission from Ref. [25] (with alterations)). The reader is encouraged to read the cited work for in-depth explanations of the notation in this figure Similar to the current study, various markers indicate experimentally observed melt pool morphologies as desireable, keyholing, undermelting (i.e. lack-of-fusion), and balling. In an effort to aid reader interpretation, the blue region was placed on top of the original point-wise map by manually tracing the region surrounding the "successful" print labels. The topology of the different melt pool morphology regions in the map agree very well with the predicted printability regions for $\mathrm{Ni}-5 \mathrm{wt} . \% \mathrm{Nb}$ in the current work shown in Fig. 3. The agreement is particularly interesting due to the fact that these observations are from an EOS M290 printer, meaning that the printabilty predictions are system-agnostic.\\ printability map itself, shown as the shaded regions surrounding each boundary in Fig. 6. The parameters are arranged in order of their influence on the boundaries with liquid conductivity $K_{L}$ being the most influential and $K_{V}$ being the least influential. Some interesting observations can be made when comparing the relative boundary thicknesses within each map. For example, $K_{S}$ has a relatively strong influence on the balling boundary as compared to the keyhole and lack-offusion boundaries. This can be interpreted as $K_{S}$ having a stronger influence on length, rather than width or depth of the melt pool. Conversely, $\alpha_{s / l}$ preferentially influences the keyhole and lack-offusion boundaries, meaning that it does not affect melt pool length as much. The primary influence of $\alpha_{v}$ is on the keyhole boundary which is consistent with its implementation as a method for approximating increased laser absorptivity during keyhole formation. When comparing boundary uncertainties among different parameters, $K_{L}$ is quite clearly the most influential for all boundaries. Unfortunately, $K_{L}$ is the least understood conductivity value and varies significantly between different Finite Element models found in the literature. This issue stems from a general lack of experimental conductivity measurements of liquid metal alloys, as well as the artificial increase of the parameter in Finite Element models as a proxy for convective heat transfer within the melt pool. The small influence of vapor conductivity values $K_{V}$ and $K_{V z}$ are the result of the relatively narrow ranges of input values provided for the uncertainty propagation. In addition to uncertainties propagated from the model inputs, there are also uncertainties associated with the threshold criteria values themselves. In order to understand the effect of these uncertainties on the overall morphology of the printability predictions, maps were calculated at threshold values $\pm 15 \%$, resulting in the 6 plots seen in Fig. 7. \subsection*{4.2. Printability maps for CoCrFeMnNi high entropy alloy} The same process used to predict the printability map for the Ni$5 \mathrm{wt} . \% \mathrm{Nb}$ alloy was applied to an equiatomic $\mathrm{CoCrFeMnNi}$ high entropy alloy system. The resulting printability maps can be seen in Fig. 8. These maps have the same general topology as the Ni-5wt.\% $\mathrm{Nb}$ maps above, but the spacing and relative size of the regions is completely different and further highlights the strong coupling between alloy and process parameter space when determining suitable protocols for AM. In contrast to the Ni-5wt.\%Nb alloy, the investigation of HEA was not as comprehensive and its printability was only investigated in a rather narrow region of the processing space. While there are not as many single track observations to indicate exactly where each print region is located experimentally, there is an obvious overprediction of the balling region in the Finite Element map. Taking a lesson from the uncertainty analysis performed in the $\mathrm{Ni}-5 \mathrm{wt} . \% \mathrm{Nb}$ system, this can be attributed to uncertainty in the liquid conductivity of this system. Nevertheless, predictions of the keyhole and lack-of-fusion boundaries agree very well with experimentally determined morphologies, shown as markers of different colors and shapes in Fig. 8. Again, the Finite Element model outperforms the predictive capability of the Eagar-Tsai model for the same reasons discussed in the Ni-5wt.\%Nb case. In the Eagar-Tsai model, oversimplification of assumptions regarding the material properties and the physics\\ \includegraphics[max width=\textwidth, center]{2024_03_10_03a3ec6f9e764fa92ed6g-09} \begin{center} \begin{tabular}{|cccc|} \hline LOF & KEY & BALL & $\square \mathrm{G}$ \\ $\square$ Exp1 & $\Delta$ Exp1 & O Exp1 & $\star$ Exp1 \\ $\square$ Exp2 & $\Delta$ Exp2 & $\bullet$ Exp2 & $\star$ Exp2 \\ \end{tabular} \end{center} Fig. 6. Uncertainty bounds calculated from a Monte Carlo based uncertainty propagation. Predicted regions are as follows: good quality (blue,G), keyholing (green,KEY), balling (purple, BALL), and Lack of Fusion (orange,LOF). Experimentally observed morphologies throughout the process parameters space are indicated by markers of different shapes that following the same color scheme as the predicted regions. Hollow and filled markers indicate if the data is from Exp1 or Exp2, respectively. The 6 plots correspond to the 6 key thermo-physical properties listed in the lower right corners. Liquid conductivity $K_{L}$ has the largest impact on all boundaries while the two absorptivity parameters $\left(\alpha_{S / L}\right.$ and $\left.\alpha_{V}\right)$ have the largest impact on the keyhole boundary which agrees with their intended purpose. Solid conductivity $K_{S}$ affects balling the most and the two vapor conductivities ( $K_{V}$ and $K_{V z}$ ) have little to no impact. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_03a3ec6f9e764fa92ed6g-10(1)} \end{center} Fig. 7. Predicted printability maps calculated at $\pm 15 \%$ of the threshold criteria values used in this work while holding the other criteria constant for $\mathrm{Ni}-\mathrm{Nb}$ alloy investigated in this work. Each row of the plot corresponds to a different threshold criteria. involved leads to melt pool dimensions that cannot be accurately calibrated over the entire process space. This is further corroborated by the predicted-actual comparison of the two models shown in Fig. 9. The melt pool width is significantly over-predicted, while the melt pool depth is under-predicted by the Eagar-Tsai model. The width comparison also shows the ability of the Finite Element model to capture the experimentally determined limit of melt pool width at $80-90 \mu \mathrm{m}$. This is attributed to the Finite Element model's ability to transition from surface to volumetric heating via inclusion of the vapor phase transformation and subsequent penetration of the laser deeper into the substrate. \subsection*{4.3. Comparison of printability} In addition to internal comparisons within each map, a direct comparison of printability between two materials in this study can also provide valuable insight. From both predictions and experiments, it is evident that $\mathrm{Ni}-5 \mathrm{wt}$.\% $\mathrm{Nb}$ has a larger printable region, under L-PBF conditions, than the CoCrFeMnNi HEA. The shape and orientation of the printable region can also tell us about the sensitivity of the material to variations in either laser power or scan speed. The more equiaxed printable region in the Ni-5wt.\%Nb case indicates an equal sensitivity to both processing parameters whereas the elongated print region in the HEA case indicates a higher sensitivity to laser power than scan speed. With this in mind we can readily conclude that the Ni-5wt.\%Nb alloy is the more printable alloy in this case, based on the available evidence and computational framework. \section*{5. Summary and conclusions} The Finite Element model and melt pool dimension based methodology presented here leads to L-PBF printability maps that\\ \includegraphics[max width=\textwidth, center]{2024_03_10_03a3ec6f9e764fa92ed6g-10} Fig. 8. Printability maps that predict melt pool morphology regions for a $\mathrm{CoCrFeMnNi}$ high entropy alloy. Predicted regions are as follows: good quality (blue,G), keyholing (green,KEY), balling (purple, BALL), and Lack of Fusion (orange,LOF). Experimentally observed morphologies throughout the process parameters space are indicated by markers of different shapes that following the same color scheme as the predicted regions. There is generally good agreement between computations and experiments here, but the size of the balling region seems to be over predicted. Four representative melt pool cross sections from each region can be seen on the right. Eagar-Tsai predictions are essentially uninformative in this case due to constant material properties and no phase transformation considerations. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) agree well with experiments. The consistency and accuracy of the framework applied to two drastically different alloy systems with only minor modifications is a strong indication that the approach is applicable for a wide range of materials. This is significant as this suggests that it is possible to use the proposed computational methodology for a priori evaluation of the suitability of an arbitrary alloy as an AM feedstock via identification of successful processing parameters, thus providing a plausible route for the design of alloys with reduced sensitivity to machine variability during the AM process. Further validation of the proposed methodology, however, will be necessary before predicted alloy printability can be used in a design framework. The predictive capability of this printability framework can be increased through more accurate predictions of uncertainty. If experimental melt pool measurements exist for a particular alloy $a$ priori, the uncertainty surrounding these boundaries can be more accurately defined by performing a Bayesian calibration of the thermo-physical parameters of the model [43]. This would result in input value distributions that are specifically defined for the particular problem at hand. This option is not necessarily viable when considering computational alloy design since the alloy being optimized has, by definition, never been experimentally tested. However better definitions of the uncertainty prior to optimization increase the chances of success. In addition to better understanding of the uncertainty, accuracy of the printable region boundaries may be increased with the inclusion of additional physics such as free surface fluid flow modeling. However, this increase in model complexity will result in an increase in computational expense that may preclude its use in\\ \includegraphics[max width=\textwidth, center]{2024_03_10_03a3ec6f9e764fa92ed6g-11} Fig. 9. Diagnostic plots showing the predictive accuracy of the Finite Element and Eagar-Tsai models for both melt pool width and depth for the CoCrFeMnNi high entropy alloy. The Finite Element model has much better agreement with the depth as would be expected with the improved laser source term. The Eagar-Tsai model over predicts width and under predicts depth. an iterative optimization scheme. With this in mind, the Finite Element based thermal model presented in this work represents a good middle ground between the fast but less accurate Eagar-Tsai approach and the slow but more accurate models that incorporate fluid dynamics. The direct connection between the composition and resultant printability of an alloy can be incorporated into an iterative optimization scheme by utilizing quantitative measurements of the size and shape of the blue printable regions in Figs. 3 and 8 as design metrics. For example, one could increase the robustness of an existing alloy to variations in processing parameters and environmental conditions by using such an optimization scheme to determine adjustments in alloy composition that would maximize the size of the printable region. Development of a more accurate method to link composition and phase-dependent thermo-physical properties (i.e. more complicated than the rule-of-mixture model used in the Ni-5wt.\%Nb case above) will need to be considered if the optimization extends beyond regions where a dilute solution approximations can be used. We would like to note that defining the printable region is just the first step in optimizing the performance of AM processed parts. Once the printable region is defined, selection of a particular set of process parameters within that region can be determined through optimization of other important material phenomena such as solidification front morphology, secondary phase evolution, and evaporative control of alloy composition. Furthermore, quantifying the uncertainty in boundary locations as shown in Fig. 6 is important when optimizing within the printable region itself and could provide further input as to the most effective uncertainty quantification exercise to carry out based on the effect of a specific quantity of interest on the variance in the printability map of a given alloy. \section*{Acknowledgements} The authors would like to acknowledge the support of the Army Research Office under Contract No. W911NF-18-1-0278. Portions of this work were also (partially supported by NASA through Grant No. NNX15AD71G. LJ would also like to acknowledge the NSF-NRT fellowship support through the National Science Foundation grant No. NSF-DGE-1545403, NRT-DESE: Data-Enabled Discovery and Design of Energy Materials (DEM). Finite Element Model simulations were carried out in the Texas A\&M Supercomputing Facility. \section*{References} [1] M. Seifi, A. Salem, J. Beuth, O. Harrysson, J.J. Lewandowski, Overview of materials qualification needs for metal additive manufacturing, J. Occup. Med. 68 (3) (2016) 747-764. [2] B. Dutta, F.H.S. Froes, The Additive Manufacturing (AM) of titanium alloys, Met. Powder Rep. 72 (2) (2017) 96-106. [3] B. Baufeld, O. Van der Biest, R. Gault, Additive manufacturing of Ti-6Al-4V components by shaped metal deposition: microstructure and mechanical properties, Mater. Des. 31 (2010) S106-S111. [4] Y. Zhu, J. Li, X. Tian, H. Wang, D. Liu, Microstructure and mechanical properties of hybrid fabricated Ti-6.5 Al-3.5 Mo-1.5 $\mathrm{Zr}-0.3 \mathrm{Si}$ titanium alloy by laser additive manufacturing, Mater. Sci. Eng. A 607 (2014) 427-434. [5] G. Dinda, A. Dasgupta, J. Mazumder, Laser aided direct metal deposition of inconel 625 superalloy: microstructural evolution and thermal stability, Mater. Sci. Eng. A 509 (1-2) (2009) 98-104. [6] G. Bi, C.-N. Sun, H.-c. Chen, F.L. Ng, C.C.K. Ma, Microstructure and tensile properties of superalloy IN100 fabricated by micro-laser aided additive manufacturing, Mater. Des. 60 (2014) 401-408. [7] W.J. Sames, K.A. Unocic, R.R. Dehoff, T. Lolla, S.S. Babu, Thermal effects on microstructural heterogeneity of Inconel 718 materials fabricated by electron beam melting, J. Mater. Res. 29 (17) (2014) 1920-1930. [8] K. Guan, Z. Wang, M. Gao, X. Li, X. Zeng, Effects of processing parameters on tensile properties of selective laser melted 304 stainless steel, Mater. Des. 50 (2013) 581-586. [9] I. Tolosa, F. Garciandía, F. Zubiri, F. Zapirain, A. Esnaola, Study of mechanical properties of aisi 316 stainless steel processed by "selective laser melting", following different manufacturing strategies, Int. J. Adv. Manuf. Technol. 51 (5-8) (2010) 639-647. [10] M. Mahmoudi, G. Tapia, B. Franco, J. Ma, R. Arroyave, I. Karaman, A. Elwany, On the printability and transformation behavior of nickel-titanium shape memory alloys fabricated using laser powder-bed fusion additive manufacturing, J. Manuf. Process. 35 (2018) 672-680. [11] J. Sam, B. Franco, J. Ma, I. Karaman, A. Elwany, J.H. Mabe, Tensile actuation response of additively manufactured nickel-titanium shape memory alloys, Scripta Mater. 146 (2018) 164-168. [12] B.E. Franco, J. Ma, B. Loveall, G.A. Tapia, K. Karayagiz, J. Liu, A. Elwany, R. Arroyave, I. Karaman, A sensory material approach for reducing variability in additively manufactured metal parts, Sci. Rep. 7 (1) (2017) 3604. [13] J. Ma, B. Franco, G. Tapia, K. Karayagiz, L. Johnson, J. Liu, R. Arroyave, I. Karaman, A. Elwany, Spatial control of functional response in 4d-printed active metallic structures, Sci. Rep. 7 (2017) 46707. [14] J.J. Lewandowski, M. Seifi, Metal additive manufacturing: a review of mechanical properties, Annu. Rev. Mater. Res. 46 (1) (2016) 151-186. [15] G. Tapia, W. King, L. Johnson, R. Arróyave, I. Karaman, A. Elwany, Uncertainty propagation analysis of computational models in laser powder bed fusion additive manufacturing using polynomial chaos expansions, J. Manuf. Sci. Eng. 140 (12) (2018), 121006-121006-12. [16] C. Kamath, B. El-dasher, G.F. Gallegos, W.E. King, A. Sisto, Density of additively-manufactured, $316 \mathrm{l}$ SS parts using laser powder-bed fusion at powers up to 400 W, Int. J. Adv. Manuf. Technol. 74 (1-4) (2014) 65-78. [17] I. Yadroitsev, A. Gusarov, I. Yadroitsava, I. Smurov, Single track formation in selective laser melting of metal powders, J. Mater. Process. Technol. 210 (12) (2010) 1624-1631. [18] I. Yadroitsev, P. Krakhmalev, I. Yadroitsava, Hierarchical design principles of selective laser melting for high quality metallic objects, Add. Manuf. 7 (2015) 45-56. [19] I. Yadroitsev, I. Yadroitsava, P. Bertrand, I. Smurov, Factor analysis of selective laser melting process parameters and geometrical characteristics of synthesized single tracks, Rapid Prototyp. J. 18 (3) (2012) 201-208. [20] G. Tapia, A. Elwany, A review on process monitoring and control in metalbased additive manufacturing, J. Manuf. Sci. Eng. 136 (6) (2014) 060801. [21] S.K. Everton, M. Hirsch, P. Stravroulakis, R.K. Leach, A.T. Clare, Review of insitu process monitoring and in-situ metrology for metal additive manufacturing, Mater. Des. 95 (2016) 431-445. [22] P. Lott, H. Schleifenbaum, W. Meiners, K. Wissenbach, C. Hinke, J. Bültmann, Design of an optical system for the in situ process monitoring of selective laser melting (slm), Physics Procedia 12 (2011) 683-690. [23] J. Trapp, A.M. Rubenchik, G. Guss, M.J. Matthews, In situ absorptivity measurements of metallic powders during laser powder-bed fusion additive\\ manufacturing, Appl. Mater. Today 9 (2017) 341-349. [24] M. Cola, S. Betts, In-Situ Process Mapping Using Thermal Quality Signatures during Additive Manufacturing with Titanium Alloy Ti-6Al-4V, Case Study for Sigma Labs, 2018, p. 29. [25] L. Scime, J. Beuth, Using machine learning to identify in-situ melt pool signatures indicative of flaw formation in a laser powder bed fusion additive manufacturing process, Add. Manuf. 25 (2019) 151-165. [26] M.H. Farshidianfar, A. Khajepour, A.P. Gerlich, Effect of real-time cooling rate on microstructure in laser additive manufacturing, J. Mater. Process. Technol. 231 (2016) 468-478. [27] J. Raplee, A. Plotkowski, M.M. Kirka, R. Dinwiddie, A. Okello, R.R. Dehoff, S.S. Babu, Thermographic microstructure monitoring in electron beam additive manufacturing, Sci. Rep. 7 (2017) 43554. [28] W. Huang, R. Kovacevic, Feasibility study of using acoustic signals for online monitoring of the depth of weld in the laser welding of high-strength steels, Proc. IME B J. Eng. Manufact. 223 (4) (2009) 343-361. [29] T.H.C. Childs, C. Hauser, M. Badrossamay, Selective laser sintering (melting) of stainless and tool steel powders: experiments and modelling, Proc. IME B J. Eng. Manufact. 219 (4) (2005) 339-357. [30] D. Tomus, P.A. Rometsch, M. Heilmaier, X. Wu, Effect of minor alloying elements on crack-formation characteristics of Hastelloy-X manufactured by selective laser melting, Additive Manufacturing 16 (2017) 65-72. [31] N.J. Harrison, I. Todd, K. Mumtaz, Reduction of micro-cracking in nickel superalloys processed by Selective Laser Melting: a fundamental alloy design approach, Acta Mater. 94 (2015) 59-68. [32] J.H. Martin, B.D. Yahata, J.M. Hundley, J.A. Mayer, T.A. Schaedler, T.M. Pollock, 3D printing of high-strength aluminium alloys, Nature 549 (7672) (2017) 365-369. [33] J. Gockel, J. Beuth, Understanding Ti-6al-4v Microstructure Control in Additive Manufacturing via Process Maps, Solid Freeform Fabrication Proceedings, Austin, TX, 2013, pp. 12-14. Aug. [34] T. Mukherjee, J.S. Zuback, A. De, T. DebRoy, Printability of alloys for additive manufacturing, Sci. Rep. 6 (2016) 19717. [35] V. Juechter, T. Scharowsky, R.F. Singer, C. Körner, Processing window and evaporation phenomena for Ti-6Al-4V produced by selective electron beam melting, Acta Mater. 76 (2014) 252-258. [36] T.H.C. Childs, C. Hauser, M. Badrossamay, Mapping and modelling single scan track formation in direct metal selective laser melting, CIRP Annals 53 (1) (2004) 191-194 [37] T. DebRoy, H. Wei, J. Zuback, T. Mukherjee, J. Elmer, J. Milewski, A. Beese, A. Wilson-Heid, A. De, W. Zhang, Additive manufacturing of metallic components-process, structure and properties, Prog. Mater. Sci. 92 (2018) $112-224$. [38] J.C. Ion, H.R. Shercliff, M.F. Ashby, Diagrams for laser materials processing, Acta Metall. Mater. 40 (7) (1992) 1539-1551. [39] G. Taguchi, A.J. Rafanelli, Taguchi on robust technology development: bringing quality engineering upstream, J. Electron. Packag. 116 (2) (1994), 161-161. [40] H.-J. Choi, A Robust Design Method for Model and Propagated Uncertainty, PhD Thesis, Georgia Institute of Technology, 2005. [41] W. Chen, M.M. Wiecek, J. Zhang, Quality utility-A compromise programming approach to robust design, J. Mech. Des. 121 (2) (1999) 179-187. [42] E. Sandgren, T.M. Cameron, Robust design optimization of structures through consideration of variation, Comput. Struct. 80 (20-21) (2002) 1605-1613. [43] M. Mahmoudi, G. Tapia, K. Karayagiz, B. Franco, J. Ma, R. Arróyave, I. Karaman, A. Elwany, Multivariate calibration and experimental validation of a 3d finite element thermal model for laser powder bed fusion metal additive manufacturing, Integrating Mater. Manuf. Innov. 7 (3) (2018) 116-135. [44] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Courier Corporation, 2013. [45] C. Körner, E. Attar, P. Heinl, Mesoscopic simulation of selective beam melting processes, J. Mater. Process. Technol. 211 (6) (2011) 978-987. [46] C.R. Noble, A.T. Anderson, N.R. Barton, J.A. Bramwell, A. Capps, M.H. Chang, J.J. Chou, D.M. Dawson, E.R. Diana, T.A. Dunn, Ale3d: an Arbitrary LagrangianEulerian Multi-Physics Code, Tech. Rep., Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States), 2017. [47] J.C. Steuben, A.P. Iliopoulos, J.G. Michopoulos, Discrete element modeling of particle-based additive manufacturing processes, Comput. Methods Appl. Mech. Eng. 305 (2016) 537-561. [48] T. Eagar, N.-S. Tsai, Temperature fields produced by traveling distributed heat sources, Weld. J. 62 (12) (1983) 346-355. [49] N. Nguyen, A. Ohta, K. Matsuoka, N. Suzuki, Y. Maeda, Analytical Solutions for Transient Temperature of Semi-infinite Body Subjected to 3-d Moving Heat Sources vol. 78, WELDING JOURNAL-NEW YORK, 1999, p. 265. [50] A. Block-Bolten, T.W. Eagar, Metal vaporization from weld pools, Metallurgical Transactions B 15 (3) (1984) 461-469. [51] C.B. Alcock, V.P. Itkin, M.K. Horrigan, Vapour pressure equations for the metallic elements: 298-2500k, Canadian Metallurgical Quarterly 23 (3) (1984) 309-313. [52] K. Karayagiz, A. Elwany, G. Tapia, B. Franco, L. Johnson, J. Ma, I. Karaman, R. Arróyave, Numerical and experimental analysis of heat distribution in the laser powder bed fusion of Ti-6Al-4V, IISE Transactions 0 (0) (2018) 1-17. [53] C.J. Smithells, W.F. Gale, T.C. Totemeier, Smithells Metals Reference Book, eighth ed., Elsevier Butterworth-Heinemann, Amsterdam ; Boston, 2004 [54] M. Laurent Brocq, A. Akhatova, L. Perrière, S. Chebini, X. Sauvage, E. Leroy Y. Champion, Insights into the phase diagram of the CrMnFeCoNi high entropy alloy, Acta Mater. 88 (2015) 355-365. [55] M.W. Chase, NIST JANAF themochemical tables, in: Tech. Rep., fourth ed, National Institute of Standards and Technology, 1998. [56] S. Roy, M. Juha, M.S. Shephard, A.M. Maniatty, Heat transfer model and finite element formulation for simulation of selective laser melting, Comput. Mech. 62 (3) (2018) 273-284. [57] I. Couckuyt, T. Dhaene, P. Demeester, ooDACE toolbox: a flexible objectoriented Kriging implementation, J. Mach. Learn. Res. 15 (1) (2014) 3183-3186 [58] M. Letenneur, A. Kreitcberg, V. Brailovski, Optimization of laser powder bed fusion processing using a combination of melt pool modeling and design of experiment approaches: density control, Journal of Manufacturing and Materials Processing 3 (1) (2019) 21. [59] I. Toda-Caraballo, E.I. Galindo-Nava, P.E.J. Rivera-Díaz-del Castillo, Unravelling the materials genome: symmetry relationships in alloy properties, J. Alloy. Comp. 566 (2013) 217-228. [60] T. Iida, R.I. Guthrie, The Thermophysical Properties of Metallic Liquids: Fundamentals, vol. 1, Oxford University Press, USA, 2015. \begin{itemize} \item \end{itemize} \end{document} \documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{hyperref} \hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,} \urlstyle{same} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage[version=4]{mhchem} \usepackage{stmaryrd} \usepackage{bbold} \usepackage{graphicx} \usepackage[export]{adjustbox} \graphicspath{ {./images/} } \usepackage{esint} \usepackage{multirow} \title{Lecture Notes in Mechanical Engineering } \author{Ulrich Halm ${ }^{1(\boxtimes)}\left(\right.$ (D) and Wolfgang Schulz ${ }^{1,2}$ (D)\\ 1 Nonlinear Dynamics of Laser Processing, RWTH Aachen University, Steinbachstr. 15,\\ 52074 Aachen, Germany\\ ulrich.halmenld.rwth-aachen.de\\ 2 Fraunhofer Institute for Laser Technology, Steinbachstr. 15, 52074 Aachen, Germany} \date{} \begin{document} \maketitle Lecture Notes in Mechanical Engineering Uwe Reisgen Dietmar Drummer Holger Marschall Editors Enhanced Material, Parts Optimization and Process Intensification Proceedings of the First International Joint Conference on Enhanced Material and Part Optimization and Process Intensification, EMPOrIA 2020, May 19-20, 2020, Aachen, Germany Lecture Notes in Mechanical Engineering (LNME) publishes the latest developments in Mechanical Engineering - quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNME. Volumes published in LNME embrace all aspects, subfields and new challenges of mechanical engineering. Topics in the series include: \begin{itemize} \item Engineering Design \item Machinery and Machine Elements \item Mechanical Structures and Stress Analysis \item Automotive Engineering \item Engine Technology \item Aerospace Technology and Astronautics \item Nanotechnology and Microengineering \item Control, Robotics, Mechatronics \item MEMS \item Theoretical and Applied Mechanics \item Dynamical Systems, Control \item Fluid Mechanics \item Engineering Thermodynamics, Heat and Mass Transfer \item Manufacturing \item Precision Engineering, Instrumentation, Measurement \item Materials Engineering \item Tribology and Surface Technology \end{itemize} To submit a proposal or request further information, please contact the Springer Editor of your location: China: Dr. Mengchu Huang at mengchu.huang @ \href{http://springer.com}{springer.com} India: Priya Vyas at \href{mailto:priya.vyas@springer.com}{priya.vyas@springer.com} Rest of Asia, Australia, New Zealand: Swati Meherishi at \href{mailto:swati.meherishi@springer.com}{swati.meherishi@springer.com} All other countries: Dr. Leontina Di Cecco at \href{mailto:Leontina.dicecco@springer.com}{Leontina.dicecco@springer.com} To submit a proposal for a monograph, please check our Springer Tracts in Mechanical Engineering at \href{http://www.springer.com/series/11693}{http://www.springer.com/series/11693} or contact \href{mailto:Leontina.dicecco@springer.com}{Leontina.dicecco@springer.com} Indexed by SCOPUS. All books published in the series are submitted for consideration in Web of Science. More information about this series at \href{http://www.springer.com/series/11236}{http://www.springer.com/series/11236} Uwe Reisgen $\cdot$ Dietmar Drummer $\cdot$ Holger Marschall Editors \section*{Enhanced Material, Parts Optimization and Process Intensification} Proceedings of the First International Joint Conference on Enhanced Material and Part Optimization and Process Intensification, EMPOrIA 2020, May 19-20, 2020, Aachen, Germany Springer \section*{Editors} \begin{center} \begin{tabular}{ll} Uwe Reisgen & Dietmar Drummer \\ Institut für Schweißtechnik und Fügetechnik & Lehrstuhl für Kunststofftechnik \\ Aachen, Nordrhein-Westfalen, Germany & der Universität Erlangen-Nürnberg \\ & Erlangen, Bayern, Germany \\ \end{tabular} \end{center} Holger Marschall Mathematical Modeling and Analysis Darmstadt, Hessen, Germany\\ Dietmar Drummer der Universität Erlangen-Nürnberg ISSN 2195-4356 ISSN 2195-4364 (electronic) Lecture Notes in Mechanical Engineering ISBN 978-3-030-70331-8 ISBN 978-3-030-70332-5 (eBook) \href{https://doi.org/10.1007/978-3-030-70332-5}{https://doi.org/10.1007/978-3-030-70332-5} (C) The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland \section*{Preface} This volume of Lecture Notes in Mechanical Engineering contains selected papers of the planned International Joint Conference on Enhanced Material and Part Optimization and Process Intensification (EMPOrIA2020), which would have taken place in Aachen/Germany on May 19-20, 2020, but had to be canceled due to the Corona Pandemic. The conference was organized by SFB 1120 Aachen (Precision Melt Engineering), SFB 814 Erlangen (Additive Manufacturing) and CCE Darmstadt (Center for Computational Engineering). Many of the results published in this volume were funded by the Deutsche Forschungsgemeinschaft e.V. (DFG, German Research Foundation). We would like to take this opportunity to express our gratitude for this support. Highest precision in the manufacturing process is preferably simple process chains with a low number of process steps-that is one of the main demands made by manufacturing companies that seek to maintain and expand stable and sustainable production in high-wage countries such as Germany at competitive costs. The Collaborative Research Center 1120 (SFB 1120) addresses these research topics with the aim to give a comprehensive description of melt-based manufacturing technologies such as casting, injection molding, welding, cutting, additive manufacturing and melt-based coating. For these processes, in which the material is at least temporarily in a liquid phase, a multi-scale description of the involved physical and material-based processes will be developed, so as to increase part precision by at least one order of magnitude. Wherever innovations and personalized products are desired: With almost unlimited freedom of design, additive manufacturing technologies open up new perspectives to achieve constructive solutions. These types of manufacturing techniques barely set any limits to the spirit of innovation. Additive manufacturing techniques follow the trend toward individual customized products and will allow for serial production in the future. To take advantage of the potentials included in additive manufacturing techniques, the Collaborative Research Center 814 (SFB 814) does fundamental research on this technology, so it can be used for the production of multifunctional components. The most important thing is to analyze the process chain from beginning to end. This not only includes design and process\\ simulation but also especially characteristics, creation and modification of suitable materials and their reactions in the fabrication process, up to the final component. Computational Engineering (CE) is an integral part of the research profile of TU Darmstadt. CE is a modern and multidisciplinary science for computer-based modeling, simulation, analysis and optimization of complex engineering applications and processes and phenomena in nature. The Centre for Computational Engineering (CCE) concentrates all activities in CE at TU Darmstadt. It is organized orthogonally and in addition to existing departments covering the relevant topical disciplines in science and engineering. By defining relevant research areas, the CCE coordinates all research activities in Computational Engineering at TU Darmstadt. CCE offers a stable platform for multidisciplinary cooperation of its members and associated investigators, which initiates joint research projects directly, also on a large scale. Broadness and relevance of $\mathrm{CE}$ are well documented by many research projects at TU Darmstadt where CE is involved. The EMPOrIA2020 is a perfect platform for efficient knowledge transfer in the field of materials processing and their applications. The EMPOrIA2020 is devoted to scientific presentations on the latest research results. The EMPOrIA2020 focuses on the latest developments as well as future trends in the field of materials processing. The conference topics address anyone who is interested in the potential of manufacturing in theory and application. It is the aim of the EMPOrIA2020 to bring together international experts from research and industry in order to match scientific advances and economic needs for mutual benefit. EMPOrIA2020 received 37 contributions. After a thorough review process, the program committee accepted 25 papers. Thank you very much to the authors for their contribution. We would like to thank members of the program committee for their efforts and expertise in contributing to reviewing, without which it would impossible to maintain the high standards of reviewed papers. This volume consists of seven parts: Welding with five papers, brazing with two papers, coating with three papers, additive manufacturing with five papers, casting with three papers, molding with five papers and cutting with two papers. We appreciate the partnership with Springer for their essential support during the preparation of EMPOrIA2020. Thank you very much for EMPOrIA Team. Their involvement and hard work were crucial to the success of the EMPOrIA2020 conference. \section*{Organization} \section*{Steering Committee} \section*{General Chair} \begin{center} \begin{tabular}{lc} Reisgen, Uwe & \begin{tabular}{c} RWTH Aachen University, "Welding \\ and Joining Institute," Germany \\ \end{tabular} \\ Co-chairs & \\ Drummer, Dietmar & Friedrich-Alexander-Universität \\ & Erlangen-Nürnberg, "Institute of Polymer \\ Marschall, Holger & Technology," Germany \\ & Technical University Darmstadt, "Mathematical \\ & Modeling and Analysis," Germany \\ \end{tabular} \end{center} \section*{Members} Akyel, Fatma Apel, Markus Bobzin, Kerstin Elgeti, Stefanie Gillner, Arnold Hopmann, Christian RWTH Aachen University, "Welding and Joining Institute," Germany ACCESS e.V., Germany RWTH Aachen University, "Chair for Laser Technology," Germany TU Wien, "Institute of Lightweight Design and Structural Biomechanics," Austria RWTH Aachen University, "Chair of Laser Technology," Germany RWTH Aachen University, "Institute for Plastics Processing," Germany Mayer, Joachim Olschok, Simon \section*{Program Committee} Apel, Markus Behr, Marek Bobzin, Kerstin Bück, Andreas Bührig-Polaczek, Andreas Drummer, Dietmar Elgeti, Stefanie Gillner, Arnold Häfner, Constantin Hopmann, Christian Körner, Carolin Marschall, Holger Mayer, Joachim Mergheim, Julia\\ RWTH Aachen University, "Community Laboratory for Electron Microscopy," Germany RWTH Aachen University, "Welding and Joining Institute,” Germany ACCESS e.V., Germany RWTH Aachen University, "Chair for Computational Analysis of Technical Systems," Germany RWTH Aachen University, "Surface Engineering Institute," Germany Friedrich-Alexander-Universität Erlangen-Nürnberg, "Chair of Particle Technology," Germany RWTH Aachen University, "Chair for Foundry Science and Foundry Institute," Germany Friedrich-Alexander-Universität Erlangen-Nürnberg, "Institute of Polymer Technology," Germany TU Wien, "Institute of Lightweight Design and Structural Biomechanics," Austria RWTH Aachen University, "Chair of Laser Technology," Germany RWTH Aachen University, "Chair of Laser Technology," Germany RWTH Aachen University, "Institute for Plastics Processing," Germany Friedrich-Alexander-Universität Erlangen-Nürnberg, "Chair of Materials Science and Engineering for Metals," Germany Technical University Darmstadt, "Mathematical Modeling and Analysis," Germany RWTH Aachen University, "Community Laboratory for Electron Microscopy," Germany Friedrich-Alexander-Universität Erlangen-Nürnberg, "Institute of Applied Mechanics," Germany \begin{center} \begin{tabular}{|c|c|} \hline Merklein, Marion & \begin{tabular}{l} Friedrich-Alexander-Universität \\ Erlangen-Nürnberg, "Chair of Manufact \\ Technology," Germany \\ \end{tabular} \\ \hline Olschok, Simon & \begin{tabular}{l} RWTH Aachen University, "Welding \\ and Joining Institute," Germany \\ \end{tabular} \\ \hline Reisgen, Uwe & \begin{tabular}{c} RWTH Aachen University, "Welding \\ and Joining Institute," Germany \\ \end{tabular} \\ \hline Schäfer, Michael & \begin{tabular}{l} Technical University Darmstadt "Numerica \\ Methods in Mechanical Engineering," \\ Germany \\ \end{tabular} \\ \hline Schmidt, Michael & \begin{tabular}{l} Friedrich-Alexander-Universität \\ Erlangen-Nürnberg, "Chair of Photonic \\ Technologies," Germany \\ \end{tabular} \\ \hline Steinmann, Paul & \begin{tabular}{l} Friedrich-Alexander-Universität \\ Erlangen-Nürnberg, 'Institute of Applie \\ Mechanics," Germany \\ \end{tabular} \\ \hline Stingl, Michael & \begin{tabular}{l} Friedrich-Alexander-Universität \\ Erlangen-Nürnberg, "Department of \\ Mathematics," Germany \\ \end{tabular} \\ \hline Weeger, Oliver & \begin{tabular}{l} Technical University Darmstadt, "Numeric \\ Methods in Mechanical Engineering," \\ Germany \\ \end{tabular} \\ \hline Zhang, Hongbin & \begin{tabular}{l} Technical University Darmstadt, "Departm \\ of Materials and Geosciences," German \\ \end{tabular} \\ \hline \multicolumn{2}{|l|}{EMPOrIA Team} \\ \hline Akyel, Fatma & \begin{tabular}{l} RWTH Aachen University, "Welding and \\ Joining Institute," Germany \\ \end{tabular} \\ \hline Lewandowsky, Marie-Luise & \begin{tabular}{l} RWTH Aachen University, "Welding and \\ Joining Institute," Germany \\ \end{tabular} \\ \hline Olschok, Simon & \begin{tabular}{l} RWTH Aachen University, "Welding and \\ Joining Institute," Germany \\ \end{tabular} \\ \hline Reisgen, Uwe & \begin{tabular}{l} RWTH Aachen University, "Welding and \\ Joining Institute," Germany \\ \end{tabular} \\ \hline \end{tabular} \end{center} \section*{Contents} Welding\\ Simulation of Phase Transformation and Residual Stress of Low Alloy Steel in Laser Beam Welding ..... 3\\ Fatma Akyel, Uwe Reisgen, Simon Olschok, and Karthik Murthy\\ Metallographic Comparison for Laser Welding of Cu-ETP and CuSn6 with Laser Beam Sources of $515 \mathrm{~nm}$ and $1030 \mathrm{~nm}$ Wavelength ..... 14\\ Marc Hummel, Christoph Schöler, and Arnold Gillner\\ Numerical Investigation of Keyhole Depth Formation in Micro Welding of Copper with $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ Laser Radiation ..... 29\\ Christoph Schöler, Markus Nießen, and Wolfgang Schulz\\ Reduction of Hot Cracks During Electron Beam Welding of Alloy-247 LC ..... 40\\ Aleksej Senger, Torsten Jokisch, Simon Olschok, and Uwe Reisgen\\ Validation of the EDACC Model for GMAW Process Simulation by Weld Pool Dimension Comparison ..... 51\\ Oleg Mokrov, Marek Simon, Ivan Shvartc, Rahul Sharma, and Uwe Reisgen\\ Brazing\\ New Opportunities for Brazing Research by in situ Experiments in a Large Chamber Scanning Electron Microscope ..... 63\\ Anke Aretz, Riza Iskandar, Joachim Mayer, Kirsten Bobzin, Alexander Schmidt, and Thomas E. Weirich\\ Phase-Field Modeling of Precipitation Microstructure Evolution in Multicomponent Alloys During Industrial Heat Treatments ..... 70\\ Michael Fleck, Felix Schleifer, Markus Holzinger, Yueh-Yu Lin, and Uwe Glatzel\\ Coating\\ $\mathrm{TiO}_{\mathrm{x}} / \mathrm{Cr}_{2} \mathrm{O}_{3}$ Heating Coatings for Injection Molding of Polyamide ..... 81\\ Kirsten Bobzin, Wolfgang Wietheger, Hendrik Heinemann, and Andreas Schacht\\ Simulation of Multiple Particle Impacts in Plasma Spraying . ..... 91\\ Kirsten Bobzin, Wolfgang Wietheger, Hendrik Heinemann, and Ilkin Alkhasli\\ Simplex Space-Time Meshes for Droplet Impact Dynamics .. ..... 101\\ Violeta Karyofylli and Marek Behr\\ Additive Manufacturing\\ Melt Pool Formation and Out-of-Equilibrium Solidification During the Laser Metal Deposition Process ..... 113\\ Jonas Zielinski, Henrik Kruse, Marie-Noemi Bold, Guillaume Boussinot, Markus Apel, and Johannes Henrich Schleifenbaum\\ Understanding Cylinder Temperature Effects in Laser Beam Melting of Polymers ..... 123\\ Sandra Greiner, Andreas Jaksch, and Dietmar Drummer\\ Additive Manufacturing of Multi-material Polymer Parts Within the Collaborative Research Center 814 ..... 142\\ Robert Setter, Thomas Stichel, Thomas Schuffenhauer, Sebastian-Paul Kopp, Stephan Roth, and Katrin Wudy\\ Extreme High-Speed Laser Material Deposition (EHLA) as High-Potential Coating Method for Tribological Contacts in Hydraulic Applications ..... 153\\ Achill Holzer, Stephan Koß, Stephan Ziegler, Johannes Henrich Schleifenbaum, and Katharina Schmitz\\ In-Situ Alloying in Gas Metal Arc Welding for Wire and Arc Additive Manufacturing ..... 168\\ Uwe Reisgen, Rahul Sharma, and Lukas Oster\\ Casting\\ Development of an In-Situ Observation Procedure for Hot Tear Formation in Aluminum Alloys in Gravity Die Casting ..... 181\\ Nino Wolff, Rahul Sharma, Uwe Vroomen, Andreas Bührig-Polazcek, and Uwe Reisgen\\ Determination of the Heat Transfer Coefficient for a Liquid-Solid Contact in Gravity Die Casting Processes ..... 191\\ Thomas Vossel, Björn Pustal, and Andreas Bührig-Polazcek\\ Micro-macro Coupled Solidification Simulations of a Sr-Modified Al-Si-Mg Alloy in Permanent Mould Casting ..... 202\\ Bei Zhou, Herfried Behnken, Janin Eiken, Markus Apel, Gottfried Laschet, and Nino Wolff\\ Molding\\ Analysis of Radial Heat Transfer in an Injection Mold with Highly Dynamic Segmented Mold Tempering ..... 215\\ Christian Hopmann, Cemi Kahve, and Cheng-Long Xiao\\ Evaluation and Transport of the Crystallization Heat in an Iterative Self-consistent Multi-scale Simulation of Semi-crystalline Thermoplastics ..... 225\\ Christian Hopmann, Jonathan Alms, and Gottfried Laschet\\ Thermal Optimisation of Injection Moulds by Solving an Inverse Heat Conduction Problem ..... 236\\ Tobias Hohlweck and Christian Hopmann\\ Reduction of Internal Stresses in Optics Through a Demand-Oriented Cooling Channel Layout in Injection Moulding ..... 246\\ Christian Hopmann and Jonas Gerads\\ Inverse Design Method for Injection Molding Cavity Shapes . ..... 256\\ Florian Zwicke and Stefanie Elgeti\\ Cutting\\ Cutting Whistle - An Original Approach for Nozzle Design in Fiber Laser Cutting of Stainless Steel ..... 267\\ M. de Oliveira Lopes, Dirk Petring, Dennis Arntz-Schröder, Frank Schneider, Stoyan Stoyanov, and Arnold Gillner\\ Optimization of Beam Shapes for Laser Fusion Cutting by 3D Simulation of Melt Flow ..... 277\\ Ulrich Halm and Wolfgang Schulz\\ Author Index. ..... 287 \section*{Welding} \section*{Simulation of Phase Transformation and Residual Stress of Low Alloy Steel in Laser Beam Welding } \begin{abstract} The inhomogeneous temperature distribution in welding processes leads to high temperature gradients between the weld seam and the base material. A heterogeneous phase transformation takes place between the areas where the austenitic transformation temperature is exceeded and those where it remains below this temperature. This leads to a residual stress state which results in distortion when the yield strength is exceeded. In order to understand the thermal history of a welded specimen and the phase transformation that has taken place, numerical simulation is used.\\ This work focuses on the temperature field simulation and the resulting phase transformation in laser beam welding. Two heat sources are combined to simulate the weld pool. Typical models from the literature are used to represent the phase transformation. Altogether a model is developed which can be used as a basis for the calculation of residual stress formation due to thermal load and phase transformation. \end{abstract} Keywords: FEM simulation $\cdot$ Residual stress $\cdot$ Conical heat source $\cdot$ Goldak heat source $\cdot$ Phase transformation \section*{1 Introduction} The use of fusion welding in manufacturing industry is wide spread. However, the local heat input in the welding process leads to an inhomogeneous temperature distribution resulting in varying temperature gradients within the whole sample. While the temperature surpasses the liquidus temperature in the fusion zone (FZ), resulting in molten material and even evaporation in this area, the temperature in the heat affected zone (HAZ) is below the solidus temperature. Areas that surpassed the austenitization temperature decompose in the cooling step into different phases depending upon the chemical composition and the cooling rate. The phase transformation and the thermal shrinkage in the cooling process superpose to residual stress or, in the case the yield point is surpassed, result in distortion of the welded specimen. A new approach to reduce the residual stresses is through targeted alloy composition. During the transformation from austenite to martensite the lattice elongates. This\\ volume expansion ensures that compressive stresses are generated around the transformation zone. With a low-alloy material such as S235JR, the martensite transformation takes place at about $400^{\circ} \mathrm{C}$. At this temperature compressive stresses build up until the transformation is complete. However, as the component cools further, the tensile stresses, generated by shrinkage, dominate the compressive stresses. By using the alloy composition, it is possible to shift the martensite start temperature $\left(M_{s}\right)$ to lower temperature. Thus, compressive stresses are induced in the tensile stress dominated weld seam, until room temperature is reached. Because the transformation takes place at reduced temperatures, this phenomenon is called the Low Transformation Temperature (LTT) effect. In order to understand this effect, a simulation model is generated, which shows the phase transformation in the base material and the weld seam. For this purpose, a model must first be created, which depicts the thermal history and the phase transformations in a specimen. In literature, many approaches are present using FEM simulation to describe the formation of residual stress within a welded specimen [1-5]. However, most simulations are used for the arc welding processes. In this work, the heat distribution of carbonmanganese steel is simulated combining a typical heat source for arc welding and beam welding, in order to depict the distribution in a laser beam welded specimen. Furthermore, the microstructure transformation is simulated by building a model, which describes the phase transformations based on the heat input. \section*{2 State of the Art} During production, each component is subject to certain environmental influences, for example static or dynamic stress. Apart from these environmental influences, additional conditions influencing internal stresses exist in the component. These are called residual stresses. Residual stresses act without external loads and can at most be in the range of the local material yield strength. If the yield strength is exceeded, plastic deformation of the component occurs. [6,7]. The local heat input in the welding process causes metallurgical processes in ferriticpearlitic steels, for instance in the weld pool and the heat-affected zone, [8]. As the austenite start temperature $A_{c 1}$ is reached, the base microstructure begins to transform into austenite. As soon as the austenite finish temperature $A_{c 3}$ is reached or exceeded, the microstructure consists only of austenite. Due to the inhomogeneous temperature distribution, the phase transformation and stress distribution is also inhomogeneous. These processes are restricted by the surrounding cool base material, which leads to local incompatibility [9]. Apart from experimental investigations, numerical simulation is used to numerically visualize phenomena that otherwise take place too quickly in the welding process itself. A significant advantage is the mathematical prediction of the residual stresses and distortion caused by the welding process. According to [10], welding simulation is divided into 3 areas. In the process simulation the fusion zone geometry and the temperature field are simulated. Thermal boundary conditions are defined and thermal material characteristics are included. With the information about the temperature cycles the material simulation can be performed. Here, the\\ processes that take place in the material are simulated. The phase volume fraction in the melt zone throughout the heat-affected zone up to the base material is depicted. With the results of the material characteristics and the thermal history, the structure simulation is used to map the residual stresses and distortion in the component. In order to be able to display the metallurgical processes and the stress states in the workpiece, it is important to determine the transient temperature field as accurately as possible. For this purpose, a so-called equivalent heat source is used to represent the heat coupling. In this context, the heat source model according to Goldak is used in particular [11]. The model describes a volumetric double ellipsoid Gaussian distribution of the heat flux density and is often used for arc welding processes. For the description of the deep welding effect in the beam welding processes, a volumetric Gaussian heat source is also used, which describes the shape of a cone [12]. Various numerical models are used to simulate the phase transformation. For diffusion controlled transformations (ferrite, perlite and bainite) the microstructure components are described by the equation according to Johnson-Mehl-Avrami-Kolomogorov (short JMAK or Avrami equation) [13-17]. Furthermore, the equation according to Koistinen and Maburger is used to describe the diffusionless martensitic phase transformation as a function of the martensite starting temperature [18]. These and other models are used to represent the boundary conditions for the numerical analysis of phase transformations. \section*{3 Welding Trials} The material used in this work is a low alloy carbon-manganese steel sheet (S235JR) with the dimensions $100 \times 50 \times 5 \mathrm{~mm}$. No filler wire was used and a bead on plate was carried out (autogenous welding). For the welding tests, a Trumpf TruDisk 16002 disk laser was used as beam generator, which has a maximum beam power of $16 \mathrm{~kW}$ and a minimum fibre diameter of $200 \mu \mathrm{m}$. The chemical composition of the base material was investigated by an OES analysis, Table 1. Table 1. Alloying elements of the base material (S235JR) in $\mathrm{m} \%$ \begin{center} \begin{tabular}{l|l|l|l|l|l|l|l|l|l} \hline & $\mathrm{Fe}$ & $\mathrm{C}$ & $\mathrm{Si}$ & $\mathrm{Mn}$ & $\mathrm{Cr}$ & $\mathrm{Ni}$ & $\mathrm{Mo}$ & $\mathrm{P}$ & $\mathrm{S}$ \\ \hline S235JR & 98.2 & 0.08 & 0.056 & 1.01 & 0.413 & 0.041 & 0.014 & 0.034 & 0.003 \\ \hline \end{tabular} \end{center} To record the temperature distribution in the specimen, type $\mathrm{K}$ thermocouples were tacked to the top of the component, Fig. 1. The distance between each thermocouple was $5 \mathrm{~mm}$. The temperature of both sides of the weld was recorded and an average built. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-018(1)} \end{center} Fig. 1. Temperature measurement in the welding process with type $\mathrm{K}$ thermocouples \section*{4 Numerical Simulation Model} A numerical model is a replica of the physical model. In order to realise a numerical model an exact definition of material properties and boundary conditions is necessary. Since the welding was performed lengthwise over the middle of the sample, only half of the sample needs to be simulated because of the symmetry. Symmetry does not only apply to geometry. Since the weld is made in the middle of the sample, the heat conduction to the sides is also the same. The temperature-dependent mechanical properties as well as thermal properties are subject to the same temperature gradients. For this reason it is sufficient to simulate half of the sample and still get a result for the whole sample. This is a common procedure to reduce the simulation calculation time. Thus, the simulated dimension of the model is $25 \times 100 \times 5 \mathrm{~mm}$ with a symmetry line along the path of the heat source. An additional method to reduce the computing time is to adjust the mesh density. In this context, the mesh density in the welding zone is defined very finely, since the temperature gradients are particularly high here, and a mesh that is too coarse can lead to errors in the calculation, Fig. 2. The mesh density reduces gradually with further distance to the weld zone. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-018} \end{center} Fig. 2. Meshed model with high mesh density in the welding zone and a total geometry of $25 \times$ $100 \times 5 \mathrm{~mm}$ The 3D finite element mesh was generated in ABAQUS CAE using the eight-node linear heat transfer brick element (DC3D8) totalling over 32.428 nodes and 27.930 elements. The smallest element size measures $0.5 \times 0.5 \times 0.5$ in the weld zone. For the volumetric heat flux the subroutine DFLUX is used. The subroutine used for the phase transformation is UMAT with solution dependent variables (SDV). \subsection*{4.1 Heat Source Model} The primary objective of the temperature field simulation is to determine the geometrical characteristics of the melt pool, as well as the temperature cycles in the melt pool and in its immediate vicinity (HAZ). The heat source is used to apply the thermal load in the weld zone. In this study a combination of a spherical and a conical heat source model is used to describe a transient heat source model, Fig. 3. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-019} \end{center} Fig. 3. Combined spherical and conical heat source model The spherical heat source is suitable for modelling the heat input into the width of the weld seam. However, the geometrical description is not sufficient to describe the heat input into the depth of the workpiece. For this reason, the cone heat source is added. \begin{equation*} Q_{\text {Sperical }}=(1-\Psi) \underbrace{\frac{6 \sqrt{3} Q}{R_{g}^{3} \pi \sqrt{\pi}}}_{\text {Energy input }} \exp \left[-3\left(\frac{x^{2}}{R_{g}^{2}}+\frac{y^{2}}{R_{g}^{2}}+\frac{[z-v \Delta t]^{2}}{R_{g}^{2}}\right)\right] \tag{1} \end{equation*} Equation 1 describes a Goldak heat source with geometric variables defined to be equal in size, thus representing a sphere with the radius $R_{g}$. This serves to simplify the equation and to reduce the variables in the numerical model. The beam power is described by the Parameter $Q$ where by $Q=U I k_{\text {eff }}$; defined by the acceleration voltage $U$, the beam current $I$ and the efficiency coefficient $k_{\text {eff }}$. The Parameter $\Psi$ describes the portion of the conical heat source and is $\leq 1$. This means for example with a $\Psi=0.7$ the conical part is effective at $70 \%$ and the spherical part at $30 \%$. The movement of the heat source is described by the expression $u=x-v t$. Here $t$ is the welding time and $v$\\ the welding speed. \begin{gather*} Q_{\text {Conical }}=\underbrace{\frac{3 \Psi Q}{\pi H R_{0}^{2}}}_{\text {Energy input }} \exp \left[-3\left(\frac{x^{2}}{R_{0}^{2}}+\frac{(z-v \Delta t)^{2}}{R_{0}^{2}}\right)\right] \underbrace{\left[1+0.01\left(\frac{H-y}{H}\right)\right]}_{\text {Inclination of flanks }} \text { step }\left(\frac{H-y}{1 m m}\right) \tag{2}\\ \text { step }=\left\{\begin{array}{c} 0 \text { if } H-y<0.0 \\ 1 \text { if } H-y>0.0 \\ 0.5 \text { if } H-y=0.0 \end{array}\right. \end{gather*} Equation 2 is used for the conical heat source. The geometrical contour of the cone is described by the radius $R_{O}$ and the cone height $H$. In addition, a term is provided in which the inclination of the cone flanks is described. The energy density distribution in the direction of the weld depth is regulated by the dimensionless step-function. The stepfunction is a simulation specification so that the heat input in y-direction never exceeds the cone height $\mathrm{H}$. If $\mathrm{y}>\mathrm{H}$, the step-function is set as 0 . If $\mathrm{y}<\mathrm{H}$, the step-function is set as 1 . If $\mathrm{y}=\mathrm{H}$, the function is set to 0.5 . To represent the total heat source, the conical and spherical heat sources are added up, Eq. 3. \begin{equation*} Q_{L B}=Q_{\text {Spherical }}+Q_{\text {Conical }} \tag{3} \end{equation*} In order to carry out the thermal analysis, it is necessary to define the thermo-physical properties of the weld plate and initial temperature distribution. \subsection*{4.2 Phase Transformation Model} The kinetics of a phase transformation in the heating and cooling cycle are described by the JMAK-equation, Eq. 4. \begin{equation*} V_{A}=\sum_{i} V_{i}^{0}\left(1-\exp \left(-b_{i} t^{n_{i}}\right)\right) \tag{4} \end{equation*} Where $V A$ describes the austenite fraction, $V i^{0}$ constitutes an initial fraction of ferrite $(\mathrm{i} \equiv \mathrm{F})$, pearlite $(\mathrm{i} \equiv \mathrm{P})$ and bainite $(\mathrm{i} \equiv \mathrm{B})$, while the constants $b_{i}$ and $n_{i}$ are material parameters and $t$ the time. The base material (S235JR) consists in its initial state of around $94 \%$ of ferrite and $6 \%$ of pearlite phase fraction. The kinetics of the phase transformation in the heating cycle from pearlite to austenite $(\mathrm{P} \rightarrow \mathrm{A})$ and ferrite to austenite $(\mathrm{F} \rightarrow \mathrm{A})$ have to be considered. Both transformations take place by nucleation and growth processes. The mathematical modelling of a $\mathrm{P} \rightarrow$ A transformation was introduced by [19] and it can be adopted to the base material. With this, Eq. 5 describes the austenite volume fraction from pearlite dissolution $V \gamma^{P}$ during the continuous heating. \begin{equation*} V_{\gamma}^{P}=V_{P_{0}}\left\{1-\exp \left(\int_{A_{c_{1}}}^{T} \frac{4 \pi}{3 \dot{\mathrm{T}}^{4}} \dot{N} G^{3} \Delta T^{3} d T\right)\right\} \tag{5} \end{equation*} Where $V_{P_{0}}$ is the initial pearlite fraction. The nucleation rate $\dot{N}$ and the growth rate $\mathrm{G}$ were expressed as a function of the activation energies $Q_{N}$ and $Q_{G}$. Equation 6 describes the activation energies as follows: \begin{equation*} \dot{N}=f_{N} \exp \left(-\frac{Q_{N}}{k \Delta T}\right) \& G=f_{G} \exp \left(-\frac{Q_{G}}{k \Delta T}\right) \tag{6} \end{equation*} The parameter $k$ is the Boltzman constant, whereas $f_{N}$ and $f_{G}$ are functions representing the influence of the structure and the heating rate on the nucleation growth rates respectively. [19] and [20] proposed the kinetics of ferrite to austenite transformation. Equation 7 shows the proposed relationship: \[ V_{\gamma}^{\alpha}=\left\{\begin{array}{c} V_{\alpha_{0}}\left[1-\frac{5.6 \dot{T}}{6 \times 10^{-12} V_{\alpha_{0}}\left(T-T_{C}\right)^{5.6}+5.6 \dot{T}}\right], T_{C}393$ & 75 \\ \hline Melting point $[\mathrm{K}]$ & 1356 & 1313 \\ \hline \end{tabular} \end{center} The striking difference is the five times higher thermal conductivity of Cu-ETP compared to CuSn6. With the same absorption as shown in Fig. 2, this results in a completely different thermal conduction of energy into the material. \section*{4 Results and Discussion} \section*{Experiments} The experimentally determined data are discussed below. Figure 5 shows the welding depth determined from cross sections. Here the dependence of laser power, feed rate and laser wavelength is of primary importance.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-032} Fig. 5. Weld seam depth of CuSn6 (left) and Cu-ETP (right) depending on laser power, feed rate and laser wavelength The graphs show the dependence of the welding depth on laser power and feed rate, whereby both laser wavelengths are compared. For CuSn6 (left), the values of the welding depth for $1030 \mathrm{~nm}$ wavelength are significantly higher than the values for $515 \mathrm{~nm}$ at a feed rate of $50 \mathrm{~mm} / \mathrm{s}$. With increasing feed rate, a different sensitivity can\\ be seen with both lasers. If the feed rate is increased to $250 \mathrm{~mm} / \mathrm{s}$, the welding depth at $1030 \mathrm{~nm}$ wavelength is reduced by up to $2100 \mu \mathrm{m}$, whereas the welding depth at $515 \mathrm{~nm}$ wavelength is only reduced by a maximum of $1350 \mu \mathrm{m}$. It can also be seen that this causes the curves to converge. At an even higher feed rate, it can be assumed that the curves would intersect between $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ wavelength. This behavior can be seen in the right diagram for $\mathrm{Cu}-\mathrm{ETP}$. This results in a range between 150 and $250 \mathrm{~mm} / \mathrm{s}$ feed rate where the laser weld seams with $515 \mathrm{~nm}$ wavelength are even deeper than those of $1030 \mathrm{~nm}$ laser wavelength. For welding applications with a wide range of different feed rates, the laser with $515 \mathrm{~nm}$ wavelength provides more consistent welding depths. Looking at the weld seam width, an opposite behavior than for the weld seam depth is visible. The graphs in Fig. 6 show the same representation, but this time with the weld seam width plotted on the y-axis.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-033} Fig. 6. Weld seam width of CuSn6 (left) and Cu-ETP (right) depending on laser power, feed rate and laser wavelength It can be seen that for both CuSn6 and Cu-ETP the seam width at $515 \mathrm{~nm}$ wavelength tends to be higher than width at $1030 \mathrm{~nm}$ wavelength. The seam width of CuSn6 with $515 \mathrm{~nm}$ wavelength and increasing feed decreases more than with $1030 \mathrm{~nm}$ wavelength. With CuSn6 the curves tend to be constant for both wavelengths. In addition, the seam width is lower in absolute terms for Cu-ETP than for CuSn6. This can be explained by the 5 times higher thermal conductivity of Cu-ETP as listed in Table 3. Calculating the aspect ratio (weld seam depth/weld seam width) from the graphs shown before, this results in a new image as shown in Fig. 7. For CuSn6, the aspect ratio for $515 \mathrm{~nm}$ wavelength is between 1 and 2 and remains constant despite increasing feed rate. On the other hand, the aspect ratio for $1030 \mathrm{~nm}$ decreases from 2.5-3.5 down to about 2. For Cu-ETP, the point of intersection is again earlier at a feed rate of about $200 \mathrm{~mm} / \mathrm{s}$. At higher feed rates from $200 \mathrm{~mm} / \mathrm{s}$ upwards, weld seams with greater aspect ratio are formed at $515 \mathrm{~nm}$ wavelength compared to $1030 \mathrm{~nm}$ wavelength.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-034} Fig. 7. Aspect ratio for CuSn6 (left) and Cu-ETP (right) depending on laser power, feed rate and laser wavelength In Fig. 8 and Fig. 9 a representation of the weld seam cross sections for both laser wavelengths and materials are shown. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-034(1)} \end{center} Fig. 8. Weld seam cross sections of CuSn6 for $1030 \mathrm{~nm}$ laser (left) and $515 \mathrm{~nm}$ laser (right) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-035(1)} \end{center} Fig. 9. Weld seam cross sections of Cu-ETP for $1030 \mathrm{~nm}$ laser (left) and $515 \mathrm{~nm}$ laser (right) In the case of CuSn6, very sharply tapered weld seams are produced at the seam base with low feed rate. With increasing feed rate, the welding depth decreases for both. However, the weld seam becomes wider at the seam base. It can also be seen, that weld seams with the $515 \mathrm{~nm}$ laser beam source have stronger pore formation than with the $1030 \mathrm{~nm}$ wavelength. For $\mathrm{Cu}$-ETP on the other hand, the weld seams show a similar geometry for both wavelengths and parameters. Once again, a stronger pore formation can be observed at $515 \mathrm{~nm}$ wavelength. In addition, the melt throw-up is more pronounced on the upper side of the seam with $515 \mathrm{~nm}$ wavelength. These results indicate a greatly increased process dynamic in the melt pool with the $515 \mathrm{~nm}$ wavelength process. Measuring the weld seam surface roughness with a 3D-microscope (Keyence VHX6000) the findings of an increased process dynamic can be confirmed. As shown in Fig. 10, the surface roughness of both materials with $515 \mathrm{~nm}$ wavelength is higher than with $1030 \mathrm{~nm}$ wavelength.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-035} Fig. 10. Weld seam surface roughness for CuSn6 (left) and Cu-ETP (right) depending on laser power, feed rate and laser wavelength These findings are also confirmed by the surface photographs shown in Fig. 11. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-036} \end{center} Fig. 11. Comparison of weld seam surface on CuSn6 (left) and Cu-ETP (right) between $515 \mathrm{~nm}$ laser (top) and $1030 \mathrm{~nm}$ laser (bottom) The weld seams produced with $515 \mathrm{~nm}$ wavelength show more irregular structures visible due to a stronger formation of spatter around the weld seam as well as a more irregular surface and stronger cratering compared to $1030 \mathrm{~nm}$ for both $\mathrm{CuSn} 6$ and $\mathrm{Cu}-$ ETP. \section*{Simulation} The experimental results from Fig. 5 and Fig. 6 are assessed using the keyhole model presented in Sect. 3 in order to identify the mechanisms leading to the different trends observed with $515 \mathrm{~nm}$ and $1030 \mathrm{~nm}$ laser radiation. The values of keyhole depths and widths (at the keyhole entry) are extracted from the calculated three-dimensional keyhole profiles as a function of the process parameters. The analysis of the keyhole properties then should be directly linkable to the weld seam properties because of a geometric correlation between them. The simulation results of the keyhole depths and widths are shown in Fig. 12. In both cases similar trends as in the experimental results are observed. The graphs of the keyhole depth show different slopes leading to deeper keyholes with the $1030 \mathrm{~nm}$ laser at low feed rates. In contrast the keyhole width acts much less sensitive to changes in the process parameters although a slightly higher sensitivity still can be seen for the $1030 \mathrm{~nm}$ laser. The values of the keyhole width are always greater for the $515 \mathrm{~nm}$ laser and do not reflect the "intersecting" behavior of the keyhole depth. It should be noted that the power values used in the simulations differ from the nominal values in the experiments. They had to be manipulated in order to obtain comparable keyhole depths. For $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ radiation $80 \%$ and $60 \%$ of the nominal values\\ were found by trial and error calculations, respectively. The reduction to effective powers can be explained by losses due to the focusing optic (approximately 10\%, the only losses considered in the calculations of the keyhole width) and by interaction with the metal vapor inside the keyhole (scattering, absorption) which is wavelength-dependent. There might be further reasons for the discrepancy like a non-stationary process in the experiments or the two-dimensional model structure (c.f. [14]). Nevertheless, it should be concluded that the attenuation of laser light by the metal vapor is much more present in case of the $515 \mathrm{~nm}$ beam (c.f. [12,13]).\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-037} Fig. 12. Calculated keyhole depth and width from numerical model for Cu-ETP Regarding the qualitative behavior of the keyhole depth, the model reproduces the influence of the wavelength correctly. The following hypotheses are put forward to explain the differences between a process with a wavelength of $515 \mathrm{~nm}$ and $1030 \mathrm{~nm}$. Laser beams with a wavelength of $515 \mathrm{~nm}$ impinging on the horizontal material surface are absorbed to a larger extent than those at $1030 \mathrm{~nm}$ wavelength. Heating and melting is intensified which leads to an increased keyhole entry diameter. Due to the enlarged opening, a larger part of the total laser radiation enters the keyhole. This is particularly pronounced for high feed rates at which the weld depth reacts much more sensitive for the $1030 \mathrm{~nm}$ radiation. Furthermore, the radiation of $515 \mathrm{~nm}$ wavelength entering the keyhole is absorbed more strongly than the radiation of $1030 \mathrm{~nm}$ wavelength during any interaction with the keyhole surface which tends to produce steeper inclinations of the keyhole wall in this process regime. At lower feed rates, however, there are two peculiar aspects that lead to deeper keyholes with the $1030 \mathrm{~nm}$ laser radiation. First, when the angle between incident radiation and surface normal exceeds a certain value, absorption according to the Fresnel equations becomes larger for $1030 \mathrm{~nm}$ than for $515 \mathrm{~nm}$ radiation (c.f. Fig. 13). This typically happens whenever the keyhole wall acquires a sufficient steepness. Second, the stronger absorption of the $515 \mathrm{~nm}$ light by the metal vapor becomes more noticeable the deeper the keyhole gets. In combination, both effects lead to the trends observed in the experiments and simulations. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-038} \end{center} Fig. 13. Angular dependence of the absorptivity of Cu-ETP for $515 \mathrm{~nm}$ and $1030 \mathrm{~nm}$ laser radiation after the Fresnel equations \section*{5 Conclusions and Outlook} In the present work, a parameter study on CuSn6 and Cu-ETP is conducted to compare the influence of the laser wavelength on the laser welding process. A laser beam source with $515 \mathrm{~nm}$ and one with $1030 \mathrm{~nm}$ wavelength are used with identical focal diameter. The resulting weld seams are compared based on metallographic evaluation of cross sections and surface measurements. The following conclusions can be drawn: i. The final weld seam depth shows lower influence on feed rate in a process with $515 \mathrm{~nm}$ laser wavelength. ii. For feed rates $<150 \mathrm{~mm} / \mathrm{s}$ the laser beam source with $1030 \mathrm{~nm}$ wavelength produces weld seams with greater depth than $515 \mathrm{~nm}$. At feed rates, for CuSn6 $>250 \mathrm{~mm} / \mathrm{s}$ and Cu-ETP $>200 \mathrm{~mm} / \mathrm{s}$, the laser produces deeper welds at a wavelength of $515 \mathrm{~nm}$. iii. The laser beam source with $515 \mathrm{~nm}$ wavelength produces weld seams with greater surface roughness and increased pore formation compared to the $1030 \mathrm{~nm}$ laser beam source. iv. For $515 \mathrm{~nm}$ laser wavelength a stronger interaction of light and copper vapor is expected. v. The trends of the weld seam depth and width are attributed to differences in Fresnel absorption and light vapor interaction by means of simulation studies. In future investigations the influence of local power modulation on the process with both laser wavelengths and identical optical parameters should be investigated. Due to the homogeneous distribution of the laser power in the material, it can be investigated\\ more precisely what influence the laser beam wavelength has on the formation of pores inside the weld seam. For the simulation, a consideration of light-vapor interaction inside the keyhole and three-dimensional heat conduction losses at the keyhole bottom are expected to give more reliable results. For the experimental proof, further in situ experiments have to be conducted to determine the geometry of the vapor capillaries, the absorption behavior of the laser radiation in the process and the position of the laser beam axis and keyhole axis. This allows to determine to which degree the laser radiation with different wavelengths actually influences the process. Acknowledgements. The presented investigations were carried out at RWTH Aachen University within the framework of the Collaborative Research Centre SFB-1120-236616214 "Bauteilpräzision durch Beherrschung von Schmelze und Erstarrung in Produktionsprozessen" and funded by the Deutsche Forschungsgemeinschaft e.V. (DFG, German Research Foundation). The sponsorship and support is gratefully acknowledged. \section*{References} \begin{enumerate} \item Breitkopf, A.: Umsatz mit Lasern weltweit in den Jahren 2006 bis 2019, 11 May 2020]. \href{https://de.statista.com/statistik/daten/studie/163232/umfrage/weltweiter-umsatz-mitlasern-seit-2006/}{https://de.statista.com/statistik/daten/studie/163232/umfrage/weltweiter-umsatz-mitlasern-seit-2006/} \item Häusler, A., Mehlmann, B., Olowinsky, A., Gillner, A., Poprawe, R.: Efficient copper microwelding with fibre lasers using spatial power modulation. Lasers Eng. LIE 36(1), 133-146 (2017) \item Poprawe, R.: Tailored Light 2. Springer, Heidelberg (2011) \item Ramsayer, R.M., Sebastian Engler, G.S.: New approaches for highly productive laser welding of copper materials. In: 1st International Electric Drives Production Conference (EDPC) (2011) \item Hummel, M., Schöler, C., Häusler, A., Gillner, A., Poprawe, R.: New approaches on laser micro welding of copper by using a laser beam source with a wavelength of $450 \mathrm{~nm}$. J. Adv. Join. Process. 1, 100012 (2020). \href{https://doi.org/10.1016/j.jajp.2020.100012}{https://doi.org/10.1016/j.jajp.2020.100012} \item Engler, S., Ramsayer, R., Poprawe, R.: Process studies on laser welding of copper with brilliant green and infrared lasers. Phys. Proc. 12, 339-346 (2011). \href{https://doi.org/10.1016/j.phpro}{https://doi.org/10.1016/j.phpro}. 2011.03.142 \item Conzen, J.H., Häusler, A., Stollenwerk, J., Gillner, A., Poprawe, R., Loosen, P.: LaserstrahlMikroschweißen von mikroelektronische Baugruppen unter Anwendung von örtlicher und zeitlicher Energiedeposition. Elektronische Baugruppen und Leiterplatten EBL (2017) \item De Bono, P., Metsios, I., Blackburn, J., Hilton, P.: Laser processing of copper and aluminium thin sheets with green $(532 \mathrm{~nm})$ and infrared $(1064 \mathrm{~nm})$ pulsed laser beam sources. In: ICALEO (2013) \item Pricking, S., Huber, R., Klausmann, K., Kaiser, E., Stolzenburg, C., Killi, A.: High-power $\mathrm{CW}$ and long-pulse lasers in the green wavelength regime for copper welding. SPIE LASE 2016:97410G. \href{https://doi.org/10.1117/12.2213293}{https://doi.org/10.1117/12.2213293}. \item Altarazi, S., Hijazi, L., Kaiser, E.: Process parameters optimization for multiple-inputsmultiple-outputs pulsed green laser welding via response surface methodology. In: International Conference on Industrial Engineering and Engineering Management 4-7 December 2016, Bali, Indonesia (2016) \item Kaiser, E., Huber, R., Stolzenburg, C., Killi, A.: Sputter-free and uniform laser welding of electric or electronical copper contacts with a green laser. In: LANE, vol. 8 (2014) \item Kaiser, E., Dold, E., Killi, A., Zaske, S., Pricking, S.: Application benefits of weling copper with a $1 \mathrm{~kW}, 515 \mathrm{~nm}$ continuous wave laser. In: 10th CIRP Conference on Photonic Technologies [LANE 2018], vol. 10 (2018) \item Haubold, M., Ganser, A., Eder, T., Zäh, M.F.: Laser welding of copper using a high power disc laser at green wavelength. Proc. CIRP 74, 446-449 (2018). \href{https://doi.org/10.1016/j.pro}{https://doi.org/10.1016/j.pro} cir.2018.08.161 \item Schöler, C., Nießen, M., Hummel, M., Olowinsky, A., Gillner, A., Schulz, W.: Modeling and simulation of laser micro welding. In: Lasers in Manufacturing Conference (2019) \item Copper, L.A.: In: Ullmann's Encyclopedia of Industrial Chemistry. Wiley-VCH Verlag GmbH \& Co KGaA, , Hoboken (2000) \item Brillo, J., Egry, I.: Surface tension of nickel, copper, iron and their binary alloys. J. Mater. Sci. 40(9-10), 2213-2216 (2005). \href{https://doi.org/10.1007/s10853-005-1935-6}{https://doi.org/10.1007/s10853-005-1935-6} \item Kramer, T., Olowinsky, A., Durand, F.: SHADOW - a new welding technique. In: SPIE 2002 (4637) (2002) \item Moeller, E. (ed.): Handbuch Konstruktionswerkstoffe: Auswahl, Eigenschaften, Anwendung, 2nd edn. Hanser, München (2014) \end{enumerate} \section*{Numerical Investigation of Keyhole Depth Formation in Micro Welding of Copper with $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ Laser Radiation } \begin{abstract} The keyhole depth formation in laser micro welding of copper is numerically investigated as a function of feed rate and laser power. The calculations of the keyhole depth are based on an approximate process model for the threedimensional steady keyhole profile and carried out for laser beams of the wavelengths $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ with equal intensity distributions in the beam waist. It is found that under standard process conditions deeper keyholes are established with the $1030 \mathrm{~nm}$ laser when the feed rate is decreased whereas under conditions that minimize the attenuation of the laser radiation by the metal vapor the $515 \mathrm{~nm}$ laser leads to an overall more efficient process. Furthermore, the results reveal a different sensitivity of the keyhole depth to feed rate and laser power for both laser beams. Based on model equations and absorption mechanisms, the different behavior towards $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser radiation is analyzed. An instructive consideration of the keyhole front in the upper keyhole part is presented and three absorption mechanisms that affect the geometrical form of the keyhole are identified: direct absorption, absorption contributions due to multiple reflections, and radiation attenuation by the metal vapor. \end{abstract} Keywords: Laser welding $\cdot$ Copper $\cdot$ $1030 \mathrm{~nm}$ vs. $515 \mathrm{~nm} \cdot$ Keyhole depth $\cdot$ Numerical simulation \section*{1 Introduction} In basic research on laser micro welding of copper it has been reported that using $515 \mathrm{~nm}$ laser radiation a more efficient process leading to deeper welds can be achieved than with a conventional $1030 \mathrm{~nm}$ laser [1]. However, this assumes that the interaction between the $515 \mathrm{~nm}$ laser radiation and the copper vapor has to be minimized in order to prevent strong radiation attenuation. Under standard process conditions, where no measures are taken to reduce the light-vapor interaction, it has been observed that the seam depths of copper welds with $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ lasers fall within the same range of values (c.f. Fig. 1). From Fig. 1 it furthermore becomes obvious that the seam depth is more sensitive to changes in feed rate for welds with the $1030 \mathrm{~nm}$ laser leading to deeper welds at small feed rates.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-042} Fig. 1. Experimental values of the seam depth of bead-on-plate welds in Cu-ETP for $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser radiation as a function of feed rate and laser power obtained with a Trumpf TruDisc 8001 and a Trumpf TruDisc Pulse 421 laser, respectively. Beam radius: $0.1 \mathrm{~mm}$ (Marc Hummel, personal communication, RWTH Aachen University, June 30, 2020) The goal of this work is to identify mechanisms of the formation of the keyhole depth which can explain the differences in seam depth and its sensitivity to changes in feed rate based on numerical simulations of the three-dimensional keyhole profile with $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser radiation. The text is structured as follow. First, an overview of the applied keyhole model is presented. Then, numerical experiments are carried out to calculate the keyhole depth as a function of feed rate and laser power for both laser wavelengths. It is verified that the observed behavior of the weld seam is reproduced by the keyhole depth calculations. Last, a discussion regarding the keyhole formation which is based on the model equations and the considered absorption mechanisms is given. \section*{2 Mathematical Modeling} Here, an outline of the model that is used to calculate the three-dimensional quasi-steady keyhole profiles is given. From these profiles the keyhole depths will be obtained in the further analysis. For a more detailed model description the reader may be referred to a previous work of the authors [2]. A simple scheme of the laser welding process showing the laser beam entering the keyhole is depicted in Fig. 2. \subsection*{2.1 Layer Model and Model Parameters} The keyhole wall is considered steep, as is typical for high aspect ratio welds. It is assumed that the continuum mechanical quantities change only slowly with depth for the most part of the keyhole. Heat and mass transfer, including phase transitions, are \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-043} \end{center} Fig. 2. Process scheme of laser welding indicating the path of a single light ray in the keyhole modeled in two-dimensional lateral layers normal to the beam axis. Coupling between the layers is conveyed by Fresnel absorption which depends on the local shape of the three-dimensional keyhole surface. Multiple reflections inside the keyhole and their absorption at the surface are realized by a ray tracing algorithm. The geometric shape of the keyhole surface in each layer is approximated by a circle which is characterized by its radius $R$ and its front position $A$. Furthermore the layer surface temperature $T_{S}$ is introduced, which takes a constant value in each layer since lateral variations of the temperature along the keyhole surface are neglected. The front position corresponds to the relative position of the keyhole front with respect to the laser beam axis. For each layer the values of the three model parameters are calculated iteratively to satisfy the set of conditional equations presented in the following. \subsection*{2.2 Conditional Equations} The conditional equations result from local and global balance considerations at the keyhole surface for which a best fit by the layer parameters $\left(R, A, T_{S}\right)$ is sought. At the front position $x=A$ the interface conditions Eqs. (1) and (2), expressing, respectively, the local conservation of momentum and heat during the transition from the liquid to the gaseous phase, are evaluated: \begin{gather*} \rho u^{2}=\gamma / R \tag{1}\\ \rho u H_{v}=q_{a}-q_{l} \tag{2} \end{gather*} where $\rho$ denotes the mass density of the gas at the phase boundary, $u$ the gas efflux velocity normal to the boundary, $\gamma$ the surface tension, $H_{v}$ the specific latent heat of vaporization, $q_{a}$ the absorbed heat flux, and $q_{l}$ the heat flux entering the liquid material. The last term in Eq. (1) represents the Laplace pressure for a cylindrical surface with curvature $1 / R$. In addition, Eq. (2) is integrated over the keyhole surface of each layer assuming that latent heat contributions due to evaporation and condensation compensate each other. This leads to the global power balance. \begin{equation*} \oiint\left(q_{a}-q_{l}\right) d S=0 \tag{3} \end{equation*} In order to evaluate Eqs. (1) to (3) information about the liquid and gaseous states is required. The mass efflux $\rho u$ and the dynamic gas pressure $\rho u^{2}$ are established from a Hertz-Knudsen evaporation model, which relates them to the gas pressure and the surface temperature $T_{s}$. The gas pressure is set to ambient pressure for further simplification. The heat flux into the liquid $q_{l}$ is obtained from a two-dimensional, analytical heat conduction solution and is a function of feed rate, thermal diffusivity of the material, and curvature of the front.[2]. \subsection*{2.3 Absorbed Heat Flux} The heat flux due to absorption of laser radiation at the keyhole surface is calculated by \begin{equation*} q_{a}=\mu A_{S}(\mu) I_{L}+q_{M R} \tag{4} \end{equation*} where $\mu=-\hat{s} \cdot \hat{n}=\cos \theta, \theta$ being the angle of incidence between the light's Poynting vector $\hat{s}$ and the local normal vector of the keyhole surface $\hat{n}, A_{S}$ is the absorptance of the material's surface, $I_{L}$ is the intensity of the direct laser light, and $q_{M R}$ is the contribution of multiple reflections. The surface elements and the local normal vectors are obtained by a three-dimensional discretization of the keyhole surface (c.f. Fig. 3). The functional dependence $A_{S}(\mu)$ results from Fresnel equations in the high conductivity limit [3] and is parametrized by a frequency- and temperature-dependent material parameter $\epsilon$. In the present work it is considered for unpolarized light for which it reads: \begin{equation*} A_{S}(\mu)=\frac{2 \epsilon \mu}{\epsilon^{2}+2 \epsilon \mu+2 \mu^{2}}+\frac{2 \epsilon \mu}{2+2 \epsilon \mu+\epsilon^{2} \mu^{2}} \tag{5} \end{equation*} With regard to Fig. 3 the contribution of multiple reflections to the total heat flux at node $(i, j)$ is calculated by the ray tracing algorithm as \begin{equation*} q_{M R}^{i j}=\sum_{k=1}^{K} \sum_{l=1}^{L_{k}} \prod_{m=1}^{M_{k l}} A_{n_{k}}^{-1}\left(1-R\left(\theta_{n_{k} l}\right)\right) R\left(\theta_{n_{k} l m}\right) P_{n_{k} l} \tag{6} \end{equation*} where $k, l$, and $m$ are local indices for surface elements, rays, and reflections, respectively, $K$ is the number of surface elements adjacent to node $(i, j), L_{k}$ is the number of rays hitting element $n_{k}, M_{k l}$ is the number of reflections of ray $l$ prior to hitting element $n_{k}$, $A_{n_{k}}$ is the area of element $n_{k}, R$ is the reflectance due to the Fresnel equations ( $R=1-A$, c.f. Eq. (5)), $\theta_{n_{k} l}$ is the angle of incidence of ray $l$ of element $n_{k}, \theta_{n_{k} l m}$ is the angle of incidence of the $m^{\text {th }}$ reflection of ray $l$ of element $n_{k}, P_{n_{k} l}$ is the initial power of ray $l$ of element $n_{k}$, and $n_{k}$ is a partial indexing for identification of the surface elements. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-045} \end{center} Fig. 3. Surface mesh with node and element indexing scheme around the node $(i, j)$ for $j \geq 1$ with $N$ nodes per layer. A partitioning of $4 \times 4$ as indicated in the upper left element is used by the ray tracer for emitting one ray per each sub-element in each iteration. It should be noted that $K, L_{k}, M_{k l}$, and $n_{k}$ are functions of the node number $(i, j)$. (For instance, $K$ equals 2 if the node is part of the first or last layer and 4 else.) The initial power of a ray is calculated from the power of the raw beam taking into account a "zeroth" reflection from the sub-element which it is emitted from (c.f. Fig. 3). Intersection handling and redirection of rays is accomplished with basic geometry. \subsection*{2.4 Limitations} The simplified model is bound to several restrictions which will cause deviations from the real process. It allows for constant material parameters only. The heating and cooling contributions from the workpiece top and the keyhole bottom are neglected. Solid and liquid are considered as one common phase. There is a uniform flow through the capillary, i.e., circulations in the weld pool are not taken into account. Neither light-vapor interaction inside the keyhole nor vapor heating are modeled, and only the effect of radiation attenuation by the metal vapor will be accounted for roughly by adjusting the laser intensity values globally during calculations with the $515 \mathrm{~nm}$ laser. \section*{3 Simulation Results} In this section numerical results of the keyhole depth obtained with the proposed keyhole model are presented. The keyhole depth is calculated as a function of feed rate and laser power for lasers of the wavelengths $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ under standard process conditions, including attenuation of the $515 \mathrm{~nm}$ radiation by the metal vapor, and under idealized conditions, neglecting the interaction between laser radiation and metal vapor. The keyhole depth results are examined with respect to the experimental results on the seam depth referred to in Sect. 1. \subsection*{3.1 Simulation Parameters} The material parameters of copper used in the simulation are summarized in Table 1. The thermal properties were obtained from literature [4]. The values of density, thermal conductivity, and specific heat are specified for room temperature. The surface tension was obtained from measured data [5] by extrapolation to the evaporation temperature. For both laser wavelengths the parameter $\epsilon$ in Eq. (5) is chosen such that the function $A_{S}(\mu)$ reproduces known values of the absorptance at normal incidence [6], i.e., for $\mu=1$. These values are listed in the last column of Table 1 for the wavelengths $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$, respectively. Table 1. Material parameters \begin{center} \begin{tabular}{l|l|l|l|l|l|l|l} \hline \begin{tabular}{l} Density \\ $\left[\mathrm{g} / \mathrm{cm}^{3}\right]$ \\ \end{tabular} & \begin{tabular}{l} Thermal \\ conductivity \\ $[\mathrm{W} / \mathrm{m} / \mathrm{K}]$ \\ \end{tabular} & \begin{tabular}{l} Specific \\ heat \\ $[\mathrm{J} / \mathrm{g} / \mathrm{K}]$ \\ \end{tabular} & \begin{tabular}{l} Heat of \\ fusion \\ $[\mathrm{J} / \mathrm{g}]$ \\ \end{tabular} & \begin{tabular}{l} Heat of \\ vaporization \\ $[\mathrm{J} / \mathrm{g}]$ \\ \end{tabular} & \begin{tabular}{l} Boiling \\ point \\ $[\mathrm{K}]$ \\ \end{tabular} & \begin{tabular}{l} Surface \\ tension \\ $[\mathrm{N} / \mathrm{m}]$ \\ \end{tabular} & \begin{tabular}{l} Absorptance \\ [] \\ \end{tabular} \\ \hline 8.93 & 394 & 0.385 & 210 & 4810 & 2868 & 0.95 & $0.10,0.45$ \\ \hline \end{tabular} \end{center} The investigated process parameters are listed in Table 2. They are chosen so that they correspond to typical parameters for setups with the Trumpf TruDisc 8001 and the Trumpf TruDisc Pulse 421 laser beam sources. The chosen Super-Gaussian beam profile (of fourth order) resembles a top hat beam profile with smoothed flanks and is motivated by measurements of the beam caustic (c.f. [2]). Note that the $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser beams share the same distributions of intensity and Poynting vector only in the focal plane because of wavelength-dependent propagation. Table 2. Process parameters \begin{center} \begin{tabular}{l|l|l|l|l} \hline \begin{tabular}{l} Laser power \\ $[\mathrm{W}]$ \\ \end{tabular} & \begin{tabular}{l} Feed rate \\ $[\mathrm{mm} / \mathrm{s}]$ \\ \end{tabular} & \begin{tabular}{l} Focal diameter \\ $[\mu \mathrm{m}]$ \\ \end{tabular} & \begin{tabular}{l} $\mathrm{M}^{2}$ beam quality \\ [] \\ \end{tabular} & Beam profile \\ \hline $3000-4000$ & $50-250$ & 200 & 20 & Super-Gaussian \\ \hline \end{tabular} \end{center} In order to account for the strong attenuation of the $515 \mathrm{~nm}$ radiation by the copper vapor under standard process conditions, i.e., conditions for which there are no external measures to minimize the interaction between laser radiation and metal vapor (c.f. [1]), the intensity values in simulations with the $515 \mathrm{~nm}$ laser are reduced by an overall factor of $20 \%$. The value is found from numerical tests and comparisons with existing experimental data (c.f. Fig. 1). It should be understood as an average relative attenuation of the laser radiation between both wavelengths. \subsection*{3.2 Calculation Results} The results of the keyhole depth calculations are shown in Fig. 4 and Fig. 5. Figure 4 shows that deeper keyholes are obtained with the $515 \mathrm{~nm}$ laser radiation for all considered feed rates and laser powers under idealized process conditions. Under standard conditions, including attenuation of the $515 \mathrm{~nm}$ laser radiation, a similar trend can be observed as in the experiments on the seam depth shown in Fig. 1. Due to their different slopes the graphs of the keyhole depth in Fig. 5 reveal deeper keyholes for the $515 \mathrm{~nm}$ laser at high feed rates and for the $1030 \mathrm{~nm}$ laser at low feed rates. This observation is compatible with the assumption that the process of keyhole depth formation is more sensitive to changes in feed rate when using $1030 \mathrm{~nm}$ laser radiation. It can also be seen that changing the laser power hardly influences the sensitivity to the feed rate which shows that the power calibration performed on the process with $515 \mathrm{~nm}$ light does not impair the conclusions of the following analysis from a qualitative point of view. It should also be noted that the absolute values of the keyhole depth in Fig. 4 and Fig. 5 will deviate from those in the real process due to the several model limitations mentioned in Sect. 2.4. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-047} \end{center} Fig. 4. Calculated values of the keyhole depth in copper for $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser radiation as a function of feed rate and laser power under idealized process conditions \section*{4 Discussion} It is rather intuitive that under idealized process conditions, neglecting attenuation by the metal vapor, deeper keyholes are obtained with $515 \mathrm{~nm}$ laser radiation since the absorptance of copper at $515 \mathrm{~nm}$ is by far greater than at $1030 \mathrm{~nm}$ (c.f. Table 1). Therefore, the focus of the discussion is on the observations under standard process conditions at \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-048} \end{center} Fig. 5. Calculated values of the keyhole depth in copper for $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser radiation as a function of feed rate and laser power under standard process conditions which attenuation of the $515 \mathrm{~nm}$ radiation by the metal vapor is present. The sensitivity of the keyhole depth is analyzed first, followed by considerations about the formation of the keyhole depth. \subsection*{4.1 Keyhole Depth Sensitivities} The different sensitivities of the keyhole depth for $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser radiation are interpreted in terms of Fresnel absorption with regard to Eqs. (4) and (5). For this, an analysis of the keyhole front in the upper part of the keyhole is performed. Based on a sensitivity analysis of the inclination of the upper keyhole front the sensitivity of the keyhole depth is deduced. Although the formation of the keyhole is a complex three-dimensional process the results on the upper front will be meaningful for all other segments of the keyhole wall where the absorbed heat flux is likewise ruled by Fresnel absorption. The sensitivity of the front inclination will thus be representative of the average keyhole wall inclination and, consequently, of the keyhole depth. From now on consider the keyhole front in a two-dimensional coordinate system containing the feed axis and the optical axis. Near the workpiece top the intensity distribution on the keyhole surface is primarily established by direct laser radiation, i.e., contributions of reflections are secondary [2]. Neglecting the term $q_{M R}$ in Eq. (4), the factor $\mu A_{S}(\mu)$ then gives the percentage of the incident intensity that is absorbed by the front as a function of the cosine of the angle of incidence $\mu$. From Fig. 6 it becomes clear that for the majority of $\mu$-values $\mu A_{S}(\mu)$ is larger for $515 \mathrm{~nm}$ laser radiation, with a maximum difference at $\mu=1$. There it corresponds to the reference value of the absorptance listed in Table 1. For smaller $\mu$-values the differences in $\mu A_{S}(\mu)$ decrease and for $\mu<0.083$ the $1030 \mathrm{~nm}$ laser even yields greater absorption. It should be noted that the\\ monotonous graphs of $\mu A_{S}(\mu)$ show different slopes which will become important in the later discussion.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-049} Fig. 6. Intensity absorption factor $\mu A_{S}(\mu)$ from Eq. (4) for $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser radiation as a function of the cosine of the angle of incidence $\theta$ By definition, $\mu$ is related to the inclination of the keyhole front. Near the workpiece top propagation distances are small compared to the Rayleigh lengths of both laser beams so that the Poynting vector is directed mainly parallel to the optical axis. In this case $\mu$ corresponds to the cosine of the front inclination angle with respect to the feed axis. That is, for large values of $\mu$ the front is flat, for small values it is steep. In order to maintain a steady keyhole front a certain value of the absorbed intensity $q_{a}$ is required according to Eq. (2). This value depends on process and material parameters and local properties at the keyhole front (e.g., the heat flux into the material, curvature of the front). In general, the higher the feed rate, the higher the value is. For a given intensity $I_{L}$ of the incident laser radiation the front will then incline to absorb the required value of $q_{a}$ according to Eq. (4). Referring to Fig. 6, the quotient of $q_{a}$ and $I_{L}$ defines a target value of $\mu A_{S}(\mu)$ which can be incorporated into the plot as a horizontal line. The intersections of this line with the graphs of $\mu A_{S}(\mu)$ define the local values of $\mu$ for both lasers. Considering a top-hat-like beam profile, there is a typical intensity value $I_{L}$ everywhere along the upper keyhole front. Following the construction above there will be a representative front inclination for each laser power and feed rate. Increasing the laser power or reducing the feed rate will lower the quotient of $q_{a}$ and $I_{L}$ and thus lower the value of $\mu$ according to Fig. 6 . However in the range $0.1 \leq \mu \leq 1$ the decrease will be much faster for the $1030 \mathrm{~nm}$ laser because of the lower slope of the graph of $\mu A_{S}(\mu)$. Hence there is a higher sensitivity of the front inclination to feed rate and laser power for $1030 \mathrm{~nm}$ radiation. Under the initial assumptions this sensitivity is reflected by the keyhole depth as observed in Fig. 5. \subsection*{4.2 Mechanisms of Keyhole Depth Formation} So far only the sensitivity of the keyhole depth but not its absolute values has been addressed. In particular, the different sensitivities were found in a range of $\mu$-values for which the $515 \mathrm{~nm}$ laser still yields greater absorption and hence steeper fronts. To conclude this discussion three mechanisms that lead to the formation of deeper keyholes with the $1030 \mathrm{~nm}$ laser radiation under standard process conditions are identified. One aspect is the stronger attenuation of the $515 \mathrm{~nm}$ laser radiation by the metal vapor which causes an overall diminution of the intensity and hence smaller front inclinations. Furthermore, there is the higher absorption of $1030 \mathrm{~nm}$ radiation at very steep fronts as per Fig. 6. (The value $\mu=0.083$ corresponds to an angle of incidence of $85.24^{\circ}$.) The required intensities do not necessarily have to be available in the laser beam directly, but can be established by multiple reflections. Finally, the intensity of reflected radiation is higher the less of it is absorbed by the keyhole surface. According to Fig. 7 this is the case for $1030 \mathrm{~nm}$ radiation for most of the $\mu$-values. Once the wall inclination becomes large enough to deflect radiation downwards, i.e., at least $45^{\circ}(\mu=0.7)$ in case of the upper keyhole front, effective into-the-depth power coupling of the $1030 \mathrm{~nm}$ laser radiation sets in. These three mechanisms together lead to deeper keyholes and thus deeper weld seams with the $1030 \mathrm{~nm}$ laser at low feed rates. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-050} \end{center} Fig. 7. Fresnel absorptance $A_{S}(\mu)$ from Eq. (5) for $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser radiation as a function of the cosine of the angle of incidence $\theta$ \section*{5 Conclusion} Using an approximate process model the keyhole depth was investigated as a function of feed rate and laser power for copper welds with $1030 \mathrm{~nm}$ and $515 \mathrm{~nm}$ laser beams. A more efficient process was found for $515 \mathrm{~nm}$ laser radiation under idealized conditions where\\ there is no radiation attenuation by the metal vapor. Under standard conditions, including attenuation of the $515 \mathrm{~nm}$ radiation, the calculations revealed deeper keyholes at low feed rates and a higher sensitivity of the keyhole depth to feed rate for the $1030 \mathrm{~nm}$ laser as observed in experiments. This behavior could be explained by a consideration of the upper keyhole front in terms of Fresnel absorption and a local energy balance, and by the identification of three absorption mechanisms that affect the formation of the keyhole. In further investigations the effects of preheating and polarization state will be investigated, and laser beam sources in the blue visible spectrum [7] as well as other copper materials will be addressed. Acknowledgement. The presented investigations were carried out at RWTH Aachen University within the framework of the Collaborative Research Centre SFB-1120-236616214 and funded by the Deutsche Forschungsgemeinschaft e.V. (DFG, German Research Foundation). The sponsorship and support is gratefully acknowledged. \section*{References} \begin{enumerate} \item Kaiser, E., Dold, E.-M., Killi, A., Zaske, S., Pricking, S.: Application benefits of welding copper with a $1 \mathrm{~kW}$, $515 \mathrm{~nm}$ continuous wave laser. In: 10th CIRP Conference on Photonic Technologies, LANE 2018. Bayerisches Laserzentrum GmbH, Erlangen (2018) \item Schöler, C., Nießen, M., Hummel, M., Olowinsky, A., Gillner, A., Schulz, W.: Modeling and simulation of laser micro welding. In: Lasers in Manufacturing 2019, World of Photonics Congress, Munich, Germany, 24-27 June 2019. WLT e.V, Erlangen (2019) \item Schulz, W., Simon, G., Urbassek, H.M., Decker, I.: On laser fusion cutting of metals. J. Phys. D Appl. Phys. 20, 481-488 (1987) \item Lossin, A.: Copper. In: Ullmann's Encyclopedia of Industrial Chemistry, vol. 1, p. 15. WileyVCH Verlag GmbH \& Co. KGaA, Weinheim, Germany (2000) \item Brillo, J., Egry, I.: Surface tension of nickel, copper, iron and their binary alloys. J. Mater. Sci. 40, 2213-2216 (2005) \item Hess, A., Schuster, R., Heider, A., Weber, R., Graf, T.: Continuous wave laser welding of copper with combined beams at wavelengths of $1030 \mathrm{~nm}$ and of 515nm. Phys. Proc. 12, 88-94 (2011) \item Hummel, M., Schöler, C., Häusler, A., Gillner, A., Poprawe, R.: New approaches on laser micro welding of copper by using a laser beam source with a wave-length of $450 \mathrm{~nm}$. J. Adv. Join. Process. 1, 100012 (2020) \end{enumerate} \section*{Reduction of Hot Cracks During Electron Beam Welding of Alloy-247 LC } \begin{abstract} Alloy-247 LC belongs to the group of precipitation hardening materials and is characterized by good creep resistance at higher temperatures. Although the material offers good cast workability, the weldability of the material is very limited due to its high crack tendency. This paper identifies and optimizes electron beam welding parameters with regard to hot crack reduction when welding conventionally cast components. The crack evaluation is carried out using scanning electron microscopy and light microscopy of the upper beads and the cross sections. In order to statistically verify the results, crack identification was carried out by micro-CT measurements. A welding speed dependent dendrite arm distance measurement additionally supports the crack investigation. Furthermore, a crack-optimized welding parameter was successfully transferred to a dissimilar joint weld (conventionally solidified to directionally solidified) and the potential for welding the high-performance material Alloy-247 LC with the electron beam was demonstrated by creep tests. \end{abstract} Keywords: Electron beam welding $\cdot$ Nickel-based alloy $\cdot$ Alloy-247 LC $\cdot$ Dendrite $\cdot$ Hot crack $\cdot$ Creep test \section*{1 Introduction} The improvements in the efficiency of gas turbines are achieved by various combinations of technological measures. These include improved cooling, development of thermal insulation layers, aerodynamic optimization of the blades, reduction of losses and the further development of materials with better high-temperature characteristics [1]. The last-named has experienced an enormous development in metallurgy over the last decades. The specific mechanical and chemical properties have been improved with increasing quantities of different alloying elements. In addition, the casting processing of the superalloy has been expanded. With the innovative alloys and the possibility of directional solidification (DS) and single crystalline solidification (SX), the efficiency and lifetime of turbine materials have been further optimized [2-4]. Alloy 247 LC is a chemically modified superalloy specially developed for directional solidified blades and guide vanes. This enables the production of complex, core-containing, thin-walled blades. From an economic point of view, a repair of the guide vanes is opportune [5]. A\\ hybrid design of the guide vanes, using different solidification states, would also have a positive influence on the economic efficiency. The broad spectrum of alloying elements constitutes a great challenge for welding technology. In particular, the weldability of the age-hardening nickel-base alloy is correlated with the aluminium and titanium content [6]. To increase strength, aluminium and titanium are withdrawn from the $\gamma$-matrix after solution heat treatment during the ageing process and a $\gamma^{\prime}$ phase $\mathrm{Ni} 3(\mathrm{Al}, \mathrm{Ti})$ is precipitated. This decreases the lattice parameter and increases the lattice distortion. The heat treatment is usually carried out after the welding process. Welding after heat treatment would soften the material in the area of the weld seam and the HAZ. However, the strengthening measure after the welding process can lead to crack formation. Due to the lower aging temperature range compared to the solution annealing temperature, aging processes already occur during the heating phase to solution annealing temperature and thus $\gamma^{\prime}$ precipitation. A superposition of the stresses resulting from the lattice distortion processes and the residual welding stresses in the HAZ that have not yet been removed can lead to the maximum material yield strength being exceeded and to failure of the component [7]. For this reason the residual welding stress should be reduced to a minimum. Furthermore, hot cracking is to be considered as critical, especially during welding. When welding nickel-base alloys, a differentiation is essentially made between two types of hot cracking. Intercrystalline liquation cracks in the HAZ, according to the mechanism of constitutional liquefaction of the low-melting phases, as well as solidification cracks in the seam. For both crack types, crack initiation is due to thermally induced stresses. Cracks in the weld metal occur mainly during solidification. Due to the different solubility of the alloying elements in the melt, the concentration changes continuously in the solidification interval. The degree of segregation depends on the solidification rate. This is generally influenced by the welding speed during welding. In addition, the solidification rate changes with the temperature gradient $\mathrm{G}$ at each location of the weld pool isotherms. Both the weld pool shape and the microstructure are determined by these two values. During the solidification interval, the solidification type changes continuously from planar to equiaxial dendritic [7, 8]. Solidification starts in the area of the highest cooling rate or the highest temperature gradient at the solidification edge to the base material. The crystals grow perpendicular to the solidification isotherms. With increasing welding speed, the weld pool shape changes from elliptical to drop-shaped with crystal growth almost perpendicular to the welding direction. The segregation front proceeds in the remaining melt with the interdendritic distance unfavourable to the shrinkage stresses resulting from the process. The consequence is crack initiation in the melt. With the electron beam, a precise and versatile tool is available. On the one hand, critical residual welding stresses can be reduced by specific heat control and on the other hand, the solidification morphology can be positively influenced. The welding process thus offers the ideal conditions for improving the seam quality in terms of crack reduction when welding Alloy 247 LC. The welding speed is investigated as a primary parameter of the process for modifying the heat control. \section*{2 Experimental Setup} \subsection*{2.1 Material} For the investigations, the precipitation-hardening nickel-based alloy Alloy-247 LC was examined in the conventionally cast (CC) state and later also in the directionally solidified state. After the casting process, the material was solution annealed at $1232{ }^{\circ} \mathrm{C}$ for $2 \mathrm{~h}$ 15 min under reduced atmospheric pressure. Subsequently, the specimens for the welding tests were eroded out of the ingots and milled to final dimension $(100 \times 60 \times 6)$. Both the $\mathrm{CC}$ and the DS base material have a coarse-grained structure with macroscopic dendrite spacing. In the interdendritic areas of the base material a multi-phase structure with $\gamma^{\prime}$ precipitations of $\mathrm{Ni} 3(\mathrm{Al}, \mathrm{Ti})$ in the $\gamma$ matrix is present. The size and shape of the $\gamma^{\prime}$ precipitates is inhomogeneously distributed due to the missing aging process after the solution heat treatment. This chemical composition is presented in Table 1. Table 1. Composition of Alloy-247 LC (wt. \%). Examined with atomic emission spectroscopy \begin{center} \begin{tabular}{l|l|l|l|l|l|l|l|l|l|l|l|l} \hline & $\mathrm{Ni}$ & $\mathrm{C}$ & $\mathrm{Si}$ & $\mathrm{Cr}$ & $\mathrm{Co}$ & $\mathrm{Mo}$ & $\mathrm{W}$ & $\mathrm{Ti}$ & $\mathrm{Al}$ & $\mathrm{Ta}$ & $\mathrm{Hf}$ & $\mathrm{Fe}$ \\ \hline Alloy-247 LC & bal. & 0.07 & 0.1 & 8.2 & 9.0 & 0.5 & 8.9 & 0.8 & 5.6 & 3.5 & 1.6 & 0.4 \\ \hline \end{tabular} \end{center} \subsection*{2.2 Process} The electron beam welding machine ProBeam K-7 with $120 \mathrm{kV}$ acceleration voltage was used as a test facility. The welding was performed at a pressure of $10^{-4}$ mbar and with a working distance of $400 \mathrm{~mm}$ to the focus lens. The focus position was left on the component surface at all beam currents. As in practice a certain welding depth is required, all tests were welded with a constant welding depth of $5 \mathrm{~mm} \pm 0.5 \mathrm{~mm}$. This also provides comparability of the results. For this purpose, a power required for the welding depth was determined for each welding speed. An overview of the parameters investigated is shown in Table 2. It can be seen that with decreasing welding speed a higher energy per unit length is required to achieve the same weld depths. Before welding, the plates were cleaned in an acetone ultrasonic bath for $10 \mathrm{~min}$ and then clamped with a vice perpendicular to the welding direction, over the entire length. A $90 \mathrm{~mm}$ long seam was welded in the middle of the $100 \mathrm{~mm}$ long sample. Table 2. Overview of the examined parameters \begin{center} \begin{tabular}{cccccccc} \hline \begin{tabular}{c} Alloy-247 \\ LC \\ \end{tabular} & & \begin{tabular}{c} Specimen \\ thickness \\ $[\mathrm{mm}]$ \\ \end{tabular} & \begin{tabular}{c} $\mathrm{E}$ \\ $[\mathrm{J} / \mathrm{mm}]$ \\ \end{tabular} & \begin{tabular}{c} $\mathrm{U}_{\mathrm{b}}$ \\ $[\mathrm{kV}]$ \\ \end{tabular} & \begin{tabular}{c} $\mathrm{I}_{\mathrm{b}}$ \\ $[\mathrm{mA}]$ \\ \end{tabular} & \begin{tabular}{c} $\mathrm{V}_{\mathrm{s}}$ \\ $[\mathrm{mm} / \mathrm{s}]$ \\ \end{tabular} & \begin{tabular}{c} Focus \\ position \\ \end{tabular} \\ \hline $\mathrm{CC}$ & BoP & 6.0 & 960 & 120 & 4.0 & 0.5 & surface \\ $\mathrm{CC}$ & BoP & 6.0 & 600 & 120 & 5.0 & 1.0 & surface \\ CC & BoP & 6.0 & 450 & 120 & 7.5 & 2.0 & surface \\ CC & BoP & 6.0 & 270 & 120 & 9.0 & 4.0 & surface \\ CC & BoP & 6.0 & 210 & 120 & 10.5 & 6.0 & surface \\ CC & BoP & 6.0 & 164 & 120 & 10.9 & 8.0 & surface \\ CC & BoP & 6.0 & 138 & 120 & 11.5 & 10.0 & surface \\ CC + DS & tack & 12.0 & 78 & 120 & 6.5 & 10.0 & surface \\ welding & & & & & & & \\ CC + DS & \begin{tabular}{c} joint \\ welding \\ \end{tabular} & 12.0 & 1680 & 120 & 14 & 1.0 & surface \\ \hline \end{tabular} \end{center} \subsection*{2.3 Evaluation Methods} In order to be able to evaluate the welding results and create a sufficient basis for interpretation, both metallographic and radiographic examinations were carried out. For this purpose, all samples were cut out of the seam according to Fig. 1. The first and last $5 \mathrm{~mm}$ of the seam were not considered in the evaluation.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-055} Fig. 1. Drawing of the mechanical sample preparation for three transverse sections and two microCT images (left) and of the sections for the dendrite investigation (right) In the first step, all samples were examined for surface cracks with the scanning electron microsope. The crack position and the total crack length were determined. These results are used as a first indication for crack evaluation. The crack identification and localization inside the weld was performed with the assistance of microCT scans. For this purpose, samples of the same size were taken from the weld samples. Due to the high density of the material, the sample geometry was limited to a maximum thickness of $3.3 \mathrm{~mm}$. One side was milled to the centre of the seam and subsequently the $3.3 \mathrm{~mm}$ thick sample was cut out. A total of 2 specimens per examined parameter were prepared for the Micro CT examination. The crack positions and crack lengths were also determined. Due to the lack of information about the types of crack, metallographic\\ examinations of transverse, longitudinal and surface sections were carried out in addition to the microCT. For this purpose the samples were etched according to Kalling-II $(100 \mathrm{~mL}$ ethanol, $100 \mathrm{~mL}$ hydrochloric acid (32\%) and $5 \mathrm{~g}$ copper(II)-chloride) at $21{ }^{\circ} \mathrm{C}$ for $45 \mathrm{~s}$ and then magnified with a microscope. Simultaneously to crack identification, the secondary dendrite arm spacing (SDAS) was measured using the metallographically prepared samples according to [9]. Due to the continuously changing welding isotherm and the associated dependence of the dendrite growth direction, the sample preparation for the determination of the primary dendrite spacing is very complex. In addition, the direction of dendrite growth changes with the welding speed and thus the effort for an adequate measurement. For this reason, the dendrite spacing was not measured within the scope of this work. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-056} \end{center} Fig. 2. Drawing of the welding preparation and the position of the creep specimen Furthermore, specimens for creep tests were welded with the crack-reduced $1.0 \mathrm{~mm} / \mathrm{s}$ parameter. For this purpose, the parameter for a $12 \mathrm{~mm}$ thick joint weld (Alloy-247 CC to Alloy-247 DS) was adjusted, Table 2. Due to the low viscosity of the melt and the resulting unacceptable weld sinkage welding in PA-position, the specimen preparation was selected according to Fig. 2. Like the preliminary tests before, the specimens were heat-treated, mechanically prepared and then cleaned with acetone. Before the joint welding, the samples were tack welded on both sides by an $80 \mathrm{~mm}$ long linear seam. The parameters are shown in Table 2. By choosing a narrow tack weld geometry, the subsequent weld ensures that the cracked tack weld is completely over-welded in the welding area. The samples for the creep tests were extracted according to Fig. 2. A total of 10 creep specimens were prepared from two joint welds. Subsequently, the samples were subjected to a three-stage heat treatment. Solution annealed at $1243{ }^{\circ} \mathrm{C}$ for $4 \mathrm{~h}$, in the stabilization annealed at $1080^{\circ} \mathrm{C}$ for $2 \mathrm{~h}$ and ageing at $870{ }^{\circ} \mathrm{C}$ for $20 \mathrm{~h}$. \section*{3 Results} \subsection*{3.1 Influence of the Welding Speed on the Welding Depth} The weld geometry has a significant influence on the heat distribution over the welding depth and thus on the stress distribution in the component. Figure 3 shows the seam geometries in relation of the welding speed. At welding speeds of $1 \mathrm{~mm} / \mathrm{s}$ and $2 \mathrm{~mm} / \mathrm{s}$ it can be seen that the weld depth of $5 \mathrm{~mm} \pm 0.5 \mathrm{~mm}$ is not achieved. Due to the low welding speed, the leading heat flow changes continuously the welding depth over the entire weld seam length. In addition, nail head formation increases and the ratio of weld depth to weld width decreases significantly. Due to the low thermal conductivity of the alloy, this effect can be observed up to a welding speed of $4 \mathrm{~mm} / \mathrm{s}$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-057} \end{center} Fig. 3. Light microscopy images of cross-sections at different welding speeds \subsection*{3.2 Influence of the Welding Speed on the Dendrite Morphology} The welding speed as a direct parameter has a significant influence on the temperature gradient $\mathrm{G}$ and the crystallization rate R. Figure 4 illustrates the influence of the welding speed on SDAS. The SDAS decreases with increasing welding speed due to the high solidification rate. Furthermore, the SDAS is inhomogeneous over the seam depth. Towards lower welding speeds, the SDAS increases in areas of the pronounced nail head. Regardless of the welding speed, the solidification rate is highest in the root zone. As a result, the dendrite arm distance in the root area is closer than in the other areas of the weld Furthermore, the inhomogeneity of the SDAS increases over the seam depth to higher welding speeds. At $1.0 \mathrm{~mm} / \mathrm{s}$ welding speed, the SDAS varies over the seam depth by only $1.2 \%$ of the maximum value. In contrast, the variation at higher welding speeds \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-058} \end{center} Fig. 4. Dendrite arm distance over the welding depth in percent depending on the welding speed. Evaluated by means of transverse, longitudinal and surface sections in three areas of the seam (upper bead, seam centre and seam root). $(6.0 \mathrm{~mm} / \mathrm{s})$ increases to approximately $50 \%$ of the maximum value. According to Whitesell [10], the SDAS is dependent on both the temperature gradient and the solidification rate. In welding, however, these two indirect parameters cannot be separated from the welding speed. The solidification rate is inevitably dependent on the temperature gradient. This allows a conclusion to be drawn about the qualitative course of the temperature gradient. \subsection*{3.3 Crack Formation Depending on the Welding Speed} The first evaluation of a weld seam is always performed visually on the surface. The result gives a first indication of the seam quality. Figure 5 shows an example of three SEM images of seam surfaces that were welded with different speeds. The energy per unit length was kept constant at $100 \mathrm{~J} / \mathrm{mm}$. It can be seen that the crack length increases with increasing welding speed. In addition, the crack position shifts from the base material in the direction of the weld seam. At high welding speeds, the crack progresses along the solidification line perpendicular to the welding isotherm. In this area, thermal stresses occur perpendicular to the dendrite growth direction and tear open the still liquid interdendritic area. With decreasing welding speed, more time is available for solidification. On the one hand, a microcracks can be filled due to the larger dendrite spacing and the subsequent melt flow, on the other hand, the thermal stress (transverse to the welding direction) only develops when the critical area (which runs transverse to the stress) has sufficient strength. According to Rappaz [11], the hot crack tendency decreases with higher SDAS and lower thermal stress. However, the residual stress states in Fig. 5 cannot be compared due to the different stiffness states. An investigation with constant welding depth minimizes the possible influence of stiffness to a minimum. Figure 6 shows the total crack length on the upper \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-059(1)} \end{center} Fig. 5. SEM Images of weld pool geometry, dendrite growth direction and crack initiation direction depending on the welding speed bead over the welding speed at constant welding depth. For this purpose all cracks were cumulated to a total crack length. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-059} \end{center} Fig. 6. Correlation between welding speed and total crack length on the upper bead at constant welding depth. Evaluated on SEM images. The total crack length increases with increasing welding speed. At higher speeds, the maximum crack length is limited by the seam width and thus the total crack length on the upper bead does not increase significantly. In addition, a differentiation is made in the following between two types of hot cracking. At higher welding speeds, the solidification crack mainly occurs in the seam. Where, on the other hand, the liquation cracks occurs in the HAZ at lower welding speeds. In the range between $2 \mathrm{~mm} / \mathrm{s}$ and $8 \mathrm{~mm} / \mathrm{s}$ welding speed, both types of hot crack are observed. For this reason, a maximum of the total crack length at $6 \mathrm{~mm} / \mathrm{s}$ welding speed is shown in Fig. 6. A microCT evaluation of the weld seams in Fig. 7 shows a similar correlation between the welding speed and the total crack length. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-060} \end{center} Fig. 7. Correlation between welding speed and total crack length in the seam at constant welding depth. Evaluated on microCT images. $2.0 \mathrm{~mm} / \mathrm{s}$ $8.0 \mathrm{~mm} / \mathrm{s}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-060(1)} \end{center} Fig. 8. Light microscopy images showing a parameter and position dependent crack formation near the nail head and in the root area of a weld for $2.0 \mathrm{~mm} / \mathrm{s}$ and $8.0 \mathrm{~mm} / \mathrm{s}$ welding speed In contrast to the evaluation of the upper bead, the total crack length in the weld seam increases linearly with increasing welding speed. A metallographic examination was carried out to identify the types of cracks. Figure 8 shows an example of the typical hot cracks when welding Alloy-247 LC. Comparable to the crack investigations on the upper bead, only predominantly hot cracks occur in the HAZ at lower welding speeds. In contrast, at higher welding speeds the solidification crack in the deep welding area cannot be avoided. According to Fig. 4, a higher temperature gradient can be assumed due to the smaller dendrite arm distance in this area. This in turn has a negative effect on the thermally induced residual stresses and the solidification rate, which are mainly responsible for the solidification cracks in the weld metal. \subsection*{3.4 Welding of Creep Specimens} The previous results indicate that at lower welding speeds, the total crack length decreases to a minimum when welding Alloy-247 LC in the CC and solution heat treated condition. A weld joint between a CC and a DS (transverse to the direction of weld) specimen was investigated in the following. Heat treatment subsequent to the welding process increases the $\gamma$ 'precipitation and thus the creep resistance to higher temperatures. For this purpose, the samples were solution annealed at $1243{ }^{\circ} \mathrm{C}$ for $4 \mathrm{~h}$ after welding, stabilised at $1080{ }^{\circ} \mathrm{C}$ for $2 \mathrm{~h}$ and aged at $870{ }^{\circ} \mathrm{C}$ for $20 \mathrm{~h}$. For the creep tests the $1.0 \mathrm{~mm} / \mathrm{s}$ welding speed parameter was preferred to the $0.5 \mathrm{~mm} / \mathrm{s}$ parameter due to the lower leading heat flow. The beam current was adjusted to the sheet thickness. Despite clamping perpendicular to the welding direction, the specimens were tack welded with a welding depth of $2.1 \mathrm{~mm}$ on both sides over a length of $80 \mathrm{~mm}$. The creep test specimens were mechanically prepared as shown in Fig. 2. The results of the creep test thus reflect the weld quality in the middle area of the weld. Figure 9 shows the results of the creep tests of welded and aged specimens, at a test temperature of $850^{\circ} \mathrm{C}$ and $950{ }^{\circ} \mathrm{C}$ in comparison with the base materials. The individual measuring points of the welded specimens are on the extrapolated minimum curve of the $\mathrm{CC}$ base material.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-061} Fig. 9. Creep rupture strengths of the hybrid weld (CC with DS) at two different test temperatures $\left(850{ }^{\circ} \mathrm{C}\right.$ and $950{ }^{\circ} \mathrm{C}$ ). Mean strength of the base materials (solid lines) and the specified minima according to Siemens (dashed lines). This shows that the liquation cracks occurring parallel to the direction of the load or the cracks that could occur during post-heat treatment have no significant influence on the creep strength. \section*{4 Conclusion} In this study it could be shown that the hot cracking tendency could be reduced with a reduced temperature gradient. As a direct parameter in electron beam welding, the welding speed has a significant influence on the temperature gradient and thus on the solidification rate and weld pool geometry while the power density distribution of the beam remains constant. At lower welding speeds the solidification crack in the seam and on the upper bead could be completely suppressed due to the lower temperature gradient. As Rappaz [11] has already shown with the hot cracking criterion, the SDAS and the temperature gradient correlate with the hot cracking probability (solidification crack). In contrast, the liquation crack in the HAZ could not be suppressed either in the area of the nail head or in the area of the deep welding. However, at lower welding speeds, the total length decreased significantly. Furthermore, creep tests have shown that possible liquation cracks in the area of the deep welding area that occurring parallel to the direction of the load (transverse to the welding direction) have no influence on the hightemperature strength. Even a heat treatment to increase strength after the welding process has no negative influence on crack formation with the optimized welding parameter. \section*{References} \begin{enumerate} \item Mom, A.J.A.: Introduction to Gas Turbines. Woodhead Publishing, Sawston (2013). https:// \href{http://doi.org/10.1533/9780857096067.1.3}{doi.org/10.1533/9780857096067.1.3} \item Betteridge, W., Shaw, S.W.K.: Development of superalloys. Mater. Sci. Technol. 3(9), 682694 (1987) \item Sims, C. T.: A history of superalloy metallurgy for superalloy metallurgists. Superalloys 1984. The Metallurgical Society of AIME, Warandale (1984) \item Harris, K., Erickson, G.L., Schwer, R.E.: Directionally solidified and single-crystal superalloys, properties and selection: irons, steels, and high-performance alloys. ASM Handbook Committee (1990) \item Harris, K., Erickson, G.L., Schwer, R.E.: MAR M 247 derivations - CM 247 LC DS alloy and CMSX single crystal alloys: properties \& performance. Superalloys 1984. The Metallurgical Society of AIME, Warandale (1984) \item Kelly,T. J.: Welding metallurgy of investment cast nickel-based superalloys. Weldability of Materials, pp. 151-157. ASM International, Materials Park, OH (1990) \item Kou, S.: Welding Metallurgy, 2nd edn. Wiley, New Jersey (2003) \item Schulze, G.: Die Metallurgie des Schweißens - Eisenwerkstoffe - Nichteisenmetallische Werkstoffe, 4th edn. Springer, Berlin (2010) \item BDG-Richtlinie VDG-Merkblatt: Bestimmung des Dendritenarmabstandes für Gussstücke aus Aluminium-Gusslegierungen, P220, BDG-Informationszentrum Giesserrei, Düsseldorf (2011) \item Whitesell, H.S., Li, L., Overfelt, R.A.: Influence of solidification variables on the dendrite arm spacings of ni-based superalloys. Metall. Mater. Trans. B. 31B, 546-551 (2000) \item Rappaz, M., Drezet, J.-M., Gremaud, M.: A new hot-tearing criterion. Metall. Mater. Trans. A. 30A, 449-455 (1999) \end{enumerate} \section*{Validation of the EDACC Model for GMAW Process Simulation by Weld Pool Dimension Comparison } \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-063} \\ and Uwe Reisgen (D) \\ Welding and Joining Institute, RWTH Aachen University, Pontstrasse 49, \\ 52062 Aachen, Germany \\ \href{mailto:simon@isf.rwth-aachen.de}{simon@isf.rwth-aachen.de}\\ \} \begin{abstract} The EDACC model (evaporation-determined arc cathode coupling) was developed to represent a more physically in depth description of the heat flux and current density distribution on the surface of the weld pool in gas metal arc welding (GMAW). To validate the model, geometry parameters available from experiments from GMAW processes were compared to the corresponding geometry parameters from simulations. The process simulation model was supplied with an approximation for the surface deformation and simulations were performed without the surface deformation and with the surface deformation for a common Gaussian heat flux and current density distribution, as well as for the EDACC model. The EDACC model parameter of the bulk plasma temperature was calibrated to match the total current. The results of the validation are presented and their fidelity is discussed. \end{abstract} \section*{1 Introduction} The gas metal arc welding (GMAW) process remains the most widely used fusion welding process among the others, when considering the amount of filler material sold in Germany [1]. Its simple use, high deposition rates and, easy automation made it widely known and usable. However, the simulation of the GMAW process remains a field of current engineering research. It consists of modeling the complex interaction of physical phenomena which occur during the welding process and which have not always been fully understood in sufficient depth. The formation of the droplets, the molten pool behavior and, the metal transfer during the welding process have remained relevant research topics throughout the years. Therefore, further research and a continuing development of new and more precise mathematical models are still relevant. The key factor, which determines the formation of the weld seam, is the flow of the molten metal in the weld pool with its visible and invisible complex physical processes [2]. The hydrodynamics, electromagnetics, heat and current distribution, momentum and mass transfer of the droplets into the molten pool as well as the free surface deformation are some of these processes [3]. The cathode region determines the distribution of the heat flux and the current density on the weld pool surface and is therefore a sensitive boundary\\ condition for the process. Until now, mainly a Gaussian distribution was assumed, but the latest development was presented with the evaporation determined model of arc cathode coupling (EDACC) [4], see Fig. 1.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-064} Fig. 1. Exemplary heat flux distribution for the Gaussian heat source model (left) and the EDACC model (right), adapted from [4] While the assumption of the Gaussian distribution was dependent of the actual conditions of the arc only, the EDACC model is based on the surface temperature of the weld pool as well as the plasma temperature and their interaction via the evaporation. This represents a deeper consideration of the underlying physics. Although a qualitative comparison of the models has been performed in [5], the results have not been compared against experimental data, yet. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-064(1)} \end{center} Fig. 2. Symbolized application of the EDACC model to the fully hydrodynamic weld pool calculation The model used in [5] was extended with an approximation of the free surface deformation (FSD) in ANSYS CFX. This allows to study the effects of the changed\\ current density distribution on the Lorentz-forces, which are considered as main drivers for the hydrodynamics in the weld pool, see Fig. 2. This allows a validation of the EDACC model in comparison with geometrical weld pool data (reinforcement, depth, length) from real welding experiments. Therefore, three different cases are examined during the investigation: the application of a Gaussian heat source model (GHSM) without FSD, the application of the GHSM with FSD and application of the EDACC model with FSD. \section*{2 Methods} \subsection*{2.1 Geometrical Data} \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-065}\\ a) \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-065(1)}\\ b) Fig. 3. Section views of the weld seam from [6] a) Cross-section b) Longitudinal section For the validation of the models (i.e. [5] with extension to the FSD) and further simulation results, the experimental data from previously generated experiments were used, see Table 1. The main geometry parameters under consideration in the present work can be seen in Fig. 3. Those are the weld bead reinforcement $(H)$, the weld bead width $(W)$, the depth of the penetration $(D)$ and the length of the molten pool $(L)$. The welding was performed on steel S235JR and the main process parameters are current $(I)$, voltage $(U)$, welding speed $\left(v_{w . s}\right)$ and wire feed rate $\left(v_{w . f . r .}\right)$ and they can be seen in Table 1. The geometrical parameters resulting from the experiments are shown in Table 2. Table 1. GMAW process parameters \begin{center} \begin{tabular}{l|l|l|l|l} \hline Experiment number, № & $\mathrm{I},[\mathrm{A}]$ & $\mathrm{U},[\mathrm{V}]$ & $\mathrm{V}_{\text {w.s }},[\mathrm{mm} / \mathrm{min}]$ & $\mathrm{V}_{\text {w.f.r., }}[\mathrm{m} / \mathrm{min}]$ \\ \hline 1 & 200 & 26.9 & 300 & 6 \\ \hline 2 & 250 & 29.4 & 300 & 8 \\ \hline 3 & 300 & 38.7 & 300 & 10 \\ \hline \end{tabular} \end{center} Table 2. Geometrical weld pool parameters. (H), (W), (D) from blown-out experiments, (L) from tracer experiments. \begin{center} \begin{tabular}{l|l|l|l|l} \hline Experiment number, № & $\mathrm{H},[\mathrm{mm}]$ & $\mathrm{W},[\mathrm{mm}]$ & $\mathrm{D},[\mathrm{mm}]$ & $\mathrm{L},[\mathrm{mm}]$ \\ \hline 1 & $3.4 \pm 0.09$ & $10.9 \pm 0.06$ & $2.8 \pm 0.2$ & $26.6 \pm 2.6$ \\ \hline 2 & $3.8 \pm 0.2$ & $12.8 \pm 0.3$ & $3.6 \pm 0.2$ & $34.4 \pm 0.9$ \\ \hline 3 & $3.6 \pm 0.1$ & $17.9 \pm 0.2$ & $5.1 \pm 0.2$ & $42.5 \pm 0.2$ \\ \hline \end{tabular} \end{center} \subsection*{2.2 Heat Source Calibration Data} Gaussian Heat Source Model. The GHSM model needed to be calibrated for the radius of the heat source $\mathbf{r}_{\text {heat_source }}$, in order to match the width of the weld pool. Additionally also the radius of the droplets $\mathbf{r}_{\text {droplet }}$ was varied to account for changes in droplet transfer with increasing current (Table 3). Table 3. Parameters for the GHSM for GMAW process \begin{center} \begin{tabular}{l|l|l} \hline Experiment number, № & $\mathrm{r}_{\text {heat_source },[\mathrm{mm}]}$ & $\mathrm{r}_{\text {droplet }},[\mathrm{mm}]$ \\ \hline 1 & 9.3 & 0.6 \\ \hline 2 & 10 & 0.5 \\ \hline 3 & 14.6 & 0.4 \\ \hline \end{tabular} \end{center} EDACC Heat Source Model The EDACC heat source, as defined in [4] and [5], also needed to be calibrated for the cathode voltage drop $\boldsymbol{U}_{\boldsymbol{d}}$, the plasma temperature $\boldsymbol{T}_{\text {plasma }}$ and the radius of the heat source $\mathbf{r}_{\text {heat_source, }}$, see Table 1 , in order to match the total current and the power of the real process. The radius was also chosen to match the width of the resulting weld pool, while the voltage and the temperature were adjusted to give a reasonable ratio between power and current. The resulting values for the plasma temperature can be considered reasonable, based on the scientific works of [7] and [8], where it is stated that the plasma temperature in GMAW can vary between $6000[\mathrm{~K}]$ and $9000[\mathrm{~K}]$. Also, for the voltage drop, the results from [9] were used for orientation, considering a small negative contribution by the anode voltage drop (Table 4). \section*{3 Results} \subsection*{3.1 Quantitative Comparison} Figure 4 presents a comparison of the simulation results with the experimental data for the weld bead reinforcement, the depth and the width. In the comparison of the weld bead reinforcement a constant underestimation can be noticed. The model for the weld bead Table 4. Parameters for the EDACC for GMAW process \begin{center} \begin{tabular}{l|l|l|l} \hline \begin{tabular}{l} Experiment number, \\ № \\ \end{tabular} & $U_{d},[\mathrm{~V}]$ & $T_{\text {plasma }}[\mathrm{K}]$ & r $_{\text {heat_source, }[\mathrm{mm}]}$ \\ \hline 1 & 16 & 6850 & 5.2 \\ \hline 2 & 18 & 6670 & 6.2 \\ \hline 3 & 20 & 6080 & 9.0 \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-067(1)} \end{center} Fig. 4. Reinforcement (left), depth (center) and width (right) error comparison with GMAW process experimental data. reinforcement was only applied in the cases where the free surface deformation was taken into account, so for the GHSM and the EDACC, the same value for the reinforcement was used. The depth seems to be very much overestimated in the cases, where the free surface was not considered. However for the comparison of the EDACC with the Gauss model, the results almost lie within 0 and $-20 \%$, i.e. slightly underestimating the depth in the simulation compared to the real experimental weld pool results. The error of the width for all cases lies within $\pm 5 \%$, which is to be expected as the width was one of the parameters, the model was calibrated for. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-067} \end{center} Fig. 5. Length comparison with experimental data for GMAW. For the length comparison as can be seen in Fig. 5, it can be seen that the length is always overestimated by the EDACC model, by $\sim 10-15 \%$. Only in Experiment 1, the low current case, the GSHM with FSD underestimates the length. It should be noted however, that the length for the experimental data was taken from tracer experiments, which rather tends to overestimate the real weld pool length. Therefore an overestimation by the simulation needs to be judged especially critical. In this perspective, the GHSM without the FSD seems to yield the most accurate results. However, since it lacks the consideration of the weld seam deformation and it gives very large errors for the depth, this agreement should not be taken as a proof of accuracy. \subsection*{3.2 Qualitative Comparison} \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-068(1)}\\ a)\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-068(2)}\\ b) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-068} \end{center} Fig. 6. Comparison between experimental weld seam cross-sections and simulation results performed with GHSM (left) and EDACC model (right) for GMAW process a) Experiment №1 b) Experiment №2 c) Experiment №3. The qualitative comparison to the cross-sections of the experiments in Fig. 6 shows that the agreement for the weld reinforcement geometry is quite good when using the model for the FSD. This seems to show that the error in reinforcement, as seen in Fig. 4 must be due to fluctuations of the welding process and the small size of the reinforcement, where already small deviations might cause a considerable relative error. However, it is clearly noticeable that the depth is clearly deviating quite strongly. Overall, the differences between the GHSM (left) and the EDACC (right) are subtle, and they both seem to capture the shape of the cross section equally well. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-069} \end{center} Fig. 7. Comparison between experimental weld seam longitudinal sections and simulation results performed with GHSM (a, b, c) for GMAW process a) Experiment №1 b) Experiment №2 c) Experiment №3. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-069(1)} \end{center} Fig. 8. Comparison between experimental weld seam longitudinal sections and simulation results performed with EDACC model (d, e, f) for GMAW process d) Experiment №1 e) Experiment №2 f) Experiment №3. The comparison of the longitudinal cross-section shows that the differences between GHSM (Fig. 7) and EDACC (Fig. 8) are subtle again. Only for the first experiment in a) and d), a noticeable difference becomes apparent. Here the GHSM is considerable shorter, which can be also seen in Fig. 5. The main differences between the experimental results and the simulations lie first in the shape of the melting front, as in all cases, a "tip" becomes apparent, where it can be seen that the surface heat source is melting the material, but the heat and momentum by the droplets have not yet affected the weld pool shape. Another noticeable difference is the angle and curvature of the solidification front. In the experiments, the shape is much more concave and the angle with the top surface of the weld seam is much more steep, while in the simulation it seems almost perpendicular. \section*{4 Discussion} The reinforcement seems to show a constant underestimation. The model for the reinforcement was based on mass conservation, i.e. it is based on the fact, that whatever comes into the system by the wire, must exit the system by the weld seam. Since the approximation for the shape seems quite good as seen from Fig. 6, it has to be concluded that more mass has entered the system than could be accounted for by the process parameters. Possibly the welding velocity was not well calibrated in the experiment. The differences in width were marginal, as was expected due to the radius of the heat source being calibrated for the resulting weld pool width. However, the error in depth was considerable, although the addition of the FSD presents a significant improvement. However the differences between GHSM and EDACC were not as pronounced as expected. This might be due to the mesh resolution and due to the omission of the consideration of the arc column, which might have even more effects when accounting for the non-axisymmetric distribution of the current density vector field and the resulting effect on the Lorentz force. Considering the qualitative comparison in Fig. 6, it can be stated that the chosen approximation for the shape of the FSD was quite suitable, while the depth was difficult to obtain by the simulation. However, as the droplet transfer was not considered with high accuracy and with the suspicion of inaccurate setting of the wire feed velocity on the wire feeding device, the agreement in depth could be improved by a more accurate treatment in these areas. The differences in length were considerable, with a general tendency to overestimate the length from the measurements, in all but Experiment 1 for the GHSM. Since the data of the measurements were taken from trace experiments, which tend to even more overestimate the weld pool length, these differences are even more concerning. The seeming agreement for the length for Experiment 1 with GHSM still lacks a clear explanation. The apparently better matching of the simulation without the FSD should not be mistaken for a better performance of this approach. Since it lacks the consideration of the weld seam reinforcement and it gives very large errors for the depth, this agreement should rather be taken as an indication that some parts in the underlying model, still need improvement. In particular, the shape of the melting front in Fig. 7 and Fig. 8 could be improved by a more accurate positioning of the droplet mass source. For improvement of the shape of the solidification front in Fig. 7 and Fig. 8 a more accurate solidification model and possibly a finer meshing will be investigated in the future. \section*{5 Conclusion} The presented validation of the EDACC model shows that the EDACC model does perform as well as the GHSM when it comes to the determination of the weld pool shape. However, the EDACC model yields the advantage of giving more realistic surface temperatures of the weld pool, i.e. below boiling temperature, as was discussed in [5]. The EDACC model will also give rise to a modified distribution of current density and heat flux, as was discussed in [4] and [5] and can be seen from Fig. 1. This proves the additional benefit of the EDACC model when performing numerical GMAW process simulations. As a next step, the very simplified solidification model will be improved. Acknowledgement. The presented investigations were carried out at RWTH Aachen University within the framework of the Collaborative Research Centre SFB1120-236616214 "Bauteilpräzision durch Beherrschung von Schmelze und Erstarrung in Produktionsprozessen" and funded by the Deutsche Forschungsgemeinschaft e.V. (DFG, German Research Foundation). The sponsorship and support is gratefully acknowledged. \section*{References} \begin{enumerate} \item Reisgen, U., Stein, L.: Fundamentals of joining technology: Welding, Brazing and Adhesive Bonding, DVS Media GmbH, Düsseldorf (2016) \item Cho, M.H., Lim, Y.C., Farson, D.F.: Simulation of the weld pool dynamics in the stationary pulsed gas metal arc welding process and final weld shape. Weld. J. 85(12), 271-283 (2006) \item Mokrov, O., et al.: Numerical investigation of droplet impact on the weld pool in gas metal arc welding. Mater. Sci. Eng. Technol. 48(12), 1206-1212 (2017). \href{https://doi.org/10.1002/mawe}{https://doi.org/10.1002/mawe}. 201700147 \item Mokrov, O., Simon, M., Sharma, R., Reisgen, U.: Arc-cathode attachment in GMA welding. J. Phys. D Appl. Phys. 52(36), 364003 (2019). \href{https://doi.org/10.1088/1361-6463/ab2bd9}{https://doi.org/10.1088/1361-6463/ab2bd9} \item Mokrov, O., Simon, M., Sharma, R., Reisgen, U.: Effects of evaporation-determined model of arc-cathode coupling on weld pool formation in GMAW simulation. Weld. World 64, 847-856 (2020). \href{https://doi.org/10.1007/s40194-020-00878-3}{https://doi.org/10.1007/s40194-020-00878-3} \item Reisgen, U., Schiebahn, A., Mokrov, O., Lisnyi, O., Sharma, R.: The experimental analysis of the influence of submerged arc welding parameters on weld bead geometry formation. CWA J. (Journal de l'ACS) 11, 90-94 (2015) \item Kozakov, R., et al.: Spatial structure of the arc in a pulsed GMAW process. J. Phys. D Appl. Phys. 46(22), 224001 (2013). \href{https://doi.org/10.1088/0022-3727/46/22/224001}{https://doi.org/10.1088/0022-3727/46/22/224001} \item Valensi, F., et al.: Plasma diagnostics in gas metal arc welding by optical emission spectroscopy. J. Phys. D Appl. Phys. 43(43), 434002 (2010). \href{https://doi.org/10.1088/0022-3727/}{https://doi.org/10.1088/0022-3727/} 43/43/434002 \item Zhang, G., et al.: Study of the arc voltage in gas metal arc welding. J. Phys. D Appl. Phys. 52, 085202 (2019). \href{https://doi.org/10.1088/1361-6463/aaf588}{https://doi.org/10.1088/1361-6463/aaf588} \end{enumerate} \section*{Brazing} \section*{New Opportunities for Brazing Research by in situ Experiments in a Large Chamber Scanning Electron Microscope } \begin{abstract} The present study demonstrates that in situ heating experiments in a LC-SEM are capable to provide hitherto not accessible insights into the kinetics of the brazing process. Continuous video documentation and temperature logging of the entire experiment yielded the on-set time of the wetting of the base material and the upper time limit that should not be exceeded to avoid quality losses of the joint. For the here investigated system of $75 \mathrm{Sn} 20 \mathrm{Cu} 5 \mathrm{Ge}$ filler metal with aluminum alloy EN AW-42100 base metal, the maximum holding time has been determined as $3.5 \mathrm{~min}$ at $450^{\circ} \mathrm{C}$. The wetting point at this temperature is reached after one minute, which proves the effectiveness of the here investigated system. \end{abstract} Keywords: Scanning electron microscopy $\cdot$ SEM $\cdot$ Large chamber $\cdot$ LC-SEM $\cdot$ In situ $\cdot$ Brazing $\cdot$ Wetting \section*{1 Introduction} The usual workflow of materials characterization by electron microscopy puts main emphasis on the pre- and post-mortem state of the sample under investigation. This traditional approach fails however, if information about intermediate stages during mechanical, chemical and/or temperature treatment of the sample are crucial to gain in detail understanding of the process. In consequence, questions related to the mechanism and how the material transforms into a certain morphology or microstructure remain frequently unanswered. To fill this knowledge-gap the development of in situ materials characterization techniques and equipment became one of the top priorities among the past two decades. Nevertheless, while the implementation of in situ capabilities is rather straightforward and became readily available for some characterization techniques, this is unfortunately not the case in conjunction with electron microscopes. For the latter, a much more elaborate instrument design is required in order to manage the high vacuum demands at elevated temperatures and/or upon varying pressure [1,2]. About 15 years ago one of the unique large-chamber scanning electron microscopes (LC-SEM) was installed at the main authors institute [3]. The main benefit of this type\\ of LC-SEM is its huge chamber that was designed to overcome the common restrictions of conventional SEMs, which do not allow implementation of in situ experiments on the larger scale. To reach this goal, the large-chamber hosts the whole column of the SEM, which enables to align the electron optics to almost any position with regard to the sample [4]. Hence, this setup allows investigation of samples with dimensions of up to $0.7 \mathrm{~m}$ in diameter and $300 \mathrm{~kg}$ in weight. Aside imaging and high-frame rate video capabilities with secondary electrons (SE), the LC-SEM is equipped with a backscattering electron (BSE) detector and a silicon-drift energy dispersive X-ray (EDX) analysis system from BRUKER. Experiments can be operated under variable pressure (VP) of up to 3000 Pa. Hence, this LC-SEM facilitates integration of even very bulky setups necessary for in situ tensile testing, laser beam micro welding or larger sample heating equipment [5]. For the here presented in situ brazing experiment we employed a heating module from Kammrath \& Weiss GmbH, Dortmund, Germany (Fig. 1). \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-074} \end{center} Fig. 1. Heating module in the LC-SEM (bottom). The electron optical column with an SE and BSE detector can be seen at the top. \section*{2 Focus Application: in situ Brazing} Throughout the joining process via brazing, locally melted phases are generated along the interface of the work pieces which form the brazing joint between the filler metal and the base material after solidification. However, melting and solidification processes as well as segregation effects might occur in the process affected zone that can lead to severe shrinkage, mismatch and even distortion of the components. Melting, solidification and segregation are temperature dependent, so the heating and cooling rate as well as the holding time of a brazing process are crucial parameters for the phase evolution and\\ microstructure along the joining zone [6]. For further improvement of the joining process, it is therefore necessary to gain a more thorough understanding of the involved time and temperature frame and to determine the onset temperature of the wetting, the ideal maximum temperature and the period of holding time. To determine all these crucial parameters a LC-SEM outfitted with a suitable in situ setup is the perfect tool that assists development of optimized brazing processes with even more precise results for long-lasting and well-functioning joints. For demonstration of the capabilities of the described approach we used the brazing system $75 \mathrm{Sn} 20 \mathrm{Cu} 5 \mathrm{Ge}$ (as filler metal) with aluminum alloy EN AW-42100 (as base material) that has been investigated by our group in an earlier study [7]. \subsection*{2.1 Experimental} A small $0.1 \mathrm{~mm} \times 0.2 \mathrm{~mm}$ chunk of $75 \mathrm{Sn} 20 \mathrm{Cu} 5 \mathrm{Ge}$ filler metal on a sheet of aluminum alloy EN AW-42100 was inserted into the heating module. The sample was then heated up under vacuum to $450{ }^{\circ} \mathrm{C}$ using a heating rate of about 2.4 degrees per sec. Due to the inertia of the temperature control loop, the temperature may overshoot the targeted temperature for a limited period of time. The holding time of $33 \mathrm{~min}$ was chosen to be relatively long compared to conventional brazing processes, in order to be able to investigate any effects even after the brazing joint has been established. The subsequent cooling took place under vacuum conditions in the LC-SEM. The temperature curve of the experiment, together with SE images recorded after certain time periods are shown in Fig. 2. The corresponding event-log of the experiment is listed in Table 1. After cooling to ambient temperature, the sample was characterized by EDX element mapping from top (Fig. 3) and in cross-section geometry (Fig. 4) for characterizing interface of the joint. A specimen for subsequent STEM-EDX element mapping in a transmission electron microscope (TEM) was prepared by focused ion beam (FIB) milling using a Dualbeam FIB FEI STRATA400 (Fig. 5) [8]. The TEM investigation was carried out with a Zeiss LIBRA200FE operated at $200 \mathrm{kV}$. Table 1. Event-log of the LC-SEM in situ experiment. \begin{center} \begin{tabular}{l|l|l|l} \hline $\#$ & Time $[\mathrm{sec}]$ & Temperature $\left[{ }^{\circ} \mathrm{C}\right]$ & Remarks \\ \hline 1 & 0 & RT & Launch of heat ramp $\left(\sim 2.4^{\circ} \mathrm{C} / \mathrm{sec}\right)$ \\ \hline 2 & 90 & 380 & First visible shrinkage of the filler metal \\ \hline 3 & 150 & 470 & Initial signs of wetting \\ \hline 4 & 210 & 450 & Complete wetting \\ \hline 5 & 270 & 450 & Grain structure of base becomes visible \\ \hline 6 & 400 & 450 & Grain structure/white rim around molten filler metal \\ \hline 7 & 1640 & 450 & Pronounced grain structure visible \\ \hline 8 & 2700 & 200 & Termination of the experiment \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-076} \end{center} Fig. 2. Temperature curve of the LC-SEM in situ experiment and SE images recorded after certain time periods. The number of the images refers to the event-log in Table 1.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-076(1)} Fig. 3. SEM image and corresponding EDX element distribution maps recorded after the in situ experiment in the LC-SEM. (a) image from the secondary electron (SE) detector (b) aluminum, (c) silicon (d) tin, (e) copper (f) germanium. \subsection*{2.2 Results} The event-log listed in Table 1 reports the first visible changes at a nominal sample temperature of $380^{\circ} \mathrm{C}(\# 2)$. This is the point when the native oxide layer of the base material is locally destroyed and becomes dissolved by the filler metal. After another minute, the until then rather structureless molten filler metal started to develop some grain structure contrast in the SE image (\#5). This must be interpreted as result of an increased surface roughness. Further annealing at $450^{\circ} \mathrm{C}$ caused formation of a white\\ rim after additional 2 min (\#6), which might go along with an increased segregation of the initial filler metal. The latter process is again characterized by a further increase of surface roughness. As seen by comparison of the SE images \#6 to \#8 in Fig. 2, these images represent the final stage of the experiment since the shape of the filler metal remains unchanged. The main difference between these three images is the contrast gain with annealing time. Inspection of the EDX element distribution maps recorded from the solidified sample proves the great inhomogeneity over the sample. As expected, the grains of the base material contain still the largest amounts of aluminum with formation of aluminumcopper phases in the central contact zone (Fig. 4b and 4e). However, the grain boundaries of the aluminum rich phase are found thoroughly decorated with silicon and it seems that the spread of tin took place along these tracks along the grain boundaries as well. As a consequence, the center of the re-solidified filler metal is significant depleted in silicon. In contrast to the latter, copper appears much less mobile and could not be detected outside the central wetting area. Moreover, low amounts of magnesium and germanium are distributed along the rim of the center part of the filler metal. Based on the SEMEDX results from the cross-section sample, it appears that the formation of copper-tin phases at the interface can be ruled out due to the missing overlap of the corresponding element maps for copper (Fig. 4e) and tin (Fig. 4f). However, the STEM-EDX element distribution maps in Fig. 6 give a more detailed view of the microstructural changes directly at the interface. These distribution maps recorded at higher magnification show that copper is also dissolved to some extend in the tin matrix. Moreover, the maps show that copper mixes also with aluminum, but not with silicon. The latter element however, binds to germanium, a finding that is also supported by the element overlaps in Fig. 4c and $4 \mathrm{~d}$.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-077} Fig. 4. SEM secondary electron (SE) image and corresponding EDX element distribution maps of a cross-section from the center part of the sample after the LC-SEM in situ experiment. The elemental maps in (b) and (e) prove formation of aluminum-copper phases at the interface. The latter are embedded in a probably pure tin matrix as seen in (f). At this magnification the formation of copper-tin phases at the interface cannot be justified due to the non-overlapping element maps for copper (e) and tin (f). However, as proven by Figs. 6e and 6f, some amounts of copper are indeed dissolved in the tin matrix. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-078(3)} \end{center} Fig. 5. Secondary electron (SE) image recorded at the interface of the cross-section sample. The length of the extracted FIB lamella for STEM-EDX analysis is indicated by the yellow arrows.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-078}\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-078(2)}\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-078(1)} Fig. 6. High-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) image of the FIB specimen in (a) and corresponding EDX element distribution maps for the key-elements in (b) to (f). This close-up demonstrates that the interface between base material and filler metal reveals highly in-homogenously and quite complex. Whereas copper (e) mixes with aluminum in (b) and tin in (f), this appears not to be the case for silicon (c). The latter however, binds to germanium (d), which is a rather unexpected finding (for comparison see also Fig. $4 \mathrm{c}$ and $4 \mathrm{~d})$. \subsection*{2.3 Discussion and Conclusions} As demonstrated in this study, in situ brazing experiments in a LC-SEM are capable to provide hitherto not accessible insights into the kinetics of the initial wetting of the base material and the evolution of intermetallic phases formed along the contact zone. Due to continuous video documentation and temperature logging of the entire experiment,\\ it is possible to identify the optimum processing parameters at the later stage of data evaluation. Although each in situ experiment is in fact a single shot experiment that requires several repetitions for statistical reasons, it does provide already good first estimates for the nearly optimum brazing conditions. Hence, we were also able within the present study to estimate the most critical parameter for brazing - the holding time - for a particular maximum processing temperature from a single in situ experiment in the LC-SEM. Thus, for the here investigated system of $75 \mathrm{Sn} 20 \mathrm{Cu} 5 \mathrm{Ge}$ filler metal with aluminium alloy EN AW-42100 base metal, the holding time should not exceed 3.5 minutes at $450^{\circ} \mathrm{C}$ in order to avoid any quality losses of the joint. Moreover, the great efficiency of the here investigated brazing system could be confirmed by determining the wetting point at one minute after reaching the target temperature. Acknowledgements. The authors gratefully thank Mr. Kevin Kistermann (GFE) for FIB sample preparation and evaluation of TEM data. This work was performed within the German Research Foundation (DFG) supported Collaborative Research Centre SFB 1120 "Precision Melt Engineering". Moreover, the DFG is acknowledged for financial support within the recent Project 163323790 . \section*{References} \begin{enumerate} \item Stokes, D.J.: Principles and Practice of Variable Pressure/Environmental Scanning Electron Microscopy (VP-ESEM). Wiley, Chichester (2008). \href{https://doi.org/10.1002/9780470758731}{https://doi.org/10.1002/9780470758731} \item Dehm, G., Howe, J.M., Zweck, J.: In-Situ Electron Microscopy: Applications in Physics, Chemistry and Materials Science. Wiley-VCH (2012). \href{https://doi.org/10.1002/978352765}{https://doi.org/10.1002/978352765} 2167 \item Aretz, A., Ehle, L., Haeusler, A., Bobzin, K., Öte, M., Wiesner, S., Schmidt, A., Gillner, A., Poprawe, R., Mayer, J.: In situ investigation of production processes in a large chamber scanning electron microscope. Ultramicroscopy 193, 151-158 (2018) \item Klein, M., Klein, S.: Adapting human behaviour for the development of a new scanning electron microscope. In: Proceedings of International Conference on Micromechatronics for Information and Precision Equipment MIPE 1997, Tokyo, Japan, p. 324-329 (1997) \item Ramazani, A., Schwedt, A., Aretz, A., Prahl, U.: Digital Image Correlation (DIC), Dual Phase Steel, EBSD, Extended Finite Element Method (XFEM), In Situ Bending Test, Kernel Average Misorientation (KAM) Map, Representative Volume Element (RVE). Key Eng. Mater. 586, 67-71 (2014) \item Schmitz, G.J., Böttger, B., Apel, M.: On the role of solidification modelling in integrated computational materials engineering "ICME". In: IOP Conference Series: Materials Science and Engineering, vol. 117, p. 012041 (2016). \href{https://doi.org/10.1088/1757-899X/117/1/012041}{https://doi.org/10.1088/1757-899X/117/1/012041} \item Iskandar, R., Schwedt, A., Mayer, J., Rochala, P., Wiesner, S., Oete, M., Bobzin, K., Weirich, T.E.: Microstructural analysis of germanium modified tin-copper brazing filler metals for transient liquid phase bonding of aluminium. Materialwiss. Werkstofftech. 48, 1257-1263 (2017). \href{https://doi.org/10.1002/mawe.201700155}{https://doi.org/10.1002/mawe.201700155} \item Giannuzzia, L.A., Stevieb, F.A.: A review of focused ion beam milling techniques for TEM specimen preparation. Micron 30, 197-204 (1999). \href{https://doi.org/10.1016/S0968-432}{https://doi.org/10.1016/S0968-432} 8(99)00005-0 \end{enumerate} \section*{Phase-Field Modeling of Precipitation Microstructure Evolution in Multicomponent Alloys During Industrial Heat Treatments } \begin{abstract} We develop a phase-field model for the simulation of chemical diffusion limited microstructure evolution. The model is applied to $\gamma^{\prime}$-precipitation under the influence of realistic multi-step aging treatments in multi-component nickel-based superalloys with industrially relevant chemical complexity. The temperature-dependent thermodynamic and kinetic input parameters are obtained from CALPHAD calculations using ThermoCalc. Further, the model accounts for the lattice-misfit between the precipitate- and the matrix-phase. The required temperature-dependent elastic stiffness and lattice-misfit can be measured using resonance ultrasound spectroscopy and high temperature $\mathrm{X}$-ray diffraction, respectively. This allows to account for realistic shaping of $\gamma^{\prime}$-particles in the simulation. The comparison to shapes of $\gamma^{\prime}$-particles in experimental microstructures serves as an important cross validation of the model. The application of the model to investigate the effect of the subsequent aging treatment on the precipitation microstructure after a brazing process is discussed. \end{abstract} Keywords: Precipitation hardening $\cdot$ Aging heat treatment $\cdot$ Phase-field modeling $\cdot$ Brazing \section*{1 Introduction} Nickel-base superalloys have various applications at elevated temperatures, especially in stationary gas turbines and airplane engines. The main strengthening mechanism, which makes these alloys applicable for high temperatures is by coherent precipitation of ordered fcc $\gamma^{\prime}$-phase ( $\mathrm{L} 1_{2}$ structure) [1]. The aim of industrial aging heat treatments is to achieve optimum precipitate sizes, a narrow size distribution and high volume fractions up to $70 \%$ of the strengthening phase $[2,3]$. This is achieved by nonisothermal multi-stage aging heat treatment, being specifically optimized for the individual alloy [4-6]. During brazing the composition of the base material is strongly altered in the extended joining zone by the imposed braze material. This poses the material science question of how to design optimal heat treatments for the joined material [7, 8]. In this work, we discuss the precipitation microstructure evolution during multi-stage, nonisothermal aging heat treatments in joining zones based on simulations. \subsection*{1.1 Precipitation Microstructure Evolution} To obtain optimal mechanical properties, it is crucial to tailor the mean precipitate size and size distribution as well as the precipitate volume fraction as a result of the aging heat treatment. Different physical mechanisms lead to a temporal evolution of the mean size and size distribution of the precipitates as well as the overall precipitate volume fraction. A general increase of the mean precipitate size is referred to as "coarsening". An individual particle can either grow due to a local supersaturation of the matrix (i.e. nonequilibrium growth) or on the expense of the surrounding, smaller particles, which are simultaneously dissolving. The latter coarsening mechanism is called "precipitate ripening", according to the commonly known Lifshitz-Slyosov-Wagner (LSW) theory of Ostwald ripening [9-11]. Which proceeds very close to the local thermodynamic equilibrium [12]. Ostwald ripening is the growth of large particles at the expense of dissolving smaller ones. The driving force is the overall reduction of interface area and thus interfacial energy. The size distribution during ripening is self-similar with respect to the mean precipitate size. Furthermore, new particles can nucleate from the supersaturated matrix, and two neighboring precipitates can coagulate, i.e. merge into a single, larger precipitate. In comparison to ripening, nonequilibrium nucleation and growth results in an increasing overall precipitate volume fraction. In an industrial aging heat treatment this typically occurs during and right after the cooling stages. The shaping and the arrangement of the precipitate particles is predominantly influenced by elastic effects, which result from the temperature dependent misfit between the $\gamma^{\prime}$-precipitates and the matrix-phase. Misfitting coherent precipitates cause an inhomogeneous strain field around the precipitates. The precipitate shape is determined by the minimum of the sum of interfacial and elastic energy [13]. The effect of elasticity on the precipitate shape rises with increasing precipitate size as bulk elastic effects then dominate the interfacial contributions [14]. With increasing misfit, the precipitate shapes become increasingly more cuboidal due to the cubic anisotropy of the elasticity $[3,15]$. \subsection*{1.2 Phase-Field Simulations of Precipitate Microstructure Evolution} The focus of this work is on the qualification of a phase-field model for the simulation of diffusion limited precipitate microstructure evolution in nickel-base superalloys. The aim is to realize the simulation of nonisothermal multi-stage aging heat treatments including cooling and heating stages for integrated computational materials engineering. The phase-field method is frequently used to study the temporal evolution of precipitation microstructures [16-21]. The required thermodynamic and kinetic input information is obtained from CALPHAD calculations using the commercial software-package ThermoCalc [22]. Considering different nickel-base superalloys, we perform simulations of\\ precipitation microstructure formation with the explicit consideration of up to ten different chemical components. Furthermore, an elastic term is included in the model to account for the misfit stresses as well as inhomogeneous elastic constants. The details concerning the present phase-field model are given basically in [12]. This model has been recently extended by the so-called "sharp phase-field method" [23, 24]. Respective extensions to the model are discussed in [25]. The temperature dependent thermodynamic and kinetic input parameters can be calculated from thermodynamic and thermo-kinetic CALPHAD databases as described in $[12,26]$. The elastic parameters have been extracted from metallurgic experiments at Metals and Alloys at the University of Bayreuth. The temperature-dependent lattice misfit between the $\gamma^{\prime}$-phase and the matrix has been measured using high-temperature $\mathrm{X}$-ray diffraction. The temperature dependent anisotropic and inhomogeneous elastic constants have been measured using resonance ultrasound spectroscopy. Highly important information about the stiffness contrast between the $\gamma$-matrix and the $\gamma^{\prime}$-precipitates [21] can be derived from carefully prepared singles-phase single-crystals [2, 12]. \section*{2 Results and Discussion} In this paper, we focus on the following two alloys from the 1st generation of nickel base superalloys: René 80 and Alloy 247 together with the braze material AMS4782. The compositions of the different alloys are given in Table 1. Table 1. Composition of the different alloys in at. \% considered in this work. \begin{center} \begin{tabular}{l|l|l|l|l|l|l|l|l|l|l|l} \hline & Co & $\mathrm{Mo}$ & $\mathrm{Cr}$ & $\mathrm{W}$ & $\mathrm{Ta}$ & $\mathrm{Al}$ & $\mathrm{Ti}$ & $\mathrm{Si}$ & $\mathrm{Hf}$ & $\mathrm{C}$ & $\mathrm{Ni}$ \\ \hline Alloy 247 & 10 & 0.7 & 8.3 & 10 & 3 & 5.5 & 1.0 & - & 1.4 & 0.1 & Bal. \\ \hline AMS4782 & - & - & 19 & - & - & - & - & 10 & - & 0.1 & Bal. \\ \hline René 80 & 9.2 & 2.4 & 15 & 1.2 & - & 6.4 & 5.7 & - & - & 0.8 & Bal. \\ \hline \end{tabular} \end{center} \subsection*{2.1 Simulation of Aging in René 80} After homogenization and quenching of René 80, a mean $\gamma^{\prime}$ precipitate size of $136 \pm 30$ $\mathrm{nm}$ was experimentally determined. Primary precipitates are observed with a volume fraction of $12 \pm 3 \%$ [6]. This is the initial configuration for a one-dimensional simulation of the coarsening during the aging heat treatment of René 80. The initial setup consists of 2000 initial precipitates with randomly distributed sizes $4 \xi12,000 \mathrm{~K}$ and $\mathrm{v}_{\mathrm{p}}>1,000 \mathrm{~m} / \mathrm{s}$ respectively [1]. Due to the high plasma temperatures, nearly any material can be brought to the liquid phase and impacted on the substrate material at relatively high velocities [2]. The liquid particles deform, cool down rapidly and solidify on the substrate surface during their impact, thereby building up a coating (Fig. 1). Measured and calculated cooling rates of the ceramic particles during the impact are reported in the literature to be in the range of $\dot{\mathrm{q}}=10^{7}$ to $\dot{\mathrm{q}}=10^{10} \mathrm{~K} / \mathrm{s}$ [3-5]. Since the dynamics of particle deformation and solidification control the resulting coating microstructure and hence the properties of the final coating, it is important to model the particle impact to increase the understanding of this process. Furthermore, the experimental observation of the particle deformation process poses challenges due to the short time frames of a few microseconds [6]. Due\\ to these reasons, several works can be found in the literature that numerically analyze the particle impact and splat formation [7-9]. While the simulation of a single particle impact improves the understanding of the dynamics of particle deformation and solidification, simulating the impact of multiple particles would allow in the future to determine the coating properties such as porosity and effective thermal conductivity. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-101} \end{center} Fig. 1. A cross-section picture of a typical $\mathrm{Al}_{2} \mathrm{O}_{3}$ coating sprayed with atmospheric plasma spraying The focus of this work is to present a multiple particle impact model where individual particles can be identified. This gives an unprecedented possibility to track the temperature evolution as well as their cooling rates during and after their impact. To the knowledge of the authors, this has not been demonstrated in the literature for computational fluid dynamics based multiple particle impact simulations. A brief overview of the numerical modelling used to simulate the particle impact and solidification will be given in the next chapter. It will be followed by a previously performed benchmark simulation of an impact of a single nickel particle to verify the model against the reference simulations in the literature [10]. This previous model was extended for this work to simulated the impact of 20 particles and the material was changed to alumina. The results of these simulations will be presented. Furthermore, the temperature evolution as well as the cooling rates will be shown for the individual $\mathrm{Al}_{2} \mathrm{O}_{3}$ particles. Hereby a better understanding of particle impact in atmospheric plasma spraying will be achieved, which in turn will enable process improvements in the long term. \section*{2 Numerical Modelling} A common way to model the particle impact in thermal spraying is the computational fluid dynamics approach, which allows to resolve the deformation and splashing of liquid\\ particles. To distinguish between the liquid particle phase and the gaseous ambient phase, a multiphase modelling approach Volume of Fluid (VOF) is used. VOF is a region following scheme, which enables the modelling of two or more immiscible fluids. This method stores the volume fraction information of each fluid phase in the cells of computational domain. Since the computational fluid dynamics approach inherently assumes the particles to be fluids, additional numerical modelling is needed to take the particle solidification and solidified splats into account. Commonly used modelling approaches in the literature are the modified viscosity method [11] and enthalpy porosity method [12]. In the modified viscosity method the solidification is modelled by assigning a temperature dependent viscosity profile to the particle material which rapidly reaches large values as the temperature decreases to the solidification temperature. A major disadvantage of this method is the numerical requirement of the time step to decrease inversely proportional to the increasing viscosity in order for the solution to converge. This, in turn, requires much larger numbers of time steps for the simulation to complete, which results in longer and often critical computation times. Contrary to the modified viscosity method, the enthalpy porosity method does not require a decrease of the time steps for the solution to converge when the particle solidification occurs and is therefore computationally much easier. Due to this advantage, the enthalpy porosity method was used to model the particle impact in this work. Since in the enthalpy porosity method, the material viscosity is not increased artificially to imitate a solidified material, its viscosity at temperatures below solidification temperatures does not affect the kinematics of the particle material. Therefore, the kinematics of the solidified material need to be controlled by an additional momentum source variable, which is included in the conservation of momentum equation in the numerical solver. In this work, the commercial computation fluid dynamics software ANSYS Fluent 19 (ANSYS. Inc. Canonsburg, United States of America) was used to model and simulate the particle impact. This software allows for the user to manipulate the momentum source with the help of a user defined function and thus to artificially accelerate or decelerate the particle depending on a flow condition. To model the solidification, the user defined momentum source was defined in such a way, that below the solidification temperature, the particle material is rapidly decelerated to imitate the inertia of a solidified material. The added momentum source term (S) can be found in Eq. (1). \begin{equation*} S=-C \cdot V F_{p} \cdot K(\rho) \cdot v \tag{1} \end{equation*} The magnitude of the deceleration force acting on the particle material is proportional to its instantaneous velocity $v$ and the particle volume fraction $V F_{p}$. The numerical constant $C$ and the density dependent parameter $K(\rho)$ control this deceleration as explained in [10]. $S$ acts on the particle material starting the moment its temperature drops below the solidification temperature, gradually diminishes as the particle slows down and virtually fades away as the particle comes to a halt in its solidified state. Although Ansys Fluent already comes with a solidification model based on the enthalpy porosity method which could be directly used out of the box, it turned out to be inapplicable for the simulation of multiple particle impacts due to a numerical artifact. The numerical artifact becomes evident when a liquid particle comes in contact\\ with an already solidified particle. To avoid this artifact while simulating the impact of more than one particle, the user defined momentum source was defined as described above. More detailed information about the enthalpy porosity method of Ansys Fluent, its numerical artifact concerning multiple particle impact and the momentum source formulation defined as a user defined function to remedy this issue can be found in the previous work of authors [10]. \subsection*{2.1 Model Validation} As mentioned earlier, experimental verification on the particle impact model is challenging due to the short time scales at which the deformation and solidification occur in thermal spraying. Due to this, the developed particle impact model was verified against a reference particle impact model found in the literature [13]. Additionally, the authors of the aforementioned study have experimentally validated their model for the impact of nickel particles. Thus, comparing the simulation results of the model developed in this work to the simulation results of an experimentally validated model found in literature serves as an indirect experimental validation. To achieve this, a benchmark simulation was built with particle parameters corresponding to those given in the reference simulation. A more detailed description of the simulation set-up as well as the material properties for the nickel particles can be found in the previous work [10]. Figure 2 gives main characteristics of the simulation set-up while visually comparing the two results. Based on the visual attributes of the formed splats as well as the flattening degrees, a good correspondence between the developed and the reference models can be concluded. a)\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-103} Nickel particle $\mathrm{D}=60 \mu \mathrm{m}$\\ b) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-103(2)} \end{center} $=73 \mathrm{~m} / \mathrm{s}$ $\mathrm{T}_{\mathrm{p}}=400^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-103(1)} \end{center} Fig. 2. Simulation results of an impact of a single nickel particle. a) model developed in this work, b) experimentally verified model found in literature [13]. Here, D corresponds to particle diameter, $v$ to particle velocity prior to the impact, $T_{p}$ to particle temperature and $T_{S}$ to substrate temperature. The image originates from [10] and is used under CC BY 3.0, slight repositioning of the text has been performed. \subsection*{2.2 Simulation Setup} After the particle impact model was verified, it was utilized to simulate the impact of 20 $\mathrm{Al}_{2} \mathrm{O}_{3}$ particles. The parameters defining the particle impact are summarized in Table 1. The particle size is within the range of commonly used particle size distribution for the feedstock material used in atmospheric plasma spraying. The particle velocity and particle temperature correspond to the characteristic particle in-flight parameters occurring during spraying of $\mathrm{Al}_{2} \mathrm{O}_{3}$ particles at a stand-off distances typical for coating deposition. The time interval between the consecutive particle impacts is defined by the impact time interval. An uncharacteristically short impact time interval of $\Delta t=5 \mu \mathrm{s}$ was chosen for this set-up to be able to simulate more particle impacts during the total simulation time of $t=100 \mu$ s than it would have been possible under realistic coating conditions. The values of the particle size, velocity, temperature as well as the impact time interval correspond to the mean values. The actual values of the aforementioned parameters were randomly varied based on the normal distribution with relatively tight standard deviations, which is given in Table 1 as SD. The particle impact locations on the substrate were generated randomly. Since the substrate temperature was held constant during the simulation without being influenced by the impacting hot particles, the material of substrate was not taken into account and therefore is not given in the table. Table 1. Simulation parameters for the 3-D multiple particle impacts \begin{center} \begin{tabular}{l|l} \hline Parameter & Value \\ \hline Particle material & $\mathrm{Al}_{2} \mathrm{O}_{3}$ \\ \hline Number of particles & 20 \\ \hline Mean particle size, SD & $30 \mu \mathrm{m}, 2 \mu \mathrm{m}$ \\ \hline Mean particle velocity, SD & $200 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}$ \\ \hline Mean particle temperature, SD & $3,000^{\circ} \mathrm{C}, 10^{\circ} \mathrm{C}$ \\ \hline Mean impact time interval, SD & $5 \mu \mathrm{s}, 0.5 \mu \mathrm{s}$ \\ \hline Substrate temperature & $20^{\circ} \mathrm{C}$ \\ \hline \end{tabular} \end{center} $\mathrm{Al}_{2} \mathrm{O}_{3}$ is a ceramic feedstock material commonly used in atmospheric plasma spraying. Its material properties are shown in Table 2, which were taken from Burcat and Ruscic [14]. The solid heat capacity is function of the material temperature and therefore is given as a temperature range. Table 2. Material properties of $\mathrm{Al}_{2} \mathrm{O}_{3}$ [14] \begin{center} \begin{tabular}{l|l} \hline Property & Value \\ \hline Melting temperature & $2,327 \mathrm{~K}$ \\ \hline Latent heat of melting & $1,060 \mathrm{~J} \mathrm{~g}^{-1}$ \\ \hline Solid material density & $3.95 \mathrm{~g} \mathrm{~cm}^{-3}$ \\ \hline Liquid material density & $2.7 \mathrm{~g} \mathrm{~cm}^{-3}$ \\ \hline Solid heat capacity & $0.6-0.9 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}$ \\ \hline Liquid heat capacity & $1.95 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}$ \\ \hline Thermal conductivity & $6 \mathrm{~W} \mathrm{~m}^{-1} \mathrm{~K}^{-1}$ \\ \hline \end{tabular} \end{center} \section*{3 Results and Discussion} Due to the nature of fluid dynamics simulation, identifying and tracking the individual particles poses a challenge once they come into contact with each other. As the particles contact each other, they merge into the unified block of the same particle phase with no distinguishing feature that would allow to differentiate one from another and to recognize the borders between the particles. This is characteristic to all particle impact modelling works found in the literature that use the computational fluid dynamics approach. Overcoming this inherent limitation would allow to track the temperature evolution and the cooling rates of individual particles. In the model developed in this work, an additional variable that holds the identity information for each particle was introduced into the solution process. Each particle is assigned a unique identifier as it emerges into the computational domain and the identifier is incremented for the next particle. In this manner, the particles are basically counted in the order of their emergence into the simulation. Figure 3 illustrates an isometric view of the simulation results after all 20 particles have impacted on the substrate and solidified. When only distinguishing between the gas and particle phases, all of the solidified particles seem to be consisting of a single block of material. While this block contains pores, the individual boundaries between singles particles cannot be distinguished. When visualizing the particles based on their unique identifier, the individual particles can be clearly differentiated. For the formation of different phases during the solidification of particles, the temperature profile and its corresponding cooling rate are of great interest. The presented model is capable of calculating the temperature evolution of the individual particles as illustrated in Fig. 4. Here it can be seen that each particle emerges into the simulation domain at the temperature of $3,000 \mathrm{~K}$, maintains this temperature for a short period of time during its flight towards the substrate and rapidly cools down upon the impact. The cooling down of the particles continues even after solidification has taken place. It is worth noting that the early particles that make direct contact with the substrate surface seem to cool down faster than the particles impacting on the already solidified particles. Another important aspect is that the particle temperatures are not strictly monotonically decreasing. The temperature of the solidified particles show significant spikes as newly emerged, hot particles impact on them. There temperature spikes can also be observed \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-106(1)} \end{center} Fig. 3. Result of the impact simulation with $20 \mathrm{Al}_{2} \mathrm{O}_{3}$ particles. Comparison of visualizing the solidified particles based on the particle volume fraction versus visualizing them based on their identifier. for the particles which do not directly contact the new and hot particles. In this case, the spikes arise with a delay, resulting from the heat transfer through the surrounding material. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-106} \end{center} Fig. 4. Temperature evolution of individual particles numbered based on their identifier A better insight into the cooling rates of the particles can be gained by differentiating the particle temperature with respect to time. Particle heating rates for the individual particles, that were obtained in this manner, are shown in Fig. 5. Here, the pronounced downward spikes in the particle heating correspond to the initial rapid cooling of the particles at the moment of their impact. The overall magnitude of the particle cooling\\ rate is in agreement with the values reported for $\mathrm{Al}_{2} \mathrm{O}_{3}$ particles in the literature [5]. Upwards spikes correspond to the heating of the particles through the contact with newly emerged and hot particles. Although the graph of the particle temperatures indicate that particles that emerge later in the simulation tend to have gentler slopes, such correlation could not be observed on the graph of the particle heating. This can be explained by the fact that the maximum magnitude of the particle heating rate occurs during the first moments of the particle impact, while the particle temperature is still high. When there is still a high temperature difference between the new and the solidified particle, how fast a particle cools down is mainly influenced by how well the liquid particle wets the solid surface. Due to this reason, no clear correlation can be observed between the maximum cooling rates of the particles and their time of impact. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-107} \end{center} Fig. 5. Heating rates of the individual particles \section*{4 Conclusion and Outlook} This work presented a computational fluid dynamics model for multiple particle impacts. The multiphase formulation to distinguish the gas phase from the particle phase was done using the volume of fluid method. Solidification was modelled by modifying momentum source with the help of user defined routines, which is adapted from the enthalpy porosity method to suit the multiple particle impact. An additional variable was assigned to each particle at the time of its emergence to identify the individual particles after the impact. With the help of this identification method, it was for the first time possible to track the temperature evolution as well as the cooling rates of individual particles separately in a multiple particle impact simulation. Identifying individual particles opens the possibility to identify the interfaces between the particles, as can be seen in Fig. 6. Interlamellar interfaces in real thermally sprayed coatings are much thinner than the splats, yet they influence the effective thermal conductivity of the coatings. Directly resolving the interlamellar interfaces in the particle impact model is challenging because the grid refinement level would be too high for practical applications. With the help of interface identification it would be possible to model the properties of the interlamellar interfaces instead of directly resolving them with grid refinement. This opens the possibility to simulate the influence of different particle in-flight properties on the resulting coating and its properties. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-108} \end{center} Fig. 6. Virtual cross-sections of the simulated coating build-up, where particles as well as the interlamellar gaps can be identified Acknowledgments. The presented investigations were carried out at RWTH Aachen University within the framework of the Collaborative Research Centre SFB1120-236616214 "Bauteilpräzision durch Beherrschung von Schmelze und Erstarrung in Produktionsprozessen" and funded by the Deutsche Forschungsgemeinschaft e.V. (DFG, German Research Foundation). The sponsorship and support is gratefully acknowledged. \section*{References} \begin{enumerate} \item Bobzin, K., et al.: A numerical investigation: influence of the operating gas on the flow characteristics of a three-cathode air plasma spraying system. In: Thermal Spray 2013: Proceedings of International Thermal Spray Conference, pp. 400-405 (2013) \item Heimann, R.B.: Plasma Spray Coating. Principles and Applications, Wiley-VCH, Weinheim (2008) \item Vardelle, A., et al.: A Perspective on plasma spray technology. Plasma Chem. Plasma Process 35(3), 491-509 (2015) \item Bianchi, L., et al.: Microstructural investigation of plasma-sprayed ceramic splats. Thin Solid Films 299(1-2), 125-135 (1997) \item Li, L., et al.: Suppression of crystallization during high velocity impact quenching of alumina droplets: observations and characterization. Mater. Sci. Eng. A 456(1-2), 35-42 (2007) \item Goutier, S., Vardelle, M., Fauchais, P.: Last developments in diagnostics to follow splats formation during plasma spraying. J. Phys.: Conf. Ser. 275, 12003 (2011) \item Vardelle, M., et al.: Influence of particle parameters at impact on splat formation and solidification in plasma spraying processes. J. Therm. Spray Technol. 4(1), 50-58 (1995) \item Chandra, S., Fauchais, P.: Formation of solid splats during thermal spray deposition. J. Therm. Spray Tech. 18(2), 148-180 (2009) \item Ghafouri-Azar, R., et al.: A stochastic model to simulate the formation of a thermal spray coating. J. Therm. Spray Tech. 12(1), 53-69 (2003) \item Bobzin, K., et al.: Modelling of particle impact using modified momentum source method in thermal spraying. J. Phys.: Conf. Ser. 480, 12003 (2019) \item Bobzin, K., et al.: Simulation of PYSZ particle impact and solidification in atmospheric plasma spraying coating process. Surf. Coat. Technol. 204(8), 1211-1215 (2010) \item Zheng, Y.Z., et al.: Modeling the impact, flattening and solidification of a molten droplet on a solid substrate during plasma spraying. Appl. Surf. Sci. 317, 526-533 (2014) \item Pasandideh-Fard, M., et al.: Splat shapes in a thermal spray coating process: simulations and experiments. J. Therm. Spray Technol. 11(2), 206-217 (2002) \item Burcat, A., Ruscic, B., Third millennium ideal gas and condensed phase thermochemical database for combustion with updates from active thermochemical tables. Argonne National Laboratory, Lemont (2005) \end{enumerate} \section*{Simplex Space-Time Meshes for Droplet Impact Dynamics } \begin{abstract} Droplet impact dynamics is an example of a complex two-phase flow. However, we manage to reduce the complexity of this problem by reducing its dimensionality. This paper highlights an axisymmetric interface-capturing method $[1,2]$. The level-set method is used for modeling the evolution of the front, because of its inherent ability to account for large topological changes of the interface [3], and is combined with a continuum surface force (CSF) model. We use a space-time finite element discretization, which is achieved by means of simplex space-time elements and leads to entirely unstructured grids with varying levels of refinement both in space and in time. Therefore, despite the complexity of the contact dynamics, the efficiency of our simulations is improved when using adaptive temporal refinement in areas of interest. Two different benchmark cases from [4] are used for verifying our numerical approach. \end{abstract} Keywords: Space-time $\cdot$ Simplex $\cdot$ Axisymmetric $\cdot$ Two-phase flows $\cdot$ Contact lines \section*{1 Introduction} Problems involving moving contact lines are common in many processes of production engineering, such as continuous liquid film coating, soldering and brazing, flow in porous media, and other critical technological areas [5]. The way that liquid droplets impact and spread is an ongoing research area, since it is encountered in several industrial applications, and the improvement of the manufacturing processes (e.g., ink-jet printing or organic light-emitting diode fabrication) depends on the knowledge of drop impingement [6]. The problem of the droplet impacting belongs to multi-phase flows and is complicated since numerous physical phenomena take place at varying timescales. When a droplet touches a surface, it starts spreading until it reaches a maximum width. Finally, the dominant capillary effects act on the droplet and force it to either stick to or rebound from the surface [7]. According to [6], the most important parameters which influence the impact of droplets are the impact velocity, the surface tension, and the surface roughness. The way a droplet spreads onto a solid can be classified into four phases, namely the kinematic, spreading, relaxation, and wetting phase. In Fig. 1, experimental data is presented, which shows the impact of a drop of water on a solid when different combinations of impact velocity and equilibrium contact angle are defined. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-111} \end{center} Fig. 1. Water droplet impacting onto either hydrophilic or hydrophobic surfaces at various time instances. Every row represents a different set of impact velocity and equilibrium contact angle. Dashed circles indicate air bubbles entrapment or droplet emission. The figure was adapted from [7]. In the current paper, we use an unstructured space-time finite element method for solving two-phase incompressible flows, including moving contact lines. During the last two decades, the growing interest in 4D simplex space-time discretizations is evident. The fourth dimension is time. In the work of Karyofylli et al. [8], a 4D simplex space-time finite element discretization was exploited in the context of mold filling since simplex space-time meshes allow for temporal refinement close to the evolving front. Therefore, the accuracy of the computations is locally increased at a reduced computational cost. The compressible Navier-Stokes equations were discretized by von Danwitz et al. [9] with unstructured space-time finite element meshes, and the compressible flow was simulated in a valve that fully closes and opens again. Gesenhues [10] computed geophysical flows and their rheology with a simplex space-time finite element solver while employing continuous rheology models. Moreover, Gaburro [11] used a space-time formulation combined with the finite volume method. Zwart [12] initially developed an integrated space-time finite volume method for transient fluid flows. This method satisfies the conservation law in space-time. \section*{2 Governing Equations of Axisymmetric Two-Phase Flows} The computational domain $\Omega$ in the case of axisymmetric two-phase flow problems is a subset of $\mathbb{R}^{2}$. It contains two immiscible Newtonian fluids depicted by the subdomains $\Omega_{1}$ and $\Omega_{2}$, where $\Omega_{1} \cup \Omega_{2}=\Omega$. Here, $\Gamma=\partial \Omega$ represents the boundary of $\Omega$, while $\Gamma_{\text {int }}=\partial \Omega_{1} \cap \partial \Omega_{2}$ denotes the interface between the two immiscible phases (Fig. 2). \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-112} \end{center} Fig. 2. Computational domain $\Omega$ of an axisymmetric two-phase flow problem, containing two fluids in the subdomains $\Omega_{1}$ (white) and $\Omega_{2}$ (light blue) (adopted and modified from [13]). We can express in terms of the coordinate $x$ and the radial coordinate $r$ the velocity as $\boldsymbol{u}=\left\{u_{x}, u_{r}, u_{\theta}\right\}$, where $u_{\theta}=0$. Moreover, the velocity $\boldsymbol{u}$, the pressure $p$, and the levelset field $\phi$, in each phase $i$ in subdomain $\Omega_{i}(t)$ are obtained by solving at each instant $t \in\left(0, t_{\text {total }}\right)$ the incompressible Navier-Stokes and the level-set transport equations: \begin{align*} \rho_{i}\left(\frac{\partial u_{x}}{\partial t}+u_{x} u_{x, x}+u_{r} u_{x, r}-g_{x}\right)+p_{, x} & =\mu_{i}\left\{u_{x, x x}+\frac{1}{r}\left(r u_{x, r}\right)_{, r}\right\}+f_{x}^{\sigma} \delta(\phi), \\ \rho_{i}\left(\frac{\partial u_{r}}{\partial t}+u_{x} u_{r, x}+u_{r} u_{r, r}\right)+p_{, r} & =\mu_{i}\left\{u_{r, x x}+\left[\frac{1}{r}\left(r u_{r}\right)_{, r}\right]_{, r}\right\}+f_{r}^{\sigma} \delta(\phi), \\ u_{x, x}+\frac{1}{r}\left(r u_{r}\right)_{, r} & =0, \\ \frac{\partial \phi}{\partial t}+u_{x} \phi_{, x}+u_{r} \phi_{, r} & =0 . \tag{1} \end{align*} where $\rho_{i}$ denotes the density, $\mu_{i}$ represents the dynamic viscosity, $f^{\sigma}$ is the surface tension force and $\delta(\phi)$ is the Dirac delta function. Partial derivatives with respect to the subsequent variable are described by commas and the components of a vector field are symbolized by subscripts. Moreover, the current phase is denoted by the indexing $i=1,2$. For the discretization of Eq. (1), we use $P 1 P 1$ finite elements, as described in [8]. The Galerkin/least-squares (GLS) stabilization method is applied [9, 14], because the aforementioned elements are not compliant with the LBB condition. In [8], we have derived the Galerkin formulation of the Navier-Stokes equation in a Cartesian coordinate system, but we did not take into consideration moving contact lines and the impact mechanism. Hence, we assumed that the equilibrium contact angle is $90^{\circ}$. Here, we demonstrate, following the examples of $[4,15]$, how the Galerkin formulation of the Navier-Stokes equation should be altered for including more complex wetting effects: \begin{align*} \int_{Q_{n}} \mathbf{w}^{h} \cdot \gamma \kappa \mathbf{n}_{\left(P_{i n t}\right)_{n}}^{h} \delta(\phi) d Q & =\int_{P_{n}} \gamma \cos \theta_{e} \mathbf{w}^{h} \cdot \mathbf{n}_{L}^{h} \delta(\phi) d P \tag{2}\\ & -\int_{Q_{n}} \gamma \underline{\nabla i d}_{\left(P_{i n t}\right)_{n}}^{h}: \underline{\nabla} \mathbf{w}^{h} \delta(\phi) d Q . \end{align*} where $\gamma$ is the surface tension coefficient and $\kappa$ is the curvature. The symbol $\mathbf{n}_{\left(P_{\text {int }}\right)_{n}}^{h}$ stands for the normal vector on $\left(P_{i n t}\right)_{n}$, whereas $\underline{\nabla}$ expresses the tangential gradient and $\mathbf{i d}^{h}$ is the identity mapping on the space-time evolving interface $\left(P_{\text {int }}\right)_{n}$, and the superscript $h$ stands for the discretization. Here, $\theta_{e}$ symbolizes the equilibrium/static angle between the moving space-time interface, $\left(P_{i n t}\right)_{n}$, and the space-time boundary $P_{n}$. The normal vector, $\mathbf{n}_{\mathrm{L}}^{h}$ is orthogonal to the contact line $\left(L_{i n t}\right)_{n}$, which is the result of the intersection of the evolving interface with the space-time boundary, and tangent to $P_{n}$. Moreover, the space-time slab is defined as $Q_{n}$ and $\mathbf{w}^{h}$ are the test functions. For expressing Eq. 2 in axisymmetric coordinate system, the reader should check the formulation in [2] regarding the tangential gradient. Furthermore, the curvature $\kappa$ can be computed in the axisymmetric case as in [1]. \section*{3 Results} \subsection*{3.1 Static Droplet on a Solid Surface} A typical benchmark case of two-phase flows is one of a static bubble inside the computational domain. In the context of contact problems, we assume a static droplet, contacting a solid surface with different equilibrium contact angles. We assume three different scenarios. The general setting is drawn in Fig. 3. In each scenario, the droplet has a radius of $r=0.1$, the surface tension coefficient is equal to $\gamma=0.5$, and the density and viscosity for both materials are equal to one. We also make use of the Navier-slip boundary condition, as defined in [8], and the Navier-slip coefficient is uniform and set to $\beta_{w}=0.05$, as in [4]. Furthermore, the time slab thickness was 0.01 in all scenarios. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-113} \end{center} Fig. 3. Axisymmetric static water droplet on a solid surface in 3D: computational domain. In the first scenario, we used an axisymmetric formulation in combination with a simplex space-time mesh (SST), and the equilibrium contact angle was equal to $\theta_{e}=$ $90^{\circ}$. An SST mesh allows a higher resolution both in space and in time close to the interface, as shown in Fig. 4 (left column). The computational domain was a square of dimensions $0.15 \times 0.15$, consisting of 84,714 elements. For the second scenario, we used an axisymmetric formulation in combination with an SST mesh again. This time, the equilibrium contact angle was equal to $\theta_{e}=120^{\circ}$, as it is shown in Fig. 4 (middle\\ column). The computational domain was a square of dimensions $0.20 \times 0.20$, consisting of 69, 529 tetrahedral elements. The third scenario is the 3D equivalent of the second scenario, and a flat space-time mesh (FST) was used, as presented in Fig. 4 (right column). The computational domain was a parallelepiped of dimensions $0.40 \times 0.20 \times 0.40$, consisting of 160, 000 tetrahedral spatial elements. According to the Laplace-Young equations, the pressure inside the bubble should be equal to $\Delta p=2 \gamma / r$, where $\Delta p$ is the pressure jump between the two phases, whereas the velocity should be zero everywhere in the domain. As we can observe in Fig. 4, the pressure jump in every scenario is equal to $\Delta p=10$, which is confirmation that our simulations were in a good agreement with the analytical prediction. Moreover, the results of the second scenario (middle column in Fig. 4) were similar to the 3D equivalent (right column in Fig. 4). Axisymmetric, SST, $\theta_{\mathrm{e}}=90^{\circ}$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-114(2)} Axisymmetric, SST, $\theta_{\mathrm{e}}=120^{\circ}$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-114(1)} 3D, FST, $\theta_{\mathrm{e}}=120^{\circ}$\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-114} Fig. 4. Grids and pressure distribution of the three different test cases. \subsection*{3.2 Impact of a Water Droplet on a Solid Surface} In this subsection, we will investigate the impact of an axisymmetric water droplet on a solid surface. The droplet reaches the solid surface and then starts spreading. Moreover, the wettability of the surface can vary. The same example was numerically examined by [4]. Its origin is a physical experiment conducted by [6]. The computational domain $\Omega$ and its dimensions are presented in Fig. 5 and it contains air and a water droplet which touches the solid surface with impact velocity: $v_{0}=0.35 \mathrm{~m} / \mathrm{s}$. Since the droplet is considered to be spherical and the domain is cylindrical, the example belongs to the category of axisymmetric two-phase flow problems. Therefore, the complexity and dimensionality of our problem can be reduced, and we are allowed to use only the purple-colored slice (see Fig. 5) for simulating this example. The material properties for water and air can be found in Table 1. In this example, we will present only the case of an equilibrium contact angle, $\theta_{e}=179^{\circ}$. As in [4], we use $179^{\circ}$ instead of $180^{\circ}$ to avoid any numerical instabilities. The computational domain consists of 80000 triangular elements and the time-slab thickness \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-115} \end{center} Fig. 5. Axisymmetric water droplet impacting on a substrate in 3D: computational domain. Table 1. Material properties of water and air. \begin{center} \begin{tabular}{l|l|l} \hline Properties (units) & Water & Air \\ \hline $\rho\left\{\mathrm{g} / \mathrm{cm}^{3}\right\}$ & 1 & 0.0012 \\ \hline $\mu\{\mathrm{g} /(\mathrm{cm} \cdot \mathrm{s})\}$ & 0.01 & 0.000182 \\ \hline $\gamma\left\{\mathrm{g} / \mathrm{s}^{2}\right\}$ & & 73 \\ \hline \end{tabular} \end{center} is equal to $\Delta t=0.01 \mathrm{~ms}$. We also make use of the Navier-slip boundary condition, as defined in [8]. The Navier-slip coefficient, $\beta_{w}$, is defined as follows: \[ \beta_{w}=\beta_{\infty} \cdot \delta_{w}(\phi)+\beta_{0}, \delta_{w}(\phi)=\left\{\begin{array}{crl} 0, & & |\phi| \leq a \tag{3}\\ \frac{|\phi|}{a}-1, & a<|\phi| & <2 a \\ 1, & & |\phi| \geq 2 a \end{array}\right. \] where $\beta_{0}$ is the wetting coefficient around the contact line, $\beta_{\infty}$ is the far-field wetting coefficient, and $a$ denotes the characteristic length scale around the interface. For this test case, we set $\beta_{0}=0.01, \beta_{\infty}=100000$ and $a=0.0025$. In Fig. 6, our results obtained with our in-house space-time solver, XNS, are shown in the bottom row. We compare them with experimental data [6] and other numerical results, computed with the solver DROPS [4]. As we can see, we represent the experimental data well. Hence, the water droplet in our computation is able to bounce back at $t=12 \mathrm{~ms}$. The shape of the XNS-simulated droplet is almost identical to the one in the experiment at every time instance. Hence, our computations preserve the droplet characteristics observed during the experiment. For example, our droplet features the same sharp tip at $t=3.5 \mathrm{~ms}$, as in the case of [6] at $t=3.55 \mathrm{~ms}$. Furthermore, our computation results do not face any issue with the spreading velocity, and the simulation timings are matching quite well the experimental ones. DROPS: \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-116(1)} \end{center} Fig. 6. The impact of a water droplet onto a solid surface with equilibrium contact angle $\theta_{e}=$ $180^{\circ}$. In the top row, the numerical results are obtained with the solver DROPS and are taken and adapted from [4]. In the bottom row, the results of our in-house solver, XNS, are presented. In the middle row, the experimental results are adapted from [6].\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-116} Fig. 7. The droplet's initial diameter (left) and spreading diameter (right). \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-116(2)} \end{center} Fig. 8. Dimensionless spreading diameter, $D^{*}$, over time. Following the example of Dong et al. [16] and Klitz [17], we compute the dimensionless droplet spreading diameter $D^{*}=D / D_{0}$ over time. Here, the spreading diameter, $D$, is computed directly at the contact line and $D_{0}$ is the droplet's initial diameter, as illustrated in Fig. 7. In Fig. 8, we present the diagram of the dimensionless spreading\\ diameter, $D^{*}$, over time. Unfortunately, Vadillo et al. [6] did not provide any experimental data regarding the spreading diameter. Therefore, we cannot compare our numerically computed dimensionless spreading diameter with the experimental one. \section*{4 Conclusion} In this paper, two examples of droplet impact dynamics were investigated. The complexity of each benchmark case is decreased by reducing its dimensionality, utilizing an axisymmetric formulation. Besides, a novel discretization approach is used, which allows arbitrary temporal refinement of the space-time slabs in the vicinity of the interfaces. Acknowledgment. The authors gratefully acknowledge the support of the German Research Foundation (DFG) under program SFB 1120 "Precision Melt Engineering". The computations were conducted on computing clusters provided by the RWTH Aachen University IT Center and by the Jülich Aachen Research Alliance (JARA). \section*{References} \begin{enumerate} \item Chessa, J., Belytschko, T.: An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension. Int. J. Numer. Meth. Eng. 58, 2041-2064 (2003). https:// \href{http://doi.org/10.1002/nme}{doi.org/10.1002/nme}. 946 \item Ganesan, S., Tobiska, L.: An accurate finite element scheme with moving meshes for computing 3D-axisymmetric interface flows. Int. J. Numer. Meth. Fluids 57, 119-138 (2008). https:// \href{http://doi.org/10.1002/fld}{doi.org/10.1002/fld}. 1624 \item Elgeti, S., Sauerland, H.: Deforming fluid domains within the finite element method: five mesh-based tracking methods in comparison. Arch. Comput. Methods Eng. 23, 323-361 (2016). \href{https://doi.org/10.1007/s11831-015-9143-2}{https://doi.org/10.1007/s11831-015-9143-2} \item Zhang, L., Reusken, A.: Numerical methods for mass transfer in falling films and two-phase flows with moving contact lines (2017). \href{https://publications.rwth-aachen.de/record/684694}{https://publications.rwth-aachen.de/record/684694}. \href{https://doi.org/10.18154/RWTH-2017-02014}{https://doi.org/10.18154/RWTH-2017-02014} \item Baer, T.A., Cairncross, R.A., Schunk, P.R., Rao, R.R., Sackinger, P.A.: A finite element method for free surface flows of incompressible fluids in three dimensions. Part II. Dynamic wetting lines. Int. J. Numer. Methods Fluids. 33, 405-427 (2000). \href{https://doi.org/10.1002/}{https://doi.org/10.1002/} 1097-0363(20000615)33:3\%3c405::AID-FLD14\%\href{http://3e3.0.CO}{3e3.0.CO};2-4 \item Vadillo, D.C., Soucemarianadin, A., Delattre, C., Roux, D.C.D.: Dynamic contact angle effects onto the maximum drop impact spreading on solid surfaces. Phys. Fluids 21, 1-8 (2009). \href{https://doi.org/10.1063/1.3276259}{https://doi.org/10.1063/1.3276259} \item Lin, S., Zhao, B., Zou, S., Guo, J., Wei, Z., Chen, L.: Impact of viscous droplets on different wettable surfaces: impact phenomena, the maximum spreading factor, spreading time and post-impact oscillation. J. Colloid Interface Sci. 516, 86-97 (2018). \href{https://doi.org/10.1016/}{https://doi.org/10.1016/} j.jcis.2017.12.086 \item Karyofylli, V., Wendling, L., Make, M., Hosters, N., Behr, M.: Simplex space-time meshes in thermally coupled two-phase flow simulations of mold filling. Comput. Fluids. 192, 104261 (2019). \href{https://doi.org/10.1016/j.compfluid.2019.104261}{https://doi.org/10.1016/j.compfluid.2019.104261} \item von Danwitz, M., Karyofylli, V., Hosters, N., Behr, M.: Simplex space-time meshes in compressible flow simulations. Int. J. Numer. Meth. Fluids 91, 29-48 (2019). \href{https://doi.org/10}{https://doi.org/10}. 1002/fld. 4743 \item Gesenhues, L.: Advanced methods for finite element simulation of rheology models for geophysical flows (2020). \href{https://doi.org/10.18154/RWTH-2020-05371}{https://doi.org/10.18154/RWTH-2020-05371} \item Gaburro, E.: Well balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for non-conservative Hyperbolic systems (2018) \item Zwart, P.J.: The integrated space-time finite volume method (1999) \item Chessa, J., Belytschko, T.: An extended finite element method for two-phase fluids. J. Appl. Mech. 70, 10 (2003). \href{https://doi.org/10.1115/1.1526599}{https://doi.org/10.1115/1.1526599} \item Pauli, L., Behr, M.: On stabilized space-time FEM for anisotropic meshes: incompressible Navier-Stokes equations and applications to blood flow in medical devices. Int. J. Numer. Meth. Fluids 85, 189-209 (2017). \href{https://doi.org/10.1002/fld}{https://doi.org/10.1002/fld}. 4378 \item Ganesan, S., Tobiska, L.: Modelling and simulation of moving contact line problems with wetting effects. Comput. Vis. Sci. 12, 329-336 (2009). \href{https://doi.org/10.1007/s00791-0080111-3}{https://doi.org/10.1007/s00791-0080111-3} \item Dong, H., Carr, W.W., Bucknall, D.G., Morris, J.F.: Temporally-resolved inkjet drop impaction on surfaces. AIChE J. 53, 2606-2617 (2007). \href{https://doi.org/10.1002/aic}{https://doi.org/10.1002/aic}. 11283 \item Klitz, M.: Numerical simulation of droplets with dynamic contact angles (2014) \end{enumerate} \section*{Additive Manufacturing} \section*{Melt Pool Formation and Out-of-Equilibrium Solidification During the Laser Metal Deposition Process } \begin{abstract} In Laser Metal Deposition (LMD) processes, a complex interplay between the blown particles, the laser beam and the substrate determines the resulting microstructure.\\ We investigate the melt pool formation during LMD in dependence of the process parameters with particular attention to kinetic effects of the particles on that change the melt pool shape, both experimentally and with means of simulations.\\ The solidification takes places far from equilibrium due to the large temperature gradients at the phase front and fast solidification velocities. With the help of phase field simulations and microstructure analysis, we will unravel the solidification process during LMD. The dendrite arm spacing is compared with experimental data to prove the validity of the simulation.\\ In this work, Inconel 718, a material common in LMD turbomachinery applications, is used. \end{abstract} Keywords: Laser Metal Deposition $\cdot$ Microstructure $\cdot$ Solidification conditions \section*{1 Introduction} \subsection*{1.1 Approach} Laser metal deposition (LMD) uses a focused laser beam to melt a substrates surface. With a powder nozzle, a stream of metal particles is blown in the formed melt pool and therefore fuses metallurgical with the substrate (after cooling down). Moving the laser beam and the powder nozzle over substrate generates a weld track that is well bonded to the material. Multiple tracks above each other allow the build op of complex 3d structures. An advantage of LMD in contrast to conventional methods is the near net shape form of the specimen and the small dilution of the added material with the substrate (or lower layers). In the last decade, LMD has become an established processing technique for the manufacturing and repair of metal parts [1]. The resulting microstructure for a specific material depends strongly on the local chemical composition and the local solidification conditions. In well-known and investigated processes, the phase front velocity and the temperature gradients are small compared to the gradients in metal Additive Manufacturing (AM) processes. The first challenge is to determine the solidification conditions at the solidification phase front. From emissivity measurements only the surface temperature can be determined. With thermal elements, the temporal temperature distribution at a fixed point, far away from the phase front (in comparison to the melt pool size) can be measured. Therefore it is advised, to combine those methods with thermal simulations of the corresponding process. In our case the Laser Metal Deposition (LMD) process with the material Inconel 718 is investigated. The dependence of the microstructure (primary and secondary dendrite arm spacing) on the process parameters and therefore indirectly on the solidification conditions is the subject of our research. The scientific question to be answered in this paper, if a pure simulation based approach is capable of determining the microstructure of an as-built LMD sample. It is also discussed which parts give rise to largest deviation due to model simplifications. In the first step, the LMD model is explained followed by a validation with single track experiments under the variation of the process parameter by changing the line energy (Laser power divided by scanning velocity) $E_{l}=P_{L} / v_{S}$ up to $\pm 30 \%$ from the default parameter. The influence of the process parameter on the solidification condition is investigated there. In the second section, the model for the calculation of the microstructure, based on the phase field model, is explained. After that, the resulting microstructure from the experiments is compared with the calculated one. In the last section, the findings are discussed and an outlook for future research is given. \section*{2 From Process Parameters to Solidification Conditions} \subsection*{2.1 Melt Pool Modelling} At the heart of most metal AM processes is the melt pool. Its behavior is strongly influenced by the first order process parameters like Laser Power $P_{L}$, the scanning velocity $v_{S}$ as well as the intensity distribution of the laser in the working plane and newly cladded material in each layer (comparable to a mass rate $\dot{m}_{p}$ ) as well as the distance of neighboring melt tracks (hatch distance $h_{S}$ ) [2]. In our work, some of the second order influence factors of the LMD process are included: particle flight path and particle interaction with the laser beam yielding a reduced transmitted laser intensity distribution in the working plane but increased particle temperature, cooling effects by radiation, absorption depending on the melt surface curvature. Higher order terms like for example the influence of gravity on the particle path and the melt behavior are neglected. The laser source is treated as a surface source with absorption values taken from literature [3]. The track geometry is determined by the solution of the Young-Laplace equation with the constraint of mass conservation from the ingoing powder particles. The powder particles are a volumetric heat source (or sink; depending on their temperature) if their kinetic energy and angle of impact is sufficient; the particles are only deflected if\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-122} Fig. 1. Temperature distribution of simulated melt track geometry side view and cross section (perpendicular to scanning direction). they are too slow to overcome the surface tension or when the angle is not steep enough. The thermophysical material properties [4] are assumed to be temperature dependent and the latent heat is included with the method of effective heat capacity. The full mathematical formulation of the model can be found in our previously published work [5]. The implementation of Marangoni flow is discussed in literature. The forces that lead to a surface force driven slow are two fold: 1) the temperature dependency of the surface tension and 2) the gradient of the chemical composition on the melt pool surface. For the first influence facto is has been shown in literature that the influence is negligible [6]. Furthermore the capillary length of nickel base alloys $(\approx 4.8 \mathrm{~mm}$ [7]) is larger than the melt pool dimension (roughly $1 \mathrm{~mm}$ ) supports the idea of neglecting Marangoni flow and also gravity. The second factor is unknown and no value can be associated with it. The temperature distribution for the default parameter set is shown in Fig. 1. As a validation for the model, the melt pool dimensions (depth, height and width) are compared with experimentally obtained single track data where the single tracks were deposited with varied process parameters. \subsection*{2.2 Melt Pool Model Validation and Influence of Volume Energy} Since the goal is to obtain the solidification conditions, which cannot be observed directly, a method is required which yields reliable results. Our model is tested in the range of $30 \%$ variation of the volume energy (or line energy); the energy that is averagely introduced per unit volume (length) in the material. The default parameter is at laser power of $300 \mathrm{~W}$ and a scanning velocity of $8.3 \mathrm{~mm} / \mathrm{s}$. The same volume energy variation can be obtained by varying either the laser power or scanning velocity (and powder mass rate) to a different (reciprocal) degree. We will investigate later if the same volume energy, in the $30 \%$ bounds, yields the same results depending on the first order process parameter that leads to the change in volume energy. The cross sections for each parameter set (take at three different points in the weld track) are compared with the calculated values of our model (2.1). The 13 different parameters with the corresponding line energy are shown in Fig. 2. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-123} \end{center} Fig. 2. Parameter variations in laser power and scanning velocity with the according line energy \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-123(1)} \end{center} Fig. 3. The effect of the powder mass flow during the LMD process on the depth, width, height and shape (symmetry) of the melt pool. The data for the depth, height and width is extracted from the isosurface of the solidus temperature for simulations and light microscopically measured from a polished cross section for experimental data (Fig. 3). The height is measured from substrate level to the highest point of the melt track in each cross section. The width is taken on substrate level and the depth is measured from substrate level to the deepest point of the melt pool. For the experimental data always the average of three measurements is used for evaluation. Also the effect of the powder on the melt pool boundary can be seen. It is evident that the first order influence is the added mass to the melt pool, resulting in the typical melt track shape. More interesting is the fact, that an asymmetric boundary between melt and substrate material is formed by the particle melt interaction. The origin\\ of the asymmetry is found in the asymmetry of the powder "beam". Therefore a scanning direction dependency of the melt pool shape (and temperature distribution) also exists in LMD even if coaxial nozzles are used (asymmetries occur more often when nozzles are slightly damaged, but still in use). Even though the asymmetry is much smaller in contrast to off-axis nozzles. The melt pool widths do not change whether powder is used in the process or not. The width grows proportionally to the volume energy. The melt pool depth and height depend on the use of powder, because the volume energy can only melt a certain volume of material, thus the depth is decreased if powder is used. Also, the depth scales proportionally with the volume energy $E_{V}$. Additionally, a remelting process without powder supply results in a height of the remelted track up to $15 \mu \mathrm{m}$. This increase in volume is due to a conversion to the tetragonal $\gamma^{\prime \prime}$ phase, which has a lower atomic packing efficiency than the Inconel fcc $\gamma$-matrix. The simulation data is always taken in a quasi-equilibrium state (where the melt pool - / temperature change within the next time step is almost zero). The comparison of experimentally obtained and simulated data is shown in Fig. 4. It can be noted, that generally the accordance between experiment and simulation is quite well with relative deviations of less than $10 \%$.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-124} Fig. 4. Comparison of track geometries for experimental samples with simulated results. On the left the volume energy is changed by changing the laser power while on the right side the scanning velocity and powder mass rate are adapted. For the variation of the scanning velocity, the melt pool depth is calculated very accurately while the variation of the laser power yields more deviating results. A possible origin of the increased deviation could be that effects of the radiation intensity on the melt pool surface are neglected or that the underestimation of particle shadowing effects and neglected evaporation effects (for higher powers) could cancel each other out at the volume energy level of the default parameter. From the transient three dimensional temperature distribution the solidification conditions (solidification velocity $v_{s o l}$, thermal gradient $\nabla T$ and cooling rate $\dot{T}$ ) can be extracted. \subsection*{2.3 Determination of Solidification Conditions} As an input for the following microstructure simulation, the solidification conditions (temperature gradient $G$, cooling rate $\dot{T}$, solidification phase front velocity $v_{\text {sol }}$ ) are required. In reality, solidification conditions vary all over the solidification phase front; thus picking a representative position is mandatory to obtain comparable $2 \mathrm{~d}$ microstructures. The assumption is, that if the melt pool geometry (temperature distribution) is calculated correctly, the solidification conditions are also correct (see validation in Sect. 2.2). Since we are interested in the microstructure inside the build volume and have to take multiple layers into account, it is not advised to pick a point in the track that would be remelted in the consecutive layer To keep the results comparable we determine an effective layer height $h_{\text {Layer }}=4 / 3 \cdot 0,9 \cdot h_{S}$ on the dependence of the experimental melt pool height and picked the point that is in the middle of the melt point and layer height above the deepest point on the solidification front. This procedure is shown for the default parameter in Fig. 5. This function for the effective layer height is chosen because it is not be remolten during the application of consecutive layers. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-125} \end{center} Fig. 5. Point (Star) chosen for the extraction of the solidification conditions, the melt pool depth and height as well as the effective layer height for the default parameter. Scanning direction from right to left. The solidification conditions and their respective process parameters are listed in Table 1 . The solidification velocity strongly depends on the scanning velocity; the effect of the laser power is 20 to $50 \%$ smaller. The temperature gradient, on the other hand is influenced more by the laser power than the scanning velocity. The cooling rate depends stronger on the scanning velocity. It can be seen, that the interplay between process parameters and solidification conditions is complex and that there is no easy way to predict them without running simulations. Table 1. Process parameters and according solidification condition. The default parameter is highlighted in grey. \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|} \hline \begin{tabular}{c} $\mathbf{P}_{\mathbf{L}}$ \\ $[\mathbf{W}]$ \\ \end{tabular} & \begin{tabular}{c} $\mathbf{d}_{\text {Laser }}$ \\ $[\boldsymbol{\mu m}]$ \\ \end{tabular} & \begin{tabular}{r} $\mathbf{V}$ scan \\ $[\mathbf{m m} / \mathbf{s}]$ \\ \end{tabular} & \begin{tabular}{c} $\boldsymbol{E}_{\boldsymbol{V}}$ Var. \\ $[\boldsymbol{\%}]$ \\ \end{tabular} & \begin{tabular}{c} $\mathbf{G}$ \\ $[\mathbf{K} / \mathbf{m}]$ \\ \end{tabular} & \begin{tabular}{c} $\dot{\mathbf{T}}$ \\ $[\mathbf{K} / \mathbf{s}]$ \\ \end{tabular} & \begin{tabular}{c} Vsol \\ $[\mathbf{m m} / \mathbf{s}]$ \\ \end{tabular} \\ \hline 300 & 1000 & 8.3 & 0 & $1,30 \mathrm{E}+06$ & $9,23 \mathrm{E}+03$ & 7.1 \\ \hline 210 & 1000 & 8.3 & -30 & $1,50 \mathrm{E}+06$ & $1,13 \mathrm{E}+04$ & 7.5 \\ \hline 390 & 1000 & 8.3 & +30 & $1,20 \mathrm{E}+06$ & $7,08 \mathrm{E}+03$ & 5.9 \\ \hline 300 & 1000 & 11.9 & -30 & $1,30 \mathrm{E}+06$ & $1,35 \mathrm{E}+04$ & 10.4 \\ \hline 300 & 1000 & 6.4 & +30 & $1,30 \mathrm{E}+06$ & $6,89 \mathrm{E}+03$ & 5.3 \\ \hline \end{tabular} \end{center} The extracted conditions are the required input for the microstructure simulation with the MICRESS software. \section*{3 From Solidification Conditions to Microstructure} \subsection*{3.1 Microstructure Modelling} In [8], we have presented phase field simulations of IN718 directional solidification under LPBF conditions including interface kinetics [9]. In this present study we apply the same technique to the conditions in the LMD process. During our investigations, we have varied the solidification speed over a wide range from $v_{s o l}=5,3 \mathrm{~mm} / \mathrm{s}$ to $v_{\text {sol }}=10,4 \mathrm{~mm} / \mathrm{s}$ (the corresponding temperature gradients and cooling rates are given in Table 1). The phase field simulations are performed using the MICRESS software, based on a multi-component phase field model [10] that is coupled to the TCNI8 ThermoCalc database. The composition of the alloy that was chosen for our simulations lies in chemical composition boundary of IN718 and is given in Table 2 (Fe as balance). Table 2. Chemical composition of Inconel 718 alloy (min-max mass percentage) in comparison to the chemical composition used for the microstructure model ( $\mathrm{Fe}$ as balance). \begin{center} \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline Ele. & $\mathrm{Ni}$ & $\mathrm{Cr}$ & $\mathrm{Nb}$ & $\mathrm{Mo}$ & $\mathrm{Ti}$ & $\mathrm{Al}$ & $\mathrm{Co}$ & $\mathrm{C}$ \\ \hline \begin{tabular}{l} Min \\ $[\mathrm{w} \%]$ \\ \end{tabular} & 50.00 & 17.00 & 4.75 & 2.80 & 0.65 & 0.20 & - & - \\ \hline \begin{tabular}{l} Max \\ $[\mathrm{w} \%]$ \\ \end{tabular} & 55.00 & 21.00 & 5.50 & 3.30 & 1.15 & 0.8 & 1.00 & 0.08 \\ \hline \begin{tabular}{l} Modell \\ $[\mathrm{w} \%]$ \\ \end{tabular} & 53.20 & 19.00 & 5.13 & 3.05 & 0.9 & 0.5 & 0.5 & 0.08 \\ \hline \end{tabular} \end{center} In the simulation, the primary gamma phase as well as $\gamma^{\prime}, \gamma^{\prime \prime}$, Laves and Sigma are implemented. The 2D domain size is $15 \mu \mathrm{m} \times 24 \mu \mathrm{m}$ and the discretization grid spacing is $12 \mathrm{~nm}$. The thermal gradient $\nabla T$ is considered homogeneous in space and constant in time (so-called frozen temperature approximation), and diffusion is neglected in the solid phase. Periodic boundary conditions are applied along the horizontal axis. The thermal gradient points upwards and the preferential growth direction $<100>$ is tilted by $10^{\circ}$. The results for the default parameter's solidification conditions are shown in Fig. 6.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-127} Fig. 6. Dendrite growth during solidification for different time steps with the solidification conditions of $\nabla T=1,3 E+06 \mathrm{~K} / \mathrm{m}, \dot{T}=1 E+04 \mathrm{~K} / \mathrm{s}$; . The primary dendrite arm spacing is $14,8 \mu \mathrm{m}$ and the secondary is $2 \mu \mathrm{m}$. The Niob content (w.\%) is color scaled. The simulations results show a strong branching behavior, normally expected for slower solidification processes with smaller thermal gradients. Even tertiary dendrites are identified, normally associated with slower solidification. In the interdendritic area Niob precipitates and as the solidification proceeds laves phase (yellow) stabilizes The determined primary/secondary dendrite arm spacings are $14.8 \pm 0.2 \mu \mathrm{m}$ and $2.0 \pm$ $0.2 \mu \mathrm{m}$, respectively. \subsection*{3.2 Comparison with Experimental Data} The experimentally obtained microstructure for the default parameter is shown in Fig. 7, the position of the sample is in the chosen according to the position given in Fig. 5. Several regions with different micro segregation patterns can be observed ranging from unidirectional growth in the plane of the image to areas of an isotropic 2D dimensional networking, indicating a dendritic growth perpendicular to the plane of the image. The occurrence of secondary dendritic arms can be detected at several points. The primary and secondary dendrite arm spacings are measured to $3.5 \pm 0.2 \mu \mathrm{m}$ and $0.9 \pm 0.2 \mu \mathrm{m}$, respectively, this is roughly a factor of 4 smaller than the simulation results. The deviation between simulation and experiment seems large at first glance, but the simulated tertiary dendrites could be mistaken, in the experiment, for primary dendrites when the branching occurs some $10 \mu \mathrm{m}$ away from the cross section plane. This would reduce the deviation down to a factor of 2, thus yielding a satisfying accordance between simulation and experiment. Further investigations have to be conducted to test this hypothesis. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-128} \end{center} Fig. 7. Microstructure sample of LMD manufactured material with the default parameter (Table 1). \section*{4 Discussion and Outlook} The melt pool simulation for LMD yields accurate results. Nevertheless a small systematic deviation can be observed and thus is topic of our ongoing research in the frame of the "Precision Melt Engineering" Collaborative Research Center SFB1120. For the default Inconel 718 parameters, however, the results are accurate enough to consider the calculated solidification conditions as reliable, and to use them as input for a phase field method based microstructure simulation (MICRESS). The calculated microstructure, primary dendrite arm spacing, is in the order of magnitude of the experimentally measured data. However, the occurrence of tertiary dendrite arms in the simulation is quite a surprise. In our continuous research work, we will try to investigate this phenomena with a sensitivity analysis of the phase field model with respect to the solidification conditions. With this approach we can finally identify whether the solidification conditions chosen (or the position) is representative/good or the LMD process/microstructure model simplifications are eligible. The point where the solidification conditions are taken is still up for debate. As in this article shown, the solidification conditions change strongly in the meltpool, thus its hard to find a representative volume. Further work could include multiple microstructure simulation domains in the meltpool with different solidification conditions. Those resulting microstructure should then tested against each other to identify the energetically favoured (similar to comparison of growth directions in [8]). Acknowledgements. All presented investigations were conducted in the context of the Collaborative Research Centre SFB1120 "Precision Melt Engineering" at RWTH Aachen University and funded by the German Research Foundation (DFG). For the sponsorship and the support we wish to express our sincere gratitude. \section*{References} \begin{enumerate} \item Poprawe, R. (ed.): Tailored Light 2: Laser Application Technology. Springer, Heidelberg (2011). (RWTH edition) \item Pirch, N., Linnenbrink, S., Gasser, A., Wissenbach, K., Poprawe, R.: Analysis of track formation during laser metal deposition. J. Laser Appl. 29(2), 22506 (2017) \item Sainte-Catherine, C., Jeandin, M., Kechemair, D., Ricaud, J.-P., Sabatier, L.: Study of dynamic absorptivity at $10.6 \mu \mathrm{m}\left(\mathrm{CO}_{2}\right)$ AND $1.06 \mu \mathrm{m}(\mathrm{Nd}-\mathrm{YAG})$ wavelengths as a function of temperature. Le Journal de Physique IV 01 C7, C7-151-C7-157 (1991) \item Pottlacher, G., Hosaeus, H., Kaschnitz, E., Seifter, A.: Thermophysical properties of solid and liquidInconel 718 Alloy*. Scand. J. Metall. 31. Nr. 3, 161-168 (2002) \item Pirch, N., Linnenbrink, S., Gasser, A., Schleifenbaum, H.: Laser-aided directed energy deposition of metal powder along edges. Int. J. Heat Mass Transf. 143, 118464 (2019) \item Pirch, N., Kreutz, E.W., Möller, L., Gasser, A., Wissenbach, K.: Melt dynamics in surface processing with laser radiation. In: Proceedings of the 3rd European Conference on Laser Treatment of Materials Coburg 1990, S. 65 (1990) \item Amore, S., Valenza, F., Giuranno, D., Novakovic, R., Dalla Fontana, G., Battezzati, L., Ricci, E.: Thermophysical properties of some Ni-based superalloys in the liquid state relevant for solidification processing. J. Mater. Sci. 51. Nr. 4, 1680-1691 (2016) \item Boussinot, G., Apel, M., Zielinski, J., Hecht, U., Schleifenbaum, J.H.: Strongly out-ofequilibrium columnar solidification during laser powder-bed fusion in additive manufacturing. Phys. Rev. Appl. 11(1), 567 (2019) \item Boussinot, G., Brener, E.A.: Interface kinetics in phase-field models: isothermal transformations in binary alloys and step dynamics in molecular-beam epitaxy. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 88(2), 22406 (2013) \item Eiken, J., Böttger, B., Steinbach, I.: Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application. Phys. Rev. e Stat. Nonlinear Soft Matter Phys. 73(6 Pt 2), 66122 (2006) \end{enumerate} \section*{Understanding Cylinder Temperature Effects in Laser Beam Melting of Polymers } \begin{abstract} Laser beam melting of polymers allows for the fabrication of highly complex parts with excellent properties. For part generation, temperatures close to the softening range of the polymer have to be set on the powder bed surface and in z-direction. These high temperatures are directly linked to high durations of the cooling phase, high delay times for part availability and progressing material aging. Within this work, the impact of the heat control in z-direction is analyzed. Therefore, the cylinder heater temperature is varied and the fabricated parts are characterized extensively. Thermal simulation of the temperature distribution within the build chamber is performed to predict the aging behavior of the material and the maximum cooling time. It could be shown that the majority of part properties is unaffected by reducing the cylinder temperature, whereas cooling time and material aging of the surrounding powder could be reduced. This indicates the possibility of a solidification-optimized processing strategy with targeted temperature control in z-direction. \end{abstract} Keywords: Additive manufacturing $\cdot$ Laser beam melting $\cdot$ Powder bed fusion $\cdot$ Laser sintering \section*{1 Introduction} Powder bed fusion of polymers, which is also called selective laser beam melting or laser sintering (SLS) has developed from a prototype production to a direct manufacturing technology [1]. Compared to conventional production technologies, such as injection molding, SLS offers high geometrical freedom and the possibility to fabricate polymer parts at low quantities at a short design to manufacturing time [2]. The emerging topics concerning advanced SLS polymer processing are the increase of material availability, enhanced reproducibility and the reduction of processing times for faster part availability [3]. All of these topics are somehow linked to the predominant transient temperature fields within the SLS process. According to several authors [4-6] especially the temperature inhomogeneities during the process affect the reproducibility of part quality characteristics and material aging. Multiple energy sources and sinks within the SLS process affect the temperature fields. The temperature distribution on the powder\\ bed surface is basically determined by the surface heating system. The powder is locally molten by laser. Every layer, surface cooling is induced by recoating a new layer of powder onto the powder bed surface. In z-direction, platform heaters and cylinder heaters (or removal chamber or frame heaters) as well as heat conduction processes affect the temperature fields. According to the findings of the authors, there is an unused potential for process optimization that can be used, when the impact of the cylinder heater on powder material and part properties is fully understood. For this reason, the basic influence of the cylinder temperature on part properties will be analyzed in the following. \section*{2 State of the Art} In Fig. 1, typical simplified temperature profiles within the three process phases of the SLS process are shown. More precisely, the heating, build and cooling phase, are shown for the surface $T_{\text {Surface }}$ or build chamber temperature $T_{B}[7]$ and the cylinder temperature $\mathrm{T}_{\text {Cylinder }}\left(\mathrm{T}_{\mathrm{C}}\right)$. In the heating phase, which lasts between two and three hours depending on the system type and the size of the build chamber, the temperature of the powder bed surface and the build cylinder is gradually increased to their target temperatures. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-131} \end{center} Fig. 1. Schematic illustration of the temperature profiles on the powder bed surface and at cylinder temperature in z-direction during the SLS-process [7]. Within the build phase, the surface and the cylinder temperatures are held at a constant temperature level. Usually, for semi crystalline thermoplastics, the surface temperature is chosen according to the model of isothermal laser sintering [8,9] slightly below the melting temperature. The temperature of the cylinder heater is set to a significantly lower temperature level, which varies for polyamide 12 (PA12) mostly in the range\\ between $130{ }^{\circ} \mathrm{C}$ and $150{ }^{\circ} \mathrm{C}$ depending on the system size. The energy to overcome the melting enthalpy of the material is locally introduced by a $\mathrm{CO}_{2}$-laser, leading to a two-phase mixture area, where the melt is coexisting with unmolten powder. Local laser energy input leads to high heating rates that usually can be neglected within the overall temperature household of the build chamber due to the quick decay time [10]. The powder coating process regularly interrupts this thermodynamically stable state, by adding new and cooler powder onto the powder bed surface. Afterwards, the surface temperature has to be raised to the target temperature, again. Amongst many other parameters, the duration of the build phase is depending on the height of the build job and the layer time and can take more than $24 \mathrm{~h}$. During the final cooling phase, all heating systems are deactivated and the system as well as the powder cake cool down passively. The duration of the cooling phase mainly depends on the thermal conductivity of the polymer powder, the thermal mass and usually corresponds to the duration of the build phase. Part cooling is accepted to happen slowly to avoid warpage by inhomogeneous shrinkage caused by locally differing cooling rates $[5,6,11]$. Due to this slow cooling, the properties of SLS parts are morphologically different from injection molded parts which solidify within a time period of seconds [12]. In Fig. 1, a strongly optimized temperature chart is shown. In reality, the interactions between different temperature fields are more complex and their observation is essential for process understanding and optimization. Regarding the three process phases, most research is performed on understanding the build phase. It is stated, that especially the amount of energy input into the SLS process determines the completeness of the melting within the part, which can for instance be adjusted by increasing the laser power, lowering the scan spacing or by setting higher surface temperatures [13]. In [14], the influence of energy density $\left(\mathrm{E}_{\mathrm{D}}\right)$ and surface temperature on part density is studied empirically and numerically, indicating a positive correlation between $\mathrm{T}_{\mathrm{B}}$ or $\mathrm{E}_{\mathrm{D}}$ and part density. Especially the temperature distribution within the molten material affects the quality of the resulting parts. Therefore, the choice of optimum exposure parameters, such as effective laser power or scan speed, has been found to be decisive for the resulting surface and melt temperatures and therefore part properties [15-19]. However, even for optimum surface and exposure parameters, an influence of part positioning within the build chamber on the part characteristics can be detected, even for identical geometries [12, 20]. Wudy [7] and Josupeit [21] showed that every parts thermal history, which is among many other influences mainly depending on the system and the position within the build chamber, is unique. This can be attributed to inhomogeneous temperature fields that are present within the build chamber and especially along the zaxis of most laser sintering systems. [7, 21] These locally varying temperature histories lead to altered part properties due to different material crystallization and solidification. Gibson [22] showed that part density and mechanical properties are affected by part orientation, and building height. Especially parts in the center of the build space tend to have higher tensile strength and part density, which was referred to lower cooling rates and more homogeneous temperature fields. Zharringhalam [13] performed experiments under variation of the cooling period, where parts were extracted from the powder bed at different time spans after fabrication. For comparison, the results are presented in Table 1. It was found that after high times to extraction, higher values for the tensile\\ strength were achieved, which is in accordance to Gibson's findings in [22]. Short times to extraction led to higher values of the elongation at break and Young's Modulus. However, no significant influence on relative crystallinity was observed, indicating that crystallization process was finished earlier [13]. Table 1. Impact of extraction time on mechanical properties and crystallinity [13]. \begin{center} \begin{tabular}{l|l|l|l|l} \hline Mechanical properties & \multirow{2}{*}{Unit} & Estimated time to extraction & & \\ \cline { 3 - 6 } & & $66 \mathrm{~h}$ & $1 \mathrm{~h}$ & $0.1 \mathrm{~h}$ \\ \hline Elongation at break & $\%$ & 13.5 & 16.8 & 19.1 \\ \hline Tensile Strength & $\mathrm{MPa}$ & 42.5 & 41.0 & 40.6 \\ \hline Young's Modulus & $\mathrm{GPa}$ & 1.69 & 1.65 & 1.80 \\ \hline Crystallinity & $\%$ & 27.9 & 27.5 & 27.2 \\ \hline \end{tabular} \end{center} The understanding of crystallization pf PA12 within the SLS process has changed significantly over the last decades. In the early 2000s, it was assumed that according to the model of isothermal laser sintering, the molten material would remain liquid until the entire part bed begins to cool down in the cooling phase [23]. Later on, Drummer [24] showed that under processing conditions and depending on the used material system, isothermal crystallization is present and the implementation of time-dependent phase transitions into the model of isothermal laser sintering is necessary to explain different material behavior. Wegner [18] summarized that the validity of the model of isothermal laser sintering was limited to a narrow period of time, which can be correlated to a low part size or build-height. In $[25,26]$ isothermal crystallization and the degree of crystallization were modelled for PA12 and polypropylene in the first ten layers considering the influence of powder coating cooler material onto the molten material. It could be shown that within 10 layers the majority of crystallization has been completed. In [27], time and temperature dependent material solidification due to isothermal crystallization of PA12 could be observed within the process and within process adapted material characterization. At a build chamber temperature of $168^{\circ} \mathrm{C}$, measurable material consolidation takes place after around $10 \mathrm{~min}$ after exposure was found. A revision of the temperature control setup of the build chamber was announced, allowing for an active cooling of the part cake in z-direction after isothermal crystallization and solidification of the material is finished. The knowledge of material consolidation under isothermal conditions in combination with the knowledge on the inadequacies of the existing technical solution must therefore lead to the temperature system of the build chamber to be reconsidered. Already in 1997, Gibson [22] proposed to improve the temperature control strategy within SLS systems to achieve more homogeneous part properties independent from positioning. In [28], Li examined the cooling of polyamide 12 (PA12) components through simulations and optimized the build chamber geometry and the cooling parameters in terms of maximum temperature homogeneity. It was found that the geometry of the build chamber has a major influence on the temperature homogeneity of the cooling process. For an optimum\\ cooling process a container width small width, long length and high height should be used [28]. Due to more uniform part temperature histories, these adaptions have the potential to increase the reproducibility of part properties and to enhance the efficiency of the SLS process significantly. Furthermore, the cooling phase would no longer determine the production time and part availability [27]. Therefore, a basic understanding on the influence of the cylinder temperature on part properties has to be generated. In the following, experiments are performed aiming for a material dependent temperature control system for an optimized SLS process. \section*{3 Materials and Methods} Within the following section, information on the used material, the experimental setup and the performed series of experiments is shown. The aim is to determine the basic influences of isothermally tempered cylinder heating on different temperature levels on the material and component properties in order to ensure the potential for process acceleration through a reduced cylinder temperature. The long-term goal is to develop a locally and temporally adapted tempering strategy in the z-direction to exploit the potential of consolidation due to isothermal crystallization of PA12 as reported in [27]. \subsection*{3.1 Material System} The experiments were conducted using PA12 powder PA 2200 from EOS GmbH (Krailling, Germany). A refreshed powder mixture of a 50:50 weight ratio of virgin and recycled powder was used. The used powder was taken from overflow containers, and therefore only slightly affected by the high ambient temperature. Therefore, a low thermal impact on the powder and the experiments can be expected. Prior to fabrication, the bulk density and viscosity number (VN) of the powder mixture were determined to $0.44 \pm 0.01 \mathrm{~g} / \mathrm{cm}^{3}$ and $56.5 \pm 1.4 \mathrm{ml} / \mathrm{g}$. \subsection*{3.2 Laser Beam Melting System} A freely parameterizable laser beam melting system was applied for the experiments. For studying the impact of cylinder temperature on the resulting part properties, a miniaturized build chamber was used. The schematic illustration of the experimental setup is depicted in Fig. 2 a). The build chamber dimensions in xy-plane are reduced from $350 \times 350 \mathrm{~mm}^{2}$ to $100 \times 100 \mathrm{~mm}^{2}$ and the build chamber height is reduced from $500 \mathrm{~mm}$ to $150 \mathrm{~mm}$. The miniaturized build chamber was applied, as tempering a small volume of powder can be correlated to a higher control over the present temperature fields, compared to the higher build volume of the standard system. The build chamber is heated by a silicone heater, which is mounted around the build cylinder (see Fig. 2 b). For setting the temperature field on the powder bed surface, eight individually controllable infrared quartz radiator arrays are installed within the system. For laser exposure, a $50 \mathrm{~W} \mathrm{CO}_{2}$-laser with a focus diameter of $0.4 \mathrm{~mm}$ was used.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-135(2)} Fig. 2. Schematic illustration of the experimental set-up depicting a) the miniaturized build chamber within the standard build chamber and b) the cylinder heating system. \subsection*{3.3 Fabrication Experiments} In order to study the influence of the cylinder temperature on the resulting part properties, multipurpose test specimens were fabricated. The dimensions of the sample are sketched in Fig. 3. Within the miniaturized build chamber, six samples can be positioned at equal distancing in one layer. Five layers of test specimens were fabricated and for process stability, all of the samples were oriented in recoating direction. For thermal isolation, 50 layers of powder were recoated before the first and after the last exposed layer, respectively. The build job setup is schematically visualized in Fig. 4. For all experiments, the exposure parameters and the build chamber temperature were kept constant. The parameters are listed in Table 2. In addition, no scaling factors were set. The cylinder temperature was varied between $100{ }^{\circ} \mathrm{C}$ and $150{ }^{\circ} \mathrm{C}$ with increments of $10^{\circ} \mathrm{C}$. A reference experiment was performed with turned off cylinder heater, which is named " $0{ }^{\circ} \mathrm{C}$ " experiment in the following sections. After fabrication and cooling to room temperature, the parts were carefully depowdered by using a brush. In addition, powder samples were extracted from material located between the tensile bars. Immediately after extraction, the 30 multipurpose test specimens were stored in a vacuum cabinet at room temperature to avoid water absorption. a) \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-135(1)}\\ b) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-135} \end{center} Fig. 3. Geometric description of test samples a) front view and b) side view.\\ a) Top view \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-136} \end{center} b) Side view\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-136(1)} Fig. 4. Schematic of the build job setup in a) top view and b) side view. Table 2. Constant processing parameters for the fabrication of specimens. \begin{center} \begin{tabular}{l|l|l} \hline Process parameter & Value & Unit \\ \hline Laser power $\mathrm{P}_{\mathrm{L}}$ & 16 & $\mathrm{~W}$ \\ \hline Scan speed $\mathrm{v}_{\mathrm{s}}$ & 2,000 & $\mathrm{~mm} / \mathrm{s}$ \\ \hline Hatch distance $\mathrm{h}_{\mathrm{s}}$ & 0.2 & $\mathrm{~mm}$ \\ \hline Layer height $\mathrm{d}_{\mathrm{h}}$ & 0.1 & $\mathrm{~mm}$ \\ \hline Energy density $\mathrm{E}_{\mathrm{D}}$ & 0.4 & $\mathrm{~J} / \mathrm{mm}^{3}$ \\ \hline Build chamber temperature $\mathrm{T}_{\mathrm{B}}$ & 174 & ${ }^{\circ} \mathrm{C}$ \\ \hline \end{tabular} \end{center} \subsection*{3.4 Temperature Measurements} The thermal boundary conditions were measured at two different sites. The temperature of the powder bed surface was determined by the systems pyrometer in the center of the powder bed. The cylinder temperature input was detected at the site of the silicon heater. For these measurements, the data acquisition rate was $25 \mathrm{~Hz}$, which means that every $40 \mathrm{~ms}$ a measuring point was recorded. \subsection*{3.5 Thermal Simulation} The thermal simulation was performed in the multiphysics software Abaqus CAE 2019 to characterize the local temperature distribution and the chemical aging of the part cake for each time step of the process. To reduce the simulation complexity, a 2D-model was used, and only half of the build chamber was modeled. This simplification was chosen based on symmetrical thermal boundary conditions. Furthermore, ten layers were combined to one simulation layer resulting in a layer height of $1 \mathrm{~mm}$ and an average layer time of $405 \mathrm{~s}$. No parts were considered in the simulation. Figure 5 shows the position of the 2D\\ xz-plane located on the top view (xy-plane) of the build chamber. In the heating phase, the initial powder layers get heated up to process temperature. Simulation model \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-137} \end{center} Build phase \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-137(1)} \end{center} Cooling phase Fig. 5. Schematic depiction of the thermal simulation. The following build phase adds layers with each simulation step. In the cooling phase, the part cake is cooled down. The thermal boundary conditions were modeled based on the temperature measurements of the experiments introduced in Sect. 3.4 (see Fig. 8). The local calculation of the $\mathrm{VN}$ is performed for each step based on the local temperatures and the model in [29]. The simulation parameters are shown in Table 3. Table 3. Boundary conditions of the thermal simulation. \begin{center} \begin{tabular}{l|l|l} \hline Simulation parameter & Value & Unit \\ \hline Heating Phase time/step time & $7,200 / 400$ & $\mathrm{~s}$ \\ \hline Layer time/step time & $405 / 40.5$ & $\mathrm{~s}$ \\ \hline Cooling phase time/step time & $36,000 / 360$ & $\mathrm{~s}$ \\ \hline Starting height & 20 & $\mathrm{~mm}$ \\ \hline Build height & 40 & $\mathrm{~mm}$ \\ \hline Layer thickness & 1 & $\mathrm{~mm}$ \\ \hline \end{tabular} \end{center} \subsection*{3.6 Material and Part Characterization} The VN value was determined for the initial powder mixture by Ubbelohde viscometer using concentrated sulphuric acid as solvent. In order to study the thermal impact of different cylinder heating levels the VN of the powder samples and the test specimens was measured, respectively. The part cake powder was extracted from spaces between the fabricated samples and homogenized. For part characterization, especially the material in the center of the specimen was analyzed in order to minimize the influence of fused particles on the surface. For basic part characterization, the part dimensions, width and height respectively, were determined by outside micrometer (measurement accuracy: $\pm 0.01 \mathrm{~mm}$ ) at three different sites for every sample. The measuring positions are highlighted in Fig. 6.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-138} Fig. 6. Schematic description of the measuring positions for the determination of the a) part width and b) part height. The morphology of the parts was characterized in terms of layer connectivity, porosity and crystallinity by transmitted light microscopy under polarized light at 25-x magnification using the microscope Axio Imager.M2 from Carl Zeiss AG (Germany). Exemplarily, samples fabricated with turned off cylinder heater and parts fabricated with cylinder temperatures of $110{ }^{\circ} \mathrm{C}, 130{ }^{\circ} \mathrm{C}$ and $150{ }^{\circ} \mathrm{C}$ were analyzed. Therefore, thin sections of approximately $10 \mu \mathrm{m}$ were extracted from the center of the tensile bars, which were located in the center of the first, third and fifth row of parts. The extraction site is depicted in Fig. 7. Subsequently, the part porosity was determined by gray value analysis in the center of the samples with a constant threshold value for binarisation of 55 . \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-138(1)} \end{center} Fig. 7. Sampling position for the extraction of the thin cuts of $10 \mu \mathrm{m}$. Part mechanics were determined by tensile tests following DIN EN ISO 527-2 using the universal testing machine Zwick 1465 from ZwickRoell GmbH \& Co. KG (Germany). For the determination of the Young's modulus, the testing speed was set to $0.5 \mathrm{~mm} / \mathrm{min}$. For failure analysis and to characterize the tensile strength and the elongation of break, the testing speed was adjusted to $25 \mathrm{~mm} / \mathrm{min}$. \section*{4 Results and Discussion} The results of the surface and cylinder temperature measurements are shown in Fig. 8. During the initial heating phase, the different heating temperature levels and plateau phases can be detected for the surface of the powder bed. The surface temperature was measured by pyrometer and the temperature of the cylinder heater was acquired by thermocouple measurements. After the end of the heating phase, the average surface temperature was determined to $174{ }^{\circ} \mathrm{C}$, which is the build chamber temperature $\mathrm{T}_{\mathrm{B}}$. Furthermore, rapid temperature rises to temperature levels of more than $200{ }^{\circ} \mathrm{C}$ are visible that can be correlated to a random detection of the exposure process. In addition, temperature reductions to temperatures levels of around $150{ }^{\circ} \mathrm{C}$ are present, which can be traced back to the heating phase after powder coating of new and cool powder layers onto the surface of the powder bed. In the build phase, the target temperatures of the cylinder temperature are reached immediately. For the untempered experiment\\ $\left(T_{C}=0\right)$ with turned off cylinder heater, an increase in cylinder temperature can be observed throughout the whole build phase, which can be correlated to heat conduction processes from heated powder to the cooler build cylinder. At the end of this phase, temperatures of more than $90^{\circ} \mathrm{C}$ are present at the measuring position. As no plateau phase was reached yet, it can be expected, that an increase in build duration would lead to a further increase of cylinder temperature. In contrast to that, the cylinder temperature is constant for the tempered experiments, although there is no active heat extraction from the system. For that reason, for this system and build setup, a thermal balance at measuring position can be expected at a cylinder temperature of around $100{ }^{\circ} \mathrm{C}$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-139} \end{center} Fig. 8. Results of the surface and cylinder temperature measurements. Within the cooling phase, an almost exponential decrease in surface and cylinder temperature is present. It can be seen, that higher cooling rates are present at the surface compared to the cylinder heaters in z-direction. Concerning cylinder heaters, the cooling rate is depending on the temperature level. The higher the initial cylinder temperature, the higher the cooling rate, especially in the beginning of the cooling phase. It can be seen, that the reduction of cylinder temperature leads to an almost identical cooling profile at the site of the build cylinder. This can be explained by the temperature gradient between the build cylinder and the surrounding air. Figure 9 shows the calculated temperature distribution of the xz-plane for different cylinder temperatures and cooling times. The thermal boundary conditions for this simulation are chosen based on the temperature measurements shown Fig. 8. Comparing the different cylinder temperatures at the end of the building phase (cooling phase: $t$ $=0 \mathrm{~h}$ ), a strong influence of the local temperature distribution in z-direction can be detected. With decreasing cylinder temperature, a three-dimensional temperature gradient develops from the surface temperature towards the colder cylinder walls. This results in a thermal history of the powder and parts, depending on the xy- and z-position in the part cake. Hence, a part build in the SLS process is not in an isothermal state over the processing time. In fact, it is cooling down to a temperature between build chamber and cylinder temperature shortly after the exposure. Furthermore, the calculated results\\ show that the temperature of the upper layers is mainly controlled by the build chamber heating system. The upper layers are not influenced by the temperature fields induced by the cylinder heaters. After turning off the heater system, the temperature of the powder bed surface decreases rapidly (cooling phase $t=0.5 \mathrm{~h}$ ). The highest calculated temperature moves from the upper layers to the center of the part cake. This leads to a core-shell temperature distribution. With ongoing cooling time, the influence of the cylinder temperature reduces, and the temperatures start to converge. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-140} \end{center} Fig. 9. Thermal simulation of the local temperature distribution of the cooling phase. Figure 10 shows the calculated maximum local temperatures over xz-plane against the cooling time. At the beginning of the cooling phase, the maximum temperature is $174^{\circ} \mathrm{C}$ for all three cylinder temperatures, which is the build chamber temperature. With continuous cooling and turned off heating systems, the maximum temperature decreases rather quickly and a temperature difference of around $10{ }^{\circ} \mathrm{C}$ can be detected between the $150^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C}$ cylinder temperature. While the cylinder temperature affects the temperature distribution significantly, the effect on the maximum temperature is rather\\ small. The maximum temperature is located in the center of the powder bed and mainly dominated by the specific heat coefficient and the heat conductivity of the powder. A higher heat conductivity, e.g. by adding fillers, could lead to higher cooling speed. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-141(1)} \end{center} Fig. 10. Thermal simulation of the maximum local temperature in the part cake during cooling. The results of the measured and calculated viscosity numbers are shown in Fig. 11. For PA12, thermal post condensation is a commonly known aging mechanism that leads to an extension of the polymer chains. By a simplifying assumption, the increase of the polymer chain length can be correlated to an increase in viscosity number. In addition, thermal degradation from laser exposure leading to a reduced polymer chain length should be considered. The VN value of the initial powder mixture was $56.5 \pm 1.4 \mathrm{ml} / \mathrm{g}$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-141} \end{center} Fig. 11. Results of the measurements of the viscosity number. It can be seen that compared to the initial powder mixture, an increase of the VN value is present for the resulting part cake powder and the resulting part, respectively. Furthermore, the VN of the part cake powder is approximately $10 \mathrm{ml} / \mathrm{g}$ higher than the\\ $\mathrm{VN}$ of the part, which can be referred to differing aging mechanism within the melt and within solid material and to the higher surface area of the small particles compared to that of the melt pool. In addition, an increase in cylinder temperature results in an increasing VN value for the part and the part cake. The calculated VN, based on the thermal simulation, fit with the measured experimental VN. However, at a cylinder temperature of $150{ }^{\circ} \mathrm{C}$ a decrease in $\mathrm{VN}$ of the part cake powder is visible while the $\mathrm{VN}$ of the simulation increases, which cannot be clearly explained. The reduction of the VN could be explained either by increasing thermal degradation at higher cylinder temperature or by insufficient definition of the powder extraction site. Both effects are not represented in the calculated value and cannot be addressed in the used model. In [5] the dependency of material aging on the position within the part cake was shown. A stronger ageing effect was measured in the center compared to outer regions of the part cake. However, to gain more reliable information on material aging, gel permeation chromatography measurements could be performed in future to determine the molecular weight of the powders and parts. The results of the geometrical characterization are shown in Fig. 12. The nominal dimension of the part width is $5 \mathrm{~mm}$. It is clearly visible, that the widths of the parts are geometrically oversized for all parameter combinations. The mean values are almost at the same level of around $5.2 \mathrm{~mm}$, with a slight decrease for cylinder temperatures of more than $110{ }^{\circ} \mathrm{C}$. However, the standard deviations are too high for a clear assessment of the influence and can be correlated to the part positioning. Furthermore, the standard deviations are decreasing with increasing cylinder temperature. This can be correlated to a theoretically more homogeneous temperature distribution along the build chamber cross-section in z-direction and local effects. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-142(1)} \end{center} Cylinder temperature in ${ }^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-142} \end{center} Fig. 12. Results of the measurements of the part width (left) and the part height (right). Considering part height, an almost similar behavior can be observed. The nominal dimension of the part height is defined to $2 \mathrm{~mm}$. In general, the samples are oversized in their height dimension, as values of around $2.2 \mathrm{~mm}$ are present for most of the parameters. Again, a slight decrease in height dimension and in standard deviation is\\ caused by an increasing cylinder temperature. This can be referred to more homogeneous temperature fields at higher cylinder temperature. In summary, it can be stated that with increasing cylinder temperature, a tendentially smaller part cross section can be expected, influencing the part mechanics. In Fig. 13, the microscope images of the thin cuts under polarized light are shown. For all cross sections, low porosity is visible within the parts, indicating sufficient energy input. For all components, adhering, unmolten particles are visible at the edges of the cross section. No clear statement can be made about the quantity of adhering particles. This result can be explained by the thermal simulations in Fig. 9. During the construction phase, almost identical thermal boundary conditions prevail for all components due to the strong influence of surface heaters. Within deeper layers, the components are influenced by the lower cylinder temperatures. Taking into account the results in [27], it can be concluded that the formation of part properties such as component geometry is mainly dependent on the surface temperature fields and is only slightly influenced by the cylinder temperature due to already performed isothermal crystallization and solidification processes.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-143} Fig. 13. Thin sections of samples fabricated with different cylinder temperatures a) untempered, b) $110{ }^{\circ} \mathrm{C}$, c) $130^{\circ} \mathrm{C}$ and $150^{\circ} \mathrm{C}$ (exemplarily shown for the third row of parts). Considering the morphology of the samples, visible pores are preferably oriented in the building direction along the build plane, which can be usually assigned to inhomogeneous particle arrangements and too low energy input. The results of the geometric\\ characterization of the components can be verified by the optical measurement of the microscopic images, since here too an oversize of the component height and the component width can be proven for all components. In addition, the typical SLS formation of a convex component bottom side and a concave component top side is visible for all components. This is due to friction and flow effects of the melt on the powder bed, respectively. Clamping this component geometry in the measuring device increases the notch effect during mechanical testing and the probability for early part failure, which would be noticeable by low values for the elongation at break. Regarding the semi crystalline structure of the parts, no significant differences can be found. In the centers of the parts fine and homogenous-looking spherulitic structures can be found. At the side areas of the parts, the layer structures are visible as layers of unmolten particles are incorporated into the melt. This can be explained by the locally differing energy input and cooling in the center and in the side regions of the parts. The results of the porosity evaluation are shown in Fig. 14. Comparatively low mean values of below $2 \%$ were measured by optical analysis of microscopy images from three different parts per parameter set. Since the surface roughness is not taken into account when calculating the porosity optically, comparably low porosity values are achieved that are subject to high standard deviations. The highest porosities are found for the untempered experiment whereas no significant difference can be observed for the tempered experiments. The inhomogeneous tempering for the untempered experiment could have led to this slightly elevated value of porosity. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-144} \end{center} Fig. 14. Results of the optical measurement of the part porosity. The results of the tensile tests are depicted in Fig. 15 and 16. The Young's modulus is determined to values of around 1,850 $\mathrm{MPa}$ and comparatively high standard deviations of mostly around $\pm 50 \mathrm{MPa}$ are present. The variation of the cylinder temperature has no significant influence on the Young's modulus or the standard deviation. The mean values of the tensile strength are determined to values of around $46 \mathrm{MPa}$, which is comparable to freshly sintered or dry PA12 samples. Again, no significant influence of cylinder temperature on the determined characteristic value was found.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-145(1)} Fig. 15. Results of the measurements of the Young's modulus (left) and the tensile strength (right). In Fig. 16, the results of the measurement of the elongation of break are depicted in dependence on the cylinder temperature. It must be emphasized that the characteristic value of elongation at break in particular is sensitive to material and process influences and therefore should be used as a significant mechanical characteristic value. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-145} \end{center} Fig. 16. Results of the measurements of the elongation of break. In some cases, very low values of less than $10 \%$ of elongation at break were achieved, which is due to the choice of test specimens scaled to the half of their original size and conditioning of the parts, which can be described as freshly sintered and dry. In addition, the shape of the cross-section promotes the notch effect during tensile testing. However, maximum values of $12.8 \%$ were measured for a cylinder temperature of $130{ }^{\circ} \mathrm{C}$, which can be described as optimum parameter for the size of the miniaturized build chamber. At cylinder temperatures between $0^{\circ} \mathrm{C}$ and $130^{\circ} \mathrm{C}$, a slight increase in the mean values of the elongation at break can be observed, while at higher temperatures there is a tendential decrease in elongation at break. Especially the latter influence cannot be\\ clearly be characterized due to the comparatively high standard deviations. Nevertheless, an influence of the cylinder temperature on the elongation of break is clearly visible, which indicates that a simple cylinder temperature reduction with unchanged part quality is not possible for process optimization. \section*{5 Summary and Outlook} Within the shown investigations, the influence of an isothermal cylinder heating system on the resulting part properties was shown in order to evaluate the possibility to reduce the cylinder temperature for an acceleration of the cooling phase. Thermal simulations indicate that within the upper layers, the samples were subjected to almost identical thermal boundary conditions, due to the strong influence of surface heaters. Within deeper layers, the components are influenced by the lower cylinder temperatures. Hence, for the used experimental setup, a minor influence of cylinder temperature on part geometry, part morphology and part mechanics, such as Young's modulus and tensile strength was observed. However, the part porosity and the elongation at break benefit from elevated temperature levels of the build cylinder. It can be concluded that the formation of most of the observed part properties is mainly dependent on the surface temperature fields and is only slightly influenced by the cylinder temperature due to already performed material solidification in the upper layers. According to these and earlier findings, a time dependent temperature profile in z-direction will be applied to the cylinder heating system. Close to the surface of the build chamber, high temperatures close to $\mathrm{T}_{\mathrm{B}}$ or the optimum cylinder temperature depending on build chamber size will be the target temperature. The temperature decrease in z-direction is realized by an active cooling system according to the progressing isothermal crystallization kinetics and the linked material consolidation. This will lead to an accelerated and more efficient SLS process in future. Acknowledgements. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 61375930 - SFB 814 “Additive Manufacturing” TP B03 and T01. \section*{References} \begin{enumerate} \item Gibson, I., Rosen, D., Stucker, B.: Additive Manufacturing Technologies-3D Printing, Rapid Prototyping, and Direct Digital Manufacturing, 2nd edn. Springer, Heidelberg (2015) \item Van Hooreweder, B., Kruth, J.-P.: High cycle fatigue properties of selective laser sintered parts in polyamide 12. CIRP Ann. 63(1), 241-244 (2014) \item Goodridge, R.D., Tuck, C.J., Hague, R.J.M.: Laser sintering of polyamides and other polymers. Prog. Mater Sci. 57, 229-267 (2012) \item Wegner, A., Witt, G.: Ursachen für eine mangelnde Reproduzierbarkeit beim Laser-Sintern von Kunststoffbauteilen. RTejournal 10 (2013) \item Josupeit, S., Schmid, H.-J.: Temperature history within laser sintered part cakes and its influence on process quality. Rapid Prototyp. J. 22(5), 788-793 (2016) \item Shen, J., Steinberger, J., Göpfert, J., Gerner, R., Daiber, F., Manetsberger, K., Ferstl, S.: Inhomogeneous shrinkage of polymer materials in selective laser sintering. In: International Solid Freeform Fabrication Symposium, pp. 298-305 (2000) \item Wudy, K.: Alterungsverhalten von Polyamid 12 beim selektiven Lasersintern. Dissertation Friedrich-Alexander-Universität Erlangen-Nürnberg (2017) \item Alscher, G.: Das Verhalten teilkristalliner Thermoplaste beim Lasersintern. Dissertation, Berichte aus der Kunststofftechnik, Shaker Verlag, Aachen (2000) \item Schmachtenberg, E., Seul, T.: Model of isothermic laser sintering, In: Society of Plastics Engineers, ANTEC 2002 conference proceedings, 3030-3035 (2002) \item Greiner, S., Wudy, K., Wörz, A., Drummer, D.: Thermographic investigation of laser-induced temperature fields in selective laser beam melting of polymers. Opt. Laser Technol. 109, 569-576 (2019) \item Yuan, M., Bourell, D., Diller, T.: Thermal conductivity measurements of polyamide 12. In: Proceedings of the Solid Freeform Fabrication Symposium, pp. 427-437 (2011) \item Bourell, D. L., Watt, T. J., Leigh, D. K., Fulcher, B.: Performance limitations in polymer laser sintering. In: International Conference on Photonic Technologies, Physics Procedia, vol. 56, pp. 147-156 (2014) \item Zarringhalam, H.: Investigation into crystallinity and degree of particle melt in selective laser sintering. Dissertation, Loughborough University (2007) \item Tontowi, A.E., Childs, T.H.C.: Density prediction of crystalline polymer sintered parts at various powder bed temperatures. Rapid Prototyp. J. 7(3), 180-184 (2001) \item Drummer, D., Drexler, M., Wudy, K.: Impact of heating rate during exposure of laser molten $\mathrm{p}$ arts on the processing window of PA12 powder. Phys. Procedia 56, 184-192 (2014) \item Drexler, M.: Zum Laserstrahlschmelzen von Polyamid 12 - Analyse zeitabhängiger Einflüsse in der Prozessführung. Dissertation, Friedrich-Alexander-Universität Erlangen-Nürnberg (2016) \item Wegner, A., Witt, G.: Understanding the decisive thermal processes in laser sintering of polyamide 12. In: AIP Conference Proceedings, vol. 1664, p. 160004 (2015) \item Wegner, A.: Theorie über die Fortführung von Aufschmelzvorgängen als Grundvoraussetzung für eine robuste Prozessführung beim Laser-Sintern von Thermoplasten. Dissertation, Universität Duisburg-Essen (2015) \item Kiani, A., Khazaee, S., Badrossamay, M., Foroozmehr, E., Karevan, M.: An investigation into thermal history and its correlation with mechanical properties of PA 12 parts produced by selective laser sintering process. J. Mater. Eng. Perform. 29, 832-840 (2020) \item Rietzel, D., Drexler, M., Kühnlein, F., Drummer, D.: Influence of temperature fields on the processing of polymer powders by means of laser and mask sintering technology. In: Solid Freeform Fabrication Symposium, pp. 252-262 (2011) \item Josupeit, S.: On the influence of thermal histories within part cakes on the polymer laser sintering process. Dissertation, Universität Paderborn, Shaker (2019) \item Gibson, I., Shi, D.: Material properties and fabrication parameters in selective laser sintering process. Rapid Prototyp. J. 3(8), 129-136 (1997) \item Kruth, J.-P., Levy, G., Klocke, F., Childs, T.H.C.: Consolidation phenomena in laser and powder-bed based layered manufacturing. Annals CIRP 56(2), 730-759 (2007) \item Drummer, D., Rietzel, D., Kühnlein, F.: Development of a characterization approach for the sintering behavior of new thermoplastics for selective laser sintering. In: LANE 2010, Physics Procedia, vol. 5, pp. 533-542 (2010) \item Amado, A., Wegener, K., Schmid, M., Levy, G.: Characterization and modeling of nonisothermal crystallization of Polyamide 12 and co-Polypropylene during the SLS process. In: Polymers \& Moulds Innovations Conference, pp. 207-216 (2014) \item Amado Becker, A. F.: Characterization and prediction of SLS processability of polymer powders with respect to powder flow and part warpage. Dissertation, ETH Zürich (2016) \item Drummer, D., Greiner, S., Zhao, M., Wudy, K.: A novel approach for understanding laser sintering of polymers. Additive Manuf. 27, 379-388 (2019) \item Li, X., Van Hooreweder, B., Lauwers, W., Follon, B., Witvrouw, A., Geebelen, K., Kruth, J.-P.: Thermal simulation of the cooling down of selective laser sintered parts in PA12. Rapid Prototyp. J. 24(7), 1117-1123 (2018) \item Drummer, D., Wudy, K., Drexler, M.: Modelling of the aging behavior of polyamide 12 powder during laser melting process. In: AIP Conference Proceedings, vol. 1664, p. 160004 (2015) \end{enumerate} \section*{Additive Manufacturing of Multi-material Polymer Parts Within the Collaborative Research Center 814 } \begin{abstract} During the past years additive manufacturing (AM) has revolutionized the manufacturing world by enabling rapid generation of geometrically-intricate designs. However, up to now in laser and beam-based AM of polymers only single powder materials whether filled or pure plastics can be processed. One aim of the Collaborative Research Center 814 (CRC 814) - Additive Manufacturing is to establish new process technologies to produce multi-material polymer parts in AM. Therefore, two different strategies basing on Laser Sintering (LS) will be explored: On the one side, selective powder deposition technologies like vibrating nozzles or electrophotography are investigated, which enable to lay down different powders beside each other in one process. On the other side, a liquid reactive UVcuring thermoset is implemented into the LS process chamber. After curing of the UV-curing thermoset the powder beside the cured thermoset is molten by the use of the $\mathrm{CO}_{2}$ laser. Both strategies allow the generation of multi-material parts consisting of material regions with different functional properties. \end{abstract} Keywords: Additive Manufacturing $\cdot$ Laser Sintering $\cdot$ Binder Jetting $\cdot$ Multi-material parts \section*{1 Introduction} Laser Sintering (LS) of polymer powders is a powerful additive manufacturing (AM) technology, which can be used to generate fully functional prototypes or complex plastic design models by performing a layer-by-layer 3D printing process [1]. Although this method provides a lot of benefits and possibilities, it also brings along a tremendous restriction: the usage of a single material within the building process. Thereby, the realization of multi-material components with combined functionalities is unfeasible. To diminish this constraint, the Collaborative Research Center 814 (CRC 814) Additive Manufacturing investigates different approaches in combination with LS which base on the one hand on the selective deposition of multiple powder materials (multimaterial powder layers) with new coating technologies and on the other hand on the implementation of a liquid reactive UV-curing thermoset in the LS process chamber in order to selectively adapt material properties. Here, the current state of the art of AM of multi-material parts is presented. After that, specific results of nozzle-based multi-material deposition, electrophotographic patterned powder layer preparation, as well as new LS routes for the melting of multi-material polymer powder layers are discussed. At last, the dynamic mechanical properties of resin infused polymer powder specimens are analyzed. \section*{2 State of the Art - Additive Manufacturing of Multi-material-Parts} According to Anstaett et al. [2] there are two ways of differentiating multi-materials parts: Discrete or graded changes of materials. A discrete change of materials is defined as a material combination, where two or more materials adjoin each other, having a defined border. A graded change of material is a transition area with a smooth change from one material to another. At this moment, there are multiple concepts in the field of AM, which attempt the combination of different types of materials as well as the local adjustment of certain properties. Fused Deposition Modeling (FDM) is an extrusion-based processing technique that is capable of building multi-material parts. An application example of this technology are additively manufactured multi-material antennas as showcased by Mirotznik et al. [3] at the University of Delaware (Newark, Delaware). Polycarbonate thermoplastic stock with different fillers was used to print dielectric and magnetic components. Poly-Jet-Modeling (PJM) and Multi-Jet Modeling (MJM) print photo reactive polymers in liquid form, which are cured by being exposed to a UV-light source implemented within the printing head. [4]. Components created by PJM/ MJM tend to negatively alter over time through exposure to daylight and oxygen, which deteriorates the mechanical and optical properties [5, 6]. Sugavaneswaran et al. [7] demonstrated that randomly oriented multi-material AM components can be created using PJM. The showcased reinforced components are specimen for tensile testing (ASTM: D412-C), which combine Tango Plus ${ }^{\mathrm{TM}}$, an elastomer like matrix material and Vero white ${ }^{\mathrm{TM}}$ as the hardplastic reinforcement. Further, Tibbits et al.[8] were able to implement shape-memory behavior into parts through multi-material PJM (a.k.a. 4D-printing). Through the additional functional implementation, they were able to create multi-material single strands, which are self-folding through energy input or change of environmental conditions. Choi et al. [9] from the University of Texas demonstrated multi-material Stereolithography with rotating vats. As in PJM, the different materials are limited to liquid photopolymers only. LS of powders is currently predominantly commercially available for the creation of mono-material parts[2]. However, laser sintered components show porous integrity, which decreases the functional utilization of the final parts [4]. Promising concepts are currently being worked on to combine different materials within LS. As described by Anstaett et al. [2], there are three different ways to allocate different powder in the building chamber: Vibrating nozzles, coater and electrophotography. Especially the use of\\ electrophotography shows to be a highly promising approach. For the accurate preparation of arbitrary multi-material powder layers for LS two techniques - the vibrating powder nozzles and the electrophotography - were explored thoroughly. Vibrating nozzles enable the highly selective discharge of small amounts of powder within the LS building chamber, which is why they are predestined for the targeted functionalization of sintered parts [9]. Electrophotography, also known as xerography, relies on a photoconductive substance, whose electrical resistance decreases when it is exposed to light. This complicated process is not only essential in the common printing industry because of its ability to handle powders very precisely and fast, but also can lead combined with AM to a powerful 3D printing technology for creating multi-material functional components [10]. However, the stacking of powder layers by electrostatic forces is challenging which was firstly shown by Kumar et al. in [10] in their pioneer work of electrophotographic 3D printing. Thus, also different approaches basing on pressure and heat are investigated to produce 3D objects [11]. \section*{3 Multi-material Concepts Within the CRC 814} \subsection*{3.1 Multi-material powder deposition} There are several approaches to pursue the goal of generating multi-material parts in the LS context, all of which are still subject of ongoing research. Vibrational powder nozzles can be employed for the deposition of fine geometric features (e. g. dots, lines) of powder materials, allowing the generation of arbitrary multi-material powder patterns. The nozzle-based approach exploits the reversible bridging mechanism of the powders within the conical nozzle body: Without external stimulus, stable powder bridges are formed in the nozzle orifice. Application of stimuli such as vibration to the nozzle causes the break-up of these bridges which initiates powder mass flow $[12,13]$. Due to the elevated processing temperature during LS and its effect on flowability, employment of a nozzle system in a LS machine requires exact control of the nozzle temperature (and hence powder temperature) to ensure constant flowability. For this reason, the used metal nozzles are equipped with internal channels allowing the continuous flow of cooling/heating liquids [14]. The electrophotographic principle applied in common printing technology uses standard toners, which mostly are made from styrene acrylic co-polymer / polyester resin with particle sizes in the range of $6 \mu \mathrm{m}$ to $20 \mu \mathrm{m}$. They are furthermore functionalized with charge control agents [15]. However, in the context of AM typically powders made of polyamide 12 (PA12), polyethylene (PE) and polypropylene (PP) are utilized [16]. The particles contained have a diameter of around $50 \mu \mathrm{m}$ or more. Since electrophotography is applied to produce two-dimensional prints on papers, the technology transfer to LS requires the solution of certain challenges[15]. Next to the different materials already mentioned, the stacking of layers in order to release a three-dimensional object is crucial. Since the part thickness is increasing with subsequent printing of layers, a transfer driven by an electric field between the photoconductor and the initial substrate plate is not useful. To meet this challenge, a new technology was developed, which allows the contactless deposition of powder picked up by a photoconductor on any substrate. The method uses a transfer metal grid with defined electric potential which is placed in close\\ distance above the substrate or the already printed layers [15] Since the distance between the grid the photoconductor is hold constant, the transfer electric field is independent from the height of the already generated part. The processing of two or more powder materials with different melting temperatures requires the adaption of the energy deposition method. Preheating and melting can be achieved by using three sources of energy: (1) IR emitters for global preheating of the build chamber to the preheating temperature of the low-melting material, (2) a $\mathrm{CO}_{2}$ laser for local, selective preheating of the high-melting polymer, and (3) a thulium laser for simultaneous melting of the multi-material part geometry [17]. However, this process requires a quick ( 1 to $5 \mathrm{~s}$ ) powder coating process to avoid shadowing of those powder areas selectively preheated by the $\mathrm{CO}_{2}$ laser radiation which leads to early crystallization and curling of the top layer. Since the production of powder layers using the vibration nozzle system already presented is slow (several minutes per layer with a size of 50x50 $\mathrm{mm}^{2}$ ), an alternate process route for the combination with vibrating nozzles was recently introduced, which just uses two energy sources [18]. While the building chamber is heated to melting temperature of the high-melting material which leads to the melting of the low-melting polymer by the IR emitters directly after its deposition by the nozzle, the high-melting material is selectively melted by a moving $\mathrm{CO}_{2}$ laser beam comparable to the classical LS process. \subsection*{3.2 Implementation of Reactive Liquids in the Laser Sintering Process} As can be seen in Fig. 1, a concept of integrating reactive resins within a laser-based AM technique is based on the combination of two processes: LS and Binder Jetting. A micro dispenser is used to selectively inject the reactive liquid into the powder bed. An infrared lamp preheats the building chamber near the melting point of the powder. Depending on the process strategy, the curing of the reactive liquid and the melting of the LS powder are performed either simultaneously or sequentially. The schematic concept in Fig. 1 is depicted for a photo reactive resin that is cured by UV radiation. Accordingly, thermoplastic elastomeric powder has to be used as the "soft" component.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-152} Fig. 1. Schematic concept and set up of a combined LS/ binder jetting process for the implementation and curing of reactive liquids within the building chamber (adapted from [19]) The overall target for the depicted process is the homogenous distribution of the reactive liquid at specific locations of the powder bed without separation of the individual\\ components. As mentioned in Sect. 2, the requirements towards the powder and the reactive liquid are dominantly dependent on the process parameter of the LS process. Besides thermal stability, injection speed and surface tension between powder and liquid component other factors like building chamber atmosphere and part shrinkage are highly influential on the successful implementation of reactive liquids in the powder bed. The approach of implementing reactive resin in LS process is highly promising towards the creation of functional multi-material parts with discrete or graded changes of materials and mechanical properties. However, there are multiple requirements towards the powder and the reactive liquid that have to be taken in account: \begin{itemize} \item Due to the preheated building chamber, the liquid component must be thermally stable near the melting temperature of the thermoplastic. \item The infiltration speed must be kept at an ideal state, which is mainly influenced by the viscosity of the liquid component and the specific characteristics of the powder. \item For sufficient wetting of the surface, a characteristic ratio in surface tension between powder and liquid component is required. \end{itemize} In the following chapters, experimental setups and results of the above described approaches for creating multi-material parts are discussed and compared to each other. \section*{4 Experimental Methodology} \subsection*{4.1 Nozzle-Based Multi-material Deposition} The setup for deposition of two powder materials with nozzles consists of a hightemperature piezo actuator providing the vibration stimulus and two metal nozzles. This construct is mounted to the standard coater of a LS machine (P380, EOS GmbH, Germany) in such a manner that nozzle movement perpendicular to that of the blade coater is enabled. The nozzles' internal fluid channels can be connected to either an oil heating unit $\left(30^{\circ} \mathrm{C}-150{ }^{\circ} \mathrm{C}\right)$ or a water cooler $\left(20^{\circ} \mathrm{C}\right)$ for precise control of the nozzle temperatures. Vibration of the actuator is controlled via a function generator creating a sinusoidal voltage signal and an analog power amplifier. A variety of LS materials (PA12, PP, TPE-A) can be used for the vibrating nozzle approach [13, 14, 20]. In Sect. 5.1, the potential of vibrating nozzles is demonstrated while they are used for the preparation of a powder pattern which represents a $2 \mathrm{D}$ gripper design, which was calculated by the CRC 814 sub project $\mathrm{C} 2$ using topology optimization algorithms [21]. The powder used is polypropylene (PP, PD0580 Coathylene, DuPont) formulated with 1 wt. \% Aerosil® (R106, Evonik) for better flowability. \subsection*{4.2 Electrophotographic Patterned Powder Layer Preparation} Figure 2 shows the individual steps for the powder development of the electrophotographic powder application method modified for powders which are used in AM [15]. First, the photoconductive plate coated with a $100 \mu \mathrm{m}$ thick layer of the positivelycharging photoconductor $\mathrm{As}_{2} \mathrm{Se}_{3}$ is charged by means of corona wire. The second step\\ is the charging of a layer of powder particles within the powder bed with a scorotron unit. The scorotron consists of a corona wire, to which high voltage is applied, and a metallic scorotron grid with a much lower voltage, which is placed between the corona wire and the powder surface. In this way the powder particles can be homogeneously charged. Simultaneously, a latent charge image is generated by selectively illuminating the photoconductive plate employing a DLP projector. Within the Discharged-Area-Development (DAD) the previously positively charged particles are hereinafter transferred to the discharged areas of the photoconductive plate. The final step (not included in Fig. 2), an electric transfer field is applied in order to deposit the powder particles from the photoconductive plate onto the substrate plate. A variety of LS materials (PA12, PA11, PP, TPU) can be used for the electrophotographic development process depicted in Fig. 2 [15]. Here, the development process is demonstrated for the preparation of a powder pattern which represents the same 2D gripper like in the Sect. 4.1. The powder used is polypropylene (PP, PD0580 Coathylene, DuPont) formulated with 1 wt. \% Aerosil® (R106, Evonik).\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-154} Fig. 2. Individual process steps of the electrophotographic powder development method. Discharged-Area-Development: Step 1: Charging of the photoconductor; step 2a: Latent charge image generation; step 2b: Charging of powder bed; step 2: Powder development \subsection*{4.3 Generation and Analysis of Multi-material Parts} Using vibrating nozzles in combination with the alternate process route (see Sect. 3.1), simple multi-layer multi-material samples can be produced. The process route used was discussed in detail in [18], so the study here focuses on the morphology of the bonding zone between the different material regions after processing. For the investigation, PP (PD0580 Coathylene, Axalta, Switzerland) formulated with 1 wt. \% Aerosil® and urethane-based TPE (TPE-U; Rolaserit PB, AM Polymer Research, Germany) were selected. 5 wt\% carbon black (Lamp Black 101, Orion Engineered Carbons, Luxembourg) was admixed to the TPE-U powder to allow the distinction between both materials and the microscopic analysis of the boundary zone. Thin sections were extracted from five-layer thick rectangular TPE-U/PP samples which possess a vertical, flat bonding zone. By means of transmitted light microscopy the boundary zone was evaluated. \subsection*{4.4 Dynamic Mechanical Properties of Resin Infused Polymer Powder Specimens} The fundamental experimental methodology for the creation of multi-material parts in a combined LS/binder jetting process concentrates on analyzing three influential categories: Material combination, process strategies/energy input and material distribution. First investigations of material combinations and the process strategies have already been documented by Wudy et al. [19,22]. This investigation concentrates on the material distribution and more specific the macroscopic dynamic properties of the transition area between reactive liquid and thermoplastic powder. Since the actual combination of reactive liquid and powder are not yet possible within a LS-based AM technique, specimens for this investigation are created within a UV oven. The specimens have dimensions of $80 \mathrm{~mm} \times 10 \mathrm{~mm} \times 2 \mathrm{~mm}$. The reactive liquid is an UV-Acrylate UV DLP Hard purchased from PhotoCentric3D, United Kingdom. It consists of acrylate and methacrylate monomers and a photoinitiator. For the powder, an unmodified PrimePart ST PEBA 2301 polyether block polyamide powder (PEBA) from the supplier EOS GmbH, Germany, is used. For the further investigations, the materials are abbreviated with TPE-A and UV-Acrylate. Specimens of 40/60, 30/70 and 20/80 TPE-A to UV-Acrylate ratios (weight percentage) are created, as well as specimens solely made of TPE-A. Furthermore, specimens exclusively made of UV-Acrylate are created with different degrees of cure of $97 \%$ and $100 \%$. The degree of cure was determined through UV-Differential Scanning Calorimetry. The curing of the UV-Acrylate was performed by exposition to UV light for $3 \mathrm{~min}$ for every specimen, except for specimens of $100 \%$ degree of cure, which were exposed to UV-light twice for 3 min. Dynamic Mechanical Analysis (DMA) is used to analyze the dynamic mechanical viscoelastic properties of the specimens. For this investigation a DMA ARES G2 of the company TA Instruments, USA is used. Frequency sweeps are performed to determine the storage modulus G', loss modulus G" and the loss factor tan $(\delta)$ at constant room temperature with increasing excitation frequencies between $0,01 \mathrm{~Hz}$ and $10 \mathrm{~Hz}$. For this, a torsion vibration DMA apparatus set up is used. The main goal of this investigation is to show, that through the implementation of a reactive resin within a thermoplastic powder the mechanical properties of the multimaterial specimen can be adjusted selectively and over a broad range. \section*{5 Results and Discussion} \subsection*{5.1 Nozzle-Based Multi-material Deposition} These mass flows through a nozzle are highly dependent on the applied voltage amplitude for the vibration excitation The PP powder pattern created by a vibrating nozzle at room temperature is depicted in Fig. 3 (left). Therefore, a nozzle movement speed of $20 \mathrm{~mm} / \mathrm{s}$ was used which led to a preparation time of about $3 \mathrm{~min}$. The powder pattern was evaluated concerning spatial characteristics (e. g. resolution, line width, layer height, homogeneity) by means of laser scanning microscopy. It has been shown that a minimum line width of about $1.25 \mathrm{~mm}$ with a height of about $0.7 \mathrm{~mm}$ was achieved; however, strong fluctuations for the line width were detected. The latter are mainly caused by uncontrolled and unspecified parasitic vibrations induced by the moving axes. The results show that\\ the application of vibration nozzles for the preparation of powder pattern can be carried out, but is slow and therefore not suitable for large-scale use. \subsection*{5.2 Electrophotographic Powder Pattern Development} If using Discharged-Area-Development for powder pattern generation, the charge image of the photoconductor shall hinder the development of the powder in certain areas. However, if the applied electric field outperforms the repulsion due to the charge image, false development occurs, which means that powder is picked up also by the charged areas of the photoconductors. In order to prevent this, the powder charge, which depends on $\mathrm{U}_{\mathrm{po}}$, and the development voltage $\mathrm{U}_{\mathrm{ph}}$ have to be adjusted. Experiments at a development distance of $1.9 \mathrm{~mm}$ showed that best results with smallest amount of false development are achieved for PP powder at an electric field of about $780 \mathrm{kV} / \mathrm{m}$ and a grid voltage $U_{\text {po }}$ of $2.0 \mathrm{kV}$. These parameters were used to create the powder pattern depicted in Fig. 3 right. The graphical analysis of Fig. 3 right shows that only minor false development occurs, while the powder pattern itself is quite homogenous with a degree of coverage close to $100 \%$. Moreover, the minimal structure details (minimal line thicknesses) are between 0.2 and $0.5 \mathrm{~mm}$ which shows that electrophotography enables much more delicate patterns than vibrating nozzles (see Fig. 3 left).\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-156} Fig. 3. Photographic images of single-layer powder pattern made out of PP powder created by nozzle discharge with vibration excitation ( $300 \mathrm{~Hz}, 30 \mathrm{~V}$ ) (left) and by electrophotographic Discharged-Area-Development deposited onto an $\mathrm{As}_{2} \mathrm{Se}_{3}$ photoconductor (right). \subsection*{5.3 Consolidation of Multi-material Powder Layers Prepared by Vibrating Nozzles} Multi-material samples were successfully sintered via the aforementioned alternate process route and analyzed according to Sect. 4.3. A typical microscopic sectional view of the boundary zone between TPE-U and PP is shown in Fig. 4. It is remarkable that the boundary zone includes a mixed zone which extends over several millimeters. This is caused by the serial powder deposition process using vibrating nozzle, whereas the powder lines are deposited next to each other with a defined overlap. Since the graded boundary zone enables a quite effective mechanical adhesion[23], combining materials, which are known to be incompatible for conventional $2 \mathrm{~K}$ injection molding processes due to the lack of intramolecular diffusion processes, is possible. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-157} \end{center} Fig. 4. Microscopic image of a thin section of a multi-material sample (left: PP; right: TPU) generated by means of vibrating nozzles in combination with the alternate process, which is based on two sources (IR heater and $\mathrm{CO}_{2}$ laser) for energy deposition. \subsection*{5.4 Dynamic Mechanical Properties of Resin Infused Polymer Powder Specimens} To analyze the dynamic mechanical properties oft resin infused polymer powder specimens, two parameters are taken in to account: Storage modulus and the loss modulus. As can be seen in Fig. 5, the storage modulus increases strongly with increasing frequency for all specimens. This is a sign for increasing stiffness of the materials for higher frequencies. Compared to specimens of plain UV-Acrylate with $97 \%$ degree of cure, a significant increase of the storage modulus for UV-Acrylate specimens with $100 \%$ degree of cure is visible. Thus, with increasing curing degree the stiffness rises. TPE-A shows the lowest storage modulus. As expected the increase of the TPE-A content within TPE-A and UV-Acrylate blends lowers the storage modulus drastically.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-157(1)} Fig. 5. Storage and Loss modulus in Pa for different TPE-A to UV-Acrylate ratios under constant room temperature during a DMA frequency sweep The aim of the investigation was to adjust a high variety of dynamic mechanical properties with the combination of the two materials TPE-A and UV-Acrylate, which is proven with these results. The loss modulus shows an atypical decrease for increasing frequencies for $100 \%$ cured UV-Acrylate specimens. This is potentially caused by premature specimen failure. Furthermore, it can be seen on a global scale, that the loss\\ modulus of all other specimens is nearly stable for the depicted frequency range. This is beneficial towards the target of a constant amount of irreversible deformation energy for increasing load frequencies. Furthermore, it can be noticed that UV-Acrylate specimens with $97 \%$ Degree of cure show a stronger increase of the loss modulus compared to TPE-A and UV-Acrylate blends. As before, a general decrease of the loss modulus for increasing TPE-A content is visible, with plain TPE-A as the global minimum. \section*{6 Conclusion} The results of the deposition of single layer test pattern made out of polypropylene using vibrating nozzles as well as electrophotography indicated that both technologies differ tremendously concerning their application potential. The powder deposition by vibrating nozzles showed itself to be relatively slow with a layer preparation time of several minutes and minimal line widths in the $\mathrm{mm}$ range. This makes vibration nozzles particularly useful for the selective functionalization of sintered components, but not for the generation of complex components from multiple materials. In contrast, electrophotography obtains high deposition speeds of a few seconds since whole layers can be prepared at once. In addition, a minimum line width down to ca. $0.2 \mathrm{~mm}$ could be achieved showing electrophotography being predestined for the generation of complex multi-material components with high precision. The microscopic analysis of the boundary zone in a multi-material sample produced by the combination of vibrating nozzles and an adapted LS melting strategy revealed a boundary zone of TPE-U and PP which includes a zone of several millimeters in which both materials are gradually mixed. Since the graded boundary zone enables a quite effective mechanical adhesion, the combination of thermodynamically immiscible materials can be realized. In the future, it is planned to combine electrophotography with a LS melting strategy in order to generate defined graded boundary zones with optimized mechanical properties. The possibility to adjust mechanical properties using multiple materials was demonstrated by a new approach basing on liquid reactive UV-curing thermoset which is implemented into the LS process chamber. After curing of the UV-curing thermoset the powder beside the cured thermoset is molten by the use of the CO2 laser. The measurement results of the storage and loss modulus for resin infused powder specimens lead to the overall conclusion, that the mechanical properties of the multi-material parts can be adjusted selectively and over a broad range. Through increase of the UV-Acrylate content within TPE-A and UV-Acrylate blends, as well as increase of the degree of cure, the storage modulus is drastically raised. However, the final process might not be able to manufacture parts in the depicted range with a fluent transition of the mechanical properties, but instead create variations consisting of two extremes like highly stiff to highly elastic. Furthermore, not all depicted ratios of reactive liquid to powder are realistically applicable for the creation of functional parts. The degree of cure has a more significant influence in terms of adjustability and improvement of the mechanical properties. Acknowledgement. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 61375930 - SFB 814, sub-project B7. \section*{References} \begin{enumerate} \item Kruth, J.P., et al.: Consolidation phenomena in laser and powder-bed based layered manufacturing. CIRP Ann. 56(2), 730-759 (2007) \item Anstaett, C., Seidel, C.: Multi-Material Processing. Laser Tech. J. 13(4), 28-31 (2016) \item Mirotznik, M.S., et al.: Multi-material additive manufacturing of antennas. In: 2016 International Workshop on Antenna Technology (iWAT) (2016) \item Gebhardt, A.: Generative Fertigungsverfahren 2016: Carl Hanser Verlag, München (2016) \item Ravve, A.: Light-Associated Reactions of Synthetic Polymers. Springer, Heidelberg (2006) \item Kaiser, W., Kunststoffchemie für Ingenieure. Carl Hanser Verlag München (2016) \item Sugavaneswaran, M., Arumaikkannu, G.: Modelling for randomly oriented multi material additive manufacturing component and its fabrication. Mat. Des. (1980-2015) 54, 779-785 (2014) \item Tibbits, S.: 4D printing: multi-material shape change. Archit. Des. 84(1), 116-121 (2014) \item Choi, J.-W., Kim, H.-C., Wicker, R.: Multi-material stereolithography. J. Mater. Process. Technol. 211(3), 318-328 (2011) \item Kumar, A., Dutta, A.: Investigation of an electro-photography based rapid prototyping technology. Rapid Prot. J. 9, 95-103 (2003) \item Rojas Arciniegas, A., Esterman, M.: Characterization and modeling of surface defects in EP3D printing. Rapid Prot. J. 21, 402-411 (2015) \item Stichel, T., et al.: Powder layer preparation using vibration-controlled capillary steel nozzles for additive manufacturing. Phys. Procedia 56, 157-166 (2014) \item Stichel, T., et al.: Mass flow characterization of selective deposition of polymer powders with vibrating nozzles for laser beam melting of multi-material components. Phys. Procedia 83, 947-953 (2016) \item Stichel, T., et al.: Multi-material deposition of polymer powders with vibrating nozzles for a new approach of laser sintering. J. Laser Micro Nanoeng. 13, 55-62 (2018) \item Stichel, T., et al.: Electrophotographic multi-material powder deposition for additive manufacturing. J. Laser Appl. 30(3), 032306 (2018) \item Kruth, J.-P., et al., Consolidation of polymer powders by selective laser sintering. In: Proceedings of the 3rd International Conference on Polymers and Moulds Innovations, pp. 15-30 (2008) \item Laumer, T., et al.: Simultaneous laser beam melting of multimaterial polymer parts. J. Laser App1. 27(S2), S29204 (2015) \item Schuffenhauer, T., et al.: Process route adaption to generate multi-layered compounds using vibration-controlled powder nozzles in selective laser melting of polymers (2019) \item Wudy, K., Budde, T.: Reaction kinetics and curing behavior of epoxies for use in a combined selective laser beam melting process of polymers. J. Appl. Polym. Sci. 136(7), 46850 (2019) \item Stichel, T., et al.: Polymer Powder Deposition using Vibrating Capillary Nozzles for Additive Manufacturing (2014) \item Stingl, M.H.D.: On a combined geometry and multimaterial optimization approach for the design of frame structures in the context of additive manufacturing. In: 7th International Conference on Additive Technologies - iCAT 2018, pp. 112-119 (2018) \item Wudy, K., Drummer, D.: Infiltration behavior of thermosets for use in a combined selective laser sintering process of polymers. JOM 71(3), 920-927 (2019) \item Laumer, T., et al.: Realization of multi-material polymer parts by simultaneous laser beam melting. J. Laser Micro Nanoeng. (2015) \end{enumerate} \section*{Extreme High-Speed Laser Material Deposition (EHLA) as High-Potential Coating Method for Tribological Contacts in Hydraulic Applications } \begin{abstract} Additive manufacturing enables the use of a variety of material compositions, especially for near-surface layers and coatings, which allows the optimization of tribological systems regarding their properties like chemical resistance. Nevertheless, it is also cost saving for various hydraulic components. By using the innovative Extreme High-Speed Laser Material Deposition (EHLA) process, a large number of different material combinations can be produced on almost any rotationally symmetrical components. In a previous publication, the authors investigated different process techniques in terms of their tribological properties and used a commonly used stainless 316L material "as printed". Since stainless steel generally has very critical tribological properties, measurements were performed with relatively low loads and velocities. In these tests, EHLA-coated surfaces achieved convincing results. Based on these findings, further measurements with more realistic loads and specialized tribological investigations were performed. Therefore, this paper examines the frictional behavior of 316L surfaces produced by laser-based EHLA treatment against different tribological pairings such as standard quenched steel as well as brass. Allowing a broad comparability, all surfaces have been post processed by lapping as most of the planar parts of hydraulic components are lapped. \end{abstract} Keywords: Tribology $\cdot$ Additive manufacturing $\cdot$ Hydraulic components \section*{1 Introduction} \subsection*{1.1 Motivation} Hydraulic applications are widely used in construction equipment, airplanes and even cars. While being used in construction equipment such as excavators and cranes, a long service life is needed. The hydraulic system needs to work for thousands of hours operating without replacing single components. Aircraft systems must of course also work reliable for many years. Passenger cars need to be designed cost efficiently and\\ environmentally friendly as they are produced in high quantity. These two points are the reason why research is being conducted on new materials for hydraulic components. In hydraulic applications, a wide variety of different materials is used. Three categories can be identified: Nitriding steel, cast iron and brass. Brass is often used as counter face of the steel or cast iron surface [13]. Due to varying pressures and rotational speed levels, all states of friction can occur within tribological contacts in hydraulic units [2, 12]. Starting with boundary lubrication in the very first moment after the speed-up, and following by a phase of mixed lubrication, about $95 \%$ hydrodynamic lubrication is strived for in the steady state of operation as it promises low friction and wear. A highpressure oil supply often allows for the use of hydrostatic bearings or pockets. However, the use of lead-free materials leads to new challenges in choosing materials. According to Czichos and van Bebber, planar contact pressures can be between $1 \cdot 10^{-3}$ and $4 \cdot 10^{3} \mathrm{MPa}$ $[2,3]$. Typically, hydraulic systems consist of various tribological contacts. These can be divided into two categories: Those with movement in longitudinal direction, like pistons, and those with rotational movement, like thrust bearings. In this work, the focus is the rotational movement. As it is very complicated to investigate in components themselves, a model test bench is used for the first measurements (see Sect. 2.4). The model test bench allows to perform comparative measurements akin to those in real hydraulic components. Especially the tribological contact cylinder block - valve plate - one of the most complicated contact in hydraulics. The contact serves as hydrostatic bearing as well as hydraulic valve and can be abstracted very well [14]. Therefore, both the geometric dimensions and the choice of materials were kept close to those of real components. The basis material used in this paper is a standard quenched and tempered steel, $42 \mathrm{CrMoV} 4$ (1.7225). The same material has been used as base for the EHLA coating, as well as reference hard-hard counterpart. Aeterna 3038, which can be considered a standard leaded brass material, was used to represent a hard-soft tribological pairing typical for hydraulics [14]. All discs have been lathe-turned and lapped. Table 2 shows the geometric parameters of the Tribo test discs. A highly productive and innovative process is available with the EHLA process, with which the surfaces can be coated individually adapted to the areas of application. Compared to thermal spraying and galvanic coating processes, EHLA produces metallurgically bonded and dense coatings. Due to the characteristics of the process, unconventional material combinations can be created and almost any coating material can be used. However, because the main energy input is into the powder materials, the process is also suitable for coating heat-sensitive substrates, such as hardened materials, aluminum and grey cast iron. In initial accompanying tests, the generated coatings have shown promising results. \subsection*{1.2 Objective} Hydraulic power components are an important field in drive technology, as they provide high forces and easy longitudinal movement. Mainly those systems use combustion engines as they do often work in remote areas. To increase the power density, hydraulic pumps have to operate at higher rotational speed, which also increases the efficiency of the diesel engine. This is a challenge for the design of the tribological joints. Almost\\ all traditional tribology pairings consist of either expensive special threatened steel, with a hardening step or containing environmentally critical lead. This work studies the possibility of replacing costly or hazardous materials by very basic steel materials equipped with a very thin but tribological active coating. It is expected, that the coated parts behave in the same way, as the coated material itself would do. There should not be any influence by the base material and no peel of the coating. Three possible outcomes are expected: Lower material use having a positive impact on the production costs, a renunciation of lead-containing materials, having a positive impact on the environment and an improved power density due to higher rotational speeds. \section*{2 Materials and Methods} \subsection*{2.1 Extreme High-Speed Material Deposition (EHLA)} Extreme High-Speed Laser Material Deposition (EHLA) is a process based on the in-situ supply of powders via a nozzle and the melting of the powder particles in flight before impinging on a substrate, forming a metallurgical bond with the substrate. In contrast to conventional LMD, the powder focus is usually set above the substrate which leads to a higher interaction time of the powder particles and the laser radiation. Simulations show that this increases the absorption of the laser beam by the powder particles [6]. Due to high superficial velocities of $500 \mathrm{~m} / \mathrm{min}$, the process is limited to depositions on rotationally symmetric parts (e.g. tubes and discs) and is often used to apply protective coatings. Since most of the laser power is absorbed by the powder in flight; the dilution \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-162} \end{center} Fig. 1. Sketch of Extreme High Speed Laser Material Deposition (EHLA) including all relevant process parameters\\ of coating and base material is low which enables a wide range of applicable material combinations [7, 8]. Typical layer thicknesses are in the range of 20 to $350 \mu \mathrm{m}$. Figure 1 is a sketch of the EHLA process and its most important parameters concerning Energy input into powder particles and substrate. The powder focus is positioned above the substrate, so that the intermediation time of the particle through the laser beam suffice to melt the particles. The most important parameters that influence the energy input into the particles are the particle velocity $v_{\text {particle }}$ and the powder mass flow $\dot{m}_{p}$ in the powder gas stream. The energy input into the substrate is mostly influenced by process speed $v_{p}$ and track displacement $f$ which is the lateral distance between one coating pass and the following. With increasing $\mathrm{v}_{\mathrm{p}}$, the interaction time between the laser beam and the substrate decreases, reducing energy input into the substrate. This leads to a reduction of melt pool size and the size of the heat affected zone. For the process development and the coating of the Tribo discs, a 4-axis machining system (Fig. 2) from Hornet with the laser source TruDisc 8001 is used. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-163} \end{center} Fig. 2. Schematic picture of the EHLA setup \subsection*{2.2 Coating Material} The material 316L has been used for the coating of the Tribo test disks. Figure 3 shows the powder analysis of the used 316L from Oerlikon. The particles are spherical and dense (see Fig. 3 a),b)). The light blue area in the particle size distribution measurement marks the manufacturer's specifications of $-53+20 \mu \mathrm{m}$ [9]. The blue line in the diagram describes the measured particle size distribution. All points on this line together add up to $100 \%$. The largest percentage of particles is in the range of approx. 30 to $45 \mu \mathrm{m}$ and thus in the range specified by the manufacturer. The chemical composition is given in Table 1. Table 1. Chemical composition 316L (Oerlikon, Diamalloy 1003-1) [18] \begin{center} \begin{tabular}{l|l|l|l|l|l} \hline $\mathrm{Fe}$ & $\mathrm{Cr}$ & $\mathrm{Ni}$ & $\mathrm{Mo}$ & $\mathrm{Si}$ & $\mathrm{C}$ \\ \hline Balanced & 17 wt.\% & 12 wt.\% & 2.5 wt.\% & 2.3 wt.\% & \begin{tabular}{l} 0.03 \\ wt.\% \\ \end{tabular} \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-164} \end{center} Fig. 3. a) REM picture of 316L paricles (Oerlikon, Diamalloy 1003-1) with the magnification of $400 \mathrm{x}, \mathrm{b})$ Incident light microscope image of 316L paricle cross sections with a magnification of 200x, c) Measured particle size distribution of used 316L powder \subsection*{2.3 Surface Finish} Contrary to the first investigations, in which the coated Tribo test discs were examined in their original state "as printed" [4], real surface treatments as usually applied in hydraulics have been examined here. In hydraulics, the geometry is typically created first by turning to an approximate shape. Then, depending on the material, the gas nitriding process takes place. Finally, the parts are getting lapped or honed. Lapping is a mainly room-bound process with geometrically undefined cutting edges. It is a production and finishing process, defined as chipping with loose grains distributed in a lapping paste which are usually guided with a shape-transferring counterpart (lapping tool) featuring ideally undirected cutting paths of the individual grains. Surfaces to be lapped are normally flat. If the work pieces have different geometric shapes, correspondingly modified method variations must be applied, in part manually and with auxiliary tools [5]. Control plates from axial piston machines, which are to be abstracted here with the Tribo test disks, can be either flat (flat control plates) or spherical (spherical control plates) [15]. One of the most interesting benefits of lapped surfaces are the undirected processing traces, which means that a pressure gradient can form without dependence on the spatial directions. Fewer connected oil pockets compared to the surface formed by the turning process. Connected grooves lead to high contact pressure peaks at the surface mountains, resulting in severe adhesive wear. The lapping process can be compared to the later lubrication situation in the tribological contact especially in the area of fluid lubrication. Lapping took place on a FLP 900 lapping machine, with a disc diameter of $900 \mathrm{~mm}$ by FLP Microprecision $\mathrm{GmbH}$, using a $\mathrm{SiC400}$ lapping paste with a grain size of 12 to 15 $\mu \mathrm{m}$. \subsection*{2.4 Tribological Approach and Parameters} A wide range of tribological contacts in hydraulic systems can be abstracted as planar contacts. These are often investigated using a disc - disc tribometer. Ifas conducts its\\ measurements with a device consisting of (see [1]) by turning two discs at a speed up to $15 \mathrm{~m} / \mathrm{s}$ and contact pressure up to $40 \mathrm{MPa}$. \section*{Test Bench} The disc - disc tribometer consists of a stator and a rotor, which are pressed together using a hydraulic cylinder. For geometrical details see Table 2. A normal force sensor constantly regulates the applied normal force. The rotor is driven by a hydraulic motor and transmits its torque to the stator, which is connected to a force sensor using a lever. The schematic drawing is shown in Fig. 4. Both discs are completely covered with a specific hydraulic fluid, which is temperature closed loop controlled. In this examinations a BECHEM Hydrostar HEP 46 EEL biodegradable high-performance hydraulic fluid has been used. Over the different tests, the fluid temperature in the basin was kept at $40^{\circ} \mathrm{C}$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-165} \end{center} Fig. 4. Cross section of the disc - disc tribometer with rotor and stator (right) [1] Based on frictional force $F_{R}$ and normal force $F_{N}$, a dimensionless friction coefficient $\mu$ is calculated: \begin{equation*} \mu=\frac{F_{R}}{F_{N}} \tag{1} \end{equation*} The $x$-axis, which shows the rotational speed in a Stribeck diagram, is also corrected for the influence of temperature, as the border between mixed lubrication and hydrodynamic lubrication depend mainly on the viscosity $\eta$, the pressure $p$ and the angular frequency $\omega$. Therefore, the Gümbel-Hersey number $\mathrm{u}$ is used. \begin{equation*} u=\frac{\eta \omega}{\bar{p}} \tag{2} \end{equation*} As - due to the measuring principle - heating always occurs in tribological contact, the influence of temperature must be corrected. This can be done by using the Arrhenius or Andrade Modell [10], approximating the actual viscosity $\eta$ by a known base viscosity $\eta_{0}$, the activation energy $E_{A}$, the gas constant $R$ and the temperature $T$. \begin{equation*} \eta=\eta_{0} \cdot \exp \left(\frac{E_{A}}{R \cdot T}\right) \tag{3} \end{equation*} This procedure makes it possible to record Stribeck curves, whereby the parameters temperature, speed and surface pressure must only be recorded accurately, but not precisely controlled, as the Gümbel-Hersey number is calculated by the measurement results of the parameters. The geometric properties of the test discs are shown in Table 2. Table 2. Geometric parameters of the Tribo test discs \begin{center} \begin{tabular}{l|l} \hline Geometric Parameter & Value \\ \hline Contact area $A_{c}$ & $946 \mathrm{~mm}^{2}$ \\ \hline Outer diameter $d_{a}$ & $70 \mathrm{~mm}$ \\ \hline Inner diameter $d_{i}$ & $59 \mathrm{~mm}$ \\ \hline Roughness $R_{z}$ & $0.4 \mu \mathrm{m}$ \\ \hline \end{tabular} \end{center} \section*{Stribeck Curves} Stribeck curves are a basic but powerful type of diagram to examine all stages of friction of lubricated tribological contacts. The examination consists of an almost load free speed up of the contact. Then, when thermal equilibrium is reached, the load is applied. Because of the high speed, fluid lubrication is usually accessed. Then the speed is reduced by a slow ramp. The tribological contact passes all stated of friction until it reaches boundary lubrication. As shown in Fig. 5, the coefficient of friction is plotted on the y-axis, while the Gümbel-Hersey number is shown on the $x$-axis. In the hydraulic application, the contact should mostly run with about $5 \%$ of solid state friction. This operation point usually meets the lowest frictional forces and leads to high efficiencies. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-167} \end{center} Fig. 5. Lubrication states shown in Stribeck curve \section*{3 Results} In the following chapter the results of two different material parings, EHLA coated 316L against 42CrMoV4 and EHLA coated 316L against an Aeterna 3038 will be shown. Due to the heavy adhesive wear of the $42 \mathrm{CrMoV} 4$, it was not possible to show a complete Stribeck curve. The coefficient of friction exceed 0.5 , what produced to much heat to be lead away. \subsection*{3.1 Coating Process} Through parameter variation during process development, a dense metallurgical bonded coating could be achieved (Fig. 7a)). Therefore, the parameters laser power $\mathrm{P}_{\mathrm{L}}$, process speed $v_{P}$, track displacement $f$, carrier gas flow $\dot{V}_{C G}$ and powder mass flow $\dot{m}_{p}$ have been varied. For the used coating the following parameters could be developed (Table $3)$. Figure 6 depicts the measurement results of the hardness measurement of the coating. On the left hand side in the diagram are the measurement results of the substrate material with an average value of $327 \mathrm{HV} 0.3$, and on the right are the results of the 316L coating with an average value of $200 \mathrm{HV} 0.3$. The measured hardness of the coating is within the range of lead-containing brass materials, typically used for hydraulic contacts. Therefore it is expected, that against the steel (hard-hard paring) the coating is soft enough and will behave like the brass material would do. We are expecting the wear to take place on the coating and not on the counterpart. The run against the brass material with the Table 3. Coating parameters \begin{center} \begin{tabular}{l|l} \hline Laser power $\left(\mathrm{P}_{1}\right)$ & $2400 \mathrm{~W}$ \\ \hline Process speed $\left(\mathrm{v}_{\mathrm{P}}\right)$ & $50 \mathrm{~m} / \mathrm{min}$ \\ \hline Track displacement $(\mathrm{f})$ & $0.25 \mathrm{~mm} / \mathrm{rot}$ \\ \hline Carrier gas flow $\left(\dot{\mathrm{V}}_{\mathrm{CG}}\right)$ & $61 / \mathrm{min}$ \\ \hline Powder Mass Flow $\left(\dot{\mathrm{m}}_{\mathrm{p}}\right)$ & $17.5 \mathrm{~g} / \mathrm{min}$ \\ \hline \end{tabular} \end{center} same hardness is more unclear. As both materials have different bases and the crystal structure is not the same, very few wear is expected. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-168} \end{center} Fig. 6. Result of the hardness measurement (hardness Vickers HV0.3) The deposited coating has been lapped and examined to determine its tribological properties. As a result of the test, the tribological active surface has been characterized by metallographic analysis (Fig. 7 b)). The cross section of the tested coating shows no cracks or other coating deviations. The contact surface has no erosion, scoring or other indications of uneven wear. The cross sections of the disc after the Stribeck curve were etched for $2 \mathrm{~min}$ at $60{ }^{\circ} \mathrm{C}$ with V2A etching solution (distilled water, hydrochloric acid and nitric acid) for microstructure analysis (Fig. 8). Furthermore, the small mixing zone can be seen by the clear bonding zone between substrate and coating. Through the etching, the individual layers and the melt bath geometry can be identified. However, the microstructure exhibits dendritic solidification. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-169} \end{center} Fig. 7. Cross sections of tribological discs: a) Cross section after EHLA coating with 50x magnification, b) Cross section after tribological test coating with 50x magnification \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-169(1)} \end{center} Fig. 8. Etched cross sections of tribological discs: a) Etched cross section after tribological test coating with 50x magnification, b) Etched cross section of the coating with $100 x$ magnification, c) Etched cross section of the bonding zone with 100x magnification \subsection*{3.2 Wear} Testing the EHLA coated disc against the reference disc (steel) shows the known mechanism of fretting, as shown in the previous publication [4]. Contrary to the former results, the wear for this pairing is very low. This can be explained with the lapped surface which allows the load to be much better distributed over the contact area. The wear profile is shown in Fig. 9. Geometrically the counterpart is in contact at about $2.5 \mathrm{~mm}$ of the measured length. Running the EHLA coated disc against the Aeterna 3038, shows a significant difference. The EHLA coated disc shows almost no visible wear and there is no distinct edge of wear. Instead, there is a smooth transition. The wear profile is shown in Fig. 10. Geometrically the counterpart is in contact at about $2.5 \mathrm{~mm}$ of the measure length. The wear track can be seen by the bare eye on both sides of the tribological pairing (Fig. 11). As there is a clear dark track, it can be assumed that the frictional energy was high enough to activate the extreme pressure additives in the hydraulic fluid [11]. \section*{EHLA after Stribeck Test against Reference} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-170} \end{center} Fig. 9. Wear profile of the EHLA coated disc after Stribeck test against reference EHLA after Stribeck Test against Aeterna 3038 \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-170(1)} \end{center} Fig. 10. Wear profile of EHLA after Stribeck test against Aeterna 3038 \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-170(2)} \end{center} Fig. 11. Optical analysis of the two Tribo test discs Calculating with the archived wear rates and the knowledge, that tribological active additives have been activated, there is no doubt that this pairing would have endured a much longer test time. Figure 12 compares the two EHLA coated discs. a) shows the severe wear of the EHLA coated disc against the $42 \mathrm{CrMoV} 4$ reference, adhesive wear is clearly visible. b) shows the color change which took place as the EP additives have been activated. On both disc the lapped surface remains on parts of the discs to provide a reference surface for determining wear.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-171} Fig. 12. Wear tracks of the Tribo test discs, a) EHLA against Reference, b) EHLA against Aeterna 3830 The EHLA coated surface against the Reference showed severe wear, which leads to a failure in very short time, whereas the Aeterna 3830 as counterpart showed mild wear. The authors assume that no state of equilibrium can be achieved with such heavy wear and that the wear progresses at the same rate. Furthermore, it was observed in the second pairing that the roughness peaks have leveled out. This process is typical for a successful run-in process, whereby both contact partners adapt to each other and a new surface roughness is formed. \subsection*{3.3 Stribeck Curves} Several Stribeck curves of the EHLA coated disc against the (leaded) Aeterna 3830, with a normal pressure of $4 \mathrm{MPa}$ have been recorded. The maximum average sliding speed was $6 \mathrm{~m} / \mathrm{s}$. The lowest coefficient of friction is 0.012 , in boundary lubrication; a coefficient of friction of 0.062 has been measured. However, these values are within the normal range of lubricated contacts [16]. The transition from fluid lubrication to mixed lubrication took place a Gümbel-Hersey number of around 10, the transition from mixed lubrication to boundary lubrication took place at a Gümbel-Hersey number of 0.5. A representative Stribeck curve for the tests performed is shown in Fig. 13. Due to the heavy adhesive wear, it was not possible to measure a Stribeck curve of the EHLA coated disc against the Reference disc. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-172} \end{center} Fig. 13. Stribeck curve of EHLA against Aeterna 3038 \section*{4 Discussion} The austenitic steel $316 \mathrm{~L}$ is corrosion as well as acid resistant and can therefore also be used with highly corrosive lubricants. The coatings generated by using EHLA are dense and do not show any coating defects even after tribological testing. Therefore, this material is suitable for use in tribological contacts with corrosive lubricants and/or in a corrosive environment [18]. Furthermore, no remaining defects or changes in the microstructure could be detected by etching to reveal microdefects and the microstructure. This demonstrates the high temperature resistance of the material as well as the fact that no critically high temperatures occurred in the test [18]. However, further metallographic investigations, such as EDX, are necessary to provide a conclusive analysis of the microstructure. Against the reference part of $42 \mathrm{CrMoV} 4$, the coating shows a wear of approx. $110 \mu \mathrm{m}$ after the test according to the wear curve in Fig. 9. However, after the metallographic cross sections, a coating with a thickness of averaged approx. $1275 \mu \mathrm{m}$ was generated, of which approx. $1090 \mu \mathrm{m}$ residual layer thickness is still present after post processing and tribological examination. As this only corresponds to a reduction of the layer thickness of approx. $185 \mu \mathrm{m}$, the initial layer thickness can be significantly reduced to less than $500 \mu \mathrm{m}$. In addition, 316L is a comparably soft material with a hardness of approx. $200 \mathrm{HV}$, so that wear and thus the layer thickness can be further reduced by using an anti-wear coating, such as a hard metal alloy or a Metal Matrix Composite (MMC). For example, MMCs have shown almost no wear in the field of brake rotors in load tests for the automotive sector (DYNO) [17]. The result showed a behavior, as expected of the coating material. The steel - EHLA approved once again, that steel on steel contacts need to be further improved as they suffer from irreconcilable as well as friction coefficients higher than $0.1[2,4,16]$. When used against the brass material, the EHLA coated disc showed a behavior, which seems to be similar to the typically used quenched or nitrated steels $[1,2,13]$. There was no grooving nor annealing colors visible, which is another indication for a steady contact. The coating did not peel off in any circumstances at the test bench. Even in severe wear conditions, where adhesive wear destroyed the surface of the coating to a depth of more than $0.1 \mathrm{~mm}$. This behavior has been observed earlier by the authors [4]. \section*{5 Conclusion and Outlook} Compared to the "as printed" surfaces measured earlier [4], lapped surfaces showed significantly less wear and lower coefficients of friction. The material used is too soft to be used in hard-hard contacts, but it is very corrosion and high temperature resistant and can therefore be used in highly corrosive environments and in areas such as the food or chemical industry. In summary, the following results were achieved. \begin{itemize} \item Through EHLA a dense metallurgically bonded coating with a thickness of approx. $1275 \mu \mathrm{m}$ of the material 316L could be produced. After post-processing and testing, the coating has a residual layer thickness of approx. $1090 \mu \mathrm{m}$. The binding between substrate and coating was well enough to maintain the link of the layer eve in heavy mixed lubrication and with almost purely adhesive wear. The subsequent metallographic analysis did not present any layer defects after the load in the tribological test. \item The highest wear occurred in the test against the reference demonstrator made of the material $42 \mathrm{CrMoV} 4$ with approx. $110 \mu \mathrm{m}$. In the test against brass there was almost no wear \item To improve the friction coefficient, which would definitely lower the wear, measurements with different materials need to be done. It has been shown, that EHLA coatings used in hard-soft parings reach good friction coefficients. \end{itemize} EHLA coated surfaces are a promising way of binding together several material properties. Over all tribology tests, even in fully adhesive wear, no signs of a peel-off of the welded layer showed. Especially the use against brass material, which can be seen as state of the art of tribological pairings in hydraulic applications showed very good results. On a tribological point of view, 316L stainless steel coatings produced by EHLA can be recommended when using as hard - soft pairing against a leaded brass material. This enables EHLA coatings to be applied on base steel layers, where it can replace the more expensive nitrated or quenched steel, which can make the production of large components in particular more cost-effective. The approach of using EHLA coated stainless steel as hard counterpart against reference steel, could not fully satisfy. For the future, other materials need to be tested, promising better tribological properties. The next step will be to improve the tribological properties by using more resistive materials as it could be done by filling in a certain amount of carbides. This would increase the strength against wear, allowing to increase the lifetime of the surface. \section*{References} \begin{enumerate} \item Otto, N.: Experimental analysis of sustainable ester- and water-based hydraulic fluids. Ph.D. thesis, RWTH Aachen University, Germany (2018) \item Czichos, H., Habig, K-H. (Hg.): Tribologie-Handbuch. Tribometrie, Tribomaterialien, Tribotechnik. 4. vollst. überarb. und erw. Aufl. Wiesbaden: Springer Vieweg, Germany (2015) \item Van Bebber, D.: PVD-Schichten in Verdr"angereinheiten zur Verschleiß- und Reibungsminimierung bei Betrieb mit synthetischen Estern. Ph.D. thesis, RWTH Aachen University, Germany (2003) \item Holzer, A., et al.: Tribological investigations on additively manufactured surfaces using Extreme High-Speed Laser Material Deposition (EHLA) and Laser Powder Bed Fusion (LPBF)". In: 12th International Fluid Power Conference, Dresden, March 9-11, Dresden, Germany (2020) \item Klocke, F., Kuchie, A.: Lapping and polishing. In: Manufacturing Processes 2. RWTHedition. Springer, Heidelberg (2009) \item Pirch, N., Linnenbrink, S., Gasser, A., Wissenbach, K., Poprawe, R.: Analysis of Track Formation During Laser Metal Deposition. Fraunhofer ILT, RWTH-Aachen Lehrstuhl für Lasertechnik (LLT) (2017) \item Schopphoven, T., Gasser, A., Backes, G.: EHLA: extreme high-speed laser material deposition. LTJ 14(4), S. 26-29 (2017). \href{https://doi.org/10.1002/latj.201700020}{https://doi.org/10.1002/latj.201700020} \item Schopphoven, T., Gasser, A., Wissenbach, K., Poprawe, R.: Investigations on ultra-high-speed laser material deposition as alternative for hard chrome plating and thermal spraying". In: Journal of Laser Applications 28 (2), S. 22501 (2016). \href{https://doi.org/10.2351/1.4943910}{https://doi.org/10.2351/1.4943910} \item Oerlikon metco: Material Product Data Sheet, Austenitic Stainless Steel Powder for Thermal Spray. Oerlikon metco (2017) \item Zerbe, C., et al.: Schmierstoffe2. In: Zerbe, C. (ed.) Mineralöle und verwandte Produkte. Springer, Heidelberg (1952) \item Burghardt, G., Wächter, F., Jacobs, G., Hentschke, C.: Influence of run-in procedures and thermal surface treatment on the anti-wear performance of additive-free lubricant oils in rolling bearings. Wear 328-329, S. 309-317 (2015). \href{https://doi.org/10.1016/j.wear.2015.02.008}{https://doi.org/10.1016/j.wear.2015.02.008} \item N.N. DIN 50281: Friction in bearings; definitions; types; conditions; physical quantities. Withdrawn, Beuth Verlag (1977) \item Paulus, A.: Reaktionsschichtbildung auf bleifreien Bronze- und Messingwerkstoffen im Kontakt von Zylinder und Steuerscheibe einer Axialkolbenpumpe. Ph.D. thesis, RWTH Aachen University, Germany (2017) \item Oberem, R.: Untersuchung der Tribosysteme von Axialkolben-Schrägscheibenmaschinen der HFA- Hydraulik. Ph.D. thesis, RWTH Aachen University, Germany (2002) \item Murrenhoff, H.: Fundamentals of Fluid Power Part 1: Hydraulics. Shaker Verlag, Aachen (2018) \item Blau, P.J. Friction science and technology. From concepts to applications, 2nd edn. CRC Press/Taylor \& Francis, Boca Raton (2009) \item Rettig, M., Grochowicz, J., Käsgen, K., Eaton, R., Wank, A., Hitzek, A., Schmengler, C., Koß, S., Voshage, M., Schleifenbaum, J.H., Verpoort, C., Weber, T.: Carbidic Brake Rotor Surface Coating Applied by High-Performance Laser-Cladding (2020) \item Oerlikon: Material Product Data Sheet - Type 316L Austenitic Stainless Steel Powders (2020) \end{enumerate} \section*{In-Situ Alloying in Gas Metal Arc Welding for Wire and Arc Additive Manufacturing } \begin{abstract} The use of low transformation temperature (LTT) alloys seems to be a promising way for reducing the residual stress level of fusion welded components. Wire and arc additive manufacturing (WAAM) is a high performance additive manufacturing process for generating large metallic components, which is based on common arc welding processes. The following article describes the investigations regarding generating LTT alloys in WAAM through in-situ alloying. Therefor a multi wire gas metal arc process in spray transfer mode is being used to generate the target LTT alloy. By using two high alloyed cold wires, it was possible to reach a chemical composition for LTT alloys, proposed by Steven and Haynes. The process showed stable behavior and it was possible to build up test specimen in form of wall shaped structures of $15 \mathrm{~mm}$ height. By establishing insitu alloying for the additive manufacturing of LTTs a new field of investigations regarding the structural behavior of LTT-injected components is being opened. \end{abstract} Keywords: Low Transformation Temperature (LTT) alloys $\cdot$ Wire and Arc Additive Manufacturing $\cdot$ Multi wire gas metal arc welding $\cdot$ In-situ alloying \section*{1 Introduction} Wire and arc additive manufacturing (WAAM) is a promising technology for the additive fabrication of large scaled metallic components and is of high interest of current research activities. In WAAM, arc welding processes are being used in the way of classical shape welding to build up components layer wise [1,2]. The most common processes that are being used for WAAM are gas metal arc welding and the cold/hot wire assisted plasma process. In both cases, an electric arc is being used as heat source to melt the filler wire. High deposition rates of over $5 \mathrm{~kg} / \mathrm{h}$, the wide spectrum of usable materials and the low limitations regarding the build volume make WAAM a key technology for large scale additive manufacturing. Two current fields of applications for WAAM processes are the aerospace industry, to reduce the amount of subtractive machining for expensive materials [3], as well as the manufacturing of spare parts with reduced delivery time for the maritime sector [4]. As a result of the high deposition rates, WAAM processes are characterized by a high heat input and therefore the manufactured components are prone to thermal distortion,\\ the formation of residual stress and a lower geometric accuracy. The underestimation of residual stress fields can lead to fatal component failure during component finishing [5]. This is, why besides of the precise knowledge of the residual stresses in the components, compensation strategies are of high interest for a safe industrial application of WAAM. Especially in welding applications, the use of Low Transformation Temperature (LTT) alloys has been a promising strategy for reducing the thermal deformation and keeping the amount of residuals stress low at the same time. The key concept of LTT alloys is to achieve a martensitic phase transformation, and therefore an expansion of volume, at reduced temperatures. As the transformation temperature is reduced, the volume increase cannot be compensated by plastic deformation, which leads to the formation of compressive stress. This compressive stress is being utilized to compensate the thermally induced tensile stress. Two important key parameters for estimating the LTT effect are the matensite start temperature $\left(M_{s}\right)$, as well as the martensite finish temperature $\left(M_{f}\right)$. To gain a maximum of stress compensation, the martensite start temperature should be as low as possible, while the martensite finish temperature needs to be over room temperature to enable full martensitic phase transformation. Different formulae exist for estimating the martensite start temperature, based on the amount of alloying elements in mass percent. Regarding LTT effect, the formula of Steven and Haynes is supposed to be most suitable, formula 1 [6]. \begin{equation*} M s\left({ }^{\circ} \mathrm{C}\right)=561-474 * \mathrm{C}-33 * \mathrm{Mn}-17 * \mathrm{Ni}-17 * \mathrm{Cr}-21 * \mathrm{Mo} \tag{1} \end{equation*} Regarding the current state of the art, a chemical composition of $10 \%$ Chromium and $8-12 \%$ Nickel, leading to a $\mathrm{M}_{\mathrm{s}}$-temperature near $200{ }^{\circ} \mathrm{C}$, is supposed to be most suitable for achieving a stress compensating LTT effect. Different research groups have been working on using LTT materials for residual stress reduction in weld seams [7-10]. Kannegiesser et al. characterized different LTT alloys regarding their transformation behaviour using high energy synchrotron diffraction as well as cold crack affinity by performing Tekken tests [8]. The experiments show, that the martensitic transformation is highly dependent on Chromium and Nickel content. Experiments on pure weld metal samples show, that also the dilution coming from the base material needs to be considered. Furthermore a certain amount of retained austenite prevents cold cracks. Additionally it is stated, that the cooling rate is of minor importance for the transformation behaviour, as the $\mathrm{M}_{\mathrm{s}}$-temperature is mainly dependant on the chemical composition. This makes the use of LTT interesting for WAAM, as the interlayer temperatures and cooing rates normally are higher compared to fusion welding. Reisgen et al. were investigating the effect of LTT wire inlays on the residual stress formation in laser beam welding [9]. Here the final alloy was generated in-situ by melting up the wire inlay and mixing it with the base material. The results show, that a reduction of thermally induced deformation of the base plate can be achieved by this approach. Other experimental work dealt with using a plasma-multi-wire process with alternating wire feed speeds to generate chemically graded fusion welds [11]. This in-situ alloying approach shows that it is possible to locally vary the chemical composition and at the same time establish a stable fusion welding process. Mochizuki et al. implemented a simulation model to estimate the LTT effect for GMA welding of a $10 \%$ Cr $10 \%$ Ni LTT filler wire. Here fillet welds were performed,\\ using a GMA process. The simulation results were referenced to physical experiments by comparing the calculated and measured strain rates of the welded component [12]. Kromm et al. investigated the LTT effect in multi layer welding [13]. As the stress compensation effects are reduced by the heat treatment of following welding layers, the investigations focussed on the transformation behaviour in dependence on the inter layer temperature. It was shown, that the stress compensation LTT effect can be used effectively as long, as the inter layer temperature is kept above the martensite start temperature $\mathrm{M}_{\mathrm{s}}$. For the fabrication of LTTs in WAAM, initial investigations have been performed by Houichi et al.. Here LTT filler wire was processed, using a GMA welding process to generate wall shaped structures. The results show, that a reduction of the longitudinal thermal distortion is possible [14]. However, the effect on the angular distortion was low, compared to the longitudinal distortion. The effect of the inter layer temperature was not kept into account. In summary it was shown, that a reduction of residual stress can be achieved by the use of LTT alloys. For wire and arc additive manufacturing though, a couple of constrains need to be considered. Especially for the manufacturing of large scaled components the use of high alloyed filler materials should be limited to cut production cost. At the same time, there is a strong need for residual stress control to minimize unexpected component failure. This is why local LTT infusion through in-situ alloying during the printing process for stress control could be a promising process development. The following works shows first results on generating LTT alloys by multi wire GMA welding for stress control in additive manufacturing. \section*{2 Experimental Setup} The experiments have been performed using a standard gas metal arc process in spray transfer mode. The welding torch was manipulated, using a linear movement. Table 1 gives an overview on the most important constant welding parameters. The electrode wire feed speed was constantly set to $8 \mathrm{~m} / \mathrm{min}$, the welding speed $80 \mathrm{~cm} / \mathrm{min}$ which Table 1. Welding parameters for in situ welding experiments. \begin{center} \begin{tabular}{l|l} \hline Parameter & Value \\ \hline Shielding gas & DIN EN ISO 14175: M20-ArC-8 \\ \hline Shielding gas flow rate & $15 \mathrm{l} / \mathrm{min}$ \\ \hline Electrode wire feed speed & $8 \mathrm{~m} / \mathrm{min}$ \\ \hline Electrode material & EN ISO 14341-A: G 3Si1 \\ \hline Cold wire material 1 & EN ISO 14343-A: G 19 9 LSi \\ \hline Cold wire material 2 & EN ISO 14343-A: G 25 20 \\ \hline Welding speed & $80 \mathrm{~cm} / \mathrm{min}$ \\ \hline Welding torch position & PA \\ \hline Substrate material & DIN EN 10025-2 S235JR \\ \hline \end{tabular} \end{center} resulted in an constant energy per unit length of $6,09 \mathrm{~kJ} / \mathrm{cm}$. As shielding gas, Argon plus $8 \% \mathrm{CO}_{2}$ was used. The contact tip to work piece distance was set to $15 \mathrm{~mm}$. The inter layer temperature was kept constant at $100{ }^{\circ} \mathrm{C}$ for all experiments. Three different material combinations were investigated, as shown in Table 2. Table 2. Welding parameters for in situ welding experiments. \begin{center} \begin{tabular}{l|l|l|l} \hline & Electrode wire & Cold wire 1 & Cold wire 2 \\ \hline Combination 1 & EN ISO 14341-A: G & EN ISO 14343-A: G 19 & \\ & 3Si1 & 9 LSi & - \\ \hline Combination 2 & EN ISO 14341-A: G & & EN ISO 14343-A: G 25 \\ & 3Si1 & - & 20 \\ \hline Combination 3 & EN ISO 14341-A: G & EN ISO 14343-A: G 19 & EN ISO 14343-A: G 25 \\ & 3Si1 & 9 LSi & 20 \\ \hline \end{tabular} \end{center} The chemical composition of the welding consumables is shown in Table 3. Table 3. Chemical composition of the wires, determined by OES analysis. \begin{center} \begin{tabular}{l|l|l|l|l|l|l} \hline & $\mathrm{Fe}$ & $\mathrm{C}$ & $\mathrm{Cr}$ & $\mathrm{Ni}$ & $\mathrm{Mn}$ & $\mathrm{Si}$ \\ \hline Electrode & 97.4 & 0.08 & 0.413 & 0.041 & 1.01 & 0.056 \\ \hline Cold wire 1 & 67.3 & 0.015 & 19.610 & 9.680 & 1.610 & 0.756 \\ \hline Cold wire 2 & 51.7 & 0.11 & 24.96 & 20.89 & 1.32 & 0.55 \\ \hline \end{tabular} \end{center} The welding torch was extended by two external cold wire feeding systems. The cold wires were fed symmetrically to the welding direction into the molten pool with an angle of $20^{\circ}$ relative to the substrate surface and $15^{\circ}$ to the movement axes of the welding torch, Fig. 1. The welding experiments were performed in order to evaluate a stable process window, as well as the maximum possible cold wire feed speeds without generating process instabilities. \section*{3 Experiments} In the beginning, the maximum possible wire feed speed was investigated using one of the wires, followed by experiments with both wires. Wall shaped specimen were produced by depositing 5-7 layers. For compensating geometric deviations in the process start and end area, the welding direction was reversed every layer. The specimen height varied between $8 \mathrm{~mm}$ and $12 \mathrm{~mm}$, depending on the cold wire feed speed. Cross sections were extracted for microscopic analysis, as well as chemical analysis via optical emission spectroscopy (OES).\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-179} Fig. 1. Left: Welding torch with cold wire feeding system. Right: schematic top view on the wire orientation. \section*{4 Results and Discussion} In total, 23 stable working points were investigated, with a summarized cold wire feeding speed, ranging from $5 \mathrm{~m} / \mathrm{min}$ to $15 \mathrm{~m} / \mathrm{min}$. For feeding the wires from the backside into the molten pool, a minimum wire feed speed was required to enable a stable droplet transfer. Table 4 shows the investigated parameters, as well as the chemical composition, measured by the OES analysis. \subsection*{4.1 Chemical Composition} The chemical composition was estimated by calculating the average value out of three OES measurements per sample. Figure 2 shows the Chromium and Nickel equivalents that were calculated from the OES analysis, drawn into the Schaeffler diagram. The Chromium and Nickel equivalents were calculated using formulae 2 and 3 : \begin{gather*} C r_{\{e q\}}=C r+M o+1.5 * S i+0.5 * T a+0.5 * N b+T i \tag{2}\\ N i_{\{e q\}}=N i+30 * C+0.5 * M n+7.5 N \tag{3} \end{gather*} It can be seen, that the estimated Chromium and Nickel equivalents are following the linear interpolation between the welding consumables as expected. Furthermore, it is visible, that the use of single wires barely reaches the Chromium and Nickel contents, that are required to reach the martensitic area. The combination of wire one and wire two enables to reach the part of the martensitic-austenitic zone, which also lets expect an LTT microstructure. Especially samples number 18 to 23 have been considered for a deeper microscopic analysis. \subsection*{4.2 Morphology} Further investigations to characterize the material were done by microscopic analysis. Figure 3 shows the macroscopic images of the multi wire samples. The images show a typical structure of wall shaped WAAM samples. A strong directional solidification can be identified for the first six layers, while the top layer partly shows a Table 4. OES results and calculated Chromium and Nickel equivalents. \begin{center} \begin{tabular}{l|l|l|l|l|l|l|l|l|l} \hline Num & \begin{tabular}{l} Cold wire \\ feed speed 1 \\ $[\mathrm{m} / \mathrm{min}]$ \\ \end{tabular} & \begin{tabular}{l} Cold wire \\ feed speed 2 \\ $[\mathrm{m} / \mathrm{min}]$ \\ \end{tabular} & Ni-Eq & Cr-Eq & C [\%] & Mn [\%] & Si [\%] & Cr [\%] & Ni [\%] \\ \hline 1 & 5 & - & 3.83 & 4.18 & 0.06 & 1.39 & 0.72 & 3.07 & 1.46 \\ \hline 2 & 6 & - & 4.02 & 4.84 & 0.05 & 1.36 & 0.69 & 3.78 & 1.73 \\ \hline 3 & 7 & - & 4.19 & 4.89 & 0.06 & 1.41 & 0.72 & 3.79 & 1.78 \\ \hline 4 & 8 & - & 4.33 & 5.08 & 0.06 & 1.40 & 0.68 & 4.03 & 1.90 \\ \hline 5 & 9 & - & 5.02 & 6.80 & 0.05 & 1.44 & 0.70 & 5.70 & 2.67 \\ \hline 6 & 10 & - & 5.17 & 7.09 & 0.05 & 1.44 & 0.68 & 6.01 & 2.83 \\ \hline 7 & - & 5 & 6.01 & 4.97 & 0.08 & 1.34 & 0.66 & 3.96 & 2.98 \\ \hline 8 & - & 6 & 7.14 & 6.41 & 0.08 & 1.38 & 0.66 & 5.39 & 3.98 \\ \hline 9 & - & 7 & 7.61 & 6.96 & 0.08 & 1.38 & 0.63 & 5.98 & 4.45 \\ \hline 10 & - & 8 & 8.56 & 7.79 & 0.09 & 1.38 & 0.63 & 6.81 & 5.12 \\ \hline 11 & - & 9 & 8.84 & 8.15 & 0.09 & 1.36 & 0.61 & 7.20 & 5.51 \\ \hline 12 & & 10 & 9.16 & 8.65 & 0.08 & 1.42 & 0.62 & 7.68 & 5.95 \\ \hline 18 & 5 & 5 & 9.71 & 11.61 & 0.08 & 1.49 & 0.63 & 10.59 & 6.95 \\ \hline 19 & 5 & 6 & 11.04 & 12.14 & 0.09 & 1.49 & 0.63 & 11.12 & 7.50 \\ \hline 20 & 5 & 7 & 11.13 & 12.90 & 0.07 & 1.49 & 0.61 & 11.91 & 8.18 \\ \hline 21 & 5 & 8 & 11.57 & 13.39 & 0.07 & 1.52 & 0.62 & 12.39 & 8.66 \\ \hline 22 & 5 & 9 & 12.13 & 13.75 & 0.07 & 1.51 & 0.61 & 12.75 & 9.13 \\ \hline 23 & 5 & 10 & 12.67 & 14.38 & 0.08 & 1.54 & 0.60 & 13.39 & 9.45 \\ \hline & & & & & & & & & \\ \hline \end{tabular} \end{center} non-directional solidification. Bright areas can be identified along the fusion lines of the weld seams, which hints to a macroscopic segregation of Chromium and Nickel. For a further evaluation of the materials, microscopic images have been prepared, Fig. 4. At higher magnitude, a strong effect of the changing chemical composition on the microstructure is visible. From sample 18 to sample 23 the Nickel content is changing from $6.95 \%$ to $9.45 \%$, while the amount of Chromium raises from $10.59 \%$ to $13.39 \%$. Especially the microstructure, which sets in from sample 21 looks very similar to the LTT microstructure, described in the literature. Kromm describes LTT cross sections, taken from weld metal in [7] as cellular martensitic microstructure, characterized by a Chromium and Nickel segregation along the martensite spots. An increasing amount of Nickel leads to larger austenitic segregation zones beside the martensitic spots. A very similar microstructure can be seen in Fig. 4, pictures 21, 22 and 23. According to this interpretation, the brighter areas show segregated austenitic phases with higher concentration of Chromium and Nickel while the darker spots represent the martensitic areas. The Chromium to Nickel relation lies below 1.5 , which is why no presence of delta ferrite is being expected. The microstructure stays \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-181} \end{center} Fig. 2. Schaeffler diagram, showing the results of Chromium and Nickel equivalents, calculated from the OES meauserments. similar over the longitudinal axis of the samples, except near the fusion line of the first layer, as well as the last layer. Due to base material dilution, the first welding layer shows a fine martensitic structure without bright segregation zones. The last weld seam shows a characteristic non-directional solidification as to be seen in the macro images. The microscopic analysis in combination with the results from the OES measurements show a high chance, that a martensitic LTT alloy was generated by the double wire approach of material combination 3. The calculated $\mathrm{M}_{\mathrm{s}}$-temperatures lie between $180^{\circ} \mathrm{C}$ (sample 18) and $81^{\circ} \mathrm{C}$ (sample 23), which makes the in-situ-alloyed samples feasible to enable an LTT effect. As the inter layer temperature was kept at $100{ }^{\circ} \mathrm{C}$, a positive effect of the martensitic phase transformation on the stress level of the base plates can not be expected. The geometrical stability of the component in wire and arc additive manufacturing highly depends on the size, viscosity and surface temperature of the molten pool. One key parameter, that has an impact on those aspects, is the inter layer temperature. In terms of processing LTT alloys in WAAM, this means that a sweet spot needs to be found between a suitable $\mathrm{M}_{\mathrm{s}}$-temperature for maximum stress compensation effect, and inter layer temperature for keeping the manufacturing process stable. The in-situ-alloying approach seems to be a highly promising way, to achieve a tailor made, locally changing chemical composition, which is adopted to the heat dissipation properties of the components geometry. In contrast to the direct use of an LTT wire as electrode, the in-situ approach is much more flexible in terms of multi material additive manufacturing.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-182} Fig. 3. Macroscopic images of the multi wire samples. The red rectangles mark the positions of microscopic images. \section*{5 Summary} The presented work shows, that it is possible, to establish a stable gas metal arc multi wire process for wire and arc additive manufacturing, that is capable of reaching a chemical composition, suitable for LTT alloys. By varying the wire feed speed, it is possible to fluently set a Chromium content between $3.07 \%$ and $13.39 \%$, as well as a Nickel content between $1.46 \%$ and $9.45 \%$. This opens a wide variety of possibilities in terms of residual stress control in WAAM. As additive manufacturing processes are characterized by an inhomogeneous material distribution, which leads to a varying thermal distortion and stress distribution. The local design of the chemical composition enables to adapt the martensite start temperature to the thermal cooling behaviour of the component. This gives the possibility to achieve a local LTT effect tailored to the components\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-183} Fig. 4. Microscopic images of double wire samples $18-23$, taken from the center of the sample. design. Future research will deal with developing a dynamic path planning and process parametrization strategy to enable a global LTT effect for a large scaled additively manufactured component. Acknowledgments. The presented investigations were carried out at RWTH Aachen University Welding and Joining Institute ISF within the framework of the Collaborative Research Centre SFB1120-236616214 "Bauteilpräzision durch Beherrschung von Schmelze und Erstarrung in Produktionsprozessen" and funded by the Deutsche Forschungs-gemeinschaft e.V. (DFG, German Research Foundation). The sponsorship and support is gratefully acknowledged. Special thanks also go to the companies ESAB AB and EWM AG for providing welding consumables and welding machines. \section*{References} \begin{enumerate} \item Pan, Z., Ding, D., Wu, B., Cuiuri, D., Li, H., Norrish, J.: Arc welding processes for additive manufacturing: a review. In: Chen, S., Zhang, Y., Feng, Z., et al. (eds.) Transactions on Intelligent Welding Manufacturing. Springer, Singapore, pp. 3-24 (2018). ISBN 978-98110-5354-2 \item Ding, D., Pan, Z., Cuiuri, D., Li, H.: Wire-feed additive manufacturing of metal components: technologies, developments and future interests. Int. J. Adv. Manuf. Technol. 81(1-4), 465481 (2015). ISSN 0268-3768. Verfügbar unter: \href{https://doi.org/10.1007/s00170-015-7077-3}{https://doi.org/10.1007/s00170-015-7077-3} \item Norsk Titanium - Unternehmenswebseite [online] [Zugriff am: 05.09.17]. Verfügbar unter: \href{https://www.norsktitanium.com/}{https://www.norsktitanium.com/} \item Wegener, V.: Ramlab - Unternehmenswebsite [online] [Zugriff am: 5. September 2017]. Verfügbar unter: \href{https://ramlab.com/}{https://ramlab.com/} \item Piehl, K.H.: Formgebendes Schweissen von Schwerkomponenten. Thyssen, Technische Berichte 1989(21, 1), 53-71 (1989) \item Steven, W., Haynes, A.G.: The temperature of formation of Martensite and Bainite in low-alloy steel. J. Iron Steel Inst. 183, 349-359 (1956) \item Kromm, A.: Umwandlungsverhalten und Eigenspannungen beim Schweißen neuartiger LTT-Zusatzwerkstoffe. Bundesanstalt für Materialforschung und -prüfung (BAM). BAMDissertationsreihe, Berlin. 72 (2011). ISBN 978-3-9813853-9-7 \item Kromm, A., Kannengiesser, T.: Characterizing PHASE TRANSFORMATIONS of different LTT alloys and their effect on RESIDUAL STRESSES and COLD CRACKING [online]. Weld. World 55(3-4), 48-56 (2011). ISSN 0043-2288. Verfügbar unter: \href{https://doi.org/10}{https://doi.org/10}. 1007/BF03321286 \item Gach, S., Olschok, S., Arntz, D., Reisgen, U.: Erratum: residual stress reduction of laser beam welds by use of low-transformation temperature (LTT) filler materials in carbon Manganese steels- in situ diagnostic: image correlation. J. Laser Appl. 30, 032416 (2018) [online]. J. Laser Appl. 32(1), 19901 (2020). ISSN 1042-346X. Verfügbar unter: \href{https://doi.org/10.2351/}{https://doi.org/10.2351/} 1.5133938 \item Reisgen, U., Olschok, S., Gach, S.: Nutzung von Low-Transformation-TemperatureWerkstoffen (LTT) zur Eigenspannungsreduzierung im Elektronenstrahlschweißprozess [online]. Materialwissenschaft und Werkstofftechnik 47(7), 589-599 (2016). ISSN 09335137. Verfügbar unter: \href{https://doi.org/10.1002/mawe}{https://doi.org/10.1002/mawe}. 201600549 \item Oster, L., Akyel, F., Reisgen, U., Olschok, S., et al.: Investigating plasma keyhole welding with multiple wires for fusion welding with chemically graded weld seams (2019) \item Mochizuki, M., Matsushima, S., Toyoda, M., Morikage, Y., Kubo, T.: Study of residual stress reduction in welded joints using phase transformation behaviour of welding material. Studies on numerical simulation of temperature, microstructure, and thermal stress histories during welding and their application to welded structures (2 nd report) [online]. Weld. Int. 19(10), 773-782 (2005). ISSN 0950-7116. Verfügbar unter: \href{https://doi.org/10.1533/wint.2005.3491}{https://doi.org/10.1533/wint.2005.3491} \item Kromm, A., Kannengiesser, T.: Effect of martensitic phase transformation on stress build-up during multilayer welding [online]. Mater. Sci. Forum: 768-769, 660-667 (2013). Verfügbar unter:\href{https://doi.org/10.4028/www.scientific.net/MSF.768-769.660}{https://doi.org/10.4028/www.scientific.net/MSF.768-769.660} \item Kitano, H., Nakamura, T.: Distortion reduction of parts made by wire and arc additive manufacturing technique using low transformation temperature welding materials [online]. Q. J. Jpn. Weld. Society 36(1), 31-38 (2018). ISSN 0288-4771. Verfügbar unter: \href{https://doi.org/}{https://doi.org/} 10.2207/qjjws. 36.31 \end{enumerate} Casting \section*{Development of an In-Situ Observation Procedure for Hot Tear Formation in Aluminum Alloys in Gravity Die Casting } \begin{abstract} Hot cracks are a widespread defect phenomenon in metal castings. In order to understand the underlying mechanisms and to evaluate numerical models to describe hot crack formation, it is important to know how hot cracks develop during the transition from the liquid to the solid state. An experimental setup is presented, which has been designed to generate hot cracks in aluminum gravity die casting in order to trace their formation during solidification by optical means. The solidification induced shrinkage is correlated with the crack formation. The alloy systems $\mathrm{AlSi}$ and $\mathrm{AlCu}$ are examined in practically relevant compositions. In addition to the development of the in-situ investigation methodology, the hot cracks produced are examined using elctron microscopy in order to determine the underlying crack mechanisms. \end{abstract} Keywords: Aluminum alloy $\cdot$ Gravity die casting $\cdot$ Hot tearing $\cdot$ In-situ observation \section*{1 Introduction} Distortion, residual stresses and hot cracks are decisive quality influencing characteristics of components in foundries and, depending on their characteristics, lead to corresponding reworking and, in the case of hot cracks, to scrap. Their reduction is therefore of great interest for cost-efficient production. In the casting process, the phenomena mentioned above result from the combination of solidification shrinkage coupled with the respective local self-feeding and the geometric constraints of the mold on the component. The work presented here was carried out within the framework of the DFG-funded Collaborative Research Center SFB1120 "Precision Melt Engineering". The long-term goal is to improve the precision of the component in permanent mold casting by creating a knowledge base in the areas of distortion and hot crack formation as well as the derivation of corresponding concepts for influencing them. In order to gain a deeper understanding under which conditions and at what point in time hot cracks form during\\ the solidification process, an experimental set-up was developed which allows the formation of hot cracks to be assigned to exact times and local temperatures and therefore to fraction solid values during solidification by means of optical recordings. The subject of hot cracking which occurs while solidifying during the casting of aluminum alloys is an already very extensively investigated area e. g. by J. A. Dantzig [1], J. Langlais [2], M. Rappaz [3] and many others. Different aluminum alloys show different susceptibilities to hot tearing mainly as a function of the width of the solidification range $[3,4]$. The system AlSi, which has good self-feeding properties at low strength, and $\mathrm{AlCu}$, which, relatively speaking, has higher strength with poorer feeding properties, are considered here in different chemical compositions. The comparison of these two systems, both in the in-situ measurements and in the subsequent considerations of the morphology, should allow conclusions to be drawn about the mechanisms of crack formation, such as possible segregation in the areas of crack formation. In-situ observation of crack initiation using optical methods has been performed by C. Davidson et al. Using an AlCu0.5 alloy [5]. The focus of that work is on the correlation of shrinkage induced stresses and crack initiation. However, the reliable recording of the forces as a result of settlement phenomena was questioned by the authors. Yamagata H. et al. Also worked on the optical records of crack formation during solidification [6]. The less hot crack susceptible alloy $\mathrm{AlSi} \mathrm{Mg} 0.3$ in a sand mold was investigated where the crack initiation was caused only by the casting geometry. Healed internal hot cracks and persistent cracks open to the surface were observed and compared. Apart from the video recording of the crack initiation, only temperature curves were recorded, and the occurring forces were taken from simulations. The difficulties in detecting the shrinkage induced forces $[5,7]$ provide motivation to correlate the crack initiation with the contraction of the cast part. In many of the previous studies, where shrinkage was detected during crack initiation, the deviations were recorded near the crack location [8] or very far away [9]. The observation that the placement of the transducers near the crack zone influences the solidification and even more the mechanical deformation, led to the approach to determine temperaturedependent shrinkage and crack formation at two different locations in the examined component. \section*{2 Development of Experimental Setup} The starting point for the setup for in-situ hot crack observation is the measuring equipment and experimental mold used in preceding studies for investigations of the cast-mold heat transfer coefficient as well as the cast part distortion [7,10,11]. The basic concept is an "F" shaped sample geometry. The mold consists of steel mold modules which enclose the contour of the "F" and are oil-temperature controlled. On the upper and lower side, the mold is closed by insulating calcium silicate plates, so that heat fluxes occur exclusively in horizontal direction into the mold modules. For the in-situ hot crack observations, corresponding mold modules were manufactured, which create a hot spot between the ribs of the "F" by integrating a further insulating plate and a quartz glass window, which also acts as an insulator. In this hotspot, where the melt is the last to solidify, hot cracks are generated due to the geometry and the solidification shrinkage. The window allows\\ the visual recording of the crack initiation and growth with a video camera. Figure 1 shows on the left side the mold already modified for hot crack observation with the lid removed from above. Temperatures are recorded by means of type " $\mathrm{K}$ " thermocouples in the area of crack formation and the area of unimpeded contraction. The contraction of the free end is detected by two linear variable differential transformers (LVDT), one coupled to the mold and one to the melt. Figure 1 shows on the right side the result of an accompanying Magma simulation (performed with Magmasoft ${ }^{\circledR}$ Version 5.3). The solid phase content in the casting is shown shortly before solidification starts everywhere in the part, the hotspot is clearly visible here.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-188} Fig. 1. The left side shows the opened mold with the hot crack area formed by the insulation and the glass window. The right side displays the calculated solid fraction during solidification and by this a hot spot where the crack is intended to form. \section*{3 Experiments} The experiments were based on ingots, made of 99.8 grade aluminum, $\mathrm{AlCu50}$ prefabrication and standard industrial A356 (AlSi7Mg0.3) and were charged according to the desired contents. Prior to casting with a superheat of $120^{\circ} \mathrm{C}$, the melt was flushed with argon for $15 \mathrm{~min}$. The mold, which was coated with an insulating coating, was thermally regulated to $150{ }^{\circ} \mathrm{C}$. For the in-situ recorded temperatures and displacements a sampling rate of $20 \mathrm{~Hz}$ was set and for the video $120 \mathrm{fps}$. A new quartz glass plate and new measuring rods were used for each test. In addition to the experiments, the Thermocalc software was used to calculate the liquidus and solidus temperatures (as equilibrium solidification) for the alloys under investigation. \section*{4 Results} As expected, the tests carried out showed no crack formation for $\mathrm{AlSi7Mg0.3}$ as well as for $\mathrm{AlSi3.5Mg0.15}$. Crack formation only became apparent when the Si content was further halved to $1.75 \mathrm{wt} \%$. Since the crack susceptibility of pure aluminum and the chosen $\mathrm{AlCu}$ alloys is relatively high, for these alloys hot cracks could be observed in each experiment. \subsection*{4.1 In-Situ Observation} The position of the thermocouple in the observed area in the immediate vicinity of the occurring hot crack allows to determine the time between filling and the first occurrence of a hot crack and to derive the corresponding temperature. For the alloy AlSi1.75Mg the first time the crack could be visually detected was at a temperature $\left(\mathrm{T}_{\mathrm{c}}\right)$ of $618{ }^{\circ} \mathrm{C}$ at the crack location. This lies within the calculated solidification interval of the alloy (649 $-575^{\circ} \mathrm{C}$ ). For the $\mathrm{AlCu}$ alloys with 2 and $4 \mathrm{wt} \%$ copper, clear hot cracks were found in both cases, each with the first appearance slightly below the solidus temperature $\mathrm{T}_{\mathrm{sol}}$. For the $\mathrm{Al} 99.8$ alloy casting the crack could be visually detected for the first time at a temperature significantly below the calculated solidus temperature of pure aluminum. This suggests that strong segregation of the secondary elements in the residual melt occurs here, which in turn could shift the solidification in the last solidified area, where crack formation is observed, to lower temperatures. These results are summarized in Table 1. Also included is the time until the first visual detection of the crack, measured from the time when the area under consideration was filled with melt. The shrinkage (S) at the temperature of the first occurrence of a hot crack can be determined by means of comparing the temperature at the point of crack formation and those of the center of the freely contracting component area where the displacements are measured. In the 99.8 grade alloy the cracking starts at the lowest shrinkage of $0.056 \%$. With AlSi1.75Mg this happens at almost double the value, which is roughly similar to $\mathrm{AlCu} 2$. $\mathrm{AlCu} 4$ shows the first signs of hot cracking at about four times the amount of shrinkage (see Table 1). The cooling curves of the test specimen at the crack area of all four alloys showing hot cracks are depicted in Fig. 2. Marked are the time and temperature points of the first visibly indications of tearing. Using the example of the experiment with $\mathrm{AlCu} 2$, it can be seen that the solidification is slower in the hotspot, where crack formation takes place, compared to the area where shrinkage is measured by temperature (Fig. 3 left). The righthand graph in Fig. 3 shows the change in length of the considered free end of the "F" shaped casting. It shows that initially the mold expands with the molten metal in it and from about $5 \mathrm{~s}$ on the shrinkage of the component begins, coupled with a corresponding gap formation (the difference between mold and component displacement). Table 1. The compositions, hot crack formation, time and shrinkage ( $\mathrm{S}$ ) of the first appearance of a crack, calculated ( $\mathrm{T}_{\text {liq }}$ and $\mathrm{T}_{\mathrm{sol}}$ ) and measured $\left(\mathrm{T}_{\mathrm{c}}\right)$ temperatures of the realized experiments. \begin{center} \begin{tabular}{l|l|l|l|l|l|l} \hline Alloy & Hot crack & Time $[\mathrm{s}]$ & $\mathrm{T}_{\text {liq }}\left[{ }^{\circ} \mathrm{C}\right]$ & $\mathrm{T}_{\text {sol }}\left[{ }^{\circ} \mathrm{C}\right]$ & $\mathrm{T}_{\mathrm{c}}\left[{ }^{\circ} \mathrm{C}\right]$ & $\mathrm{S}[\%]$ \\ \hline $\mathrm{Al} 99.8$ & Yes & 55 & - & 660 & 606 & -0.056 \\ \hline $\mathrm{AlCu} 4$ & Yes & 60 & 649 & 571 & 568 & -0.194 \\ \hline $\mathrm{AlCu} 2$ & Yes & 52 & 655 & 610 & 604 & -0.107 \\ \hline AlSi7Mg0.3 & No & - & 617 & 568 & - & - \\ \hline AlSi3.5Mg0.15 & No & - & 638 & 572 & - & - \\ \hline AlSi1.75 & Yes & 47 & 649 & 575 & 618 & -0.085 \\ \hline \end{tabular} \end{center} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-190} \end{center} Fig. 2. The cooling curves of the test specimen at the crack area of the four samples with hot cracks. Marked are the time and temperature points of the first visible indications of tearing.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-190(1)} Fig. 3. The different cooling curves of the crack location and the free contracting casting area for the ALCu2 casting on the left side. The measurements of the displacements of the casting at the area with free contraction are shown on the right for this casting. \subsection*{4.2 Chemical Composition} The chemical composition of the samples with cracks was determined by means of optical emission spectroscopy (OES) with spatial resolution in order to detect segregations near the crack. Measurements were taken at eight points from the outer side of the sample part towards the crack along the solidification direction. Measurements were taken with a spot diameter of $5 \mathrm{~mm}$. Overlapping of the measurement spots with intermittent grinding accounted for $50 \%$ of the spot diameter. No significant concentration differences were found at different distances from the crack. It occurs that the accompanying elements of AL 99.8 are mainly $\mathrm{Si}(0.17 \mathrm{wt} \%)$ and $\mathrm{Fe}(0.074 \mathrm{wt} \%)$. The measured values are summarized for the most significant elements in Table 2. Table 2. Measurements of the secondary elements. \begin{center} \begin{tabular}{l|l|l|l|l} \hline & \begin{tabular}{l} $\mathrm{Al}$ \\ 99.8 \\ \end{tabular} & $\mathrm{AlCu} 4$ & $\mathrm{AlCu} 2$ & AlSi1.75 \\ \hline $\mathrm{Si}[\mathrm{wt} \%]$ & 0.170 & 0.110 & 0.130 & 1.730 \\ \hline $\mathrm{Cu}[\mathrm{wt} \%]$ & 0.002 & 3.780 & 1.920 & 0.001 \\ \hline $\mathrm{Fe}[\mathrm{wt} \%]$ & 0.074 & 0.080 & 0.078 & 0.076 \\ \hline $\mathrm{Mg}[\mathrm{wt} \%]$ & 0.004 & 0.002 & 0.002 & 0.091 \\ \hline \end{tabular} \end{center} \subsection*{4.3 Morphology} After the test castings, the areas with hot cracks were cut out and examined optically as well as by means of scanning electron microscopy (SEM). Macroscopicx. First pictures taken from the side of the casting facing the insulation plate show the last solidified area around the hot crack. In Fig. 4 it can be seen how a dendritic structure becomes more and more apparent on the surface of all samples towards the crack. This suggests that the remaining melt near the crack flows into the structure by capillary action between the already formed dendrites shortly before the end of solidification in order to compensate for volume deficits due to solidification shrinkage. Figure 5 taken with a magnification of 50 shows that for samples of the $\mathrm{AlCu}$ alloy system a more coherent dendrite structure near the crack front is noticeable compared to the two other alloys. What they all have in common is that it is noticeable that complete dendritic structures are clearly visible towards the crack front and that the crack runs mainly between them without dissecting them. Only the sample of Al 99.8 alloy shows torn apart dendrites in the hot crack (see Fig. 5 upper left).\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-191} Fig. 4. Macroscopic images of the hot cracks taken with a magnification of five.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-192} Fig. 5. Macroscopic images of the hot cracks taken with a magnification of 50. At the upper left picture of $\mathrm{Al} 99.8$ the broken dendrite is encircled. SEM Analyses. The SEM images of the prepared fracture surfaces show mostly intact dendrite structures in all samples. In Fig. 6 no ductile structures or structures clearly damaged by the crack are visible on the pictures taken with a magnification of 100 . From this it can be concluded that the hot cracks were caused by separation of the remaining interdendritic residual melt in all cases. From a purely qualitative point of view, the dendrite structures appear to differ in their roundness for the various alloys. The AlSi1.75 in particular has the roundest forms. This can indicate different permeabilities of the structures during solidification and thus, via the influence on the interdendritic feeding, finally the hot cracking tendency. Clearly visible differences in the sizes of the dendrite structures were not detected. Figure 7 shows the surface of dendrites of the Al 99.8 alloy on the left. Wrinkles can be seen in the interdendritic surface, which can be explained by the solidification shrinkage of the residual melt located above the dendrites. The right picture of the $\mathrm{AlCu} 4$ alloy using backscatter diffraction (BSD) shows dendrite structures of primary aluminum and interdendritic a heavier phase, where the composition and the proportions will be $\mathrm{Al}_{2} \mathrm{Cu}$. A significant difference between the crack appearances in the samples was found when considering the Al 99.8 sample (Fig. 8, left) in a higher magnification. In this picture, several broken dendrite arms could be seen. This indicates that the tearing occurred partly after a coherent net of dendrites has formed. Light-optical microscopy\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-193(1)} Fig. 6. SEM pictures of the dendrite structures at the crack surface for $\mathrm{Al} 99.8, \mathrm{AlCu} 4, \mathrm{AlCu} 2$ and AlSi1.75.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-193} Fig. 7. On the left side a closer look at the last solidified interdendritic melt of the $\mathrm{Al} 99.8$ alloy and on the right side the primary aluminum dendrite structure with interdendritic $\mathrm{Al}_{2} \mathrm{Cu}$ in the $\mathrm{AlCu} 4$ alloy. images of this sample (Fig. 8 right) show interdendritic segregations, which indicate that the small solidification interval of $\mathrm{Al} 99.8$ is locally widened due to enrichment of accompanying elements (mainly $\mathrm{Si}$ ) in the residual melt.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-194} Fig. 8. Torn dendrite arms of the Al 99.8 sample (right) and segregations of interdendritic melt enriched with accompanying elements (Si) visible on a light-optical-microscopy image (left). \section*{5 Conclusions} It can be stated that the chosen method for in-situ observation of hot cracking allows to determine the time of the beginning of tearing to be about one second. Thus, the crack formation can be clearly assigned to an associated temperature and via this to an associated shrinkage. The cast specimen allow macroscopic as well as SEM analysis of the crack locations. The observation and comparison of the four specimens with pronounced hot cracks also provides the following findings: \begin{itemize} \item The SEM images of the cracks suggest that the crack formation of all samples was comparable, mainly due to separation in the remaining interdendritic residual melt. \item The OES measurements do not show any conspicuous segregation towards the crack location, which is also consistent with the cooling curves at the crack location that matches the respective alloy compositions. \item The low temperature of the first crack occurrence in 99.8 alloy, compared to the calculated $\mathrm{T}_{\text {sol }}$ suits the found micro segregations of $\mathrm{Si}$ in the interdendritic melt and the torn apart dendrites which indicates that on this sample the crack occurred partly in the already coherent net of dendrites. \end{itemize} In conclusion, the observations made suggest that a more detailed quantitative investigation of the dendrite structures using automated image analysis, especially with regard to roundness and size, will provide further information. This, together with the consideration of the theoretical behavior of the solidification, promises a deeper understanding of the hot cracking susceptibility of the different alloys. Acknowledgments. The presented investigations were carried out at RWTH Aachen University within the framework of the Collaborative Research Centre SFB1120 - 236616214 "Bauteilpräzision durch Beherrschung von Schmelze und Erstarrung in Produktionsprozessen" and funded by the Deutsche Forschungsgemeinschaft e.V. (DFG, German Research Foundation). The sponsorship and support is gratefully acknowledged. \section*{References} \begin{enumerate} \item Dantzig, J. A., Rappaz, M.: Solidification, 2nd edn., EPFL Press, Lausanne (2016) \item Langlais, J.: Fundamental study of hot tearing mechanisms of aluminum-silicon alloys. Department of Mining, Metals and Materials Engineering McGill University, Montreal (2006) \item Rappaz, M., Jacot, A., Boettinger, W.J.: Last stage solidification of alloys: a theoretical study of dendrite arm and grain coalescence. Metall. Mater. Trans. A 34A, 467-479 (2007) \item Phillion, A.: Hot tearing and constitutive behaviour of semi-solid aluminum alloys. The University of British Columbiax (2007) \item Davidson, C., Viano, D., Lu, L., StJohn, D.: Observation of crack initiation during hot tearing. Int. J. Cast Metals Res 1(19), 59-65 (2006) \item Yamagata, H., Tachibana, H., Kijima, S., Adachi, M., Koiwai, S.: Direct observation of hot tearing of Al-7\%Si-0.35\%Mg alloy. Adv. Mater. Process. Technol. 3(4), 480-492 (2018) \item Wolff, N., Vroomen U., Bührig-Polaczek, A.: Development and Evaluation of an Experimental Setup to Investigate and Influence Component Distortion in Gravity Die Casting. AFS Transactions (2020) \item Sadayappan, K., Aguiar, A.M., Shankar, S.: Development of a hot tear test procedure for aluminum casting alloys. Mater. Sci. Technol. 2019, 1094-1102 (2019) \item Nasresfahani, M.R., Niroumand, B.: Design of a new hot tearing test apparatus and modification of its operation. Met. Mater. Int. 16(1), 35-38 (2010) \item Wolff, N., Pustal, B., Vossel, T., Laschet, G., Bührig-Polaczek, A.; Development of an A356 die casting setup for determining the heat transfer coefficient depending on cooling conditions, gap size, and contact pressure. Mater. Sci. Eng. Technol. 48(12), 1235-1240 (2017) \item Vossel, T., Pustal, B., Bührig-Polaczek, A.: Modellierung der Erstarrungskinetik kolumnarer und äquiaxialer Kornstrukturen zur gefügebasierten Interpolation der Werkstoffeigenschaften im Hinblick auf die Verzugsvorhersage. Gießerei Special 2, 130-134 (2017) \end{enumerate} \section*{Determination of the Heat Transfer Coefficient for a Liquid-Solid Contact in Gravity Die Casting Processes } \begin{abstract} The description of the heat transfer coefficient represents a core element when defining a system's heat balance. Especially in foundry processes, high temperature melts get in contact with low temperature molds. While solid-solid contacts have been the focus of numerous investigations, liquid-solid contacts are rarely described in literature. This paper will present and compare different approaches to describe the phenomena and properties necessary for modeling the contact between a liquid melt and a solid mold surface with microscopical roughness. This includes a topographical analysis of the interface and the estimation of the wettability of the surface. The resulting models will determine the heat transfer coefficient for application in thermomechanical simulations of a gravity die casting process. Identifying the model best suited for modeling the melt-mold contact in a foundry process represents the first step towards a physical model that describes the entirety of a casting process. \end{abstract} Keywords: HTC model $\cdot$ Heat transfer coefficient $\cdot$ Liquid-solid contact \section*{1 Introduction} Numeric simulations are commonly used as a tool for predicting the result of gravity die casting processes. In such simulations the heat balance is of high importance to determine the local cooling conditions. Especially the heat transfer coefficient (= "HTC") for the melt-mold contact is rarely discussed in literature. A model suitable to describe the heat transfer coefficient at the contact interface of a liquid and solid material has to deliver information on two aspects of the contact: \begin{enumerate} \item Defining an expression to calculate the heat transfer coefficient at the interface with regard to its microscopically rough surface as the result of a topographical analysis \item Describe the wetting of the surface asperities derived from a mechanical analysis in order to estimate the contact area between liquid and solid regions \end{enumerate} This paper presents several different modeling approaches and evaluates the respective HTC predictions. These results are finally benchmarked against experimental data gathered from gravity die casting experiments and inverse simulations. \section*{2 Topographical Analysis} As real surfaces feature a microscopical roughness, it is important to include a topographical analysis in order to give a good representation of the respective surface. In terms of a liquid-solid contact, this is important for two reasons: On the one hand, just as for solid-solid contacts, only certain regions of the solid body will be in contact with the other one i.e. especially the surface asperities with maximum height. On the other hand, a liquid-solid contact, in contrast to a solid-solid contact, is not about just the rather few asperity contact spots, but due to the possibilities of the liquid medium to wet the surface of the solid body, the actual contact area can be significantly larger. For these reasons, the topographical analysis not only needs to come up with an appropriate description of the rough solid surface but must also describe the area in contact with the liquid material. All presented models apply the idea of wetting the solid surface up to a certain height level. The remaining gap between the wetting height and the base of the asperity is considered to be filled with gas, i.e. air. As it is either not possible or feasible to scan the entire surface of a mold, some simplifications and assumptions have to be made in order to create a model. All presented models share the following assumptions: \begin{enumerate} \item The rough surface is represented by a continuing sequence of asperities. \item The asperities themselves are considered to be conical in form with a constant slope along its surface line. \item Material properties are assumed to be constant. \item Surfaces are clean. \item Radiation heat transfer can be neglected for liquids with low melting points and/or low emissivity. \end{enumerate} \subsection*{2.1 Surface Profile Model 1} The first profile model as presented by Prasher [1] and reviewed by Somé et al. [2] further simplifies the surface structure. The asperities are considered to be of identical height and uniformly distributed. Their average height is equal to the standard deviation $\sigma$ of the asperity distribution. A schematic depiction of this approach is shown in Fig. 1. In order to define the heat transfer coefficient, its basic definition is applied which divides the effective thermal conductivity $\lambda_{\text {eff }}$ by a wall thickness $\delta$. An equivalent expression to the wall thickness can be derived by evaluating the surface in contact with liquid melt. The term $\frac{A_{\text {ratio }}}{\sigma}$ applying the ratio of wetted and total asperity surfaces $A_{\text {ratio }}$ is used as shown in Eq. (1). \begin{equation*} \left.h_{\text {model } 1}=\frac{\lambda_{\text {eff }}}{\delta}=\lambda_{\text {eff }} \cdot \frac{A_{\text {ratio }}}{\sigma} \right\rvert\, \text { with } \lambda_{\text {eff }}=\frac{2 \cdot \lambda_{1} \cdot \lambda_{2}}{\lambda_{1}+\lambda_{2}} \tag{1} \end{equation*} Equation (2) shows the calculation for the frustrum area i.e. the area defined by the height of the liquid wetting the conical surface roughness. This gives all the needed information for the heat transfer coefficient as shown in Eq. (3). \begin{gather*} \left.A_{\text {ratio }}=\frac{A_{\text {wet }}}{A_{\text {total }}}=\frac{\left[2 \cdot r_{\text {base }}-X \cdot \cot (\varphi)\right] \cdot \sqrt{X^{2}+(X \cdot \cot (\varphi))^{2}}}{r_{\text {base }} \cdot \sqrt{r_{\text {base }}^{2}+1^{2}}} \right\rvert\, \text { with } \varphi=\arctan \left(\frac{\sigma}{r_{\text {base }}}\right) \tag{2}\\ h_{\text {model } 1}=\frac{\lambda_{\text {eff }}}{\sigma} \cdot \frac{\left[2 \cdot r_{\text {base }}-X \cdot \cot (\varphi)\right] \cdot \sqrt{X^{2}+(X \cdot \cot (\varphi))^{2}}}{r_{\text {base }} \cdot \sqrt{r_{\text {base }}^{2}+1^{2}}} \tag{3} \end{gather*} While the wetting height $\mathrm{X}$ will be described by the mechanical analysis of the liquidsolid contact, all other variables are defined by the material and surface properties. The dimension of $r_{\text {base }}$ can be obtained from a topographical scan as the parameter for average groove width $R_{s m}$ which represents the asperity diameter. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-198} \end{center} Fig. 1. Liquid-solid interface for a microscopically rough surface following profile model 1 \subsection*{2.2 Surface Profile Model 2} The second profile model by Hamasaiid et al. [3] adapts the modeling approach commonly used to describe solid to solid contacts and the corresponding heat transfer coefficient. As direct contact between two rough surfaces only is present at certain local spots, flux tube theory as described by Cooper et al. [4] can be applied. The final expression shown in Eq. (4) uses the size and density of circular contact spots to describe the heat transfer coefficient. \begin{equation*} h_{\text {model } 2}=2 \cdot \lambda_{\text {eff }} \cdot \frac{r_{\text {contact }} \cdot \varrho_{\text {spots }}}{\left(1-\frac{r_{\text {contact }}}{r_{\text {base }}}\right)^{1.5}} \tag{4} \end{equation*} The parameters used in Eq. (4) can be obtained from the topographical analysis. While also treating the asperities of the rough surface as a conical geometry, their height,\\ base size and slope can be different individually. In order to give a description of such a complex surface structure the distribution of asperities is assumed to follow a Gaussian normal distribution. The average base radius of the asperities following the normal probability $\Phi(y)$ can thus be obtained as described in Eq. (6). \begin{gather*} \Phi(y)=\frac{1}{\sqrt{2 \cdot \pi} \cdot \sigma} \cdot \exp \left(-\frac{y^{2}}{2 \cdot \sigma^{2}}\right), \quad \forall y \in(-\infty ;+\infty) \tag{5}\\ r_{\text {base }}=\frac{1}{m} \cdot \int_{y=0}^{y=\infty} y \cdot \Phi(y) d y=\frac{\sigma}{\sqrt{2 \cdot \pi} \cdot m}=\frac{R_{s m}}{2} \tag{6} \end{gather*} Here $\sigma$ describes the standard deviation of the asperity heights and $R_{s m}$ represents the average peak distance. An expression for the density of contact spots $\varrho_{\text {spots }}$ and the contact spot radius $r_{\text {contact }}$ can be found as only peaks larger than the wetting height $\mathrm{W}$, describing the thickness of the entrapped air layer, will be in contact with the liquid. Using the normal probability function describing the surface leads to the following expressions according to Hamasaiid et al. [3]: \begin{gather*} \left.\varrho_{\text {spots }}=\frac{1}{2.5 \cdot \pi} \cdot\left(\frac{m^{2}}{\sigma^{2}+R_{a}^{2}}\right) \cdot \operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right) \right\rvert\, \text { with } m=\frac{2 \cdot \sigma}{\sqrt{2 \cdot \pi} \cdot R_{s m}} \tag{7}\\ r_{\text {contact }}=\frac{1}{m} \cdot\left[\frac{\sigma}{\sqrt{2 \cdot \pi}} \cdot \exp \left(-\frac{W^{2}}{2 \cdot \sigma^{2}}\right)-\frac{W}{2} \cdot \operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right)\right] \tag{8} \end{gather*} Applying these equations in Eq. (4) leads to the final expression for the heat transfer coefficient for surface profile model 2 : \begin{equation*} h_{\text {model } 2}=\frac{0.8}{\pi} \cdot \frac{\lambda_{\text {eff }} \cdot m}{\left(\sigma^{2}+R_{a}^{2}\right)} \cdot \frac{\operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right) \cdot\left[\frac{\sigma}{\sqrt{2} \cdot \pi} \cdot \exp \left(-\frac{W^{2}}{2 \cdot \sigma^{2}}\right)-\frac{W}{2} \cdot \operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right)\right]}{\left[1-\frac{\sqrt{2 \cdot \pi}}{\sigma} \cdot\left(\frac{\sigma}{\sqrt{2 \cdot \pi}} \cdot \exp \left(-\frac{W^{2}}{2 \cdot \sigma^{2}}\right)-\frac{W}{2} \cdot \operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right)\right)\right]^{1.5}} \tag{9} \end{equation*} \subsection*{2.3 Surface Profile Model 3} Another analytical model to describe the surface topology and the respective calculation for the heat transfer coefficient was developed by Hamasaiid et al. [5]. It relies on the same approach for defining the HTC coming from solid-solid contacts. In contrast to model 2, the asperities are assumed to have their base on the same zero level height as depicted in Fig. 2. The idea of leveling the asperity bases changes their slope and height distribution. Therefore, the asperity distribution function $\Phi(y)$ has to be modified to $\Phi_{B}(y)$ as shown in Eq. (10). \begin{equation*} \Phi_{\mathrm{B}}(y)=\frac{2}{\sqrt{2 \cdot \pi} \cdot \sigma_{B}} \cdot \exp \left(-\frac{y^{2}}{2 \cdot \sigma_{B}^{2}}\right), \quad \forall y \in[0 ;+\infty) \tag{10} \end{equation*} While the definition for the asperity base radius $r_{\text {base }}$ remains identical, the contact spot radius $r_{\text {contact }}$ and density of microcontact spots $\varrho_{\text {spots }}$ have to be adapted: \begin{gather*} \varrho_{\text {spots }}=\frac{8}{\varepsilon \cdot \pi^{2} \cdot R_{s m}^{2}} \cdot \operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right) \tag{11}\\ r_{\text {contact }}=\frac{1}{2} \cdot \sqrt{\frac{\pi}{2}} \cdot \frac{R_{s m}}{2 \cdot \sigma} \cdot\left[\frac{2 \cdot \sigma}{\sqrt{2 \cdot \pi}} \cdot \exp \left(-\frac{W^{2}}{2 \cdot \sigma^{2}}\right)-W \cdot \operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right)\right] \tag{12} \end{gather*} The factor $\varepsilon$ adjusts the contact spot density to incorporate the area that exists inbetween the assumed conical shapes and the potential contacts they might have. For circular bases, a value of $\varepsilon \approx 1.5$ can be approximated statistically [5]. Applying the adapted parameters to Eq. (4) leads to the final equation for the HTC: \begin{equation*} h_{\text {model } 3}=\frac{8}{\varepsilon \cdot \pi^{2}} \cdot \frac{\lambda_{\text {eff }}}{R_{S m}} \cdot \operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right) \cdot \frac{\left[\frac{1}{2} \cdot \sqrt{\frac{\pi}{2}} \cdot \frac{R_{s m}}{\sigma} \cdot\left(\frac{2 \cdot \sigma}{\sqrt{2 \cdot \pi}} \cdot \exp \left(-\frac{W^{2}}{2 \cdot \sigma^{2}}\right)-W \cdot \operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right)\right)\right]}{\left[\frac{R_{s m}^{2}}{2}-\left(\frac{1}{2} \cdot \sqrt{\frac{\pi}{2}} \cdot \frac{R_{s m}}{\sigma} \cdot\left(\frac{2 \cdot \sigma}{\sqrt{2 \cdot \pi}} \cdot \exp \left(-\frac{W^{2}}{2 \cdot \sigma^{2}}\right)-W \cdot \operatorname{erfc}\left(\frac{W}{\sqrt{2} \cdot \sigma}\right)\right)\right)\right]^{1.5}} \tag{13} \end{equation*} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-200} \end{center} Fig. 2. Liquid-solid interface for a microscopically rough surface following profile model 3 \subsection*{2.4 Surface Profile Model 4} The fourth surface model proposed by $\mathrm{Xu}$ et al. [6] uses the modeling idea presented in model 3. When introducing a common base level height, the profile parameters $R_{a}$ and $\mathrm{R}_{\mathrm{sm}}$ remain the same while the slope changes. The partially significantly decreased slope this way results in an increased size of the conical asperities, leading to a changed surface profile with increased contact area as the outcome. As a result, the calculated heat transfer coefficient will be overestimated. The slope value can be preserved though by moving the asperities in parallel to the surface's mean plane while applying a leveling\\ needed for a uniform description of the wetting height. The proposed way for achieving this is doubling the parameter $R_{a}$ i.e. $R_{a_{n}}=2 \cdot R_{a}$. This leads to a new distribution function requiring an update for contact spot density and contact spot radius: \begin{gather*} \Phi_{\mathrm{n}}(y)=\frac{1}{\sqrt{2 \cdot \pi} \cdot \sigma_{n}} \cdot \exp \left(-\frac{\left(y-R_{a_{n}}\right)^{2}}{2 \cdot \sigma_{n}^{2}}\right), \quad \forall y \in[0 ;+\infty) \tag{14}\\ \varrho_{\text {spots }}=\frac{4}{\varepsilon \cdot \pi^{2} \cdot R_{s m}^{2}} \cdot \operatorname{erfc}\left(\frac{W-2 \cdot R_{a}}{2 \cdot \sqrt{\pi-2 \cdot R_{a}}}\right) \tag{15}\\ r_{\text {contact }}= \\ \sqrt{1-\frac{2}{\pi}} \cdot \frac{R_{s m}}{4} \cdot \exp \left[\frac{-\left(W-2 \cdot R_{a}\right)^{2}}{4 \cdot R_{a}^{2} \cdot(\pi-2)}\right]+\frac{R_{s m}}{8 \cdot R_{a}} \cdot\left(2 \cdot R_{a}-W\right) \cdot\left[1 \pm \operatorname{erf}\left(\frac{W-2 \cdot R_{a}}{2 \cdot \sqrt{\pi-2 \cdot R_{a}}}\right)\right] \tag{16} \end{gather*} Inserting these equations in Eq. (4) gives the final description of the HTC: \begin{align*} & h_{\text {model } 4}=\frac{8}{\varepsilon \cdot \pi^{2}} \cdot \frac{\lambda_{\text {eff }}}{R_{\text {sm }}} \cdot \operatorname{erfc}\left(\frac{W-2 \cdot R_{a}}{2 \cdot \sqrt{\pi-2 \cdot R_{a}}}\right) \\ & \cdot \frac{\frac{1}{4} \cdot \sqrt{1-\frac{2}{\pi}} \cdot \exp \left[\frac{-\left(W-2 \cdot R_{a}\right)^{2}}{4 \cdot R_{a}^{2} \cdot(\pi-2)}\right]+\frac{2 \cdot R_{a}-W}{8 \cdot R_{a}} \cdot \operatorname{erfc}\left(\frac{W-2 \cdot R_{a}}{2 \cdot \sqrt{\pi-2 \cdot R_{a}}}\right)}{\left[1-\frac{1}{2} \cdot \sqrt{1-\frac{2}{\pi}} \cdot \exp \left[\frac{-\left(W-2 \cdot R_{a}\right)^{2}}{4 \cdot R_{a}^{2} \cdot(\pi-2)}\right]+\frac{2 \cdot R_{a}-W}{4 \cdot R_{a}} \cdot \operatorname{erfc}\left(\frac{W-2 \cdot R_{a}}{2 \cdot \sqrt{\pi-2 \cdot R_{a}}}\right)\right]^{1.5}} \tag{17} \end{align*} \section*{3 Mechanical Analysis} During the casting process, gas i.e. air is pressed into the small notches of the rough surface where it can be compressed due to external forces. The exact amount of this compression, which is crucial to the wetted height level, is the result of a pressure equilibrium. Important to the equilibrium state during wetting are: \begin{itemize} \item The initial pressure of the entrapped air inside the surface cavity $p_{0}$ \item The capillarity pressure due to surface energies $p_{\gamma}$ \item The metallostatic pressure as result of the height $h$ of the liquid column $p(h)$ \item The externally applied pressure $p_{\text {ext }}$ \end{itemize} Considering the air inside a notch, Boyle-Mariotte's law applies with state 0 representing the conditions prior to casting and state 1 representing the state after pouring: \begin{equation*} p_{1} \cdot V_{1}=p_{0} \cdot V_{0} \tag{18} \end{equation*} When applying the ideal gas law and when considering that the amount of substance $n$ remains constant due to the air being entrapped, Eq. (18) can be extended including the respective temperatures and thermal effusivities $b$ : \begin{equation*} \left.\frac{p_{1} \cdot V_{1}}{T_{1}}=n \cdot R=\frac{p_{0} \cdot V_{0}}{T_{0}} \right\rvert\, \text { with } T_{1}=\frac{T_{\text {sol }} \cdot b_{\text {sol }}+T_{l i q} \cdot b_{l i q}}{b_{\text {sol }}+b_{l i q}} \text { and } b=\sqrt{\lambda \cdot \varrho \cdot c_{p}} \tag{19} \end{equation*} The following models will show different approaches to estimate the wetting height level while assuming that the solid material is formed by a non-porous medium and that the entrapped air can be described like an ideal gas. \subsection*{3.1 Wetting Model A} Hamasaiid et al. [3] formed an equation based on the simplifying approach that surface tension is negligible. While for a gravity die casting process $p_{0}$ will be equal to normal barometric pressure, pressure $p_{1}$ depends on the process conditions. The respective volumes can be approximated by the following equations: \begin{gather*} V_{0}=\frac{\pi}{3 \cdot m_{n}^{2}} \cdot \int_{y=0}^{y=+\infty} \Phi(y) \cdot y^{3} d y=\frac{\pi}{3} \cdot \sqrt{\frac{2}{\pi}} \cdot \frac{\sigma^{3}}{m_{n}^{2}} \tag{20}\\ V_{1}=\frac{\pi}{3 \cdot m_{n}^{2}} \cdot \int_{y=0}^{y=W} \Phi(y) \cdot y^{3} d y \approx \frac{\pi \cdot W^{3}}{3 \cdot m_{n}^{2}} \tag{21} \end{gather*} Combining Eqs. (21) and (22) with Eq. (19) allows for the calculation of the wetting height $\mathrm{W}$ as shown in Eq. (22). \begin{equation*} W=\sqrt[3]{\frac{p_{0} \cdot T_{1}}{p_{1} \cdot T_{0}}} \cdot \sqrt[6]{\frac{2}{\pi}} \cdot \sigma \tag{22} \end{equation*} \subsection*{3.2 Wetting Model B} While still ension and when applying the adapted asperity distribution function $\Phi_{B}$ as presented in surface profile model 3 , the equation for the wetting height changes to: \begin{equation*} W=\sqrt[3]{2 \cdot \frac{p_{0} \cdot T_{1}}{p_{1} \cdot T_{0}}} \cdot \sqrt[6]{\frac{2}{\pi}} \cdot \sigma \tag{23} \end{equation*} \subsection*{3.3 Wetting Model C} Hamasaiid et al. [5] also presented modeling approach including surface tension influences. When modelling the surface roughness as conical structure with circular bases, the case of a circular tube with low Bond number can be assumed due to the low size of the notches. This simplifies the Laplace-Young differential equation for the pressure difference $\Delta p$ across the fluid interface. The new expression depends on surface tension $\gamma$ and curvature radius $r_{\text {curv }}$ which can be approximated as a function of $p_{1}$ as shown in Eq. (24) leading to the wetting height depicted in Eq. (25). \begin{gather*} p_{\gamma}=\frac{2 \cdot \gamma}{r_{\text {curv }}} \approx 0.87 \cdot p_{1} \tag{24}\\ W=\sqrt[3]{2 \cdot \frac{p_{0} \cdot T_{1}}{\left[p_{1}-p_{\gamma}\right] \cdot T_{0}}} \cdot \sqrt[6]{\frac{2}{\pi}} \cdot \sigma \tag{25} \end{gather*} \subsection*{3.4 Wetting Model D} Prasher proposed a model for determining the wetting height based on a surface chemistry approach which includes the surface tension $\gamma_{l i q}$ influences. It applies the actual wetted height $\mathrm{X}$ instead of the thickness of the entrapped air $\mathrm{W}$ though. For a notch as shown in Fig. 1, the capillary pressure can be described as given in Eq. (26). The pressure equilibrium can be described by the expression in Eq. (27). \begin{gather*} p_{\gamma}=\frac{2 \cdot \gamma_{l i q} \cdot \sin (\theta+\varphi)}{r_{\text {base }}-X \cdot \cot (\varphi)} \tag{26}\\ p_{1}+\frac{2 \cdot \gamma_{l i q} \cdot \sin (\theta+\varphi)}{r_{\text {base }}-X \cdot \cot (\varphi)}=p_{0} \cdot \frac{r_{\text {base }}^{3}}{\left(r_{\text {base }}-X \cdot \cot (\varphi)\right)^{3}} \tag{27} \end{gather*} Equation (27) can be solved for $\mathrm{X}$ when assuming that for a $p_{1} \approx p_{0}$ condition, as is the case in most gravity die casting processes, the term $X \cdot \cos (\varphi)$ will be small compared to the base radius. The wetting height $X$ then can be calculated via Eq. (28). \begin{equation*} X=\frac{2 \cdot \gamma_{l i q} \cdot \sin (\theta+\varphi)}{3 \cdot p_{0} \cdot \cot (\varphi)} \tag{28} \end{equation*} \subsection*{3.5 Wetting Model E} Yuan et al. [7] introduced an extension to the empiric Hamasaiid approach for the surface tension influence by integrating the surface chemistry approach described by Prasher which corrects the calculated wetting height $W_{0}$ for no surface tension influences as shown in Eq. (29). \begin{equation*} W \approx \frac{1}{\Gamma-\frac{2 \cdot \gamma_{l i q} \cdot \sin (\theta+\varphi)}{3 \cdot \Gamma \cdot p_{0} \cdot W_{0}^{3} \cdot \frac{T_{1}}{T_{0}} \cdot \cot (\varphi)}} \left\lvert\, \Gamma=3 \sqrt{\frac{p_{1}^{2}}{\sqrt{4 \cdot p_{0}^{2} \cdot W_{0}^{6} \cdot\left(\frac{T 1}{T 0}\right)^{2}}-\frac{8 \cdot \gamma_{l i q}^{3} \cdot \sin ^{3}(\theta+\varphi)}{27 \cdot p_{0}^{3} \cdot W_{0}^{9} \cdot\left(\frac{T_{1}}{T_{0}}\right)^{3} \cdot \cot ^{3}(\varphi)}}+\frac{p_{1}}{2 \cdot p_{0} \cdot W_{0}^{3} \cdot \frac{T 1}{T 0}}}\right. \tag{29} \end{equation*} \section*{4 Comparison of Wetting and HTC Predictions} Figure 3 left shsows the predictions of the wetting height models examined as a function of $R_{a}$ as $\sigma=R_{a} \cdot \sqrt{\pi / 2}$. All models show a linear dependency of the resulting wetting height level and, with exception of model $\mathrm{C}$, predict absolute numbers of similar magnitude. Model $\mathrm{C}$, which introduces an empiric surface tension influence compared to model B, predicts wetting height values that are 2-3 times larger in comparison to the other models. Even though the absolute differences between all the models are rather small, there is a strong impact on the HTC results. This can be seen in Fig. 3 right where the surface profile model predictions are examined as a function of $H T C(W)$. For model 1, a parabolic shape of its function can be seen delivering values up to $1000 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}$ in a limited range of up to a roughness of $9 \mu \mathrm{m}$. The model by Prasher for this reason is not\\ suitable to describe the HTC in gravity die casting processes. All other models show an exponential behavior and are rather similar to each other with the main difference being a shift considering at which point lower wetting heights lead to very strong increases in the HTC prediction. For this reason even small changes in the wetting height prediction can lead to substantial differences in the predicted HTC which can be seen in Table 2 and 3. Here the models are applied to two different gravity die casting experiments with experimentally determined HTC by Xu [6] and Vossel [8] labeled as "GDC-A" and "GDC-B". Table 1 shows the respective differences in process parameters. Although the wetting height predictions are all in the same magnitude and might only be different for less than $1 \mu \mathrm{m}$, the results in predicted HTC can be profoundly different. Models i.e. model combinations giving results close to the experimentally determined HTCs, thus suitable for an application as HTC model inside a numeric simulation, are color coded green for models with high and orange for models with moderate agreement to the experimental values. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-204} \end{center} Fig. 3. Model prediction of wetting height prediction over $R_{a}$ (left) and model prediction of HTC over applied wetting height level (right) Table 1. Process parameters \begin{center} \begin{tabular}{|c|cccc|} \hline \multirow{4}{*}{"GDC-A"} & $R_{a}[\mathrm{~m}]$ & $\sigma[\mathrm{m}]$ & $R_{s m}[\mathrm{~m}]$ & $\varphi\left[^{\circ}\right]$ \\ \cline { 2 - 5 } & $3.52 \mathrm{E}-06$ & $4.41 \mathrm{E}-06$ & $1.35 \mathrm{E}-04$ & 3.74 \\ & $T_{0}[\mathrm{~K}]$ & $T_{1}[\mathrm{~K}]$ & $p_{0}[\mathrm{~Pa}]$ & $p_{1}[\mathrm{~Pa}]$ \\ \cline { 2 - 5 } & 300 & 409 & $1.013 \mathrm{E}+05$ & $1.047 \mathrm{E}+05$ \\ \hline \multirow{5}{*}{"GDC-B"} & $R_{a}[\mathrm{~m}]$ & $\sigma[\mathrm{m}]$ & $R_{s m}[\mathrm{~m}]$ & $\varphi\left[{ }^{\circ}\right]$ \\ \cline { 2 - 5 } & $4.84 \mathrm{E}-06$ & $6.42 \mathrm{E}-06$ & $4.72 \mathrm{E}-04$ & 15.22 \\ & $T_{0}[\mathrm{~K}]$ & $T_{1}[\mathrm{~K}]$ & $p_{0}[\mathrm{~Pa}]$ & $p_{1}[\mathrm{~Pa}]$ \\ \cline { 2 - 5 } & 300 & 724 & $1.013 \mathrm{E}+05$ & $1.047 \mathrm{E}+05$ \\ \hline \end{tabular} \end{center} Table 2. Resulting HTC values for "GDC-A" process parameters $\left[\frac{W}{m^{2} \cdot K}\right]$ Experimentally determined HTC: $5950 \mathrm{~W} /\left(\mathrm{m}^{2 *} \mathrm{~K}\right)$ \begin{center} \begin{tabular}{l|cccc} \hline & Model 1 & Model 2 & Model 3 & Model 4 \\ \cline { 2 - 5 } Model A & 1010 & 2120 & 23100 & 278000 \\ Model B & 931 & 694 & 7580 & 144000 \\ Model C & -1360 & 1 & 14 & 6380 \\ Model D & 1010 & 2340 & 25600 & 296000 \\ Model E & 845 & 405 & 4420 & 107000 \\ \hline \end{tabular} \end{center} Table 3. Resulting HTC values for "GDC-B" process parameters $\left[\frac{W}{m^{2} \cdot K}\right]$ \begin{center} \begin{tabular}{l|cccc} \multicolumn{5}{c}{Experimentally determined HTC: $2000-2500 \mathrm{~W} /\left(\mathrm{m}^{2 *} \mathrm{~K}\right)$} \\ \hline & Model 1 & Model 2 & Model 3 & Model 4 \\ \cline { 2 - 5 } Model A & 238 & 2580 & 1440 & 392000 \\ Model B & 175 & 634 & 108 & 175000 \\ Model C & -816 & 1 & 1 & 2050 \\ Model D & 226 & 26100 & 59900 & 1820000 \\ Model E & -37 & 50 & 1 & 45200 \\ \hline \end{tabular} \end{center} \section*{5 Conclusion} The presented HTC models were applied for two different gravity die casting processes where the respective heat transfer coefficients have been determined experimentally. While some models failed to predict appropriate HTC values, the surface profile model by Hamasaiid et al. [5] and especially the approach by $\mathrm{Xu}$ et al. [6] in combination with a wetting model by Hamasaiid et al. [5] managed to predict HTC values close to the experimentally derived ones. Predicting the HTC for a gravity die casting process represents a challenging task as the formula are very sensitive to the surface roughness where quite strong deviations in HTC predictions could be presents within the standard deviation of a roughness measurement used as input parameter. Acknowledgment. The presented investigations were carried out at RWTH Aachen University within the framework of the Collaborative Research Centre SFB1120-236616214 "Bauteilpräzision durch Beherrschung von Schmelze und Erstarrung in Produktionsprozessen" and funded by the Deutsche Forschungsgemeinschaft e.V. (DFG, German Research Foundation). The sponsorship and support is gratefully acknowledged. \section*{References} \begin{enumerate} \item Prasher, R.S.: Surface chemistry and characteristics based model for the thermal contact resistance of fluidic interstitial thermal interface materials. J. Heat Transfer 123, 969-975 (2001) \item Somé, S.C., Delaunay, D., Gaudefroy, V.: Comparison and validation of thermal contact resistance models at solideliquid interface taking into account the wettability parameters. Appl. Therm. Eng. 61, 531-540 (2013) \item Hamasaiid, A., Dargusch, M.S., Davidson, C., Loulou, T., Dour, G.: A Model to predict the heat transfer coefficient at the casting-die interface for the high pressure die casting process. AIP Conf. Proc. 907, 1211 (2007) \item Cooper, M.G., Mikic, B.B., Yovanovich, M.M.: Thermal contact conductance. Int. J. Heat Mass Transf. 12(3), 279-300 (1969) \item Hamasaiid, A., Dargusch, M.S., Loulou, T.: Dour, G: A predictive model for the thermal contact resistance at liquid-solid interfaces: analytical developments and validation. Int. J. Therm. Sci. 50, 1445-1459 (2011) \item Xu, R., Li, L., Zhang, L., Zhu, B., Bu, X.: An improved model for predicting heat transfer coefficient peak value at the casting-die interfaces. Indian J. Eng. Mater. Sci. 21, 628-634 (2014) \item Yuan, C., Duan, B., Li, L., Shang, B., Luo, X.: An improved model for predicting thermal contact resistance at liquid-solid interface. Int. J. Heat Mass Transf. 80, 398-406 (2015) \item Vossel, T., Pustal, B., Bührig-Polaczek, A.: Influence of gap formation and heat shrinkage induced contact pressure on the development of heat transfer in gravity die casting processes. In: Proceedings of Liquid Metal Processing \& Casting Conference 2019 (LMPC 2019), pp. 275284 (2019) \end{enumerate} \section*{Micro-macro Coupled Solidification Simulations of a Sr-Modified Al-Si-Mg Alloy in Permanent Mould Casting } \begin{abstract} Casting simulations incorporating solidification models are commonly applied to improve the dimensional accuracy of casting components. Challenging for a predictive casting simulation is the precise description of the solidification process of the casting alloy. For Sr-modified Al-Si-Mg casting alloys (e.g. A356), the Scheil-Gulliver model fails to describe the effect of Strontium on the solidification path. In this work, a dedicated micro-macro simulation approach is applied to a permanent mould casting component with Sr-modified A356 alloy. Microstructure simulations in both 2D and 3D based on multicomponent multiphase-field method were performed to study the effect of $\mathrm{Sr}$-modification, as well as the impact of cooling rate on solidification path. Casting simulations coupled with 2D and 3D microstructure simulation were compared and validated with experimental results. \end{abstract} Keywords: A356 alloy $\cdot$ Sr-modification $\cdot$ Phase-field simulation $\cdot$ Multiscale simulation \section*{1 Introduction} In commercial Al-Si casting alloys, Strontium ( $\mathrm{Sr}$ ) is often added to improve the mechanical properties. With an amount ranging from of $100 \mathrm{ppm}$ to $400 \mathrm{ppm}$, Sr transforms the eutectic morphology from coarse plate-like structure to fine coral-like fibrous networks [1, 2]. A great number of experimental and numerical studies [3-5] focused on the mechanism of Sr-modification to the Al-Si eutectic solidification and showed that $\mathrm{Sr}$ has impacts on both growth and nucleation of eutectic Si phases. In practice, the Scheil-Gulliver approximations are commonly employed in thermomechanical casting simulations to estimate the solidification path, i.e., the temperature dependent fraction of solid $f_{\mathrm{s}}(T)$, while experimental DSC (differential scanning calorimetry thermal analysis) data are used to describe the latent heat release. However, the Scheil-Gulliver model does not describe the effect of Sr on the nucleation and growth of eutectic Si, in particular the growth undercooling. Hence, it leads to an inaccurate description of the solidification path, latent heat release as well as temperature dependent\\ effective mechanical and thermal properties. Therefore, for Sr-modified Al-Si alloy, it is necessary to get insight into the microstructure formation process and understand the effect of $\mathrm{Sr}$ on the solidification process. In a previous study [6], the impact of Sr on eutectic solidification has been studied based on 2D microstructure simulations. A dedicate multiscale simulation method based on a self-consistent homoenthalpic approach [7] has been proposed and applied to simulate a permanent mould casting process component with Sr-modified A356 alloy. The spatially resolved microstructure simulations were performed using a Calphad-based multicomponent multiphase-field (MMPF) model [8]. The effect of Sr-modification was modelled by adjusting the nucleation model for eutectic Si phase, and by calibrating a growth parameter which characterizes the critical length scale of the eutectic microstructure. The 2D microstructure simulation were coupled to the thermomechanical finite element casting simulation based on a common enthalpy-temperature relationship. In this approach, the local heat extraction rate $\dot{Q}$ obtained by macroscopic casting simulation was applied as boundary conditions in microstructure simulations. Improved description of solidification path and latent heat release have been obtained by 2D microstructure simulations, and resulted in a more predictive casting simulation. For practical applications, casting simulation combined with 2D MMPF simulations are timesaving. However, inherent simplifications and approximations in a 2D MMPF model may also lead to an inaccurate description of the enthalpy-temperature relationship. In this paper, 3D MMPF simulations coupled to the same permanent mould casting simulations will be discussed. Results for 2D and 3D MMPF simulations were compared. Moreover, in the previous study [6], 2D MMPF simulation results based on the local heat extraction rate read from one single location of the casting component were applied for all integration points in FE thermomechanical simulation. In order to identify the impact of local cooling rate on the solidification process, 3D MMPF simulations with different local extraction rates for different locations are compared. \section*{2 The Casting Experiments} Casting experiments were performed using the experimental set-up presented in [9], see Fig. 1. It mainly consists of an inner steel core, a steel mould, a sand core on the top and the axisymmetric bowl-like casting component. The bowl component has an outer diameter of $155 \mathrm{~mm}$ and a wall thickness that gradually varies from $15 \mathrm{~mm}$ up to $30 \mathrm{~mm}$. The insulation on bottom and the sand core on top of the bowl assured a radial flow of the heat flux. Cooling channels were embedded in the mould in order to control the mould temperature. The experiment was carried out with an initial melt temperature at $720^{\circ} \mathrm{C}$ and a mould temperature of $30^{\circ} \mathrm{C}$. Thermocouples embedded in the mould wall as well as in melt were used to measure the temperature and the temperature gradients during the cooling process. In order to validate the heat transfer coefficient (HTC), the gap width between the mould wall and melt, as well as the contact pressure at the inner core were measured by quartz rods together with linear variable differential transformers (LVDTs). The commercial A356 with Sr-modification and grain refinement (TiB5) has been applied as casting alloy. The grain refinement ensured a relatively homogeneous grain\\ size distribution and an equiaxial growth of fcc-Al dendrites over all the casting component. A mean grain diameter of $400 \mu \mathrm{m}$ and an average secondary dendrite arm spacing (SDAS) of $19.5 \mu \mathrm{m}$ have been measured experimentally.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-209} Fig. 1. The experiment set-up (left) and the geometry of the casting component (right). \section*{3 Macroscopic Casting Simulation Model} \subsection*{3.1 The FE Simulation Model} The thermomechanical casting simulation were performed by using the finite element (FE) software Abaqus. The FE model, including mould set and the casting component were meshed with temperature-displacement coupled 4-node linear tetrahedron (C4D4T) elements. As the steel mould was built up with three identical $120^{\circ}$ segments including cooling channels and thermo-elements, one third of the entire set-up was modelled for FE simulations. The bowl casting component was modelled as a thermoelastoplastic material, whereas the mould and core parts as thermo-elastic material. According to the experiment, the melt, i.e., the bowl region had an initial temperature of $720^{\circ} \mathrm{C}$, while the mould temperature was set to be $30^{\circ} \mathrm{C}$. \section*{Modelling of Gap Formation} As the bowl component undergoes a volume shrinkage during the solidification process, an air gap could be formed between the casting component and the mould. For the precision of the simulation, the contact condition between the bowl component and its surrounding mould distinguishes between fluid-solid contact and solid-solid contact. By modelling of the solid-solid contact condition, the impact of the formed air gap on the heat transfer coefficient (HTC) has been taken into account. In this case, the HTC is modelled as a function of the local gap width and the local contact pressure [10]. The gap conduction model was implemented in Abaqus via the GAPCON subroutine. \section*{Modelling of Phase Transformation} In thermomechanical casting simulations, the casting alloys are treated as a liquid/solid two-phase system, which is characterized by the temperature dependent fraction solid\\ $f_{\mathrm{s}}(T)$. During solidification, the local average enthalpy of the mixture can be expressed as a function of fraction solid \begin{equation*} \langle\rho h\rangle=\int_{T_{0}}^{T}\left\langle\rho c_{p}(\tilde{T})\right\rangle \mathrm{d} \tilde{T}+\langle\rho\rangle L_{f}\left[1-f_{s}(T)\right] \tag{1} \end{equation*} in which $\rho$ and $h$ denote the density and specific enthalpy, respectively. $c_{\mathrm{p}}$ is the specific heat capacity and $L_{\mathrm{f}}$ represents the latent heat, i.e. the enthalpy of melting. Here, $\langle\cdot\rangle$ represents the volume average of a quantity in the two-phase system. According to the local energy balance in terms of specific enthalpy, the local energy balance in absence of external heat sources can be formulated as \begin{equation*} \left(\left\langle\rho c_{p}\right\rangle+\langle\rho\rangle L_{f} \frac{\partial f_{s}}{\partial T}\right) \frac{\partial T}{\partial t}+\nabla \cdot\langle\rho h \mathbf{v}\rangle=\dot{\mathrm{Q}} \tag{2} \end{equation*} with $\mathbf{v}$ representing the velocity vector and $\dot{Q}$ being the local heat flux. In the Abaqus FE model, the HETVAL subroutine in conjunction with the USDFLD subroutine were applied to define the source term related to the latent heat release in Eq. (2). Normally, the heat capacity $c_{\mathrm{p}}$, the total latent heat $L_{\mathrm{f}}$ and the fraction solid-temperature relation$\operatorname{ship} f_{\mathrm{s}}(T)$ are obtained by the Scheil approximation of solidification and experimental measurements. In the micro-macro coupled approach presented here, they are obtained from the Calphad-based MMPF microstructure simulation. As an example, the simulated temperature evolution during the solidification process in the bowl is shown in Fig. 2. The grey colour indicates temperatures higher than liquidus temperature, whereas the black colour in the right picture represents temperature lower than the solidus temperature.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-210} Fig. 2. Temperature $\left({ }^{\circ} \mathrm{C}\right)$ evolution during solidification with the grey and black coloured region indicating pure liquid and pure solid, respectively. \section*{4 Microstructure Simulation} Microstructure simulations were performed using the software MICRESS ${ }^{\circledR}$, which is based on the multicomponent multiphase-field model described in [8]. The Calphaddatabase are coupled via the TQ-interface. The alloy system is defined by $92.7 \mathrm{wt} \%$ $\mathrm{Al}, 7 \mathrm{wt} \% \mathrm{Si}$ and $0.3 \mathrm{wt} \% \mathrm{Mg}$. Further chemical elements normally also present in commercial A356 alloys, such as Mn and Fe, are not considered. During the simulation,\\ the nucleation of primary fcc-Al, eutectic Al-Si and $\mathrm{Mg}_{2} \mathrm{Si}$ phase were considered. According to the experimentally measured average grain size, a simulation domain with a dimension of $320 \mu \mathrm{m} \times 320 \mu \mathrm{m} \times 320 \mu \mathrm{m}$ and the grid resolution of $2 \mu \mathrm{m}$ has been used. Compared to primary fcc-Al dendrites, the interdendritic eutectic has a much finer microstructure, which cannot be resolved with a $2 \mu \mathrm{m}$ grid resolution. Therefore, the two-phase eutectics was handled as an effective single phase. The simulation started from $100 \%$ liquid phase at $615{ }^{\circ} \mathrm{C}$. Heat extraction rate was applied as the boundary condition. As shown in Fig. 3, an equiaxed single fcc-Al dendrite growths at the beginning of the solidification. At around $f_{\mathrm{s}}=0.5$, the first interdendritic eutectic phases were formed between primary fcc-Al dendrites and residual melt, leading to a rather complex microstructure at the end of the solidification process. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-211(2)} \end{center} $f_{\mathrm{s}}=0.02, T=600^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-211} \end{center} $f_{\mathrm{s}}=0.52, T=571^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-211(1)} \end{center} $f_{\mathrm{s}}=0.71, T=570^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-211(3)} \end{center} $f_{\mathrm{s}}=0.99, T=521^{\circ} \mathrm{C}$ Fig. 3. Results of a 3D microstructure simulation \subsection*{4.1 Effect of Sr-Modification on the Eutectic Solidification} The modelling of Sr-modification in the course of the eutectic solidification were achieved by applying appropriate nucleation and growth parameters for the effective eutectic phase. Specifically, the effect of $\mathrm{Sr}$ on the growth was simulated by calibrating a parameter which characterize the critical length scale of the eutectic morphology, whereas its effect on the nucleation of eutectic Si was realized by adjusting the number of initial nuclei for the eutectic phase. In the case of unmodified A356 alloy (see Fig. 4), a potentially unlimited number of nuclei for the eutectic phase were seeded in the RVE at the beginning of eutectic solidification $\left(f_{\mathrm{s}}=0.52, T=572.3^{\circ} \mathrm{C}\right)$, i.e., the number of grains is governed by the interplay of cooling rate and latent heat release during growth. The microstructure size parameter was set to be $0.1 \mu \mathrm{m}$. For the Sr-modified case (see Fig. 5), only 8 nuclei for the eutectic phase were allowed to grow up. The microstructure size parameter was set to be $0.01 \mu \mathrm{m}$. As illustrated in Fig. 6(a), in the unmodified case the eutectic growth temperature is very close to the equilibrium temperature obtained by Scheil approximation, while by $\mathrm{Sr}$-modified alloy it is nearly $5^{\circ} \mathrm{C}$ lower. Additionally, recalescence has been observed in the primary solidification (fcc-Al). Consequently, the fraction solid curve differs to the Scheil approximation, see Fig. 6(b). \subsection*{4.2 Impact of Cooling Rates on Solidification Path} For coupling to the macroscopic casting simulation, 3D MMPF simulations were performed by taking the local heat extraction rate $\dot{Q}$ obtained in casting simulations as \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212(1)} \end{center} $f_{\mathrm{s}}=0.52, T=572.3^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212(8)} \end{center} $f_{\mathrm{s}}=0.72, T=573.2^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212} \end{center} $f_{\mathrm{s}}=0.90, T=569.7^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212(6)} \end{center} $f_{\mathrm{s}}=0.99, T=516.9^{\circ} \mathrm{C}$ Fig. 4. Growth of effective eutectic grains during solidification of unmodified A356 alloys. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212(9)} \end{center} $f_{\mathrm{s}}=0.52, T=570.8^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212(7)} \end{center} $f_{\mathrm{s}}=0.71, T=570.3^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212(2)} \end{center} $f_{\mathrm{s}}=0.90, T=570.0^{\circ} \mathrm{C}$ \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212(4)} \end{center} $f_{\mathrm{s}}=0.99, T=521.1^{\circ} \mathrm{C}$ Fig. 5. Growth of effective eutectic grains during solidification of Sr-modified A356 alloys. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212(5)} \end{center} (a) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-212(3)} \end{center} (b) Fig. 6. Comparison between simulation results of Sr-modified A356 and unmodified A356 alloy: (a) temperature evolution; (b) fraction solid curve. boundary condition. The resulting fraction solid, latent heat release and heat capacity in dependency of temperature can then be applied for improving the macroscopic process simulation. However, in the casting simulation, the local heat extraction rates are not identical in the entire casting component. It is very expensive to perform MMPF simulation on each integration point of the FE model. In order to study the impact of cooling rate variation on the solidification, MMPF simulations were performed with heat extraction rate obtained on two locations, i.e., on the bottom middle (BM) and the top middle (TM) of the bowl component. As shown in Fig. 7(a), the cooling rate on point\\ $\mathrm{BM}$ is significantly higher than on point TM. Although the heat extraction rates on these two points differ from each other, see Fig. 7(b), the fraction solid curve and enthalpytemperature relationship obtained from both MMPF simulations are quite similar, as shown in Fig. 8. Hence, in the present casting simulation, a uniform fraction solid curve and enthalpy-temperature relationship were applied for the entire component. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-213(1)} \end{center} (a) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-213} \end{center} (b) Fig. 7. Temperature evolution (a) and the local heat extraction rate (b) on the bottom middle (BM) point and top middle (TM) point of the bowl calculated by FE casting simulation. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-213(3)} \end{center} (a) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-213(2)} \end{center} (b) Fig. 8. Comparison of faction solid curves (a) and the enthalpy-temperature relationship (b) obtained by MMPF simulations on two locations. \section*{5 Results of Micro-macro Coupled Simulation} The micro-macro coupled simulations were performed in two iterative loops. It began with a FE casting simulation with a fraction solid curve approximated by the Scheil solidification model. One should note that the result from the Scheil model does not consider different cooling rates, i.e. the Scheil curve is independent from the local temperature history. The local heat extraction obtained on the point BM was then applied as boundary condition for the temperature calculation in the 2D or 3D MMPF simulation. In Fig. 9,\\ the 3D MMPF simulation results are compared with the 2D MMPF simulation using the same boundary condition and nucleation model. In the second FE simulation, the new fraction solid curve and latent heat release obtained from the microstructure simulation was applied. For validation, the simulated temperature evolutions in four different bowl locations have been compared with the experimental measurements, see Fig. 10. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-214(2)} \end{center} (a) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-214} \end{center} (b) \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-214(1)} \end{center} (c) Fig. 9. 2D and 3D MMPF simulation results: (a) temperature evolution; (b) fraction solid curve; (c) enthalpy-temperature relationship.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-214(3)} Fig. 10. Temperature evolutions obtained by FE casting simulations on four experimentally observed locations, which are labelled as TM (top middle), TS (top surface), BM (bottom middle) and BS (bottom surface). As illustrated in Fig. 10, the FE simulation with the Scheil approximation supplied good temperature predictions in locations TM and TS. Whereas on the bottom of the bowl\\ (locations BM and BS) where the cooling rate is higher, the predicted temperature was significantly higher than in the experiment, especially at the later stage of solidification. By applying the fraction solid-temperature relationship and the latent heat release from the MMPF simulation, a better temperature prediction was obtained on locations BM and BS. Although the 2D MMPF simulation results show a slightly different recalescence and eutectic growth undercooling compared to the 3D simulation (see Fig. 9), the results of coupled casting simulations with 2D and 3D MMPF are quite similar. However, the temperature predictions for some regions, e.g., BS, still deviated from the experimental data. One further iteration with micro-macro simulations has been performed, but no obvious improvement in the temperature prediction was achieved. Likely reasons are the complexity of the casting geometry including thermomechanical effects like gap formation, which is related to a wide spread in the local cooling conditions, or the high complexity in the microstructure evolution of the Sr modified Al-Si alloy. Therefore, one potential solution for minimization of the remaining error could be further calibration of the number of potential nuclei and the microstructure size parameter of the eutectic phase. Moreover, instead of a uniform fraction solid curve and enthalpy-temperature relationship, locally different relationships could also lead to a more precise temperature prediction in casting simulation. \section*{6 Conclusions and Outlooks} In the present work, the MMPF based microstructure simulation effectively depict the effect of Sr-modification on the nucleation and growth of eutectic Si. It is confirmed that a uniform fraction solid curve and enthalpy-temperature relationship can be to apply to every integration point in FE casting simulation model, if a relatively homogeneous grain size distribution and equiaxial growth of fcc-Al dendrites all over the casting component are ensured. With the improved thermodynamic description of the solidification path provided by both 2D and 3D MMPF simulations, a more precise temperature prediction can be obtained, especially in regions with high cooling rate. It is worth noting that Sr-modification has not only impact on the solidification path and the latent heat release, but also on the morphological structure of the eutectic phase. Therefore, as the next step, the effective mechanical properties of the mushy zone during the solidification process will be extracted based on the fine fibrous eutectic morphology. Acknowledgments. This work is kindly supported by the German Research Foundation (DFG) in the framework of the Collaborative Research Centre SFB1120 "Precision Melt Engineering". \section*{References} \begin{enumerate} \item Sigworth, G.K.: The modification of Al-Si casting alloys: important practical and theoretical aspects. Int. J. Metalcast. 2(2), 41 (2008) \item Timpel, M., Wanderka, N., Schlesiger, R., Yamamoto, T., Lazarev, N., Isheim, D., Schmitz, G., Matsumura, S., Banhart, J.: The role of strontium in modifying aluminium-silicon alloys. Acta Mater. 60(9), 3920-3928 (2012) \item Lu, S.Z., Hellawell, A.: Growth mechanisms of silicon in Al-Si alloys. J. Cryst. Growth 73(2), 316-328 (1985) \item Dahle, A.K., Nogita, K., McDonald, S.D., Dinnis, C., Lu, L.: Eutectic modification and microstructure development in Al-Si Alloys. Mater. Sci. Eng. A 413-414, 243-248 (2005) \item Eiken, J., Apel, M., Liang, S.M., Schmid-Fetzer, R.: Impact of $\mathrm{P}$ and $\mathrm{Sr}$ on solidification sequence and morphology of hypoeutectic Al-Si alloys: combined thermodynamic computation and phase-field simulation. Acta Mater. 98, 152-163 (2015) \item Zhou, B., Laschet, G., Eiken, J., Behnken, H., Apel, M.: Multiscale solidification simulation of Sr-modified Al-Si-Mg alloy in die casting. In: IOP Conference Series: Materials Science and Engineering, vol. 861 (2020) \item Böttger, B., Eiken, J., Apel, M.: Phase-field simulation of microstructure formation in technical castings - a self-consistent homoenthalpic approach to the micro-macro problem. J. Comput. Phys. 228(18), 6784-6795 (2009) \item Eiken, J., Böttger, B., Steinbach, I.: Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 73(6), 1-9 (2006) \item Wolff, N., Pustal, B., Vossel, T., Laschet, G., Bührig-Polaczek, A.: Development of an A356 die casting setup for determining the heat transfer coefficient depending on cooling conditions, gap size, and contact pressure. Materialwiss Werkstofftech 48(12), 1235-1240 (2017) \item Laschet, G., Jakumeit, J., Benke, S.: Thermo-mechanical analysis of cast/mould interaction in casting process. Zeitschrift für Metallkunde 95(12), 1087-1096 (2004) \end{enumerate} \section*{Molding} \section*{Analysis of Radial Heat Transfer in an Injection Mold with Highly Dynamic Segmented Mold Tempering } \begin{abstract} The demand for precise injection molded parts is continuously increasing. One of the main effects that negatively influence the geometrical part properties is warpage due to inhomogeneous shrinkage. By homogenizing the specific volume and thus the shrinkage potential, warpage is expected to be reduced. The following work addresses the homogenization of the specific volume by controlling the local part temperature with 18 individual tempering zones in the mold, which are capable of rapid heating and cooling.\\ To control the tempering elements precisely, a model predictive control (MPC) approach has been developed, which predicts mold and melt temperature for each tempering zone based on a discretized one-dimensional heat transfer equation. Due to radial heat transfer processes in the mold cavity and the part, the temperature of one tempering zone is expected to have an influence on neighboring tempering zones. By additional consideration of the radial heat transfer in the mold and the part, the heating and cooling output of each tempering zone can be adapted according to the heat input from the neighboring tempering zones. \end{abstract} To quantify the reciprocal thermal influence of the tempering zones, heating trials have been performed and recorded with a thermographic camera. Keywords: Injection molding $\cdot$ Precision molding $\cdot$ Mold tempering $\cdot$ Process control $\cdot$ PvT-optimization $\cdot$ Modeling \section*{1 Introduction} The process of injection molding offers many advantages regarding cost and efficiency for mass production. However, the manufactured parts always undergo shrinkage and often warpage, negatively affecting the geometrical part properties. One of the main material properties influencing shrinkage and thus the warpage is the pressure-specific volume-temperature behavior (pvT-behavior). According to the pvT-behavior, illustrated in Fig. 1 for a semi-crystalline polymer, melt temperature and pressure during the molding process have a major impact on the specific volume and thus the shrinkage [1,2].\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-219} Fig. 1. Specific volume distribution of plate geometry at the packing phase (left); inhomogeneous shrinkage and warpage due to locally varying pressures and temperatures (right) [3]. As illustrated in Fig. 1 for a platen shaped geometry, the specific volume varies depending on the relative position to the sprue, due to locally varying melt pressures and temperatures. This leads to inner stress during the solidification and ultimately results in warpage. To minimize part warpage, the specific volume needs to be homogenized prior to ejection. According to the pvT-behavior, the specific volume can mainly be manipulated by controlling the local melt pressure or temperature [1,2]. The local pressure can be influenced by compression zones, which alters the local part geometry and is therefore not suited for most applications. This project therefore aims to manipulate the local specific volume without altering the local part geometry, by controlling the local melt temperature. \section*{2 Injection Mold with High Segmented Temperature Control} To achieve highly dynamic temperature changes during the injection molding process, a mold has been developed, which consists of 18 individually controllable tempering zones. An overview of the mold and a cross-sectional view of one tempering zone is given in Fig. 2. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-219(1)} \end{center} Fig. 2. Movable side of the mold with segmented temperature control (left); cross-sectional view of one tempering zone (right) [3]. In the first setup, a platen-shaped geometry $(170 \mathrm{~mm} \times 170 \mathrm{~mm} \times 3 \mathrm{~mm})$ is used and segmented into 9 tempering zones. As shown in Fig. 2, right, each tempering zone consists of a ceramic heating element with a maximum power of $1300 \mathrm{~W}$ and a $\mathrm{CO}_{2}$ expansion chamber for cooling. These evaporation chambers are filled with $\mathrm{CO}_{2}$ by magnetic valves which can be turned either fully on or off. When the liquid $\mathrm{CO}_{2}$ reaches the evaporation chamber, it evaporates due to the rapid decrease in pressure and thus cools the tempering zone with a temperature minimum of approximately $-78{ }^{\circ} \mathrm{C}$ [4]. The ribbed copper shield between $\mathrm{CO}_{2}$ expansion chamber and ceramic heating element dampens mechanicals loads on the ceramic element and enhances the heat transfer between $\mathrm{CO}_{2}$ and copper. In the center of each tempering zone, an infrared temperature sensor is located to measure the local part temperature [5]. Infrared temperature sensors excel regarding the reaction time, the sample rate as well as the precision. The sensors in tempering zones 2, 5 and 8 are combined infrared temperature and piezoelectric pressure sensors to measure the in-mold pressure at three different positions along the flow path. Due to the coat-hanger shaped melt distributor, a nearly straight flow front is expected, such that the measured pressures can be extrapolated for neighboring zones. As indicated in Fig. 2, right, the distance between cavity surface and $\mathrm{CO}_{2}$ evaporation chamber is $18 \mathrm{~mm}$. Therefore, heat transfer processes underlie thermal delays, meaning that approximately three seconds elapse between the actuation of a tempering zone and the actual change of the cavity surface temperature. Because of this delay, the process control strategy that actuates the heating and cooling elements need to contain a predictive element. Furthermore, each tempering zone is expected to have a thermal influence on adjacent zones. A controller which considers the heat transfer mechanisms from the tempering elements to the cavity surface therefore allows for an optimal control of each zone. \section*{3 Model Predictive Control Approach} The model predictive control approach (MPC) is able to predict the temperature in the mold and the part by calculating the heat transfer from the part center up to the tempering element. This allows a precise actuation of the heating and cooling elements while considering the thermal delay in the mold. \subsection*{3.1 Prediction and Control Mechanism} The temperature prediction is based on five discrete heating/cooling scenarios that are simultaneously calculated for all 18 tempering zones every $100 \mathrm{~ms}$. The prediction horizon is set to three seconds since the thermal delay inside the mold is approximately three seconds. For all scenarios, the temperature $T_{i}^{t}$ at the corresponding tempering element is calculated depending on the according power output or the $\mathrm{CO}_{2}$ valve position. To calculate the temperature from timestep $t$ to the next timestep $t+\Delta t$, a physical model is needed that describes the thermal processes in the mold and the part. In a first step, heat transfer processes are simplified to one dimension. For this the one-dimensional\\ heat equation derived from Fourier's law is used: \begin{equation*} \frac{\partial T}{\partial t}=a_{e f f} \cdot \frac{\partial^{2} \mathrm{~T}}{\partial x^{2}} \tag{1} \end{equation*} The thermal diffusivity $a_{\text {eff }}$ describes the effective material specific rate of heat transfer dependent on the thermal conductivity $\lambda$, the density $\rho$ and the heat capacity $c$. The heat conduction within each material is currently calculated by using individual non-temperature-dependent material properties. The heat transfer is simplified to heat conduction with a reduced conductivity. To solve Eq. 1 for each timestep and tempering zone, the equation is discretized using the Crank-Nicolson discretization scheme. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-221} \end{center} Fig. 3. Temperature prediction based on one-dimensional temperature nodes [3]. Equation 2, allows the calculation of the temperature in the part and the mold using discretization nodes. Figure 3 shows the calculated temperature distribution for one tempering zone at $3.2 \mathrm{~s}$. The black discretization nodes allow to dynamically overwrite the current temperature according to the measured melt temperature from the infrared sensors, the calculated heating ceramic temperature, or a fixed temperature at the $\mathrm{CO}_{2}$ expansion chamber of $-78{ }^{\circ} \mathrm{C}$. Using this one-dimensional finite difference approach allows a precise calculation of the individual part temperature. However, this setup cannot consider the reciprocal influence of adjacent tempering zones. \subsection*{3.2 Simulation and Modelling of Radial Heat Transfer} In the current configuration, the calculated temperature for each tempering zone is assumed to be uniformly distributed. Furthermore, the reciprocal influence of neighboring tempering zones cannot be considered, which is expected to be significant. To qualitatively examine both hypothesis in a first step, a finite element simulation has been conducted using all heating ceramics in the movable mold side at a power of $650 \mathrm{~W}$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-222} \end{center} Fig. 4. Distribution of discretization nodes for radial heat transfer on the cavity surface for tempering zone 3 . Figure 4 shows the cavity surface temperature and illustrates that the temperature distribution of one tempering zone is not uniform as assumed with the one-dimensional approach. Furthermore, the cavity plate allows radial heat transfer between adjacent tempering zones. By combining the current linear heat transfer model with radial heat transfer, both phenomena can be considered. Rewriting Fourier's law for the case that heat is transferred through a cylindric wall with the thickness $r$ yields the equation for radial heat transfer [7]: \begin{equation*} \frac{\partial T}{\partial t}=a_{e f f}\left(\frac{1}{r} \frac{\partial T}{\partial r}+\frac{\partial^{2} T}{\partial r^{2}}\right) \tag{2} \end{equation*} with $a_{\text {eff }}$ being the effective thermal diffusivity, and $r$ radial the distance. As with the linear heat transfer equation, Eq. 2 needs to be discretized using the Crank-Nicolson discretization scheme, such that it can be connected with the linear heat transfer nodes as indicated in Fig. 4. The connection of linear and radial heat transfer nodes creates a threedimensional heat transfer model. Using the three-dimensional discretization scheme will allow to consider the reciprocal thermal impact of the neighboring tempering zones as well as the uninform temperature distribution in each tempering zone. \section*{4 Heating Trials to Quantify the Impact of Radial Heat Transfer} The development of an optimal discretization scheme for the cavity surface and the part requires knowledge about the exact temperature distribution for a given tempering scenario. Furthermore, the impact of radial heat transfer on the temperature zone needs to be examined quantitatively. Within the scope of these trials, the MPC was not used to activate the heating elements. Each element was activated manually to have full control over each zone. In order to address both issues, heating trials have been performed using the ceramic heating elements in the movable mold side. The cavity surface temperature was recorded by a thermographic camera FLIR A645sc, FLIR Systems AB, Sweden. Due to space restrictions resulting from the thermographic measuring setup, the mold could not be\\ setup on an injection molding machine. The trials were conducted without general mold tempering. During all trials in the sections below, the ceramic heating power was set to approximately $650 \mathrm{~W}$. The maximum power the MPC can actuate is limited to $650 \mathrm{~W}$, since it already suffices for high heating rates. The heating duration was set to $10 \mathrm{~s}$. These parameters are additionally listed in Table 1 for a better overview and are equally used throughout all scenarios. Table 1. Important parameters for the heating trials. \begin{center} \begin{tabular}{l|c|l} \hline Parameter & Value & Unit \\ \hline Mold temperature & 23 & ${ }^{\circ} \mathrm{C}$ \\ \hline Heating ceramic power & 650 & $\mathrm{~W}$ \\ \hline Heating duration & 10 & $\mathrm{~s}$ \\ \hline Cycle time & 50 & $\mathrm{~s}$ \\ \hline \end{tabular} \end{center} \subsection*{4.1 Calibration of the Ceramic Heating Elements} In a first approach, it was examined whether the temperature of each tempering zone is similar for a given voltage. The power of the ceramic heating elements can be expressed as a function of the voltage $U$ and the electrical resistivity $R(t)$ according to Eq. 3: \begin{equation*} P(t)=\frac{\mathrm{U}^{2}}{\mathrm{R}(\mathrm{T})} \tag{3} \end{equation*} For a rising resistivity, more voltage is needed to hold the power level. The resistivity of the ceramic elements generally tends to rise with higher element temperature decreasing the maximum power output for a given voltage. More importantly, the ceramic heating elements that were used in the cavity have varying resistivities. According to the manufacturer datasheet, the resistivity $R_{20}$ at $20^{\circ} \mathrm{C}$ of each heating element can vary up to $\pm 25 \%$ [8]. Assuming the same applied voltage, this would result in significantly varied power output and temperature distribution for different tempering zones. As shown in Fig. 5, left, the temperature of all 9 tempering zones varies significantly for the same applied voltage due to variations in the individual resistivity. Thereby, the average zone temperature is $49.3{ }^{\circ} \mathrm{C}$ with a standard deviation of approximately $5.6{ }^{\circ} \mathrm{C}$ across all zones. The voltage therefore has been adjusted with the aim to homogenize the power output and with that the temperature of all tempering zones. The resulting temperatures as well as the average zone temperature and the standard deviation are illustrated in Fig. 5 (center and right). As it can be seen in the thermographic recording, the temperature distribution is visually homogenized. The average zone temperature is $48.9^{\circ} \mathrm{C}$ at a standard deviation across all zones of $1.6^{\circ} \mathrm{C}$. Adapting the voltage of all heating elements significantly reduced the standard deviation of the average zone temperature.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-224} Fig. 5. Recorded cavity temperature distribution without adjusted voltages (left) and with adjusted voltages (center) as well as the average zone temperature with standard deviation (right). \subsection*{4.2 Analyzing the Impact of Radial Heat Transfer} After successfully adjusting the heating output for the ceramic heating elements, the impact of radial heat transfer can be analyzed. For this, investigations on multiple heating scenarios have been conducted using a varying amount of simultaneously activated heating elements. For the following sub sections, two distinct tempering scenarios are selected and presented. \section*{Heating Scenario 1: Impact of One Activated Heating Element on Cavity Tem-} perature In a first approach tempering zone 5 is solely activated for $10 \mathrm{~s}$ to examine the impact of one activated heating element on the temperature of the adjacent tempering zones. Figure 6 shows the recorded temperature for the movable mold side as well as the corresponding temperature legend. The cavity surface temperature is shown for two different recording times to highlight the heat flux. Figure 6 shows the temperature distribution after $10 \mathrm{~s}$, which also equals the heating time.\begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-224(1)} \end{center} Fig. 6. Recorded cavity surface temperature for heating scenario 1 after $10 \mathrm{~s}$ (left); and $20 \mathrm{~s}$ (right). After $10 \mathrm{~s}$, there is no significant impact on tempering zones 1, 3, 7 and 9 . The average temperature of the remaining tempering zones raised approximately $1{ }^{\circ} \mathrm{C}$ and is\\ therefore negligible. The results show that there is no short-term impact for one activated heating zone. Although the ceramic heating element is turned off after $10 \mathrm{~s}$, the average temperature of zone 5 raises from 42.8 to $48.8^{\circ} \mathrm{C}$ due to linear and radial diffusion processes in the mold. Zone 1, 3, 7 and 9 still show no significant increase regarding their average zone temperature. The temperature of the remaining zones raised approximately $2{ }^{\circ} \mathrm{C}$ for the maximum power output of approximately $650 \mathrm{~W}$. For this configuration, the short- and long-term impact on the adjacent tempering zones is negligible. \section*{Heating Scenario 2: Impact of Two Activated Heating Elements on the Cavity} Temperature. In a next step, tempering zones 7 and 9 were activated simultaneously. Based on the first results, tempering zones 1, 2 and 3 are expected to be uninfluenced. Regarding tempering zones 4, 5 and 6, the average temperature increase is assumed to be around $1-2{ }^{\circ} \mathrm{C}$. Zone 8 is expected to experience the most influence, since it is located between zones 7 and 9 . In this heating scenario, the cavity surface temperature will be recorded for $120 \mathrm{~s}$, in order to investigate the long-term thermal impact for the complete injection cycle. Figure 7 illustrates the cavity surface temperature for heating scenario 2 after 10 and $50 \mathrm{~s}$, respectively. In Fig. 7 left, the temperature of zone 1 and 3 is slightly elevated, which can be attributed to prior infrared recordings. Similar to heating scenario 1, the short-term impact on the temperatures of the adjacent zones is not large. At $10 \mathrm{~s}$, the average temperature of zones 4 and 6 raised $0.5^{\circ} \mathrm{C}$. The temperature of tempering zone 8 raised $1{ }^{\circ} \mathrm{C}$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-225} \end{center} Fig. 7. Recorded cavity surface temperature for heating scenario 2 after $10 \mathrm{~s}$ (left); and $50 \mathrm{~s}$ (right). At $50 \mathrm{~s}$, which equals to the cycle time, the long-term impact of radial heat transfer becomes evident. The average temperature of zones 4 and 6 raised approximately $2{ }^{\circ} \mathrm{C}$. The temperature of zone 8 raised approximately $5^{\circ} \mathrm{C}$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-226} \end{center} Fig. 8. Temperature distribution of tempering zone 8 for heating scenario 2 . In order to highlight the temperature distribution in zone 8, the temperature curves of six temperature nodes are shown in Fig. 8. Node 1 is located at the center of zone 8 while node 6 is on the border to zone 9 . The nodes in-between 1 and 6 are evenly distributed as indicated. Based on the local temperatures of tempering zone 8, node 6 reaches its peak temperature at $18 \mathrm{~s}$ with $42^{\circ} \mathrm{C}$. The temperature of nodes 1 and 2 on the other hand keep rising even after the cycle time of $50 \mathrm{~s}$ and plateau at $29^{\circ} \mathrm{C}$ for another $60 \mathrm{~s}$, such that the cavity surface temperature is altered in the second injection cycle. Similar behavior can be seen with the average zone temperature. This long-term alteration of a non active tempering zone is currently not considered by the MPC and will significantly influence the temperature control precision. \section*{5 Conclusion and Outlook} For a precise and on-time actuation of the tempering elements, a model predictive controller was developed based on a one-dimensional heat equation. To describe the reciprocal thermal impact of neighboring tempering zones, radial heat transfer needs to be considered. To validate and calibrate the radial heat transfer model, multiple heating scenarios were analyzed, of which two were presented. It could be seen that the short-term impact on the adjacent tempering zones can be neglected due to the low thermal diffusivity of the cavity plate. However, it could be shown that the long-term impact was not negligible. The temperature of non-active and directly neighboring tempering zones rose significantly after the actual heating time. For a tempering zone located between two active tempering zones, which were activated for $10 \mathrm{~s}$ at a power of $650 \mathrm{~W}$, the long-term zone temperature\\ rose $5^{\circ} \mathrm{C}$. This rise in temperature plateaued for additional $60 \mathrm{~s}$, exceeding the actual cycle time, and thus influencing the temperature profile of the next cycle. Considering additional radial heat transfer in the MPC model will help in detecting such phenomena and therefore lead to a significantly better local temperature control. Regarding future research, additional simulations will be conducted to consider further parameters influencing the thermal balance of the mold such as the melt temperature and the mold tempering. The simulation will be calibrated to match the conducted heating trials such that the thermal simulation during the molding process has a high validity. The additional simulated results will be used to optimize the future radial heat transfer model. Acknowledgments. All presented investigations were conducted in the context of the Collaborative Research Centre SFB1120 "Precision Melt Engineering", subproject B3 "Self-optimizing Process Control Strategies for a Highly Segmented Injection Mould Tempering" at RWTH Aachen University and funded by the German Research Foundation (DFG). For the sponsorship and the support, we wish to express our sincere gratitude. \section*{References} \begin{enumerate} \item Wang, J., Hopmann, Ch., Röbig, M., Hohlweck, T., Kahve, C., Alms, J.: Continuous twodomain equations of state for description of the pressure-specific-volume-temperature behavior of polymers. Polymers 12, 409 (2020) \item Johannaber, F., Michaeli, W.: Handbuch Spritzgießen. Carl Hanser Verlag, München (2004) \item Hopmann, C., Kahve, C.E., Schmitz, M.: Development of a novel control strategy for a highly segmented injection mold tempering for inline part warpage control. Polym. Eng. Sci. 60, 2428-2438 (2020) \item Berghoff, M.: Perspektiven bei der Temperierung von Problemzonen im Werkzeug, \href{https://www.isk-iserlohn.de/fileadmin/medien/Dokumente/co2_temperierung_fachbeitrag}{https://www.isk-iserlohn.de/fileadmin/medien/Dokumente/co2\_temperierung\_fachbeitrag}. pdf. Accessed 11 Feb 2020 \item Giese E.: Infrared temperature sensor for plastics molds, Datasheet. \href{https://www.fos-messte}{https://www.fos-messte} \href{http://chnik.de/MTS%20408_IR_BTS_STS_XSR_2017.pdf}{chnik.de/MTS 408\_IR\_BTS\_STS\_XSR\_2017.pdf}. Accessed 28 Jan 2020 \item Thomas, J. W.: Numerical Partial Differential Equations: Finite Difference Methods (1995). ISBN: 978-1-4899-7278-1. \item Kneer, R: Wärme-und Stoffübertragung I/II, RWTH-Aachen (2014) \item NN: Heating elements, Details of Standard. \href{https://www.bachrc.de/print.html?category=cer}{https://www.bachrc.de/print.html?category=cer} amic-8\&group $=1$ \&product $=0$ \&language=en. Accessed 23 Apr 2020 \end{enumerate} \section*{Evaluation and Transport of the Crystallization Heat in an Iterative Self-consistent Multi-scale Simulation of Semi-crystalline Thermoplastics } \begin{abstract} In the injection molding process of semi-crystalline thermoplastics, the melt is subjected to a complex deformation and temperature history. This leads to an inhomogeneous microstructure over the component and thus to local inhomogeneities in the component's effective properties. To predict the component properties precisely, a multi-scale simulation is used, which couples the filling simulation at the component level with a microstructure simulation at the scales of microns (SphaeroSim). The influence of the crystallization heat is considered in the filling simulation with an averaged empirically determined degree of crystallization. To achieve higher precision in the microstructure simulation the influence of the crystallization heat is considered at the microscale of SphaeroSim. SphaeroSim is extended by the calculation of a local crystallization degree, which is used to calculate the amount of local crystallization heat and heat transport calculations. \end{abstract} Keywords: Semi-crystalline polymers $\cdot$ Polymer crystallization $\cdot$ Injection molding $\cdot$ Multiscale simulation \section*{1 Introduction} The manufacturing of high-quality injection molded parts requires a deep understanding of material properties, process parameters and product design [1]. The material behavior of injection molded components highly depends on the formation of microstructures during manufacturing, which in turn is linked to the macroscopic heat and material flow during manufacturing [2]. In semi-crystalline thermoplastics two types of microstructures must be distinguished at different scales: the formation of molecular chain folded lamellae at the nanoscale and the formation of superstructures, named spherulites, at the microscale. Each spherulite contains lamellae structures originating from a single nucleus. The lamellae are surrounded by amorphous material, which in the case of isotactic polypropylene (iPP) makes up $47 \%$ of the solidified material [3, 4]. The form and distribution of superstructures as well as crystalline-amorphous composition of each spherulite has a high impact on the macroscopic thermal and mechanical properties [5, 6]. A precise calculation of superstructures provides deep insights into the thermal and mechanical properties of an injection molded component. Due to the huge computational effort to calculate the molecular behavior at the scale of a component, a 4 step multiscale simulation chain for semi-crystalline thermoplastics is developed within the collaborative research center SFB 1120, "Precision Melting Engineering" (see Fig. 1) [4]. The simulations are performed at three different levels of scale: The macroscale, a coupled filling, heat transfer and solidification simulation is performed using COMSOL Multiphysics, COMSOL Multiphysics GmbH, Göttingen [3]; at the microscale, an cellular-automata solver, SphaeroSim, is developed to calculate the form and distribution of superstructures and at the nanoscale, at which a Representative Volume Element (RVE) of the bi-lamella formed from crystalline and amorphous phases, is discretized and homogenized within HOMAT [7]. As both phases co-exist always, their pure phase properties are calculated by molecular-dynamics simulations [7]. HOMAT simulates the crystalline-amorphous composition of the bi-lamellae formation within the superstructures of iPP. This is combined with the properties resulting from the bilamella homogenization, to calculate the effective thermal and mechanical properties of the superstructures. Using the distribution of superstructures on the RVE, its effective mechanical and thermal properties are evaluated by adopting a special 3D spherulite model [2]. The simulation on the three different scales and the homogenizations allow the computation of effective properties in a reasonable time. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-229} \end{center} Fig. 1. The multiscale simulation scheme developed within the collaborative research center SFB 1120 Currently, SphaeroSim uses thermal and velocity fields calculated by filling simulation (FS) as starting conditions without calculating internal thermal diffusion during\\ solidification. This leads to neglecting the crystallization heat at the point of solidification at the microscale. The consideration of the crystallization heat at the microscale was found to impact the microstructure and thus the effective properties $[8,9]$. Böttger et al. [10] developed a self-consistent multiscale simulation scheme for metallic alloys, which correlates the thermal fields calculated at the macro- and microscale in an iterative way, to ensure that the thermal fields and the cooling behavior are consistent at both scales. To incorporate a similar approach to the multiscale simulation chain for semi-crystalline thermoplastics, parameters to link microstructure simulation (MS) and FS are determined in Sect. 2. Since the consideration of crystallization heat at the microscale impacts the superstructure formation, the release of crystallization heat (Sect. 4) and its propagation (Sect. 3) are implemented in SphaeroSim. \section*{2 The Self-consistent Approach Within the Multiscale Simulation Chain} \subsection*{2.1 Self-consistency of the Multiscale Simulation Scheme} Böttger et al. [10] discovered that crystallization heat at the microscale cannot be averaged from the macroscale and the cooling behavior must be the same at both scales otherwise a completely different microstructure is formed. Since the crystallization heat and its thermal diffusion influences the microstructure of polymers, this approach is suitable to improve the multiscale simulation chain for semi-crystalline thermoplastics $[8,9]$. In the original formulation of self-consistent iterative multiscale simulation, the FS uses process-related boundary conditions (e.g. geometric, thermal) applied on the RVE for the microstructure nucleation and growth simulation. In turn, MS is used to provide an accurate calculation of solid fraction, crystallization heat release and the temporal enthalpy change at a much smaller scale than FS. From MS, the solid fraction and thermal calculations are fed back to the FS and adjustments are done to reduce the differences between both simulations. Updated thermal and velocity fields based on the adjustments are used in another microstructure evolution simulation run. This iterative feedback-loop between FS and MS is performed until consistency within thermal fields, solid fraction and release of crystallization heat is reached. A much more realistic temperature-time curves was reached in comparison to widely used macroscale models [10]. This approach is transferred here to the multiscale simulation chain of semicrystalline thermoplastics. Here, both simulations benefit from the iterative selfconsistent framework, where MS cannot consider geometric or thermal boundary conditions (e.g. mold wall, melt temperature) on the scale of the component, the FS is equipped to provide the necessary calculations. At selected locations, the FS benefits from solidification calculations at a 1,000,000 times finer grid within the MS. To implement the iterative self-consistent approach both simulations must provide a description of crystallization degree, solid fraction and crystallization heat release including thermal diffusion. Those parameters can be calculated within SphaeroSim to a much higher accuracy than in FS. An improvement of the FS is expected if the FS parameters are adjusted accordingly. \subsection*{2.2 Macroscale Filling Simulation} The FS performs the filling simulation and heat transfer calculations within the cavity in the injection molding process. This takes into account many boundary conditions set by production-related parameters. Phase change, cooling and unsteady flow behavior of the melt are considered during the injection molding process. The melt flow description is provided by incompressible viscous Navier-Stokes flow based on the conservation equations of mass, momentum and energy. This is implemented in a dedicate finite element model, which is implemented in the multiphysics solver, COMSOL $[3,11]$. The solidification is calculated using a simple Avrami-equation to predict the solid fraction $\xi$, which depends on time $t$ and the non-isothermal kinetic rate constant $K_{a}$ : \begin{equation*} \xi=1-\exp \left\{\left[K_{a} t\right]^{n_{a}}\right\} \tag{1} \end{equation*} where $n_{a}$ is the Avrami-exponent, which can take values in the interval between 1 and 4 and characterizes the spherulitic growth mechanism [2, 12-14]. The solid fraction states the relative amount crystallized material in relation to the maximum reachable crystallization degree. The Avrami-equation therefore yields the amount of crystallized material with time depending on the non-isothermal kinetic rate constant and time. The change in solid fraction is then used within the heat transfer equations to calculate the crystallization heat release $\dot{Q}$ during solidification in the form of: \begin{equation*} \dot{Q}=\xi_{m a x}^{a b s} \Delta h_{m, 0} \frac{\partial \xi}{\partial t} \tag{2} \end{equation*} where $\xi_{\max }^{a b s}$ is the maximum reachable crystallization degree (here $53 \%$ ); and $\Delta h_{m, 0}$ the change in enthalpy for ideal $100 \%$ crystallization [3, 15]. Overall, this calculates the emitted local heat by the solidification processes for local, temporal and thermal evolution. However, the maximum reachable crystallization degree is assumed to be fixed and equal throughout the component. Here, SphaeroSim provides a significant improvement by calculating a local crystallization degree depending on crystallization kinetics and on a much finer grid. This leaves the identification in SphaeroSim, how the crystallization heat is calculated and a description of the solid fraction within a simulation volume. \subsection*{2.3 Microscale Superstructure Simulation (SphaeroSim)} SphaeroSim is a cellular-automata solver, which solves the Avrami-equation modified by the Hoffman-Lauritzen nucleation and growth theory. To simulate the microstructure within a support location, the area is usually discretized into voxels of $1 \times 1 \times 1 \mu^{3}$, since this is the actual maximum fineness within SphaeroSim [4]. The starting conditions (thermal and velocity fields) from FS are interpolated to the finer grid for each time step calculated in SphaeroSim. Currently this setup allows disregarding of all thermal behavior on the microscale since the considerations of crystallization heat and thermal diffusion are provided by the microscopic local temperature. However, due to the finer grid size and the findings of Böttger et al., the local impact of crystallization heat on the formation of spherulites is high. Therefore, the calculation of crystallization heat released during solidification at the microscale and thermal diffusion are now implemented. \section*{3 Implementation of the Thermal Transport in the Microstructure Simulation} The three-dimensional heat transfer equation is derived from Fick's second law of diffusion and describes the diffusion of heat over time and space [16]: \begin{equation*} \frac{\partial T}{\partial t}=D\left(\frac{\partial^{2} T}{\partial \boldsymbol{x}^{2}}+\frac{\partial^{2} T}{\partial \boldsymbol{y}^{2}}+\frac{\partial^{2} T}{\partial z^{2}}\right) \tag{3} \end{equation*} where $x, y, z$ are the three-dimensional relative coordinates. The thermal diffusion coefficient $D$ needs to be treated for anisotropic material, since every voxel calculated by SphaeroSim has a unique crystallization degree $k_{i}$ based on its temperature history. Additionally, the thermal conductivity $\lambda$, the specific heat capacity $c_{p}$ and the density $\rho$ depend on the local crystallization degree [7]. \begin{equation*} D_{i}\left(k_{i}\right)=\frac{\lambda\left(k_{i}\right)}{c_{p}\left(k_{i}\right) \rho\left(k_{i}\right)} \tag{4} \end{equation*} A unique $D_{i}$ must be calculated for each voxel $i$ to ensure precise thermal calculations. To simplify the determination of the local diffusion coefficient, it is assumed that the material properties in an undercooled melt do not change until solidification. Once solid, a voxel can neither remelt, nor change its crystallization degree. These assumptions allow the initialization of $D_{i}$ with material parameters of only molten material. At the time of state change the corresponding crystallization degree is calculated from $T_{c}$ and $D_{i}$ is updated. It is to note, that in the initial formulation of the iterative self-consistent multiscale scheme, Böttger et al. used a one-dimensional description of heat diffusion in their simulation [10]. This is not possible in the case of three-dimensional unique diffusion coefficients and a 3D-heat transfer is implemented. An analytical solution for the heat-equation is obtained by Fourier analysis in the form of: \begin{equation*} T(x, y, z, t)=\frac{1}{\sqrt{4 \pi D t}^{3}} \exp \left(-\frac{x^{2}+y^{2}+z^{2}}{4 D t}\right) \tag{5} \end{equation*} Equation (5) is the so-called fundamental solution of the heat-equation. The function can be used to find a general solution for the heat-equation over certain domains with simple boundary conditions [16]. Since the starting conditions received from the FS are discrete and heat sources (crystallization heat) are not covered in this solution, the usage of the fundamental solution must be adopted. The fundamental solution is used for the purpose of propagating temperature within SphaeroSim by treating each voxel as a separate heat source calculating unhindered thermal diffusion within a small timeframe $t$. The superposition of the thermal diffusion of all voxels lead to the temperature diffusion throughout the whole simulation volume. The timeframe $t$ must be chosen small enough to ensure a negligible difference of the local diffusion coefficients $D_{i}$ in the affected neighborhood. The continuous formulation of the fundamental solution allows the calculation of the temperature influence of each voxel to all other voxels in the simulation area. The\\ calculation of temperature influences to all voxels is CPU time consuming, however it allows to choose the size of the neighborhood by variation of the time $t$ for the diffusion to propagate. The discretization, once a time step size is chosen, is performed by integration of the fundamental solution over each voxel in the neighborhood, where the neighborhood is here defined as each voxel within $99.5 \%$ of the distributed heat. This ensures the validity and accuracy of the thermal diffusion throughout the simulation area, while keeping the calculation time reasonable. \section*{4 Crystallization Heat in SphaeroSim} \subsection*{4.1 Implemented Crystallization Kinetics Model} As well as the FS, the Avrami-equation is used within SphaeroSim to determine solidification of single voxels, but in a modified form. The non-isothermal kinetic rate constant $K_{a}$ can be further split into a geometric factor, a term connected to the nucleation rate and a growth function determined by the type of spherulitic growth (see Eq. (6)) [17]. At first, the type of spherulitic growth is determined to be spherical, which demands an Avrami-exponent of at least 3. The addition of a nucleation rate $\dot{N}$, adds another degree of freedom, which sets the Avrami-exponent to 4. The final form of the kinetic rate constant used in SphaeroSim: \begin{equation*} K=\frac{\pi}{3} \dot{N}(T, \Delta g) G^{3}(T, \Delta g) \tag{6} \end{equation*} where $G(T)$ is the growth rate function of the spherulites, which is derived from the Hoffman-Lauritzen nucleation and growth theory [17, 18] (explicit forms for $\dot{N}$ and $G$ can be found in [4] p. 31). The nucleation rate as well as the growth rate are dependent on the temperature $T$ and the change in Gibbs free energy $\Delta g$, which in turn is dependent on the temperature and material constants. The implementation of SphaeroSim splits $\Delta g$ into a melt flow dependent term and a melt flow independent term $\Delta g_{v, q}$, which states the change of Gibbs free energy in quiescent conditions. In order to determine the crystallization heat, the flow dependent term can be ignored, since it only contributes to the nucleation rate (shear induced nucleation) but not to the growth rate, in the current model. The change in Gibbs free energy in quiescent conditions is implemented from the Hoffman-Lauritzen theory as: \begin{equation*} \Delta g_{v, q}=\Delta h_{m, 0} f \frac{T_{m, 0}-T}{T_{m, 0}} \tag{7} \end{equation*} where $\Delta h_{m, 0}$ is the crystallization heat for an ideal crystallization degree of $100 \% ; T_{m, 0}$ is the equilibrium melting temperature; and $f$ is a correction factor proposed in Hoffman et al. to widen the application of $\Delta g_{v, q}$ to a large range of undercooling [19,20]. During cooling the iPP melt passes $T_{m, 0}\left(194{ }^{\circ} \mathrm{C}\right)$ and becomes undercooled. In the undercooled melt the formation of nuclei and the growth of spherulites is possible. Since variations in cooling rate of injection molding between $60 \mathrm{~K} / \mathrm{min}$ at the core of the component and up to $3,000 \mathrm{~K} / \mathrm{min}$ at the mold walls is common, large undercooling must be considered [21]. Measurements using a Flash-DSC 2+, Mettler-Toledo, Columbus, \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-234} \end{center} Fig. 2. The heat flow normalized with the cooling rate of each cooling cycle of iPP using the Flash-DSC 2+, Mettler-Toledo, Columbus, USA. The sample is heated to $240{ }^{\circ} \mathrm{C}$ using a constant heating rate of $100 \mathrm{~K} / \mathrm{s}$, followed by rapid cooling down to $40^{\circ} \mathrm{C}$ for each measurement. USA are performed to measure the crystallization heat during crystallization at very fast cooling rates from $600 \mathrm{~K} / \mathrm{min}$ to $300,000 \mathrm{~K} / \mathrm{min}$ (see Fig. 2). The crystallization process is described by the onset temperature and the peak temperature. The onset temperature shows the point at which the first nucleus forms and the solidification starts. The peak temperature shows the highest solidification rate per time. Both temperatures are dependent on the cooling rate (see Fig. 3), however measurements taken with cooling rates of $60,000 \mathrm{~K} / \mathrm{min}$ and $300,000 \mathrm{~K} / \mathrm{min}$ do not show any crystallization peak. The rapid cooling suppresses molecular movement to the point where no molecular chain folding is possible, and the melt solidifies purely in an amorphous phase. This points out, that the increasing cooling rates lead to a reduction in crystallization degree and therefore to a reduced crystallization heat. In order to compensate for the reduction in crystallization heat at high undercooling, the correction factor $f$ is introduced in the Hoffman-Lauritzen theory. \begin{equation*} f=\frac{2 T}{T_{m, 0}+T} \tag{8} \end{equation*} $f$ describes the reduction in crystallization heat released into the melt, therefore it is interpreted as the factor defining the crystallization degree during the simulation. In the implementation of SphaeroSim, voxels are either in a molten state or in a solid state and no solid fraction within a voxel is considered. The crystallization degree of a voxel is therefore calculated from the factor $f\left(T_{c}\right)$ at the point of phase change and the solidification temperature $T_{c}$. The point of phase change of a voxel is calculated from the Avrami-equation reaching a solid fraction of $50 \%$. This approximation simplifies the assignment of a voxel to a spherulite to the point of half crystallization time and \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-235} \end{center} Fig. 3. The crystallization onset temperature and the peak temperature of iPP measured at constant cooling rates ranging from $2 \mathrm{~K} / \mathrm{min}$ to $6,000 \mathrm{~K} / \mathrm{min}$ cooled from $240{ }^{\circ} \mathrm{C}$ to $40{ }^{\circ} \mathrm{C}$ using the FlashDSC 2+ and DSC Q2000, TA Instruments, New Castle, USA for cooling rates up to $20 \mathrm{~K} / \mathrm{min}$. reduces the amount of data generated during simulation significantly [4]. Furthermore, all crystallization heat of a voxel is released at the time of phase change. This simplifies the treatment of the temperature change to a simple addition to the solidified voxel. \subsection*{4.2 Comparison of the Calculation of Crystallization Heat at micro- and Macroscale} The crystallization heat release during solidification plays a major role within the selfconsistent approach. To compare the amount of crystallization heat released in both simulations, MS and FS, thermal calculations of a simulation volume of step-plate component are performed. The selected volume is $3 \mathrm{~mm}$ thick, spanning from one mold wall to the other one with an area of $0.5 \times 0.5 \mathrm{~mm}^{2}$. To calculate the crystallization heat released throughout the solidification within FS is performed by temporal integration of Eq. (2): \begin{equation*} \int_{0}^{\infty} \dot{Q} d t=\xi_{\max }^{a b s} \Delta h_{m, 0} \tag{9} \end{equation*} The integration of the change in solid fraction $(\partial \xi / \partial t)$ limits to 1 for a completely solidified component; with the crystallization heat for $100 \%$ crystallinity $\Delta h_{m, 0}=$ $0.14 \mathrm{~J} / \mathrm{mm}^{3}$ the released heat is calculated to $Q=55.6 \mathrm{~mJ}$. The calculation of crystallization heat in SphaeroSim cannot be performed by integration since no gradual increase of crystallinity is calculated, but a sudden phase change from melt to solid at $50 \%$ relative crystallinity. It is therefore assumed, that all crystallization heat is released at this point in time and temperature. From Eq. 7 the crystallization heat can be derived in the form of $f \Delta h_{m, 0}$. The comparison of both formulations suggests that $f$ should resemble the reached crystallization degree of each voxel. However, the solidification temperature for $f=0.53$ is $-104.6^{\circ} \mathrm{C}$. This temperature is well below the\\ glass transition temperature of iPP, therefore the assumption of a crystallization process starting at that temperature is wrong. The average crystallization degree calculated by ShpaeroSim via $f \Delta h_{m, 0}$ is $88 \%$ and crystallization heat released within the simulation volume is $92.3 \mathrm{~mJ}$. At this point some problems of the currently implemented correction factor $f$ must be pointed out: The Hoffman-Lauritzen theory from which the factor originates, was developed assuming isothermal solidification conditions with small undercooling. The formulation in general was proven to be valid for several non-isothermal cases, but the Avrami-equation in which the growth-function $G$ is embedded only predicts a relative crystallinity. In the formulation of solidification in both simulations the relative crystallinity is assumed to be a solid fraction. This disregards the crystallization degree reached at a given solidification temperature. The factor $f$ is used to compensate for the reduction in crystallization degree at higher undercooling but shows that additional parameters must be introduced to model solidification of semi-crystalline polymer in injection molding processes. It is necessary to introduce a function that calculates the crystallization degree depending on the cooling rate up to the point at which formation of lamellae is completely suppressed. This ensures, that the crystallization heat can be correctly calculated even for extreme cooling rates, which are found in injection molding processes. This still leaves the Avrami-model valid to determine solid fraction, but it would result in the amount of crystallized phase present in a voxel, disregarding amorphous material as part of the solid. \section*{5 Conclusion and Outlook} The formation of microstructures during the solidification of semi-crystalline thermoplastics has a major impact on the effective thermal and mechanical properties of the final component. The multiscale simulation chain was developed to predict the microstructure in a simulation chain across macro-, micro- and nanoscale. Since the macro- and microscale simulation both simulate solidification but on different scales, the iterative self-consistent approach is proposed. This uses the accuracy of the microscale simulation to improve the accuracy of the macroscale simulation results. In order to link both simulations, the thermal fields, crystallization degree and solid fraction are determined. Since the microscale simulation relied purely on the calculated thermal fields provided by the macroscale simulation, thermal calculations are implemented into the microscale simulation. The diffusion of temperature during solidification is calculated via the fundamental solution of the heat diffusion equation. The fundamental solution allows the choice of the time step size for the thermal diffusion, due to its continuous formulation. The thermal diffusion is implemented to consider crystallization heat emitted during the solidification at the microscale, since the crystallization heat has a major impact on the microstructure formation. The comparison of the crystallization heat from the mircoand macroscale showed significant differences in scale and thermodynamic treatment of the calculation of the crystallization heat. The microscale simulation uses the correction factor $f$ from the Hoffman-Lauritzen theory to determine the amount of crystallization\\ heat released to the system, which is not sufficient to determine the crystallization in according to experimental data and should be replaced. The correction factor $f$ has certain shortcomings, such as the overestimation of crystallization heat release. For semi-crystalline thermoplastics, a functional relationship between the crystallization degree reached and cooling rate of a sample will be developed in future works. This function will enable the Avrami-model to describe the amount of crystallized material at a given time and temperature, which is preferable, since it neglects the amorphous material as part of the solid. Acknowledgments. The depicted research was funded by the Deutsche Forschungsgemeinschaft (DFG) as part of the collaborative research center SFB 1120 "Precision Melt Engineering". We would like to extend our thanks to the DFG. The authors wish to thank Prof. R. Spina (Politecnico di Bari, Italy) for providing the simulation results of the injection molding process with COMSOL. \section*{References} \begin{enumerate} \item Spina, R., Spekowius, M., Hopmann, C.: Analysis of polymer crystallization with a multiscale modeling approach. In: Key Engineering Materials, vol. 611, pp. 928-936. Trans Tech Publications Ltd (2014) \item Laschet, G., Apel, M., Wipperfürth, J., Hopmann, C., Spekowius, M., Spina, R.: Effective thermal properties of an isotactic polypropylene ( $\alpha$-iPP) injection moulded part by a multiscale approach. Materialwiss. Werkstofftech. 48(12), 1213-1219 (2017) \item Spina, R., Spekowius, M., Hopmann, C.: Multi-scale thermal simulation of polymer crystallization. Int. J. Mater. Form. 8(4), 497-504 (2015) \item Spekowius, M.: A new microscale model for the description of crystallization of semicrystalline thermoplastics. Verlagsgruppe Mainz GmbH, Aachen (2017) \item Zhao, S., Xu, N., Xin, Z., Jiang, C.: A novel highly efficient nucleating agent for isotactic polypropylene. J. Appl. Polym. Sci. 123(1), 108-117 (2012) \item Drogelen, M., Erp, T., Peters, G.: Quantification of non-isothermal, multi-phase crystallization of isotactic polypropylene: the influence of cooling rate and pressure. Polymer 53(21), 47584769 (2012) \item Laschet, G., Spekowius, M., Spina, R., Hopmann, C.: Multiscale simulation to predict microstructure dependent effective elastic properties of an injection molded polypropylene component. Mech. Mater. 105, 123-137 (2017) \item Foks, J.: The influence of latent heat release on polymer morphology. In: Crystallization of Polymers, pp. 337-343. Springer, Dordrecht (1993) \item Raimo, M., Cascone, E., Martuscelli, E.: Review Melt crystallisation of polymer materials: the role of the thermal conductivity and its influence on the microstructure. J. Mater. Sci. 36(15), 3591-3598 (2001) \item Böttger, B., Eiken, J., Apel, M.: Phase-field simulation of microstructure formation in technical castings-a self-consistent homoenthalpic approach to the micro-macro problem. J. Comput. Phys. 228(18), 6784-6795 (2009) \item Spina, R., Spekowius, M., Dahlmann, R., Hopmann, C.: Analysis of polymer crystallization and residual stresses in injection molded parts. Int. J. Precis. Eng. Manuf. 15(1), 89-96 (2014) \item Mubarak, Y., Harkin-Jones, E., Martin, P., Ahmad, M.: Modeling of non-isothermal crystallization kinetics of isotactic polypropylene. Polymer 42(7), 3171-3182 (2001) \item Hao, W., Yang, W., Cai, H., Huang, Y.: Non-isothermal crystallization kinetics of polypropylene/silicon nitride nanocomposites. Polym. Testing 29(4), 527-533 (2010) \item Isayev, A.I., Chan, T.W., Shimojo, K., Gmerek, M.: Injection molding of semicrystalline polymers. I. Material characterization. J. Appl. Polym. Sci. 55(5), 807-819 (1995) \item Galera, V., Marinelli, A.: Determination of non-isothermal crystallization rate constant for pseudo-experimental calorimetric data. Mater. Res. 12, 151-157 (2009) \item Evans, L.C.: Partial Differential Equations, vol. 19. American Mathematical Society, Rhode Island (2010) \item Hammami, A., Spruiell, J., Mehrotra, A.: Quiescent nonisothermal crystallization kinetics of isotactic polypropylenes. Polym. Eng. Sci. 35(10), 797-804 (1995) \item Lauritzen, J.I., Hoffman, J.D.: Theory of formation of polymer crystals with folded chains in dilute solution. J. Res. Natl. Bureau Stand. Sect. A Phys. Chem. 64(1), 73 (1960) \item Hoffman, J., Davis, G., Lauritzen, J.I.: The rate of crystallization of linear polymers with chain folding. In: Treatise on Solid State Chemistry, pp. 497-614. Springer, Boston (1976) \item Hoffman, J., Miller, R.: Kinetic of crystallization from the melt and chain folding in polyethylene fractions revisited: theory and experiment. Polymer 38(13), 3151-3212 (1997) \item Wang, J., Hopmann, C., Röbig, M., Hohlweck, T., Kahve, C., Alms, J.: Continuous twodomain equations of state for the description of the pressure-specific volume-temperature behavior of polymers. Polymers 12(2), 409 (2020) \end{enumerate} \section*{Thermal Optimisation of Injection Moulds by Solving an Inverse Heat Conduction Problem } \begin{abstract} The thermal design of injection moulds is a complex process and is often conducted manually by the mould maker. However, manufacturing of highly precise parts has become more and more important over the last years. The focus is laid especially on part warpage and reproducible results in the context of a stable process.\\ In this paper, a simulative approach for an automatic cooling channel layout via an inverse heat conduction problem is presented. Based on previous results, the methodology is extended using an improved objective function. This approach minimizes the thermal inhomogeneity in the part during the holding and cooling phase by evaluating the heat flux distribution in the mould. In this project, a virtual methodology is developed for an efficient thermal mould design. Exemplary simulations with two different geometries and materials validate this approach. For a thick-walled lens geometry produced with an amorphous material, a significant improvement of the resulting temperature distribution can be shown. For the second, technical geometry with a semi-crystalline thermoplastic, the results are very close to the solution with the previous objective function. \end{abstract} Keywords: Injection moulding $\cdot$ Thermal mould design $\cdot$ Thermal optimisation \section*{1 Introduction} Injection moulding is widely used for the large-scale production of complex thermoplastic parts with short cycle time. In order to manufacture high quality parts, the injection moulding process needs optimal process conditions as well as a high reproducibility. Quality criteria such as weight, density, shrinkage and warpage determine the mechanical and dimensional integrity of the product and directly correlate to the corresponding process conditions. In this process, the design phase is the most time consuming and most costly step of the construction of an injection mould. Especially the thermal design phase requires a lot of experience by the mould designer. Every mould is as unique as the parts, which are produced. Therefore, it is highly complex to develop a thermal design with reproducible quality assuring a minimum part warpage at optimal cycle time. Conventional, analytical thermal mould design relies on the calculation of the cooling error at the cavity surface wall [1]. This calculation method is easy and suitable for conventionally drilled cooling channels but it does only give an estimation of the temperature\\ at the cavity surface rather than the actual temperature distribution in the part. Hot spots in small areas can only be detected very difficultly. It becomes even more complex for cooling channels manufactured with the freedom of the additive manufacturing (AM). Nowadays, simulation tools such as Moldflow, Moldex3D, Sigmasoft etc. are the state of the art in industrial mould-making and heavily needed to identify possible challenges already in the design phase. Consequently, process simulation requires experience of mould designers on the one hand for setting up correctly the simulation and on the other hand for interpreting correctly the calculated results. It is not assured that an optimal solution can be found $[2,3]$. This is why currently research focusses on the investigation how to design cooling channels for injection moulds in an automatic and reproducible way. After a discussion of the current state of the art on automatic cooling channel generation, this paper presents a revised method to evaluate objectively the quality of a thermal mould design by solving an inverse heat conduction problem and an improved objective function, which has been developed in previous research. \section*{2 State of the Art on Automatic Cooling Channel Generation} Putting cooling channels close to the cavity, increases the cooling capacity but increases also mechanical weaknesses of the mould steel. Jahan et al. developed an elaborate approach and proposed a thermo-mechanical design optimisation of cooling channels. This way it is ensured that the injection mould is mechanically and thermally stable and is able to take up the arising heat fluxes. The cooling channels cannot bear any mechanical forces, so that channels close to the cavity create high stresses in the remaining material. This lead to the conclusion that not every cooling channel design that would create an optimal thermal result for the part is suitable for a production process with high pressure in the filling phase. Therefore, further factors as the created stress in the mould material were considered. Jahan et al. parameterize the geometry: the diameter and the pitch distance between the centreline of the cooling channel and the simple cup-shaped part were varied. By a design of experiments (DoE) several cooling channel designs were tested and the best design was chosen by the criteria of minimum yield stress and minimum cooling time. In conclusion, the outcome of this study heavily depends on the weighting of the input parameters of the user, which does not assure that a global optimum can be found. Also, the resulting part warpage is not considered but only the achievable cooling time [4]. Several authors have taken the cooling demand of the part into the focus of their research. Using an objective function to evaluate the cooling quality, they developed a quality criterion at the end of the cooling phase such that an optimisation software can solve the thermal problem: Agazzi et al. decoupled the optimization process from the generation of the cooling channel system in a new approach. By solving an inverse heat conduction problem, the heat dissipation was determined on an outer contour surrounding the part. Within that part, there was a homogeneous starting temperature distribution related to a selected reference temperature. A uniform demoulding temperature is the goal to achieve on the surface of the moulded part at the defined point of ejection. The homogeneity of the\\ temperature distribution was evaluated by a objective function that adds up the local differences in temperature. This sum was minimized iteratively in a thermal optimization. The temperature control system was then derived based on isothermal surfaces of the calculated temperature field. In contrast to an analytical design, this method takes into account the heat conduction within the part and the mould as well as the heat transfer between these two components. However, no starting positions for the location of the cooling channels have to be defined and thus the boundary conditions are free of user influences. In contrast, the method developed by Agazzi et al. neglects the physical density properties of thermoplastics, which show a pronounced dependence on pressure and temperature [5, 6]. Therefore, the proposed objective function of Agazzi et al. considering only thermal effects has been extended with a second term taking into account the local difference in density by Nikoleizig et al. \begin{equation*} Q\left(T_{C}\right)=\sum_{i=1}^{m} \int\left(\frac{T_{E j}-T_{P l}\left(x_{i}, t, T_{C C_{0}}\right)}{\omega_{1}}\right)^{2} d A_{p a r t}+\sum_{\mathrm{j}=1}^{k} \int\left(\frac{\bar{\rho}_{P l}-\rho_{P l}\left(x_{j}, t, T_{C C_{0}}\right)}{\omega_{2}}\right)^{2} d A_{o f f} \tag{1} \end{equation*} This objective function $\mathrm{Q}\left(\mathrm{T}_{\mathrm{C}}\right)$ addresses a quick cooling through the first term, where a desired ejection temperature $\mathrm{T}_{\mathrm{Ej}}$ for the surface $A_{\text {part }}$ of the part is given and compared to the actual local temperatures $\mathrm{T}_{\mathrm{Pl}}\left(\mathrm{x}_{\mathrm{i}}, \mathrm{t}, \mathrm{T}_{\mathrm{CC}_{0}}\right)$ of the part. The second term addresses the density homogeneity, with the differences of local density $\rho_{\text {loc }}\left(\mathrm{x}_{\mathrm{i}}, \mathrm{t}, \mathrm{T}_{\mathrm{CC}_{0}}\right)$ compared to a average density $\overline{\rho_{\text {Ejec }}}$, which should be reached on an offset surface $\mathrm{A}_{\text {off }}$ within the part. Both terms are summed over their respective areas and can be weighted with the variable $\omega_{1 / 2}$. The temperatures $T_{C}$ on the outer mold contour are varied to minimize the objective function. This approach is purely thermal, which means that no filling effects are calculated. Nikoleizig et al. have also added a realistic starting temperature distribution to the methodology, which shows better results. Starting from the temperature distribution after the end of filling the optimal temperature distribution in the mould during the holding and cooling phase is iteratively calculated, such that at the end of the cooling phase the above-mentioned differential function is minimal and the part has a homogeneous temperature and density distribution [7, 8]. This approach has been used and optimised for the injection moulding process in recent years at IKV. In the following, this approach is further developed to a tempering system for optical lenses. \section*{3 Thermal Optimization - Revising the Objective Function} The methodology of Nikoleizig et al. shown in the precedent chapter is further investigated here. The core aspect of the thermal optimisation of the mould is the definition of the objective function. This function returns a specific value to the optimisation software such that the thermal state around the mould can be changed for an optimal heat flux from part to mould. This definition of the objective function is now revised: To take into account the compressible character of the plastic melt, Nikoleizig et al. have added the consideration of the density into the objective function (see Eq. 1). The two terms can be weighted individually by the terms $\omega_{1}$ and $\omega_{2}$. These weighting factors represent an absolute number and needs to be adapted to every moulded part. A series\\ of thermal optimisations have to be performed in order to find the best weighting for the specific part and process. Exemplary calculations have shown, that the value of the two terms can differ by several orders of magnitude. Changes in density are in the range of $0.1 \mathrm{~g} / \mathrm{cm}^{3}$ whereas Temperatures may differ up to $100 \mathrm{~K}$ from each other over the part's surface. Therefore, it is proposed to normalise the two terms of the function by $T_{\text {ejec }}$ and $\overline{\rho_{0}}$ respectively. This causes the two terms to be in the same order of magnitude and the whole term becomes unitless. In a second step, this weighting can now be changed and adapted by $\omega_{1 / 2}$, but in a way that the optimal weighting needs to be found only one time. The optimisation function proposed by Nikoleizig et al. does also weight implicitly more complex regions by not taking into account mesh effects. Regions that have a lot of e.g. edges and complex geometry features are usually meshed more densely than areas with low geometric complexity. As in the proposed objective function (1) the integral becomes numerically a sum. This is why in this function the sum operator is used. The respective node density from the mesh leads to an implicit weighting of the optimisation function. Based on this effect, the following revised objective function is proposed: \begin{equation*} Q\left(T_{C}\right)=\sum_{i=1}^{m}\left(\frac{T_{E j}-T_{P l}\left(x_{i}, t, T_{C C_{0}}\right)}{T_{e j} * \omega_{1}}\right)^{2} \cdot \frac{A_{e l, i}}{A_{p a r t}}+\sum_{\mathrm{j}=1}^{k}\left(\frac{\bar{\rho}_{P l}-\rho_{P l}\left(x_{j}, t, T_{C C_{0}}\right)}{\overline{\rho_{p l}} * \omega_{2}}\right)^{2} \cdot \frac{A_{e l, j}}{A_{O f f}} \tag{2} \end{equation*} This equation is normalised in the described way such that the two terms are now in the same order of magnitude and do not implicitly affect the cooling quality through numerical effects. $A_{\text {part }}$ represents the surface of the part, whereas $A_{O f f}$ is the offset surface inside the part where the density function is evaluated $A_{e l, i / j}$ represents the share of the surface of each element $i / j$ on this surface. The dependency of the thermal optimisation of the mesh size should be reduced by this new formulation. In general, the methodology is not dependent on the mesh size as long as enough mesh elements are chosen because this affects the precsion of the heat transfer calculations. Over the part's thickness, at least three elements are chosen. Over the part's surface, differences in mesh density are now evened out. To show the advantages of this new formulation of the objective function firstly thermal optimisations are performed with a lens geometry with very few features and a thick-walled mid-section. Secondly, a more complex part containing freestanding ribs, deep boxes and changes in wall thickness are investigated. \section*{4 Experimental - Thermal Optimisations} As described in Sect. 2, in this approach only the holding and cooling phase without flow effects are considered as these two phases make up the most of the cooling time of the injection moulding cycle. The melt is already in full contact with the cavity and the flow effects are neglected here. The temperature distribution after the injection phase is calculated with commercial injection moulding software. A constant mould temperature close to the final solutions is chosen and no cooling channels are used. A heat up process of the mould over a series of injections is calculated to use a starting temperature distribution, which is close to the final solution. This distribution is mapped\\ into the software environment Comsol, Comsol AB, Stockholm, Sweden. This starting temperature distribution is used for the part as well as for the surrounding mould contour. In order to save calculation time, a constant offset around the part of $10 \mathrm{~mm}$ is used. The temperature distribution directly around the part influences the part quality critically. The resulting temperature distribution is then approximated by a derived cooling channel design. The first geometry is a typical convergent lens. Due to the low refractive index of plastics the part is considerably thick, with a maximum wall thickness of $10.21 \mathrm{~mm}$. The part is visualised in Fig. 1. The used material is a Polymethyl methacrylate (PMMA) of the type Plexiglas $7 \mathrm{~N}$ by the manufacturer Roehm GmbH, Weiterstadt, Germany. The moulding parameter can be found in Table 1. The temperatures are taken from the calculation of the commercial software calculation.\\ \includegraphics[max width=\textwidth, center]{2024_03_10_9cdc4dee3b1ef59d6c5ag-243} Fig. 1. Exemplary lens geometry and moulding parameters Table 1. Parameter of the thermal optimisation for the lens geometry \begin{center} \begin{tabular}{l|l} \hline Moulding parameter & Value \\ \hline Cooling time & $240[\mathrm{~s}]$ \\ \hline Melt temperature distribution & $198-241\left[{ }^{\circ} \mathrm{C}\right]$ (depending on distance to the gate) \\ \hline Mould temperature & $83-93\left[{ }^{\circ} \mathrm{C}\right]$ \\ \hline \end{tabular} \end{center} In a second step, a reference geometry that has been used in earlier publications [9], is investigated to show the improvement by the new objective function. This geometry is visualised in Fig. 2. The geometry has specific elements, which are common for plastic parts, such as boxes, freestanding ribs and changes in wall thickness. These features are potentially prone to severe warping. With this exemplary geometry for technical parts, a comparison between the existing and the revised objective function is performed. For this part a Polybutylene terephthalate (PBT) B4520 from the company BASF SE, Ludwigshafen, Germany, is used. The calculation parameters are summarized in Table 2. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-244} \end{center} Fig. 2. Complex reference geometry Table 2. Process parameters for the thermal optimisation of the complex geometry \begin{center} \begin{tabular}{l|l} \hline Moulding parameter & Value \\ \hline Cooling time & $10 \mathrm{~s}$ \\ \hline Melt temperature & $168-281^{\circ} \mathrm{C}$ (depending on distance to the gate) \\ \hline Mould temperature & $88-65^{\circ} \mathrm{C}$ \\ \hline Ejection temperature & $110^{\circ} \mathrm{C}$ \\ \hline \end{tabular} \end{center} \section*{5 Results and Discussion} After finishing the thermal optimisations, an optimal temperature distribution can be extracted from the Comsol environment. In Fig. 3, a comparison between the new and the previous objective function is made. In this figure, the temperature on the mould contour can be seen. According to the calculation using the previous objective function, a warm ring on the upper side is necessary to cool down more slowly the outer area of the lens while the thicker parts need to be cooled more quickly. With the revised objective function, this ring of higher temperature is also visible and the inside belonging to the thick-walled lens area is cooled more strongly showing a more realistic result. Furthermore, in the mid-plane, a warm area can be seen, indicating a slow cooling of the side plane of the lens. Comparing the temperature distribution on and inside the lens shows a similar result. In Fig. 4, the resulting temperature distribution can be seen. Using the previous objective function, an overheated section in the middle of the part occurs with temperatures above $130{ }^{\circ} \mathrm{C}$, which is highly above glass transition temperature and the outer areas of the lens are already too cold. The whole temperature level is closer to the required ejection temperature $T_{e j e c}=110^{\circ} \mathrm{C}$. The effects of the mesh size and the unequal order of magnitude of the two terms are now considered. This should result in a better optical quality due to less part warpage, which will be validated in future work. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-245(2)} \end{center} Fig. 3. Comparison of the temperature distribution on the mould contour Previous objective function \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-245(3)} \end{center} \section*{Extended objective function} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-245} \end{center} Perspective view \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-245(1)} \end{center} Section cut Fig. 4. Temperature distribution of the lens at the point of ejection In the next step, the second geometry is investigated. In this case, the analysis of the resulting temperature distribution is not as obvious because the temperature distribution cannot be analysed easily due to many geometric features blocking the vision on the part. The overview on the temperature distribution (cf. Fig. 5) on the mould contour shows for the previous objective function a set of complex patterns with a slightly higher temperature level at the end of the flow path. This higher temperature distribution at the end of the flow path is more visible for the extended objective function. This takes into account, that the wall thickness is lower due to the drafting angle and cools down more quickly at the same mould temperature. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-246(1)} \end{center} \section*{Extended objective function} \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-246} \end{center} Fig. 5. Comparison of the temperature distribution in the mould contour These differences in the mould temperature distribution are barely visible on the part. In Fig. 6, the comparison of the temperature distributions on the part are shown. In contrast to the lens geometry, it can be seen, that the two temperature distributions are quite close to the required ejection temperature of $110{ }^{\circ} \mathrm{C}$. The extended objective function shows slightly higher gradients on the ribs, whereas the temperature gradients in the box section are more distinctive for the previous objective function. Both optimisations have problems to cool sufficiently corners of parts. These elevated gradients especially in these areas prone for warpage may lead to future unwanted deviations of the geometry after the derivation of the cooling channel design. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-246(2)} \end{center} Fig. 6. Comparison of the temperature distribution on the part To investigate this temperature distribution in more detail, the resulting average surface temperatures on the part and average density on the offset surface are visualised in Table 3. Table 3. Average surface temperature and density of the part \begin{center} \begin{tabular}{l|l|l|l|l} \hline Quality function & \begin{tabular}{l} Av. temperature \\ $\left[{ }^{\circ} \mathrm{C}\right]$ \\ \end{tabular} & \begin{tabular}{l} Std. deviation \\ $\left[{ }^{\circ} \mathrm{C}\right]$ \\ \end{tabular} & \begin{tabular}{l} Av density \\ $\left[\mathrm{kg} / \mathrm{m}^{3}\right]$ \\ \end{tabular} & \begin{tabular}{l} Std. deviation \\ $\left[\mathrm{kg} / \mathrm{m}^{3}\right]$ \\ \end{tabular} \\ \hline Previous & $110.19^{\circ} \mathrm{C}$ & 5.30 & 1219.56 & 10.04 \\ \hline Extended & $110.87^{\circ} \mathrm{C}$ & 6.23 & 1219.37 & 10.02 \\ \hline \end{tabular} \end{center} By comparing these results, it becomes obvious, that the thermal optimisation works quite well for both objective functions and the objective of an optimal homogeneity can be reached with both objective functions. The marginal differences can be neglected. So far it is not obvious, why for this part the differences are this small for this box geometry and very obvious for the lens geometry. Generally, the extended objective function shows better or same results and should therefore be used in future works. The reason for the different behaviour needs to be investigated in further research. \section*{6 Conclusion and Outlook} In this paper, a methodology for an automatic thermal optimisation of a mould for the injection moulding process has been discussed. Based on previous research, a revision of the objective function of the thermal optimisation has been proposed. This objective function now includes an automatic weighting of the different objectives by normalising the respective term. Furthermore, the numerical effects of different mesh sizes are evened out by taking only into account the respective part of every element of the whole surface. This revised objective function has been tested at two different geometries representing two main sectors of injection-moulded products. The lens geometry has shown a significant improvement as especially the mid-section of the lens is now more homogeneously cooled down. The part with ribs is more difficult to evaluate as the graphical evaluation can be misleading. The analysis of the average temperature and density distribution shows a slight decline of the homogeneity of the two objectives. In the next steps, an analysis about the reasons for these results will be conducted in order to receive further insights on the behaviour of this optimisation methodology. Furthermore, an extensive study will be conducted to investigate the influence of further weighting factors on the resulting temperature distribution and part warpage. Acknowledgement. The presented investigations were carried out at RWTH Aachen University within the framework of the Collaborative Research Centre SFB1120-236616214 "Bauteilpräzision durch Beherrschung von Schmelze und Erstarrung in Produktionsprozessen" and funded by the Deutsche Forschungsgemeinschaft e.V. (DFG, German Research Foundation). The sponsorship and support is gratefully acknowledged. \section*{References} \begin{enumerate} \item Hopmann, Ch., Menges, G., Michaeli, W., Mohren, P.: Spritzgießwerkzeuge, 7th edn. Hanser, Munich \item Baur, E., Osswald, T.A., Rudolph, N.: Saechtling Kunststoff Taschenbuch, 31st edn. Hanser, Munich \item Karlinger, P., Hiken, F.: Mold design. In: Mennig, G., Stoeckhert, K. (eds.) Mold-Making Handbook, vol. 3, pp. 301-331. Hanser, Munich \item Jahan, S.A., Wu, T., Zhang, Y., Zhang, J., Tovar, A., Elmounayri, H.: Thermo-mechanical design optimization of conformal cooling channels using design of experiments approach. Procedia Manuf. 10(5), 898-911 (2017) \item Agazzi, A., Sobotka, V., Legoff, R., Garcia, D., Jarny, Y.: A methodology for the design of effective cooling system in injection moulding. Int. J. Mater. Form. 3(1), 13-16 (2010) \item Agazzi, A., Sobotka, V., Legoff, R., Jarny, Y.: Uniform cooling and part warpage reduction in injection molding thanks to the design of an effective cooling system. Key Eng. Mater. 556(31), 1611-1618 (2013) \item Nikoleizig, P.: Inverse thermische Werkzeugauslegung. Dissertation. RWTH, Aachen (2018) \item Hohlweck, T., Fischer, T., Hopmann, C.: Simulative and experimental validation of an inversed cooling channel design for injection molds. In: Proceedings of the SPE ANTEC Conference, Detroit, pp. 1-6 (2019) \item Hopmann, C., Wehr, H., Schmitz, M., Schneppe, T., Theunissen, M.: Digitalisierung der Werkzeugentwicklung im Spritzgießen. In: Internationales Kolloquium Kunststofftechnik. Shaker Publishers Verlag, Düren (2018) \end{enumerate} \section*{Reduction of Internal Stresses in Optics Through a Demand-Oriented Cooling Channel Layout in Injection Moulding } \begin{abstract} The production of plastic optics creates great challenges for the injection moulding process. The lens geometry is designed to fulfil the optical requirements and often contradict the plastic design guidelines. Especially thick-walled lenses with changes in wall thickness are challenging not only in the classic injection moulding process but also in injection-compression moulding processes, as the compression pressure can lead to internal stresses and thus to reduced optical properties. In order to increase the optical performance of thick-walled plastic lenses, a methodology developed at the Institute of Plastics Processing is being adapted for the inverse calculation of the cooling requirements of plastic components. Based on this, a cooling channel design is derived and validated in injection moulding simulations. With this method, lower peak values of residual stress and birefringence can be achieved. Furthermore, it can be shown that the developed cooling channel layout significantly reduces the cooling time required to reach the glass transition temperature. \end{abstract} Keywords: Injection moulding $\cdot$ Cooling channel design $\cdot$ Plastic optics \section*{1 Introduction} The manufacturing of optical plastic parts using injection moulding or injection compression moulding is a challenge for mould, machine and process, as the geometry of the optical components often contradicts any conventional, process-oriented design guidelines. Conventional injection moulding processes often reach their limits when it comes to the high demands on moulding accuracy and internal properties, which directly influence the optical properties. Initially during the injection phase of the injection moulding process, the cavity is completely filled and then during the holding pressure phase the material shrinkage is compensated by further transport of melt through the sprue channel into the cavity. The melt movement causes inhomogeneous internal component properties such as orientation and internal stresses. The pressure distribution drops along the flow path towards the end of the part and is only effective in the areas close to the sprue. The pressure gradient induces further stresses in the moulded part, which have a negative effect on the optical\\ properties. As soon as the sprue has completely solidified (sealing point), the holding pressure phase is over and shrinkage processes can no longer be compensated [1]. This is why injection compression moulding has become established in many optical applications [2,3]. Depending on the process variant, the compression phase is used to mould the part and to compensate for shrinkage. At the beginning of the compression process, the cavity is reduced at a defined velocity until a desired compression force or pressure is reached. Afterwards, the system switches over to a force- or pressurecontrolled compression process. During the compression phase, the pressure is introduced over the entire surface of the component, so that, in contrast to injection moulding, the pressure distribution over the component is significantly more homogeneous. However, for thick-walled lenses with large wall thickness differences, which contradict a plastic-compatible design, the homogeneous pressure distribution during injectioncompression moulding represents a challenge. Injection-compression moulded parts with large wall thickness variations sometimes have poorer properties than injectionmoulded parts [4]. Due to the long compression phase which is necessary for the thick-walled area to compensate for the local shrinkage. This introduces stresses in the already solidified thin-walled areas (Fig. 1). These stresses and can lead to birefringence, whereby a lens is not correctly focused. The residual stresses therefore lead to a reduction in the optical performance of the moulded lens $[5,6]$. \begin{center} \includegraphics[max width=\textwidth]{2024_03_10_9cdc4dee3b1ef59d6c5ag-250} \end{center} Fig. 1. Optical properties of a biconvex lens with different measuring range In order to avoid deformation of already solidified areas of the moulded part, a compression pressure profile would be preferable, which applies a higher pressure to thick-walled areas than to thin-walled areas. However, a profiled compression pressure cannot be realised in terms of tooling. A uniform mould cavity pressure over the lens surface, as is present in injection compression moulding over the entire lens surface, would be appropriate if the same cooling conditions were present for thick-walled and thin-walled areas. This can be achieved by means of cooling channels adapted to requirements. In this way, thick-walled and thin-walled areas of the lens can be cooled to different intensities. \section*{2 Inverse Thermal Cooling Channel Design} The current thermal mould design method is a forward iterative process based on empirical experience. Up to now, thermal mould design has usually been designed in such a way that a mould designer adapts the design of the cooling channels in order to create a homogeneous temperature distribution at the cavity. By means of digital process simulation to calculate the temperature distribution, the forward iterative method could be used more effectively and at a lower cost. In the next step, the mould designer changes the position of the cooling channels, based on personal experience, so that hot spots are minimized. This procedure is highly dependent on the experience of the individual mould designer [7]. For this reason, current process simulation software such as Sigmasoft (SIGMA Engineering GmbH, Aachen, Germany) or Moldflow (Autodesk Inc., San Rafael, USA) offer an optimization of the mould design through virtual test plans (DoE) [8, 9]. This optimization is based on the degrees of freedom given by the designer. By choosing different geometries or process parameters, the designer can define the optimization space. Several designs can be calculated automatically one after the other. Although an optimised draft is found in the end, it is not guaranteed that it is generally an optimum. At the Institute of Plastics Processing (IKV), within the framework of the collaboration research centre 1120 "Precision from Melt", a new methodology was developed for the automatic, demand-oriented design of cooling channels in injection moulds. The aim of the research project is to achieve uniform shrinkage behaviour to reduce part warpage. An inverse heat conduction problem is solved on the basis of a homogeneous temperature and density distribution within the moulded part and then the local cooling demand is determined [9]. This methodology is adapted in the current research project to create a homogeneous cooling condition throughout a thick-walled plastic lens manufactured using injection compression moulding principle. The methodology for determining the appropriate mould temperature design can be implemented with significantly less time and cost. In this paper the automatic thermal mould design for optical parts is considered and validated with injection moulding simulations. The focus will be on the birefringence caused by residual stresses. \subsection*{2.1 Calculation of an Inverse Demand-Oriented Cooling Channel Design} The methodology for inverse cooling channel design was originally developed by Agazzi et al. and further developed by Nikoleizig et al. and Hohlweck et al. [9-11]. In a first step, the method calculates the optimum temperature distribution in the mould so that after the cooling phase a thermally homogeneous component is obtained. To evaluate the temperature distribution, a function was developed to analyse the weighted temperature and density distribution in the part. In addition, the temperature distribution on a mould envelope around the component is calculated and optimised. It is assumed that a homogeneous temperature and density distribution leads to minimal warpage. \begin{equation*} Q\left(T_{K K 0}\right)=\sum_{i=1}^{m} \int_{0}^{t_{\text {cool }}} \frac{\left(T_{\text {ejec }}-T_{F}\left(x_{i}, t ; T_{K K 0}\right)\right.}{\omega_{T}} d t+\sum_{j=1}^{n} \int_{0}^{t_{\text {cool }}} \frac{\left(\overline{\rho_{F}}-\rho_{F}\left(x_{j}, t ; T_{K K 0}\right)\right.}{\omega_{\rho}} d t \tag{1} \end{equation*} The temperatures $T_{K K 01} ; \ldots ; T_{K K 0 n}$ are calculated on the mould envelope $\Gamma_{W}$ surrounding the moulded part, in a way that the error square sum of the quality function $\mathrm{Q}$ is minimized for all $T_{K K 0 i} \in[a, b]^{n}$ for $0