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\title{Dynamics of pore formation during laser powder bed fusion additive manufacturing }


\author{Aiden A. Martin', Nicholas P. Calta', Saad A. Khairallah', Jenny Wang1, Phillip J. Depond', Anthony Y. Fong²,\\
Vivek Thampy', Gabe M. Guss', Andrew M. Kiss², Kevin H. Stone (1) 2, Christopher J. Tassone ${ }^{2}$,\\
Johanna Nelson Weker [i] ${ }^{2}$, Michael F. Toney [i] ${ }^{2}$, Tony van Buren ${ }^{1} \&$ Manyalibo J. Matthews ${ }^{1}$}
\date{}


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ARTICLE

\href{https://doi.org/10.1038/s41467-019-10009-2}{https://doi.org/10.1038/s41467-019-10009-2}

Laser powder bed fusion additive manufacturing is an emerging 3D printing technique for the fabrication of advanced metal components. Widespread adoption of it and similar additive technologies is hampered by poor understanding of laser-metal interactions under such extreme thermal regimes. Here, we elucidate the mechanism of pore formation and liquidsolid interface dynamics during typical laser powder bed fusion conditions using in situ X-ray imaging and multi-physics simulations. Pores are revealed to form during changes in laser scan velocity due to the rapid formation then collapse of deep keyhole depressions in the surface which traps inert shielding gas in the solidifying metal. We develop a universal mitigation strategy which eliminates this pore formation process and improves the geometric quality of melt tracks. Our results provide insight into the physics of laser-metal interaction and demonstrate the potential for science-based approaches to improve confidence in components produced by laser powder bed fusion.
\footnotetext{${ }^{1}$ Lawrence Livermore National Laboratory, Livermore, CA 94550, USA. ${ }^{2}$ Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA. Correspondence and requests for materials should be addressed to T.B. (email: \href{mailto:vanbuuren1@llnl.gov}{vanbuuren1@llnl.gov}) or to M.J.M. (email: \href{mailto:matthews11@%7Clnl.gov}{matthews11@|lnl.gov})
}
aser-based additive manufacturing (AM) approaches such as laser powder bed fusion (LPBF) hold the potential to revolutionize manufacturing of complex metal components in the aerospace, medical, and automotive industries 1 . LPBF is particularly attractive as it permits the production of otherwise impossible geometries via a layer-by-layer strategy to print components from a thin layer of metal powder spread on a solid metal substrate, using only a computer-aided design (CAD) file to guide the scanning of a high-power laser ${ }^{2}$. This strategy allows LPBF to avoid the geometric limitations and extensive tooling requirements present in conventional subtractive fabrication methods. Despite its significant advantages, widespread adoption of LPBF remains limited due to concerns over component quality and consistency ${ }^{3}$. Reports of mechanical properties for LPBFproduced components vary widely, which presents a significant challenge for designers ${ }^{4-7}$ and certification authorities ${ }^{8}$. This variability in material quality arises from both the unusual thermal history and rapid solidification of material imposed by laserinduced heating ${ }^{9-11}$ as well as defects introduced during the process $^{12,13}$. To improve the confidence in components built by LPBF, a greater understanding of laser-metal interaction in this extreme thermal regime and its correlation with defect generation during the LPBF process is required.

A particularly ubiquitous class of defects in LPBF-produced components are keyhole pores ${ }^{14}$, which form when excess energy is imparted by the laser to the melt pool. These pores act as stress concentrators and have a negative effect on mechanical properties ${ }^{4,13}$. While keyhole porosity is somewhat stochastic in nature, such pores have been observed in regular patterns within fabricated components ${ }^{15}$. These patterns of pores have been attributed to melt pool dynamics at the point where the laser turns off at the end of a linear scan routine and/or laser turn points in serpentine scan patterns ${ }^{16}$. Since these regions can occur thousands of times in a single component and typically near the edges of the component where the impact to mechanical properties is the most pronounced, an understanding of the laser-metal interaction process during these events could have major outcomes for the quality of components produced by LPBF.

Ex situ studies of the LPBF process have shown that overheating during changes in laser scan velocity, such as at laser turn points leads to increased evaporation of metal from the surface causing a deep keyhole depression to form. The keyhole depression is unstable and can collapse to trap inert shielding gas, such as argon, in pores within the substrate ${ }^{17-19}$. However, direct observation of the formation dynamics of such pores has proven elusive because any viable monitoring technique must probe subsurface, micron scale dynamics at time scales on the order of ten microseconds to capture process-relevant phenomena ${ }^{20}$. High-speed, in situ transmission X-ray imaging is an emerging technique for probing subsurface phenomena during LPBF processing $^{21-23}$. The technique provides information complementary to the large body of literature describing LPBF process physics using high-speed, in situ optical probes ${ }^{24-30}$ and has been applied to multiple materials and LPBF processing conditions to understand the physics of spatter $^{31}$ and melt pool dynamics in unsupported overhang regions ${ }^{23}$. However, critical subsurface information such as mechanisms of pore formation and melt pool geometry under typical processing conditions, which are ideal for study by in situ X-ray imaging, remain relatively unexplored.

Here, we perform in situ transmission X-ray imaging to probe laser-metal interactions during LPBF processing and elucidate the mechanisms leading to pore formation. We show experimentally, in a common titanium alloy (Ti-6Al-4V) used for critical applications in aerospace ${ }^{32}$ and biomedical industries ${ }^{33}$, that the formation of pores during changes in laser scan velocity such as at laser turn points proceeds via the rapid collapse of the vapor depression at the surface and subsequent trapping of argon by liquid metal flowing into the void. Complementary multiphysics simulations provide high-definition insight into general trends in metal-laser interactions during LPBF processing and confirm the pore formation mechanism detailed in the experimental efforts. Based on these experimental and simulated observations, we devise and implement a successful mitigation strategy to prevent pore formation at laser turn points by modulating the laser power to compensate for melt pool overheating. An analytical model defining the dimensionless quantity normalized enthalpy ${ }^{18,34}$ as a function of laser power, scan speed, and beam size applied to the mitigation strategy reveals that a near-constant vapor depression depth can be realized by varying the laser power to maintain a constant normalized enthalpy during laser scanning. The successful mitigation strategy is straightforward to implement and can be deployed on virtually any commercial machines using existing hardware. More profoundly, the results enhance the understanding of laser-metal interaction under realistic LPBF processing conditions and reveal a mechanism leading to the formation of pores which ultimately give rise to material performance degradation in fabricated components. The pore mitigation strategy revealed here reduces the probability of pore formation and holds the potential to significantly reduce defect density and therefore improve the reliability of a component fabricated by LPBF.

\section*{Results}
Pores formed at the laser turn point. The properties of pores formed at a laser turn point during LPBF processing of Ti-6Al-4V were determined as a function of laser power and scan speed. Laser power and scan speeds used for LPBF processing were consistent with typical build parameters ${ }^{35}$. Five hundred-micrometer-thick Ti-6Al-4V substrates with and without an approximately $60-\mu \mathrm{m}$-thick powder layer on the surface were irradiated by a $1070 \mathrm{~nm}, 50 \mu \mathrm{m}$ diameter laser beam over a $2.5 \mathrm{~mm}$ long single turn scan pattern with $50 \mu \mathrm{m}$ hatch spacing (Fig. 1). Transmission X-ray images were captured at 20 $\mathrm{kHz}$ while performing LPBF processing and the resulting image time series was analyzed to determine pore properties and formation kinetics. Figure 2a reveals the pore depth as a function of distance from the turn point under various processing conditions (for a full description of pore depth, cross-sectional area, and distance from turn point see Supplementary Fig. 1). The maximum depth of pores formed at the turn point increases as a function of laser power, and this trend is independent of steadystate scan speed. A key finding from this study is that pores are primarily formed within $200 \mu \mathrm{m}$ of the turn point under all investigated processing conditions, with $87 \%$ of the pores observed during this study observed in this region, which is consistent with ex situ observations from full builds in stainless steel ${ }^{36}$. Furthermore, pores closer to the turn point are generally deeper in the material than pores formed farther from the turn point. Inspection of an X-ray image time series captured at each respective processing condition reveals that pores form very quickly on time scales comparable to the sampling rate of our measurement $(50 \mu \mathrm{s})$. Therefore, we did not attempt to resolve from these data the time it takes for a pore to form, but instead treat pore formation as a discrete event and note the time (referred to hereafter as pore initiation time, $\tau_{\mathrm{p}}$ ), when pores form relative to the laser turn time, $t_{\text {turn }}=0$ in Fig. $2 \mathrm{~b}$. All pores observed in this study are formed after the laser passes the turn midpoint, and nearly all pores are formed $200-1000 \mu$ after this midpoint regardless of the set scan speed (Fig. 2b). While nearly all pores associated with the turn point form during this time

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\section*{g}
Process laser

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Fig. 1 Description of a laser turn point condition and experimental configuration. a-c A laser turn point is defined as the condition during laser powder bed fusion (LPBF) where the laser reaches the end of a track, decelerates, shifts a prescribed hatch spacing, changes the scan direction by $180^{\circ}$, and then accelerates along a new track parallel and adjacent to the previous track. The black dashed line indicates laser trajectory. $\mathbf{d}$-f Time difference $\left(t-t_{0}\right)$, transmission X-ray images of a turn point region in Ti-6Al-4V performed at a laser power of $200 \mathrm{~W}$, and scan speed of $1000 \mathrm{~mm} \mathrm{~s}^{-1}$. d The laser is scanning from the left to right with spatter and powder motion above the substrate surface and a depression in the surface of the melt pool due to vapor recoil below. The titanium-argon interface is indicated by the white dashed line. $\mathbf{e}$ The laser enters the turn point region and shifts by the prescribed hatch spacing. $\mathbf{f}$ The laser is moving right to left after the turn point forming a new adjacent track and leaving behind keyhole pores. $\mathbf{g}$ Simplified schematic of the experiment configuration. A white-beam X-ray source is provided by experimental station 2-2 at the Stanford Synchrotron Radiation Lightsource (SSRL). The X-ray field of view is coincident with the $1070 \mathrm{~nm}$ processing laser at the Ti-6Al-4V substrate surface. Images are captured using a scintillator-based high-speed optical system\\
\includegraphics[max width=\textwidth, center]{2024_03_10_a60fd84fbf000be70a8bg-03(1)}

Pore initiation time $(\mu s)$

Fig. 2 Properties of pores formed during LPBF of Ti-6AI-4V in the laser turn point region as a function of laser power and steady-state scan speed. All turn point condition scans were performed at full laser power. a Depth of pore relative to the substrate surface as a function of distance from the turn point of the laser. $\mathbf{b}$ Histograms of the pore initiation time, $\tau_{\mathrm{p}}$, after the laser completed the turn point for three different scan speeds where $t_{\text {turn }}=0 \mu \mathrm{s}$. Each histogram includes pores produced with all laser powers (50-300 W) at the specified scan speed with (blue line) and without (red line) powder. No pores were formed in the turn point region prior to the laser turn in these experiments\\
\includegraphics[max width=\textwidth, center]{2024_03_10_a60fd84fbf000be70a8bg-04}

Fig. 3 Vapor depression depth during LPBF of Ti-6AI-4V. All laser turn conditions were performed at full laser power. a Depression depth in the steadystate scan regime where the laser is at full scan speed as a function of laser power and scan speed. b Maximum depth of the vapor depression during the laser turn as a function of laser power and set point scan speed. Note the different $Y$-axis scale between the two panels

window, $\tau_{\mathrm{p}}$ does appear to correlate with set scan speed, as pores at $1000 \mathrm{~mm} \mathrm{~s}^{-1}$ predominantly occur ( $89 \%$ of the time) in less than $500 \mu$ s compared to $27 \%$ and $36 \%$ of the time at 600 and 800 $\mathrm{mm} \mathrm{s}^{-1}$ scan speeds, respectively. Furthermore, the results show that while careful ex situ studies can locate pores relative to scan position, only time resolved, in situ X-ray probes can with certainty, identify the time dependence of pore formation.

Changes in surface morphology at the laser turn point. To elucidate the mechanism of pore formation, the geometry of the melt pool surface (vapor-liquid interface) was quantitatively tracked throughout the turn point. Under these process conditions, the melt pool surface forms a depression whose shape is dominated by recoil pressure generated by metal vaporization at the melt pool surface ${ }^{26}$. The depth of this vapor depression during steady-state scanning and at the turn point was determined using the same processing and X-ray imaging conditions presented in Fig. 2. The vapor depression depth in Ti-6Al-4V as a function of laser power is presented in Fig. 3. Under steady-state scan conditions, the vapor depression depth increases linearly with laser power and increases with decreasing scan speed (Fig. 3a). Variations in vapor depression depth can be described in terms of changes in the localized energy density, which varies the rate of metal vaporization and therefore recoil pressure. Increasing the energy density increases the recoil pressure which drives the melt pool surface deeper into the material ${ }^{17,26}$. A linear scaling of vapor depression depth with laser power is not necessarily expected for keyhole mode heat transport where strong vaporization and melt pool dynamics play important roles. In this keyhole regime, the melt is rapidly displaced away from the laser beam under the effect of recoil momentum and Marangoni shear flow. The absorbed laser energy therefore not only leads to melting, but also to melt motion. The linear dependence observed here appears to indicate that the absorbed laser energy is spent mainly to melt the solid even in the keyhole regime, which helps to explain the linear scaling of melt depth behavior with power. The addition of a $60-\mu \mathrm{m}$ powder layer on the surface did not appear to influence the dynamics of pore formation at the turn point, likely due to denudation of metal powder along the laser scan path ${ }^{25}$. Interestingly, for the case of the maximum vapor depression depth during the turn point, the depression relationship with power is also linear (Fig. 3b); however, the depression depth as a function of laser power is identical for all steady-state scan speeds. Inspection of the velocity of galvanometer-based $\mathrm{X}-\mathrm{Y}$ scanning mirrors during the turn point indicates that at the turn point itself, the programmed steadystate scan speed has no influence on the measured scan speed (see Supplementary Fig. 2 for scanning mirror properties). Instead, the physical response time ( $650 \mu$ s step response time) of the mirrors dictates the actual scan speed during the turn point. The measured deceleration and acceleration of the mirrors approximately $500 \mu$ s pre- and post-turn varied between the scan speeds used here and approached a maximum of $1.4 \times 10^{6} \mathrm{~mm} \mathrm{~s}^{-2}$ at a programmed steady-state value of $1000 \mathrm{~mm} \mathrm{~s}^{-1}$. As the laser approaches the turn point, the mirrors decelerate and then accelerate back to full steady-state scan speed immediately after the turn. When the laser scan speed approaches zero at the turn point, the instantaneous energy density increases, leading to localized overheating and an increase in depression depth.

To further probe how the change in depression depth correlates with pore formation, the depression depth was determined as a function of time with a set scan speed of 1000 $\mathrm{mm} \mathrm{s}^{-1}$ and laser power of 100,200, and $300 \mathrm{~W}$ (Fig. 4). The vapor depression depth is at steady state when it is approximately $1000 \mu$ s from the turn point. As the laser approaches $500 \mu$ s from the turn point the vapor depression depth begins to increase until it approaches a maximum at approximately $100 \mu$ s post-turn. The maximum vapor depression depth occurring post-turn is caused by a build-up of heat in the turn point region from the long dwell time of the near-stationary laser. This increase in vapor depression depth highlights a transition between the onset of keyhole mode present during steady state and a deep keyhole mode regime at the turn region. During LPBF, ideally the melt pool depth is sufficient to melt a few layers of previously processed material at the surface (up to approximately $100 \mu \mathrm{m}$ ) to fuse this material to the powder. For the case of keyhole mode welding the power density of the laser is sufficient to evaporate metal from the surface and initiate a plasma plume ${ }^{18}$. Evaporation of metal from the surface during keyhole mode allows the laser to drill into the material leading to the formation of a vapor depression. When the depression exceeds a depth on the order of $100 \mu \mathrm{m}$ the deep keyhole regime is entered and a dramatic increase in the absorption of the laser power is realized due to multiple interactions between the melt pool and reflected laser ${ }^{37}$. This increase in laser absorption and therefore localized energy density is accompanied by formation of a high aspect ratio keyhole vapor depression as observed in Fig. 1e. After the turn, the vapor depression depth reduces to a near-steady-state regime at a time of $1000 \mu$ s post-turn. The steady-state vapor depression depth during the post-turn scan is higher than the pre-turn scan due to thermal lag associated with preheating of the material (this can be directly observed in Fig. 1a-c). Pores form at all laser powers under these processing conditions, with pores forming only post-turn during vapor depression collapse. From these direct observations, we ascribe the mechanism of pore formation at laser turn points to rapid collapse of the vapor depression. After the depression depth increases during the laser turn, the mirrors accelerate away from the turn too quickly for the

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Fig. 4 Vapor depression depth as a function of time for various laser powers at a laser turn point with a programmed steady-state scan speed of $1000 \mathrm{~mm} \mathrm{~s}^{-1}$. These scans used a constant power, and time zero corresponds to the midpoint of the turn $\left(t_{\text {mid-point }}=0 \mu \mathrm{s}\right)$. The laser is at steady-state scan speed before it begins to decelerate at approximately $-900 \mu$ s to initiate the turn. Minimum laser scan speed is reached at $0 \mu s$ after which it immediately starts to accelerate, returning to steady-state scan speed at approximately $1200 \mu$ s. The turn midpoint was determined by analysis of the in situ X-ray images. Black circles denote pore formation events. Error bars represent uncertainty in the distance between the base of the vapor depression and the surface caused by surface roughness

depression to smoothly return to the steady state, prompting a rapid collapse of the depression. This is exemplified in Fig. 2b where the histogram of $\tau_{p}$ is shifted to shorter times at a steadystate scan speed of $1000 \mathrm{~mm} \mathrm{~s}^{-1}$ compared to the $800 \mathrm{~mm} \mathrm{~s}^{-1}$ case, which is caused by an increase in the mirror acceleration out of the turn point at the higher scan speed. The collapse of the vapor depression and subsequent pore formation can be described by hydrodynamics, and the exertion of force by gaseous metal on the molten pool surrounding the depression. Increased localized energy density in material at the turn point leads to an increase in the vapor pressure of gaseous metal above the base of the vapor depression. The increase in vapor pressure causes metal to rapidly be ejected from the vapor depression driving the depression deep into the substrate and the recoil pressure of gaseous material inside the depression overcomes the force of molten metal flow into the void. Once the scan speed returns to steady state and a decrease in temperature at the depression surface is realized the recoil pressure from evaporating metal is reduced exponentially. As the surface temperature is reduced the surface tension of the melt pool increases overcoming the force from the recoil pressure and the depression collapses ${ }^{17}$. Argon filled pores are then trapped in place by the quickly freezing melt pool, leaving pores trapped in the solidified material. This collapse mechanism is distinct from the traditional view of pore formation during keyhole mode, in which instabilities at the liquid metal-vapor interface stochastically form pores even in steady state ${ }^{38}$. Under turn point conditions where laser scan acceleration is maximum, pores are formed due to the transition of the vapor depression into a deep keyhole regime and the associated collapse of the walls of vapor depression, which is too rapid for the system to smoothly accommodate without the formation of pores.

Multi-physics simulation. To further our understanding of pore formation, a series of simulations were performed to ascertain the dynamics of the collapsing vapor depression. Simulations were performed using the ALE3D multi-physics software tool ${ }^{39}$ and parameters for the validated, stainless steel (SS316L) simulation environment. The model solves the Navier-Stokes equations coupled with the heat diffusion equation in an energy-conserving scheme, while accounting for the vapor recoil pressure and evaporative cooling as boundary conditions using Anisimov's model $^{40}$. Simulated laser rays strike the surface from the source in a direct line of sight and the energy deposited into the sample is determined by an effective absorption coefficient (0.25). Note that we do not employ the polarization-dependent Fresnel equations since the fiber laser source used in this study is unpolarized and thus yields a negligible absorptivity dependence on incident angle up to $\sim 60^{\circ}$. The bulk of the incident laser energy is deposited over the front inclined wall of the vapor depression which consists of a flat liquid surface. The energy deposited into the front wall location dominates the melt pool response and melt pool depth via the recoil pressure. This is due to the exponential temperature dependence of the recoil physics and because the highest surface temperature is realized immediately below the laser at the point of incidence. Previously, the model was shown to predict melt pool dimensions, as well as explain the formation mechanism of other defect modes such as end-of-track pore defects ${ }^{17}$. Here, simulations were used to dynamically resolve the melt flow and defect formation during the turn, at high temporal $(1 \mu \mathrm{s})$ and spatial resolution $(3 \mu \mathrm{m})$, allowing confirmation of our experimental observations. Furthermore, the simulation enables probing of the generality of the vapor depression dynamics observed in the materials.

First, to confirm turn point dynamics in the simulated case of SS316L followed the same trend observed experimentally in $\mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V}$, vapor depression and melt pool depth as a function of laser power during the laser turn point was simulated using the ALE3D multi-physics model (for further details of the simulation see Supplementary Note 1 and Supplementary Movie 1). The simulated steady-state vapor depression depth correlates with the low energy density regime $\left(75 \mathrm{~W}, 1000 \mathrm{~mm} \mathrm{~s}^{-1}\right)$ measured experimentally in Ti-6Al- $4 \mathrm{~V}$ when compared using the thermal scaling laws for $\mathrm{LPBF}^{34}$, and the transition in vapor depression depth from steady state to turn point is similar to the $50 \mathrm{~W}, 1000$ $\mathrm{mm} \mathrm{s}^{-1}$ condition in $\mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V}$ ( 23 to $70 \mu \mathrm{m}$ and 32 to $62 \mu \mathrm{m}$ for the SS316 simulation and Ti6Al-4V experiment, respectively). The linear dependence of vapor depression depth with respect to the laser power was also reproduced in the SS316L simulation (see Supplementary Fig. 3a). The simulation reported a peak metal evaporative flux of approximately $1000 \mathrm{~mol} \mathrm{~m}^{-2} \mathrm{~s}^{-1}$ directly below the laser spot on the front inclined wall of the vapor depression during the turn point.

A single frame of the 3D simulation is shown in Fig. 5 for 200 $\mathrm{W}$ and $1500 \mathrm{~mm} \mathrm{~s}^{-1}$ laser scanning conditions, with temperature contour lines highlighting the liquid-solid interface and color map describing the thermal gradients in the material. The steadystate-simulated vapor depression depth is $\sim 23 \mu$ m (Fig. 5a). As the laser approaches the end of track and decelerates, the vapor depression depth increases to $\sim 70 \mu \mathrm{m}$ (Fig. 5b). This is a direct result of the increase in laser dwell time as the scan speed decreases for execution of the turn, and more energy is absorbed in the local volume causing the depth to increase. A small decrease in depth is observed during the simulation at the turn point due to the laser traveling across the hatch spacing of $100 \mu \mathrm{m}$ and encountering colder material that requires additional energy to heat to melt pool temperatures. As the laser finishes the turn, a more pronounced depth increase occurs because the accumulated residual heat is higher in this pre-heated location compared to entry into the turn point. Immediately following this melt pool depth maximum, the vapor depression depth rapidly decreases as the laser accelerates away from the turn point (Fig. 5c). A significant increase of the vapor depression depth due to this overheating followed by rapid collapse (Fig. 5d) gives rise to pore formation, as liquid metal cannot fill the deep depression before\\
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Fig. 5 Cross-section of multi-physics simulation of turn point dynamics in SS316L performed using ALE3D. The laser power was $200 \mathrm{~W}$, and the steadystate scan speed is $1500 \mathrm{~mm} \mathrm{~s}^{-1}$ and reduced during the turn point as per the physical system. The black contour line represents the melt pool boundary

rapidly solidifying due to the extreme $\left(\sim 10^{6} \mathrm{~K} \mathrm{~s}^{-1}\right)$ cooling rate at the pore location (Fig. 5e). The rapidly moving $\left(0.3 \mathrm{~m} \mathrm{~s}^{-1}\right)$ solidification front thus traps gaseous material forming the pore (Fig. 5f) confirming our experimental observation. The simulations show that at the turn point the process enters a deep keyhole regime and large pore defects are generated as the process returns to steady state, agreeing with the experimental observations in Ti-6Al-4V. These complementary observations strongly suggest that this behavior is universal and occurs regardless of material in turn points during LPBF.

Pore formation mitigation strategy. From our experimental and modeling results, the increase in depth followed by a rapid collapse of the vapor depression is the mechanism that gives rise to the formation of pores during the laser turn point. This behavior is caused by a transient increase in energy density deposited by the laser and can therefore be mitigated by adjusting process parameters to keep energy density approximately constant. Turning the laser off at the turn point (a so-called sky writing method) is not a viable solution for pore mitigation as it has previously been shown to result in pore formation ${ }^{16}$. Incidentally, the formation of pores at the end of a written track when using the sky writing method can also be explained by the observations here describing the collapse of the vapor depression and the subsequent formation of pores. The vapor depression collapse when the laser is turned off likely exhibits behavior comparable to the conditions described due to the removal of laser power within the $6.5 \mu$ s measured for the $\mathrm{Yb}$-fiber laser used in this study. In the laser off condition the transition from keyhole mode to zero laser input power would be even more abrupt than at the turn point. Given the physical limitations of the mirror-based laser scanning system, the only practical option available to stabilize the energy density during the turn point is to vary the laser power, which can be controlled at time scales on the order of 20 ps in modern Yb-fiber lasers. A scan strategy for mitigation of pore formation has the following mechanistic and physical requirements: (i) the vapor depression must not transition into the keyhole regime at the turn region, (ii) laser power must be controlled with no rapid oscillations, (iii) the power must be sufficient to maintain the melt pool during scanning of the hatch spacing, and (iv) the laser power must not increase rapidly when accelerating out of the turn point into the pre-heated region. A power profile strategy was devised to conform to these constraints and applied to LPBF of Ti-6Al-4V using a steady-state laser power of $100 \mathrm{~W}$ and a scan speed of $1000 \mathrm{~mm} \mathrm{~s}^{-1}$ (Fig. 6a). Transmission X-ray imaging of the process shows that the mitigation strategy results in a near uniform vapor depression depth during the entire scan pattern (see Supplementary Movie 2 and Supplementary Note 2 for in-process videos of the constant power and mitigation scan strategy cases). Most importantly, pores were not detected in the processed track using this scan strategy. When combined with contour and border hatch scan strategies which have been shown to reduce porosity ${ }^{41}$ this power modulation scan strategy could further improve final component quality. This is particularly important in island scan sequences where the number of turn points per volume slice is increased significantly ${ }^{42}$.

An analytical approach, utilizing normalized enthalpy ${ }^{18,34,43}$, was used to investigate the outcomes of the mitigation strategy. Normalized enthalpy is a term commonly used in the welding literature ${ }^{43,44}$ and recently has expanded to characterize LPBF conditions $^{18,34}$. Previous studies have shown a linear dependence on the depth of molten material with normalized enthalpy under varied laser conditions. The normalized enthalpy $\left(\frac{\Delta H}{h_{\mathrm{s}}}\right)$ is equal to $\frac{A P}{\pi \rho C T_{\mathrm{m}} \sqrt{D u a^{3}}}$, where $\Delta H$ is the specific enthalpy, $h_{\mathrm{s}}$ is the enthalpy at melting, $A$ is the absorptivity of the material (assumed to be 0.6 under all conditions), $P$ is the laser power $\rho$ is the density $(4.43 \mathrm{~g}$ $\left.\mathrm{cm}^{-3}\right)^{45}, C$ is the specific heat capacity $\left(0.83 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}\right)^{45}, T_{\mathrm{m}}$ is the melting temperature $(1923 \mathrm{~K})^{45}, D$ is thermal diffusivity of the molten material $\left(0.086 \mathrm{~cm}^{2} \mathrm{~s}^{-1}\right)^{45}, u$ is the laser scan speed, and $a$ is the $\frac{1}{e}$ radius of the laser beam $(a=\sigma \sqrt{2})$. The normalized enthalpy approach was applied to the vapor depression depth as a function power data in Fig. 3a collected at varied laser scan speeds (see Supplementary Fig. 4). This reveals that the vapor depression depth is linear with normalized enthalpy and the relationship is identical for different laser scan speeds under these material processing conditions.

Normalized enthalpy as a function of laser position for the constant power and mitigation scan strategy are shown in Fig. 6b. During steady-state scanning at $1000 \mathrm{~mm} \mathrm{~s}^{-1}$ and $100 \mathrm{~W}$, the normalized enthalpy is approximately equal to 12.4. For the case of the turn point performed at constant power the normalized enthalpy is greater than the steady-state case in the region $500 \mu \mathrm{m}$ before and after the turn point and reaches a maximum value of 63.2 at the turn. This increase in $\Delta H$ results in severe material overheating and the formation of a deep keyhole which ultimately leads to pore formation as the laser completes the turn. During the mitigated scan strategy, the normalized enthalpy is near constant, peaking at a value of 31.6 for approximately $100 \mu$ s at the turn point when the scan speed is reduced to $44 \mathrm{~mm} \mathrm{~s}^{-1}$. The laser power was not reduced farther than $50 \mathrm{~W}$ in this region as\\
a

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Fig. 6 Mitigation of vapor depression depth change during LPBF of Ti-6AI-4V. a The black line (left axis) corresponds to vapor depression depth as a function of time during a $100 \mathrm{~W}$ peak power pore mitigation scan strategy. Error bars represent uncertainty in the distance between the base of the vapor depression and the surface caused by surface roughness. Also shown is the commanded laser power as a function of time used in the scan strategy (red line). Depression depth values were measured for the case of a bare plate experiment because depression depth measurements in bare plate were less uncertain than the powder case, but the same trend is observed in both cases. b Normalized enthalpy $\left(\frac{\Delta H}{h_{\mathrm{s}}}\right)$ represented by the magenta-green color scale as a function of laser position during the turn point for the full power and mitigated cases at $1000 \mathrm{~mm} \mathrm{~s}^{-1}$ steady-state scan speed

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_a60fd84fbf000be70a8bg-07(2)}
\end{center}

Fig. 7 Quality of LPBF-AM tracks in Ti-6AI-4V. a, b Top-down optical image and side-on X-ray image of a LPBF-AM track in the turn point region produced using a constant power of $100 \mathrm{~W}$. Pores formed during LPBF are highlighted in b. c, d Top-down optical image and side-on X-ray image of an LPBF track produced using the $100 \mathrm{~W}$ peak power pore mitigation scan strategy shown in Fig. 5b. No pores were detected in d. All scale bars are $500 \mu \mathrm{m}$

this approaches the cut-off power of the laser resulting in complete collapse of the depression and possible underheating. This short increase however did not result in a transition to a deep keyhole vapor depression likely due to thermal lag required to induce changes in overall melt pool behavior under these conditions. Regarding the effect of preheating, it is observed that under steady-state conditions the depression depth for all scan speeds probed is approximately $250 \mu \mathrm{m}$ when the normalized enthalpy value equals 31.6 (see Supplementary Fig. 4). Comparing this behavior to the turn point case we observe that a brief increase to this level of normalized enthalpy for $100 \mu$ s during the turn does not cause the formation of a deep keyhole vapor depression and a depression depth of only $70 \mu \mathrm{m}$ was realized. The analytical normalized enthalpy analysis reveals that for successful implementation of a defect mitigation scan strategy the normalized enthalpy should be kept near constant and below the transition point into the keyhole regime.

Quality of tracks produced by pore mitigation strategy. A pore mitigation strategy is not viable if the resulting track is of low quality (e.g., discontinuous). Figure 7 shows top-down optical and side-on transmission X-ray images of LPBF-AM turn point tracks produced on Ti-6Al- $4 \mathrm{~V}$ with a single $60 \mu \mathrm{m}$ powder layer produced using constant power $(100 \mathrm{~W})$ and the mitigation strategy, respectively (for further examples see Supplementary Fig. 5). The track produced using constant power (Fig. 7a) exhibits a bulge at the turn point caused by overheating and expansion of the melt pool in this region with a track width $40 \%$ wider at the turn point than during the steady-state scan. The turn point using constant power also contains pores at depths up to approximately $250 \mu \mathrm{m}$ beneath the substrate surface (Fig. 7b). For the case of the track produced using the mitigation strategy, Fig. 7c shows a clear improvement in track geometry. There is no longer a bulge at the end of the track caused by overheating. This reveals that not only is the formation of pores mitigated using this scan strategy (Fig. 7d), the quality of the resulting track with respect to the geometry and minimum track resolution is also improved. The mitigation strategy not only improves quality of material fabricated by LPBF-AM, but also is simple to implement, because it only requires linear ramping of the laser power over a few hundred microseconds. This sort of power adjustment can be implemented with the hardware available in most commercial LPBF machines by constructing power maps with the 3D slicer\\
software that converts the component geometry defined by a CAD file into machine instructions ${ }^{46}$.

\section*{Discussion}
In summary, we have uncovered the mechanism of pore formation during laser turn points, a critical defect mode in serpentine scan-based LPBF. The pore formation process is observed experimentally in Ti-6Al- $\mathrm{V}$ and via multi-physics modeling of SS316L, revealing the general nature of the mechanism. Pores form at laser turn points due to the emergence and subsequent collapse of a deep keyhole depression caused by the deceleration and acceleration of the galvanometer-based scanning mirrors during the turn which results in dramatic variations in the local normalized enthalpy at the material surface. As the laser accelerates away from the turn point, the keyhole depression collapses and molten metal fills the void, trapping gaseous argon which ultimately forms a pore as the material solidifies. This understanding based on in situ X-ray imaging and multi-physics modeling was harnessed to devise a pore mitigation strategy based on laser power modulation and implemented under typical Ti-6Al-4V build conditions. The mitigation strategy effectively prevents pore formation at the laser turn point by removing the rapid variation in depression depth inherent in the unmitigated case and improves the geometric tolerance of fabricated tracks by avoiding overheating. Conceptually similar strategies should be applicable to any abrupt laser on/off points during LPBF. The successful mitigation strategy presented here illustrates the potential of in situ X-ray measurements coupled with high fidelity modeling for driving process improvements and paves the way to increasing the quality of LPBF-built components.

\section*{Methods}
LPBF system and processing conditions. LPBF was performed using a laboratory-scale test bed described and characterized in detail elsewhere ${ }^{22}$. The LPBF system utilized a $1070 \mathrm{~nm}$, continuous wave (CW) Yb-fiber laser (500 W maximum power, YLR-500-WC-Y14, IPG Photonics) coupled to a galvanometer scanning mirror system (Nutfield Technology, 3XB 3-Axis Scan Head) for processing. The laser was focused to a spot size of approximately $50 \mu \mathrm{m}$ in diameter $(D 4 \sigma)$ for all experiments and passed through an anti-reflective coated laser entry window into the vacuum chamber, normal to the sample surface. The optical working distance between the scanning mirrors and the sample surface was approximately $380 \mathrm{~mm}$, and the laser beam Rayleigh range was $1.8 \mathrm{~mm}$. The vacuum chamber containing the sample was evacuated to $5 \times 10^{-2}$ Torr prior to being filled with 730 Torr argon inert gas environment for processing. Argon was constantly flowed through the vacuum chamber during experiments at 500 SCCM. During processing, the laser was scanned using various laser power and scan speed conditions onto a region of a Ti-6Al-4V substrate (TMS Titanium, Poway, CA, USA). Each substrate was approximately $500 \mu \mathrm{m}$ thick in the X-ray probe direction and $10 \mathrm{~mm}$ in depth. Experiments were performed with and without a $60 \pm 20-\mu \mathrm{m}$ thick layer of $\mathrm{Ti}-6 \mathrm{Al}-4 \mathrm{~V}$ powder $(30 \pm 10 \mu \mathrm{m}$ powder diameter; Additive Metal Alloys, Maumee, OH, USA) on the surface. The Ti-6Al- $4 \mathrm{~V}$ substrate was sandwiched between two 1-mm-thick glassy carbon sheets which provided a trench to contain Ti-6Al- $4 \mathrm{~V}$ powder on the substrate surface.

Laser turn-around scanning conditions were programmed using the Waverunner scan control software and Pipeline-2 scan controller (Nutfield Technology) which compiled the required instruction routine for the galvanometer scanning mirrors and laser power interface. Two parallel, $2.5 \mathrm{~mm}$ long tracks were compiled in the software with a hatch spacing of $50 \mu \mathrm{m}$. The laser was programmed to irradiate this geometry based on internal triggering from the scanning mirror position. The geometry treated the hatching shift at the end of the track as an additional $50 \mu \mathrm{m}$ long track and unless stated, the laser remained at full power during the turn. The mitigated scan strategy was implemented using a custom field-programmable gate array (FPGA)-based laser interface module (USB-7856; National Instruments). The galvanometer scanning mirrors were controlled by the Pipeline- 2 controller for all cases, with mitigation achieved by disabling the Pipeline- 2 controller laser power interface and initializing the FPGA module to control the laser power via an analog voltage signal. The FPGA module controlled the laser power as a function of time using a lookup table. Scanning mirror position was sampled at a rate of $1 \mathrm{MHz}$ using an FPGA module, and the analog output converted to position via a calibration routine.

Imaging and data processing. In situ X-ray imaging was performed at SSRL beam line 2-2. The white-beam X-ray spectrum generated by the $1.25 \mathrm{~T}$ bend magnet was utilized for the experiments (X-ray critical energy $7.4 \mathrm{keV}$ ). The beam was aligned coincident with the Ti-6Al-4V substrate surface in the center of the vacuum chamber and the laser aligned to scan through the X-ray imaging system field of view during processing. Transmission X-ray images of the LPBF process were captured using a scintillator-based optical system. The imaging system comprised an X-ray shutter (Uniblitz), 100- $\mu$ m-thick YAG:Ce scintillator crystal (Crytur), $\mathrm{Ag}$ coated turning mirror (Thorlabs), 10x long working distance infinity corrected objective lens (0.28 NA; Mitutoyo), tube lens (Thorlabs), and FASTCAM SA-X2 $1080 \mathrm{~K}$ high-speed camera (Photron). This imaging assembly yields an effective pixel size of $2 \mu \mathrm{m}$ per pixel for all X-ray images. Images were captured with a field of view of $1024 \times 672$ pixels at $20 \mathrm{kHz}$ and an exposure time of $25 \mu$ s. The X-ray shutter was placed in front of the scintillator and actuated to the open position approximately $50 \mathrm{~ms}$ before the laser entered the field of view and then closed after a total time of $150 \mathrm{~ms}$ to protect the detector system from damage by the X-ray beam. Synchronization of the laser and imaging system was realized using a custom FPGA-based timing circuit.

X-ray images were analyzed using Image $J^{47}$ and Mathematica (Version 11.1.1) ${ }^{48}$ software packages. Time difference X-ray images were produced through division of the uncorrected time resolved image $\left(A_{\mathrm{t}}\right)$ by the initial, pristine substrate image $\left(A_{0}\right)$ (image $=\frac{\ln \left(A_{4}\right)}{\ln \left(A_{0}\right)}$. This routine provided an image where darker regions reveal a decrease in X-ray absorption (or material) and lighter regions reveal an increase in X-ray absorption (or material). A custom script in Mathematica utilized the built-in Binarize contrast threshold method to identify and characterize pores in the processed Ti-6Al-4V substrate. Optical images of processed tracks were captured ex situ using a Keyence VR-3000 wide-area 3D measurement system and analyzed using the Keyence VR-3000 G2 and ImageJ software packages.

Multi-physics simulation. Simulations were performed using the ALE3D multiphysics software tool which utilizes arbitrary-Lagrangian-Eulerian technique ${ }^{39,49}$ To simulate the thermal response and melt flow in the material, the heat conduction equation was coupled with the Navier-Stokes equations via operator splitting ${ }^{17}$. Material parameters for stainless steel (316L) were used for the simulation ${ }^{17}$. The substrate was modeled as a flat, bare plate surface with a boundary of $600 \times 300 \times 100 \mu \mathrm{m}$. Powder was not included as it significantly increases the physical complexity of the simulation and experimental results showed no significant change in the trend in pore formation between bare plate and powder. The simulation was performed using a high-resolution mesh to enable a feature detection limit of $3 \mu \mathrm{m}$. A series of simulations was performed as a function of laser power during the turn point. Under each condition, a turn point track was simulated where the laser power reduced from a steady-state laser power of $200 \mathrm{~W}$ to a constant value during the turn point. At each $1 \mu$ s simulation time step the full thermal and laser reflection profile in the material was recorded. The maximum melt depth as a function of time was determined as a function of turn point laser power. All simulations were performed using a steady-state scan speed of $1500 \mathrm{~mm}$ $\mathrm{s}^{-1}$, and assuming a constant absorptivity of 0.25 . A scan speed of $1500 \mathrm{~mm} \mathrm{~s}^{-1}$ was required due to the exhaustive computational requirements of multi-physics simulation. The laser followed a scan geometry and turn point scan speed informed by measurements of the galvanometer scan mirror response, which comprised of a straight line stretch ending in a turn point. The speed of the laser through the turn was reduced to $400 \mathrm{~mm} \mathrm{~s}^{-1}$ to ensure the simulation stayed within bounds (see Supplementary Fig. 3).

\section*{Data availability}
The data that support the findings of this study are available from the corresponding author on reasonable request.

\section*{Code availability}
The ALE3D software routine and custom Mathematica script are not publicly available. All data generated using this code are available from the corresponding author on reasonable request.

Received: 20 November 2018 Accepted: 2 April 2019

Published online: 30 April 2019

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\section*{Acknowledgements}
This material is based upon work supported by the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE) under the Advanced Manufacturing Office, CPA agreements 32035, 32037, and 32038. Lawrence Livermore National Laboratory (LLNL) is operated by Lawrence Livermore National Security, LLC, for the U. S. Department of Energy, National Nuclear Security Administration under Contract DEAC52-07NA27344. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515.

The authors acknowledge experimental assistance from Doug Van Campen, Ron Marks, Tim J. Dunn, and Matthew Latimer, sample preparation by the LLNL Precision Machine Shop, graphics assistance by Veronica Chen at LLNL, and helpful discussions with Matthew Kramer, Peter Collins, Ryan Ott, Jianchao Ye, and Wayne King.

\section*{Author contributions}
A.A.M, N.P.C. and S.A.K wrote the article with contributions from all authors. A.A.M., N.P. C., J.W., P.J.D., A.Y.F., V.T. and A.M.K. performed the in situ X-ray imaging experiments. J.W. performed the optical imaging measurements. G.M.G. and A.A.M. contributed to laser control electronics design. S.A.K. performed the multi-physics simulations. M.J.M. and T.v.B. supervised work at LLNL. M.F.T., J.N.W., C.J.T. and K.H.S supervised work at SSRL.

\section*{Additional information}
Supplementary Information accompanies this paper at \href{https://doi.org/10.1038/s41467019-10009-2}{https://doi.org/10.1038/s41467019-10009-2}

Competing interests: The authors declare no competing interests.

Reprints and permission information is available online at \href{http://npg.nature.com/}{http://npg.nature.com/} reprintsandpermissions/

Journal peer review information: Nature Communications thanks Marco Simonelli and the other anonymous reviewer for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. (c) (i) Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as 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. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit \href{http://creativecommons.org/}{http://creativecommons.org/} licenses/by/4.0/.

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\title{Additive Manufacturing of Copper-based Alloy by Laser Powder Bed Fusion }


\author{Powder Characterization}
\date{}


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Binghao Lu

University of Central Florida

Part of the Metallurgy Commons

Find similar works at: \href{https://stars.library.ucf.edu/etd2020}{https://stars.library.ucf.edu/etd2020}

University of Central Florida Libraries \href{http://library.ucf.edu}{http://library.ucf.edu}

This Masters Thesis (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations, 2020- by an authorized administrator of STARS. For more information, please contact \href{mailto:STARS@ucf.edu}{STARS@ucf.edu}.

\section*{STARS Citation}
Lu, Binghao, "Additive Manufacturing of Copper-based Alloy by Laser Powder Bed Fusion" (2020). Electronic Theses and Dissertations, 2020-. 94.

\href{https://stars.library.ucf.edu/etd2020/94}{https://stars.library.ucf.edu/etd2020/94}

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\section*{ADDITIVE MANUFACTURING OF COPPER-BASED ALLOY BY LASER POWDER BED FUSION }
by

\section*{BINGHAO LU}
B.S. Harbin Institute of Technology 2016

2020

(C) 2020 Binghao Lu

\begin{abstract}
Copper $(\mathrm{Cu})$ and $\mathrm{Cu}$-alloy are good candidates for the engineered components that require good thermal and electrical conductivity. Since industry often needs sophisticated components that cannot be made easily by traditional methods, such as casting, forging and machining, research for additive manufacturing of copper-based alloy is on demand. Therefore, this thesis focuses on the optimization of laser powder bed fusion (LPBF) of Cu-10 wt.\% Sn alloy and pure Cu based on their characteristics such as relative density/porosity, surface roughness, phase constitutes, melt pool dimension, and dendrite arm spacings dimension, determined by optical microscopy, X-ray diffraction and Scanning electron microscope. LPBF, also known as selective laser melting, was carried out for the Cu-10Sn alloy with varying parameters of laser power from $200 \mathrm{~W}$ to $350 \mathrm{~W}$, laser scan speed from $100 \mathrm{~mm} / \mathrm{s}$ to $1000 \mathrm{~mm} / \mathrm{s}$, hatch spacing from $0.06 \mathrm{~mm}$ to $0.21 \mathrm{~mm}$, and slice thickness of $0.03 \mathrm{~mm}$. Relative density of $98 \%$ to $100 \%$ by Archimedes Principle and nearly $100 \%$ by image analysis were obtained for a large range of parameters for Cu10Sn samples, which shows a very good printability of Cu10Sn over a large window of processing parameter. $\alpha$-FCC Cu, $\delta$ - $\mathrm{Cu}_{41} \mathrm{Sn}_{11}$ eutectoid phase and $\alpha$-FCC Cu phase were observed on the printed Cu10Sn samples. Flaws related to keyhole was observed according to the energy input estimated by energy density of LPBF. Melt pool of all samples were measured, and its dimension had a linear relationship with the energy density. LPBF of pure Cu was also explored with varying parameters of laser power from $200 \mathrm{~W}$ to $350 \mathrm{~W}$, laser scan speed from $50 \mathrm{~mm} / \mathrm{s}$ to $800 \mathrm{~mm} / \mathrm{s}$, with a constant slice thickness of $0.03 \mathrm{~mm}$. Relative density of the LPBF pure $\mathrm{Cu}$ varied from $80 \%$ to $88 \%$, and the flaws were mostly non-spherical, suggesting the lack of fusion to fully melt the Cu powder.
\end{abstract}

\section*{ACKNOWLEDGMENTS}
I want to thank Lord for his effort to bring faith to human being, it is because of the faith that I can endure the hard time of life and keep positive mind site. I want to thank my academic advisor Dr. Yongho Sohn for his help and supervision, and the research opportunity he brought me. I also want to thank every students and co-workers in research laboratory for their training and help throughout my research, especially Dr. Zhou for his constant advice on my research and spending time on my thesis and presentation modification, in addition to my parents and friends for their love and support.

\section*{TABLE OF CONTENTS}
LIST OF FIGURES ..... vii\\
LIST OF TABLES ..... $x$\\
CHAPTER ONE: INTRODUCTION ..... 1\\
CHAPTER TWO: LITERATURE REVIEW ..... 3\\
Additive Manufacturing ..... 3\\
Laser Source Melting ..... 4\\
Electron Beam Melting ..... 4\\
Comparison of SLM and EBM. ..... 5\\
Copper-based Alloy ..... 7\\
CuSn (bronze) ..... 7\\
Pure $\mathrm{Cu}$.... ..... 8\\
Additive Manufacturing of Cu-Sn Alloys ..... 10\\
Cu10Sn Additive Manufacturing ..... 10\\
Cu15Sn Additive Manufacturing ..... 11\\
Cu4Sn Additive Manufacturing ..... 11\\
Additive Manufacturing of Pure $\mathrm{Cu}$ ..... 12\\
Challenges Associated with Pure $\mathrm{Cu}$ ..... 12\\
Previous Pure Cu Additive Manufacturing Research ..... 12\\
CHAPTER THREE: EXPERIMENTAL DETAILS ..... 15\\
Powder Characterization ..... 15\\
Laser Powder Bed Fusion ..... 15\\
Sample Preparation and Characterization ..... 17\\
CHAPTER FOUR: FINDINGS ..... 20\\
Powder Characterization ..... 20\\
Laser Power Bed Fusion ..... 25\\
Sample Characterization ..... 27\\
Relative Density by Archimedes Principle on Cu10Sn and pure copper LPBF parts ..... 27\\
Cross-sectional Analysis for Porosity and Surface Roughness on Cu10Sn Samples ..... 29\\
Cross-sectional Analysis for Porosity on Pure Cu Samples ..... 38\\
Melt Pool Measurement on LPBF Cu10Sn Samples ..... 39\\
XRD Analysis on Cu10Sn LPBF Parts and Powder ..... 40\\
SEM on LPBF Cu10Sn Part and Dendrite Measurement ..... 40\\
Demonstrative Cu10Sn Component Manufactured by LPBF. ..... 42\\
CHAPTER FOUR: CONCLUSION ..... 44\\
LIST OF REFERENCES ..... 45

\section*{LIST OF FIGURES}
Figure 1 Metal additive manufacturing process...................................................................... 3

Figure 2 Cu-Sn phase diagram [18] .......................................................................................... 7

Figure 3 SEM micrographs for the Cu-10Sn fabricated by (a-c) SLM and (d) casting showing the ( $\alpha+\delta$ )-eutectoid (bright phase) and $\alpha$-dendrites (dark phase). [26] ...................................... 10

Figure 4 Room-temperature stress-strain curves under tensile loading for the cast and SLM Cu-

10Sn bronze and (inset) Cu-10Sn bronze propeller fabricated by SLM. [26] ............................ 11

Figure 5 Micrographs of copper specimens polished cross-sections: a) specimen N1 horizontal cross-section; b) specimen N1 vertical cross-section; c) specimen N3 horizontal cross-section; d) specimen N3 vertical cross-section [29]................................................................................. 13

Figure 6 Relative density of SLM-built cubes of pure Cu [30] ................................................ 14

Figure 7 Schematic diagram of the Cu10Sn sample cutting and characterization cross-section.. 18

Figure 8 Schematic diagram of the pure Cu sample cutting and characterization cross-section.. 18

Figure 9 An example of melt pool measurement from an etched cross-sectional sample............ 19

Figure 10 XRD pattern of Cu10Sn powders............................................................................. 20

Figure 11 XRD pattern of pure Cu powders ............................................................................ 21

Figure 12 Cu10Sn powder size distribution by laser diffraction particle size analyzer .............. 22

Figure 13 Pure copper powder size distribution by laser diffraction particle size analyzer ......... 22

Figure 14 Cross-sectional optical microscopy confirms spherical morphology of Cu10Sn

powders (a) 150× magnification, (b) 300× magnification........................................................ 23

Figure 15 Cross-sectional optical microscopy confirms spherical morphology of pure copper powders (a) 150× magnification, (b) 300× magnification....................................................... 23

Figure 16 SEM micrographs of Cu10Sn powders at different magnifications and EDS pattern of the Cu10Sn powders 24

Figure 17 SEM micrograph of pure copper powders at different magnifications and EDS pattern of the pure copper powder 25

Figure 18 LPBF builds of Cu10Sn cylinder samples with different parameters ......................... 26

Figure 19 LPBF build of pure copper samples with different parameters.................................. 27

Figure 20 Relative density of Cu10Sn samples measured by Archimedes Principle, (a) as a function of laser scan speed, (b) as a function of energy density, (c) as a function of hatch spacing ........................................................................................................................................... 28

Figure 2116 Relative density of pure copper samples with different laser power and laser scan speed measured by Archimedes Principle 29

Figure 22 Optical micrographs from Cu10Sn samples produced with 350W laser power .......... 30

Figure 23 Optical micrographs from Cu10Sn samples produced with 300W laser power .......... 30

Figure 24 Optical micrographs from Cu10Sn samples produced with 250W laser power .......... 31

Figure 25 Optical micrographs from Cu10Sn samples produced with 200W laser power .......... 31

Figure 26 Relative density determined from samples produced with 350W laser power ............ 32

Figure 27 Relative density determined from samples produced with 300W laser power ............ 32

Figure 28 Relative density determined from samples produced with 250W laser power ............ 33

Figure 29 Relative density determined from samples produced with 200W laser power ............ 33

Figure 30 Surface roughness observed from the cross-section optical micrographs for samples produced with 350W laser power ............................................................................................... 34

Figure 31 Surface roughness observed from the cross-section optical micrographs for samples produced with 300W laser power . 34

Figure 32 Surface roughness observed from the cross-section optical micrographs for samples produced with 250W laser power 35

Figure 33 Surface roughness observed from the cross-section optical micrographs for samples produced with 200W laser power . 35

Figure 34 Quantification of surface roughness method............................................................ 36

Figure 35 Surface roughness determined from samples produced with 350W laser power......... 36

Figure 36 Surface roughness determined from samples produced with 300W laser power......... 37

Figure 37 Surface roughness determined from samples produced with 250W laser power........ 37

Figure 38 Surface roughness determined from samples produced with 200W laser power......... 38

Figure 39 Optical micrograph from LPBF pure Cu................................................................. 38

Figure 40 Cu10Sn melt pool depth and width with laser parameter......................................... 39

Figure 41 Cu-10Sn melt pool depth and width with energy density ......................................... 39

Figure 42 XRD of printed Cu10Sn part with SLM parameter and Cu10Sn Powder................... 40

Figure 43 Secondary and backscatter electron micrographs of etched Cu10-Sn sample made with recommended parameters (350w, 750mm/s, 0.12mm)............................................................. 41

Figure 44 Primary dendrite arm spacing.................................................................................. 42

Figure 45 Demonstrative Component Manufactured by LPBF of Cu10Sn10 (Power=350W, Scan

Speed $=750 \mathrm{~mm} / \mathrm{s}$, Hatch Space=0.12mm) Double Layered Pipe ( $\sim 5 \mathrm{~cm}$ in Diameter)with Internal

Cooling Channels and Grit-blasted Surface Finish................................................................... 43

\section*{LIST OF TABLES}
Table 1 Processing parameters examined during LPBF optimization study for Cu10Sn............ 16

Table 2 Processing parameters examined during LPBF optimization study for pure copper ...... 17

\section*{CHAPTER ONE: INTRODUCTION}
Copper-based alloys have many desirable properties that suits a wide range of applications because of high electrical conductivity, high thermal conductivity, good strength, excellent ductility and good corrosion resistance. Pure copper, of course has one of the best electrical and thermal conductivities among all metals, and over half of the copper produced is used for electrical applications. Copper can also be easily alloyed with a wide range of elements, and produce many commercially important alloys such as brass (copper-zinc alloy), bronze ( coppertin alloy), gunmetal (copper-tin, zinc, lead alloy), copper-nickel alloy, nickel silver alloy (copper-nickel-zinc), and Beryllium-copper. [1] Bronze is an alloy of copper and tin with high ductility and low friction coefficient. Bronze has been used in architecture for design and structural purpose, in bearing, and for musical instruments, electrical contacts, coins and ship propellers. [2] Today, copper and copper-based alloy play an important role in the development of new technology, renewable energy, architecture, information and communication technology, health and sanitation. Copper production is a very important part of our economy.

Additive manufacturing (AM) is a technological process of making physical objects from 3D computer files. The manufacturing of the parts is built typically by a layer by layer strategy, and is commonly called 3D printing in a consumer-friendly way. [3] Benefits of metal additive manufacturing includes: parts can be produced directly from a 3D computer file which reduces production time; eliminate tooling and other production support process; environmental-friendly since metal powders can be re-used; reduced cost for product design; and offer an efficient way to produce sophisticated parts. [4]

Therefore, this thesis focuses on the additive manufacturing (AM) of Cu10Sn and pure Cu by laser powder bed fusion (LPBF) technology. Both Cu10Sn and pure Cu samples were produced by varying the important parameters of LPBF, namely laser power, laser scan speed, hatch spacing and slice thickness. Relative density and microstructure of Cu10Sn and pure Cu samples were examined to optimize the parameters of LPBF, and to help understand the mechanism of LPBF process.

\section*{CHAPTER TWO: LITERATURE REVIEW }
Additive manufacturing (AM), which is also called 3D printing, is a process of building threedimensional object from a computer-designed model, and the objects are usually built layer by layer [3]. AM is different from other conventional subtractive processes, like casting or forging, where material is required to be machines to manufacture component with desired geometry. AM can provide sophisticated components with less energy and time than the traditional manufacturing methods. It is currently employed to process plastics, metals and alloys, ceramics, composites and biological materials. [5]

For AM of metals and alloys, raw material can have the form of powder or wire, which are melted and/or sintered by an energy source. Metal AM are usually classified into two groups: Powder Bed Fusion (PBF) and Directed Energy Deposition (DED). These are further classified based on their energy source: laser and electron beam. The additive manufacturing process was illustrated in Figure 1.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-14}
\end{center}

Figure 1 Metal additive manufacturing process

\section*{Laser Source Melting}
In PBF technology, certain regions of the powder bed are selectively fused by the thermal energy. [3] Typical representatives are selective laser sintering/melting (SLS/SLM), Direct Metal Laser Sintering (DMLS) and electron beam melting (EBM). SLS is the process to use laser power to selectively coalesce powders by a layer by layer strategy to form the final 3D part. SLM is a more advanced technology than SLS, which can fully melt the powder by the laser. Most of the laser power for these technologies range from $200 \mathrm{~W}$ to $1000 \mathrm{~W}$. Inert atmosphere is provided within the chamber: typically, nitrogen for non-reactive material and argon for reactive material. The main parameters for these processes are laser power, scan speed, layer thickness, hatch spacing. [6] Powder layer thickness usually varies from $20 \mu \mathrm{m}$ to $100 \mu \mathrm{m}$ based on the material. A wide range of metallic material can be printed densely with these processes, for example titanium alloys, Inconel alloys, cobalt alloys, aluminum alloys and ferrous alloys. The laser based PBF has a relatively slow building speed of $5-20 \mathrm{~cm}^{3}$ and build size limitation is usually $250 \times 250 \times 325 \mathrm{~cm}^{3}$, which limits the PBF to the field of printing small parts and increases its costs. So recently the research has focusing on increasing the build speed and size to make mass printing available.

\section*{Electron Beam Melting}
Electron beam melting (EBM) is another kind of PBF technique that uses electron beam as a source to melt the powder bed. EBM is similar to SLM, and the only difference is EBM uses electron beam instead of laser to fuse powders. [7] The electron beam is emitted by a high temperature tungsten filament, and focused and controlled by electro-magnetic fields. The electron beam is focused by focus coil to the desired diameter down to $0.1 \mathrm{~mm}$ and is moved by\\
deflection coil to certain positions of the powder bed. [8] [9] After the high-speed electron beam bombards the powder bed, the kinetic energy of the electron transforms to thermal energy and melt the metal powder bed. [10] Each powder layer experiences two stages during EBM: preheating and melting. During the preheating stage, the high current and speed electron beam scans the powder bed multiple times to make sure the powders achieve the preheating temperature, which is usually $0.4-0.6 \mathrm{~T}_{\mathrm{m}}$. During the melting stage, low current and speed electron beam melts the metal powders. [11] After scanning the first layer, the stage will move down and pave another layer of powder and repeat the same procedure as the first layer. During the melting process, a small amount of inert gas helium is added to the chamber to avoid the powder being charged. It also has a system to allow the beam to be divided into multiple beam to control the powder to be heated, sintered or melted. [12] Important parameters for EBM process are: electron beam power, current, diameter of the focus, preheating temperature, and layer thickness. The typical layer thickness for EBM ranges between 50 and 200 pm. [8] EBM can work for many metallic alloys, such as titanium, cobalt chrome, titanium aluminide, Inconel, stainless steels, tool steels, copper, aluminum alloys, beryllium, etc.

\section*{Comparison of SLM and EBM}
Due to the high energy density and high scan speed, EBM often has a higher building rate than SLM, but it has inferior dimension accuracy and surface quality. [12] In both SLM and EBM, residual stress within the component is created because of the high heating and cooling rate. The preheating reduces the residual stresses on the powder layer, which can eliminate the residual stress and post-build heat-treatment process. Preheating can also make the powders agglomerate together, which serves as the support structure for some overhanging area. Therefore, the support structure in EBM only needs to conduct the heat not for support function. This can reduce the\\
support structure required for printing and increase the ability to print sophisticated parts. During LPBF, preheating of the powder bed can be done by the platform heating.

The EBM needs a high vacuum to operate because of electron beam use. [13] Vacuum environment can eliminate thermal convection, thermal gradient and the oxidation of the alloy parts. [12] However, metals and alloys that evaporate easily cannot be used in EBM. In contrast, SLM uses Argon as protective gas for reactive metal to prevent oxidation and contamination, and Nitrogen for non-reactive material. [14] Even though EBM has many advantages, it is still not as popular as SLM, because of its high cost, lack of accuracy and limited build volume that requires vacuum.

AM technologies of metals and alloys started to get attention in the fields of aerospace, marine, oil and gas, automobile, because of their unique advantages. The first advantage is its high material utilization ratio, the traditional subtractive manufacturing methods such as forging or machining has a very low material utilization. The ratio is usually 1:20 or 1:10 for some aerospace parts. The additive in contrast has a very high material utilization ratio, which can nearly reach 1:1. [15] [16] Second, through finite element analysis, it can be used for structure optimization to reduce the material weight.

Traditional manufacturing method usually finishes an engineered component in several steps including rolling, machining, wielding. However, AM technologies can make the final component within only one step. AM can also finish the component without any resembling components. AM has the advantages of less time, material consumption, better mechanical properties, and less manufacturing procedures. [17]

\section*{Copper-based Alloy}
\section*{CuSn (bronze)}
Bronze is a Cu-based alloy with an alloying addition of 12 to $12.5 \mathrm{wt} . \%$ Sn, the addition of alloying addition often provides enhanced properties, such as higher stiffness, ductility, and machinability. The Cu-Sn phase diagram is shown in Figure 2.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-18}
\end{center}

Figure 2 Cu-Sn phase diagram [18]

The bronze is first widely used as a hard metal in Bronze Age. The Bronze Age dates to the 4mid millennium BC in India and Western Eurasia, 2 millennium BC in Ancient China, and other places. There are many kinds of bronze alloys, but the most common one is with $88 \mathrm{wt} \% \mathrm{Cu}$ and 12 wt.\% Sn. [19] Bronze is usually non-magnetic, but the addition of iron or nickel can make it magnetic.

Alpha Bronze consists of alpha solid solution of tin in face-centered cubic copper. The alpha bonze with 4-5 wt.\% Sn is used to manufacture springs, blades, turbines and coins. During Bronze Age, there were two kinds of bronze used: classical bronze has a Sn concentration about 10 wt.\% and it was commonly used for casting; while mild bronze has a Sn content about 6 wt.\% and it was used from an ingot to be hammered to sheets.

Bronze is a very ductile metal (i.e., more ductile than cast iron), and only oxides superficially and passivates. However, if the copper chlorides are formed, the corrosion will then destroy the whole sample. [20] Bronze usually has a relatively low melting point than cast iron or steel. The density of bronze is usually 10\% lower than steel. Bronze has a higher electrical and heat conductivity than steel, but the cost of bronze is usually higher than ferrous alloys, although lower than nickel-alloys.

\section*{Pure Cu}
Copper has a symbol of $\mathrm{Cu}$ with the atomic number of 29 and has a good thermal and electrical conductivity with soft and ductile property. It has a pinkish and orange color in its original form. It can be used as a heat or thermal conductor, build material or the base for different copper alloys.

Copper is in the 11 group of the element periodic table, it has one s-orbital electron on top of the filled d-orbital electron shell, which give its high ductility, thermal and electrical\\
conductivity. The filled d-shell contributes little to the interatomic bond, which is dominated by the s-electron. Unlike other metallic element with an incomplete d-shell, copper with only selection contributing to the metallic bond lacks the property of covalent bonds and is therefore considered fragile. This is the reason why single crystal copper has a high ductility and low hardness. [21] On the macroscopic scale, the introduction of the defects, such as grain boundary, will hinder the motion of dislocation and increase the hardness of the material.

This partially explains the reason why copper has a high electrical conductivity (59.6×106 S/m), which is the second highest among all pure metal, second to pure silver. [22] This is because the obstruction of the electron flow primarily comes from the thermal vibration of the electrons, which are very low in soft material. [21] The maximum current density allowed in the copper cross-section in an open air is $3.1 \times 106 \mathrm{~A} / \mathrm{m}^{2}$, and above which the copper is going to heat up extensively. [23] Copper is one of the few metals that has an orange-like appearance instead of gray or silver, [24] and it will have a reddish tarnish on the surface after exposure to the air. The reason for this characteristic is because of the energy difference between the filled 3d electron orbital and the half-filled 4s orbital. Galvanic corrosion will happen if the copper is in contact with other elements. [25]

Copper doesn't react with water, but it does react with oxygen at atmospheric environment to form a thin layer of brown-black corrosion, unlike the corrosion in iron, this kind of thin layer protects the inner part and prevents it from further corrosion.

\section*{Additive Manufacturing of Cu-Sn Alloys}
\section*{Cu10Sn Additive Manufacturing}
Using LPBF with laser power of $271 \mathrm{~W}$, laser scan speed of $210 \mathrm{~mm} / \mathrm{s}$, powder layer thickness of $90 \mu \mathrm{m}$, hatch spacing of $90 \mu \mathrm{m}, \mathrm{S}$. Scudino, et al. [26] could print $99.7 \%$ relative density parts.

Similar to as-cast Cu10Sn alloy, SLM Cu10Sn sample had microstructure consisting of $\alpha-\mathrm{Cu}$ (FCC) and the eutectoid $(\alpha+\delta)$ as shown in Figure 3. However, due to the high cooling rate during the SLM process, the microstructure in general was finer than the cast, which contributed to the better mechanical property in SLM samples. The yield strength (YS), ultimate tensile strength (UTS) and elongation reported were, respectively, $120 \mathrm{MPa}, 180 \mathrm{MPa}, 7 \%$ for cast sample and 220MPa, 420MPa, 17\% for SLM samples as shown in Figure 4.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-21}

Figure 3 SEM micrographs for the Cu-10Sn fabricated by (a-c) SLM and (d) casting showing the $(\alpha+\delta)$-eutectoid (bright phase) and $\alpha$-dendrites (dark phase). [26]

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-22}
\end{center}

Figure 4 Room-temperature stress-strain curves under tensile loading for the cast and SLM Cu10Sn bronze and (inset) Cu-10Sn bronze propeller fabricated by SLM. [26]

\section*{Cu15Sn Additive Manufacturing}
Z Mao, et al. [27] were able to print Cu15Sn bronze with 99.6\% relative density by LPBF with laser power of $187 \mathrm{~W}, 185 \mathrm{~mm} / \mathrm{s}$ scan speed and $0.17 \mathrm{~mm}$ hatch spacing. During the LPBF process, the rapid cooling produced refined cellular and dendrite structures, which significantly improved the mechanical properties of the printed parts with the UTS of 661MPa and YS of 436MPa, both of which are significantly higher than the traditionally manufactured alloy with similar composition. The annealing process significantly improved the elongation to $20 \%$ although it reduced the UTS to 545MPa - still higher than traditionally manufactured alloy with similar composition.

\section*{Cu4Sn Additive Manufacturing}
Relative density of 93.68\% was obtained by using LPBF with parameters of laser power 195W, scan speed $50 \mathrm{~mm} / \mathrm{s}$ and hatch spacing of $0.06 \mathrm{~mm}$ by Z Mao, et al. [28].

\section*{Additive Manufacturing of Pure $\mathrm{Cu}$}
\section*{Challenges Associated with Pure Cu}
Due to the high thermal conductivity of pure $\mathrm{Cu}$, the melting area experience extremely high thermal gradient and rapid cooling, both of which will induce cracking, curling or delamination. In addition, due to the high laser reflection of the pure $\mathrm{Cu}$, energy absorption by the $\mathrm{Cu}$ powder bed can be too low for efficient melting. The reflected laser can also cause damage to the additive manufacturing instrument.

\section*{Previous Pure Cu Additive Manufacturing Research}
By using LPBF, Lykov et al. [29] successfully printed pure Cu cubes with the relative density of 88\% using the parameter set consisting of laser power $200 \mathrm{~W}$, scan speed $100 \mathrm{~mm} / \mathrm{s}$, layer

thickness of $0.05 \mathrm{~mm}$, hatch spacing of $0.12 \mathrm{~mm}$. The cross-section of the highest density(N1) and lowest density(N3) are shown in Figure 5.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-24}
\end{center}

Figure 5 Micrographs of copper specimens polished cross-sections: a) specimen N1 horizontal cross-section; b) specimen N1 vertical cross-section; c) specimen N3 horizontal cross-section; $d$ ) specimen N3 vertical cross-section [29]

Ikeshoji et al. [30] managed to print pure Cu samples by different hatch spacing range from

$0.025 \mathrm{~mm}$ to $0.12 \mathrm{~mm}$ with $800 \mathrm{~W}$ laser power, scan speed of $300 \mathrm{~mm} / \mathrm{s}$ and powder thickness of 0.05mm by LPBF. The maximum relative density of $96.6 \%$ was obtained by the hatch spacing of 0.1 mm. The chart of relative density with hatch spacing was shown in Figure 6.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-25}
\end{center}

Figure 6 Relative density of SLM-built cubes of pure Cu [30]

Colopi et al. printed pure Cu by LPBF by using the laser power, ranging from 200W to 1000W, laser scan speed, ranging from $1000 \mathrm{~mm} / \mathrm{s}$ to $4000 \mathrm{~mm} / \mathrm{s}$, layer thickness of $0.05 \mathrm{~mm}, 0.1 \mathrm{~mm}$. The highest relative density of $97 \%$ was reported with the use of laser power at 600W. [31]

\section*{CHAPTER THREE: EXPERIMENTAL DETAILS}
\section*{Powder Characterization}
Powder characterization was conducted for the gas atomized Cu10Sn powders supplied by the SLM Solutions (Germany) and pure Cu powder supplied by Sandvik (Germany). Powder characterization in this research included: X-ray diffraction (XRD) to identify the phase constituents of the powders; laser diffraction particle size analyzer to determine particle size measurement; optical microscopy to examine the cross-sectional characteristics; scanning electron microscopy to observe the microstructure, and X-ray energy dispersive spectroscopy (XEDS) to determine the elemental composition of the powders.

XRD was conducted for the Cu10Sn and copper powders by using PANalytical Empyrean $^{\mathrm{TM}}$ diffractometer with $\mathrm{Cu}$ target $\mathrm{K} \alpha$ radiation with the operating parameters of $40 \mathrm{~mA}$ and $45 \mathrm{kV}$ to identify the phases. The particle sizes of the powders were measured using the laser diffraction particle size analyzer (Beckman Coulter LSTM 13 320). Powder morphology was then examined by using a field-emission scanning electron microscope (FE-SEM, Zeiss Ultra55). Cross-sections of the powders were prepared metallographically by polishing down to $0.04 \mu \mathrm{m}$ using colloidal silica to examine the microstructure by optical microscopy and FE-SEM. Composition of the Cu10Sn and $\mathrm{Cu}$ powders were measured by XEDS equipped on FE-SEM.

\section*{Laser Powder Bed Fusion}
SLM® 125HL (SLM Solutions, Germany), a laser powder bed fusion instrument with the maximum power $400 \mathrm{~W}$ was used to produce samples made up of Cu10Sn alloy and pure copper. 40 cylinder samples of the Cu10Sn and 17 cubic samples of pure $\mathrm{Cu}$ were produced. Even\\
though there are many manufacturing parameters, four of them are critical in influencing the printing outcome: they are laser power, laser scan speed, hatch spacing, layer thickness. SLM Solutions recommended parameter for Cu10Sn is $350 \mathrm{~W}$ laser power, $750 \mathrm{~mm} / \mathrm{s}$ laser scan speed, $30 \mu \mathrm{m}$ layer thickness, $120 \mu \mathrm{m}$ hatch spacing. There is no recommended parameter for pure copper powder since it is considered not printable.

The three main LPBF parameters varied in this parametric study of Cu10Sn were laser power, laser scan speed, and hatch spacing. Slice thickness was held constant at $0.03 \mathrm{~mm}$. Four laser power values (200W, 250W, 300W and 350W) and laser scan speed range from 100mm/s to $1000 \mathrm{~mm} / \mathrm{s}$ were examined in the Cu10Sn investigation. Hatch spacing range from $60 \mu \mathrm{m}$ to $210 \mu \mathrm{m}$ were examined while laser power, scan speed and layer thickness were held constant at $350 \mathrm{~W}, 750 \mathrm{~mm} / \mathrm{s}$, and $0.03 \mathrm{~mm}$, respectively. These parameters are listed in Table 1.

Table 1 Processing parameters examined during LPBF optimization study for Cu10Sn

\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Power $(\mathrm{W})$ & Scan speed $(\mathrm{mm} / \mathrm{s})$ & Hatch spacing $(\mathrm{mm})$ & Layer thickness (mm) \\
\hline
350 & \begin{tabular}{c}
$300,400,500,600,700,750$, \\
$800,900,1000$ \\
\end{tabular} & 0.12 &  \\
\cline { 1 - 3 }
350 & 750 & \begin{tabular}{c}
$0.06,0.09,0.12,0.15$, \\
$0.18,0.21$ \\
\end{tabular} &  \\
\cline { 1 - 3 }
300 & \begin{tabular}{c}
$200,300,400,500,600,700$, \\
$750,800,900$ \\
\end{tabular} & 0.12 & \multirow{2}{*}{0.03} \\
\cline { 1 - 3 }
250 & \begin{tabular}{c}
$100,200,300,400,500,600$, \\
$700,750,800$ \\
\end{tabular} & 0.12 &  \\
\cline { 1 - 3 }
200 & \begin{tabular}{c}
$100,200,300,400,500,600$, \\
700,750 \\
\end{tabular} & 0.12 &  \\
\hline
\end{tabular}
\end{center}

Only the laser power and laser scan speed were varied to conduct to examine the feasibility of LPBF for pure Cu: laser power varied at 200W, 300W and 350W, laser scan speed varied from $50 \mathrm{~mm} / \mathrm{s}$ to $800 \mathrm{~mm} / \mathrm{s}$, while the layer thickness was $0.03 \mathrm{~mm}$ and hatch spacing was $0.12 \mathrm{~mm}$. These parameters are listed in Table 2.

Table 2 Processing parameters examined during LPBF optimization study for pure copper

\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Power (W) & Scan speed $(\mathrm{mm} / \mathrm{s})$ & Hatch spacing $(\mathrm{mm})$ & Layer thickness (mm) \\
\hline
350 & \begin{tabular}{c}
$50,100,150,200,300,500$, \\
700,800 \\
\end{tabular} & \multirow{2}{*}{0.12} &  \\
\hline
300 & $50,100,150,200,300,500$ &  &  \\
\hline
200 & $50,100,200$ &  &  \\
\hline
\end{tabular}
\end{center}

\section*{Sample Preparation and Characterization}
The printed Cu10Sn and pure Cu samples were sectioned from the build plate and support structure was removed from the bottom surface of the samples by polishing. The determination of the relative density was based on the Archimedes method. The absolute density of Cu10Sn was chosen as $8.85 \mathrm{~g} / \mathrm{mm}^{3}$, while the absolute density value for pure $\mathrm{Cu}$ was chosen as 8.96 $\mathrm{g} / \mathrm{cm}^{3}$. The formula to calculate relative density is:


\begin{equation*}
\text { Relative Density }=\frac{\rho_{1} \times w_{1}}{\rho_{2} \times w_{2}} \tag{1}
\end{equation*}


where $\rho_{1}$ is water density, $\rho_{2}$ is theoretical density of the alloy, $\mathrm{w}_{1}$ is the measured dry weight of the sample, $\mathrm{w}_{2}$ is the measured water-immersed weight of the sample. Measurement was done 3 times for each sample to determine the average and uncertainty.

The cylinder Cu10Sn samples and cubic pure Cu samples were then sectioned to prepare the XY and XZ cross-sections. As presented Figure 7, the Cu10Sn samples were first sectioned along the XZ cross-section to get the entire cross-section along the build direction (Z), then one of the half sample was sectioned along the XY cross-section. The cubic pure copper samples were sectioned in the same way as the cylinder as illustrated in Figure 8. The full XZ crosssection and half XY cross-section of Cu10Sn and pure Cu samples were mounted with epoxy resin for metallographic preparation.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-29(1)}
\end{center}

Figure 7 Schematic diagram of the Cu10Sn sample cutting and characterization cross-section

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-29}
\end{center}

Figure 8 Schematic diagram of the pure Cu sample cutting and characterization cross-section The mounted Cu10Sn samples were first ground and polished by the MetPrep $3^{\mathrm{TM}}$ grinding and polishing machines made by Allied Electronics \& Automation company. First the samples were ground by the SiC grinding pad with the lubricant of water, gradually from coarse pad to fine pad, i.e., 240, 400, 600, 800, 1200 grits. Then, the polishing was carried out using the $1 \mu \mathrm{m}$ diamond pad with the lubricant of mineral oil. VibroMet ${ }^{\mathrm{TM}} 2$ Vibratory Polisher (Buehler

Company) was used for final polishing: the amplitude was set at $10 \%$ for 45 minutes using the polishing fluids of colloidal silica and distilled water. The polishing procedure for pure $\mathrm{Cu}$ samples was the same as Cu10Sn.

The metallographically polished Cu10Sn and pure Cu samples were examined by optical microscopy on both XZ and XY cross-sections. The amount of flaws due to insufficient or excessive melting was quantified on both the XZ and XY cross-sections of the samples by ImageJ software. The polished Cu10Sn surfaces were then etched with a solution of distilled water, ammonium hydroxide and 3\%-hydrogen peroxide mixed by volumetric ratio of 5:5:1. Etching was carried out for less than a second. [32] From the etched Cu10Sn cross-sections, the melt pool dimension from each sample was quantified from the top layer of the sample by optical microscope, as illustrated in Figure 8. XRD was first carried out to determine the phase constituents in the Cu10Sn sample manufactured with SLM recommended parameter from both XZ and XY cross-section. FE-SEM was carried out to examine the detailed microstructure of MPBF Cu10Sn samples.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-30}
\end{center}

Figure 9 An example of melt pool measurement from an etched cross-sectional sample.

\section*{CHAPTER FOUR: FINDINGS }
XRD patterns from the Cu10Sn and pure Cu powders are shown in Figures 10 and 11, respectively. There are two phases ( $\left.\alpha=\mathrm{FCC} \mathrm{Cu}, \delta=\mathrm{Cu}_{41} \mathrm{Sn}_{11}\right)$ in the Cu10Sn powders and the main phase is $\alpha=$ FCC Cu. Only one phase, $\alpha=$ FCC Cu, was detected from pure Cu powder as presented in Figure 11.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-31}
\end{center}

Figure 10 XRD pattern of Cu10Sn powders

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-32}
\end{center}

Figure 11 XRD pattern of pure Cu powders

Figures 12 and 13 presents particle size distribution of Cu10Sn and pure Cu powders determined by laser diffraction particle size analyzer. The average particle size of the Cu10Sn powder was $40.4 \mu \mathrm{m}$ and the D10, D50, D90 values were $20.6 \mu \mathrm{m}, 40.4 \mu \mathrm{m}$ and $60.5 \mu \mathrm{m}$, as reported in Figure 11. The average particle size of the pure Cu powders was $42.65 \mu \mathrm{m}$, and the D10, D50, D90 values were $33.05 \mu \mathrm{m}, 42.28 \mu \mathrm{m}$ and $52.82 \mu \mathrm{m}$, respectively, as reported in Figure 13.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-33(1)}
\end{center}

Figure 12 Cu10Sn powder size distribution by laser diffraction particle size analyzer

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-33}
\end{center}

Figure 13 Pure copper powder size distribution by laser diffraction particle size analyzer

The optical micrographs presented in Figures 14 and 15 demonstrates, in general,

spherical shape of the Cu10Sn and pure Cu powders with very few irregularities.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-34(1)}

Figure 14 Cross-sectional optical microscopy confirms spherical morphology of Cu10Sn powders (a) 150x magnification, (b) 300x magnification\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-34}

Figure 15 Cross-sectional optical microscopy confirms spherical morphology of pure copper powders (a) 150x magnification, (b) 300x magnification

Secondary electron micrographs in Figures 16 and 17 presents the surface morphology of the Cu10Sn powder and pure copper powder, respectively. They are mostly spherical with smooth surface. Randomly, 10 powders were selected determined the chemical composition by XEDS. XEDS spectrum from Cu10Sn powder and pure copper powder are also presented in Figures 16 and 17, respectively. Chemical composition of the Cu10Sn powder was 89 wt.\% Cu\\
and 11 wt.\% of Sn, which is very close to the nominal composition of the Cu10Sn powder.

Chemical composition of the pure copper powder was nearly $100 \%$ copper.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-35}

Figure 16 SEM micrographs of Cu10Sn powders at different magnifications and EDS pattern of the Cu10Sn powders\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-36}

Figure 17 SEM micrograph of pure copper powders at different magnifications and EDS pattern of the pure copper powder

\section*{Laser Power Bed Fusion}
40 cylindrical samples of Cu10Sn and 17 cubic samples of pure copper were made by LPBF as presented in Figure 18 and 19, respectively. Some of the Cu10Sn samples had extraneous materials attached to the cylindrical geometry, this only occurred for samples printed with very low scan speed $(100 \mathrm{~mm} / \mathrm{s}$ or $200 \mathrm{~mm} / \mathrm{s})$ when the high energy density "sintered" powders adjacent to the laser scan. Pure copper cubes printed well with good surface finish as demonstrated by the sample identification number clearly exhibited on top surface as seen in Figure 19.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-37}
\end{center}

Figure 18 LPBF builds of Cu10Sn cylinder samples with different parameters

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-38}
\end{center}

Figure 19 LPBF build of pure copper samples with different parameters

\section*{Sample Characterization}
Relative Density by Archimedes Principle on Cu10Sn and pure copper LPBF parts

The measured relative density of the Cu10Sn samples is present Figure 20. The relative density increased with an increase in laser scan speed in general. The relationship between energy\\
density and relative density is revealed in Figure 20, as the energy density increased, the relative density decreased. The energy density is defined as:


\begin{equation*}
E=\frac{P}{v \times h \times t} \tag{2}
\end{equation*}


where $\mathrm{P}$ is the laser power $(\mathrm{W}), \mathrm{v}$ is the laser scan speed $(\mathrm{mm} / \mathrm{s}), \mathrm{h}$ is the hatch spacing $(\mathrm{mm}), \mathrm{t}$ is the layer thickness (mm). [33] Energy density is a very simple factor that normalizes all four critical parameters. Finally, the relative density increased with an increase in hatch spacing.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-39}

Figure 20 Relative density of Cu10Sn samples measured by Archimedes Principle, (a) as a function of laser scan speed, (b) as a function of energy density, (c) as a function of hatch spacing

Relative density of pure copper sample was measured as shown in Figure 21. Highest relative density observed was $88 \%$. The relative density was higher when $350 \mathrm{~W}$ power was employed in general. The relatively low value of relative density observed suggested that the overall energy input and/or energy absorption is insufficient to fully melt the pure copper powders.

\section*{Relative Density with Laser Parameter}
\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-40}
\end{center}

Figure 2116 Relative density of pure copper samples with different laser power and laser scan speed measured by Archimedes Principle

Cross-sectional Analysis for Porosity and Surface Roughness on Cu10Sn Samples

Optical micrographs from the XZ and XY cross-sectional Cu10Sn samples are presented in Figures 22 through 25 . They were mostly dense, but with some pores with relatively circular shape. This demonstrates that the energy input was enough to fully melt the Cu10Sn powders and the reason for these circular pores is the gas entrapment. [34]\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-41(20)}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(9)}
\end{center}

Cu-10Sn $350 \mathrm{~W} 800 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(2)}
\end{center}

Cu-10Sn $350 \mathrm{~W} 800 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(19)}
\end{center}

Cu-10Sn $350 \mathrm{~W} 900 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(17)}
\end{center}

Cu-10Sn 350W 900mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(1)}
\end{center}

Cu-10Sn $350 \mathrm{~W} 600 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(10)}
\end{center}

Cu-10Sn 350W $1000 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(12)}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(6)}
\end{center}

Cu-10Sn 350W $700 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41}
\end{center}

Cu-10Sn 350W 700mm/s

Figure 22 Optical micrographs from Cu10Sn samples produced with 350W laser power

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(18)}
\end{center}

Cu-10Sn 300W $700 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(16)}
\end{center}

Cu-10Sn 300W 700mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(4)}
\end{center}

Cu-10Sn 300W $750 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(3)}
\end{center}

Cu-10Sn 300W $750 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(7)}
\end{center}

Cu-10Sn 300W $800 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(13)}
\end{center}

Cu-10Sn $300 \mathrm{~W} 400 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(11)}
\end{center}

Cu-10Sn 300W $800 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(15)}
\end{center}

Cu-10Sn 300W $900 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(8)}
\end{center}

Cu-10Sn 300W $900 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(5)}
\end{center}

Cu-10Sn 300W $600 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-41(14)}
\end{center}

Cu-10Sn 300W 600mm/s

Figure 23 Optical micrographs from Cu10Sn samples produced with 300W laser power\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-42(21)}

Cu-10Sn 250W 600mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(4)}
\end{center}

Cu-10Sn $250 \mathrm{~W} 200 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(20)}
\end{center}

Cu-10Sn 250W $700 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(7)}
\end{center}

Cu-10Sn 250W 200mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42}
\end{center}

Cu-10Sn 250W $700 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(1)}
\end{center}

Cu-10Sn 250W 300mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(11)}
\end{center}

Cu-10Sn 250 W $750 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(3)}
\end{center}

Cu-10Sn $250 \mathrm{~W} 300 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(14)}
\end{center}

Cu-10Sn 250 W $750 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(9)}
\end{center}

Cu-10Sn 250W $400 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(5)}
\end{center}

Cu-10Sn 250W $800 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(24)}
\end{center}

Cu-10Sn 250W 400mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(23)}
\end{center}

Cu-10Sn 250W $800 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(2)}
\end{center}

Cu-10Sn $250 \mathrm{~W} 500 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(17)}
\end{center}

Cu-10Sn 250W 500mm/s

Figure 24 Optical micrographs from Cu10Sn samples produced with 250W laser power

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(18)}
\end{center}

Cu-10Sn 200W 600mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(19)}
\end{center}

Cu-10Sn 200W 600mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(12)}
\end{center}

Cu-10Sn 200W 700mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(16)}
\end{center}

Cu-10Sn 200W 700mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(6)}
\end{center}

Cu-10Sn 200W $300 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(22)}
\end{center}

Cu-10Sn 200W $750 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(10)}
\end{center}

Cu-10Sn 200W $750 \mathrm{~mm} / \mathrm{s}$\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-42(15)}

Cu-10Sn 200W 500mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(13)}
\end{center}

Cu-10Sn 200W 400mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-42(8)}
\end{center}

Cu-10Sn 200W 500mm/s

Figure 25 Optical micrographs from Cu10Sn samples produced with 200W laser power

From these micrographs, the amount of flaws was determined for each sample from 5 of the XZ cross-section optical micrographs with ImageJ software. Results were plotted as relative\\
density (1 - flaw fraction) in Figures 26 through 29. The variation in density as a function of scan speed did not agree between the two methods employed, Archimedes method and image analysis. Samples with nearly $100 \%$ density was documented via optical micrographs and image analysis at any laser power demonstrated that the range of laser power examined in this study was sufficient to melt the Cu10Sn powders, at selected scan speeds. In particular at 350W Cu10Sn alloy appeared fully dense using the scan speed of $750 \mathrm{~mm} / \mathrm{s}$, which is the SLM recommended parameters.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-43}
\end{center}

Figure 26 Relative density determined from samples produced with 350W laser power

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-43(1)}
\end{center}

Figure 27 Relative density determined from samples produced with 300W laser power

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-44}
\end{center}

Figure 28 Relative density determined from samples produced with $250 \mathrm{~W}$ laser power

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-44(1)}
\end{center}

Figure 29 Relative density determined from samples produced with 200W laser power

In order to clarify the inconsistency in density measurement presented in Figures 26 through 29, surface roughness of the samples were quantified, because, as shown in Figure 18, there were powder coalescence in some samples which may significantly change the surface roughness that can interfere with Archimedes method. Figures 29 through 32 presents typical surface roughness observed in LPBF Cu10Sn samples. The RMS value of the surface roughness\\
was then determined for each sample as shown in Figure 33. First vertical lines (white lines in Figure 33) with equal distance was drawn on the optical micrograph, then the length of each line was measured to calculate the root-mean-square. Variation in RMS surface roughness is presented for each sample as a function of scan speed in Figures 34 through 37, and the roughness clearly decreased with an increase in scan speed. This trend observed in Figures 34 through 37 is exactly opposite of trend observed for density measured by Archimedes method presented in Figures 25 and 28. Therefore for the Cu10Sn samples, the surface roughness interfered with the measurement of relative density by Archimedes method, i.e., trapped water bubble. The relative density measured by image analysis appears to be more correct in characterizing the Cu10Sn samples produced by LPBF.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-45(7)}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(9)}
\end{center}

Cu-10Sn $350 \mathrm{~W} 800 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(5)}
\end{center}

Cu-10Sn 350W $900 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(8)}
\end{center}

Cu-10Sn 350 W $1000 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(2)}
\end{center}

Cu-10Sn 350W $700 \mathrm{~mm} / \mathrm{s}$

Figure 30 Surface roughness observed from the cross-section optical micrographs for samples produced with 350W laser power

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(3)}
\end{center}

Cu-10Sn 300W $200 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(10)}
\end{center}

Cu-10Sn 300W $700 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(1)}
\end{center}

Cu-10Sn 300W $300 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45}
\end{center}

Cu-10Sn 300W $750 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(12)}
\end{center}

Cu-10Sn 300W $400 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(6)}
\end{center}

Cu-10Sn 300W $800 \mathrm{~mm} / \mathrm{s}$\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-45(11)}

Cu-10Sn 300W 900mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-45(4)}
\end{center}

Cu-10Sn 300W $600 \mathrm{~mm} / \mathrm{s}$

Figure 31 Surface roughness observed from the cross-section optical micrographs for samples produced with 300W laser power

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(8)}
\end{center}

Cu-10Sn 250W $100 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(9)}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(4)}
\end{center}

Cu-10Sn 250W 600mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(1)}
\end{center}

Cu-10Sn 250W $200 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(14)}
\end{center}

Cu-10Sn 250W 700mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(11)}
\end{center}

Cu-10Sn $250 \mathrm{~W} 300 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(15)}
\end{center}

Cu-10Sn 250W $750 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(6)}
\end{center}

Cu-10Sn 250W 400mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(10)}
\end{center}

Cu-10Sn 250W 800mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(3)}
\end{center}

Cu-10Sn $250 \mathrm{~W} 500 \mathrm{~mm} / \mathrm{s}$

Figure 32 Surface roughness observed from the cross-section optical micrographs for samples produced with 250W laser power

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(12)}
\end{center}

Cu-10Sn 200W 100mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(13)}
\end{center}

Cu-10Sn 200W 600mm/s

\begin{center}
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Cu-10Sn 200W 200mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46}
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Cu-10Sn 200W 700mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(5)}
\end{center}

Cu-10Sn 200W $300 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(2)}
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Cu-10Sn 200W $750 \mathrm{~mm} / \mathrm{s}$

\begin{center}
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Cu-10Sn 200W 400mm/s

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-46(17)}
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Cu-10Sn 200W 500mm/s

Figure 33 Surface roughness observed from the cross-section optical micrographs for samples produced with 200W laser power

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-47(1)}
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Figure 34 Quantification of surface roughness method

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Figure 35 Surface roughness determined from samples produced with 350W laser power

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Figure 36 Surface roughness determined from samples produced with 300W laser power

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Figure 37 Surface roughness determined from samples produced with $250 \mathrm{~W}$ laser power

\begin{center}
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Figure 38 Surface roughness determined from samples produced with 200W laser power Cross-sectional Analysis for Porosity on Pure Cu Samples

Representative optical micrograph from the LPBF pure $\mathrm{Cu}$ is presented in Figure 39, and they show large irregular pores because the laser energy was insufficient to fully melt the pure $\mathrm{Cu}$ powder. [34]

\begin{center}
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$300 \mathrm{~W} 300 \mathrm{~mm} / \mathrm{s} \mathrm{XZ}$ cross-section

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$300 \mathrm{~W} 300 \mathrm{~mm} / \mathrm{s}$ XY cross-section

Figure 39 Optical micrograph from LPBF pure Cu

\section*{Melt Pool Measurement on LPBF Cu10Sn Samples}
The top layer of the melt pool has the actual width and depth of laser melted volume that solidified at the end of the sample production. Width and depth were measured by ImageJ software. As presented in Figure 40, melt pool depth and width decrease with an increase in laser scan speed, which corresponds well to the increase in both depth and width with an increase in energy density as shown in Figure 41. This can be directly related to deeper laser penetration.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-50}

Figure 40 Cu10Sn melt pool depth and width with laser parameter

\begin{center}
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\end{center}

Figure 41 Cu-10Sn melt pool depth and width with energy density

XRD patterns from the XZ and XY cross-sections of LPBF Cu10Sn samples are presented in Figure 42. For comparison, XRD pattern from the starting Cu10Sn powders is also included. They have similar patterns and have the same phases consisting of $\alpha-\mathrm{FCC} \mathrm{Cu}$ and $\delta-\mathrm{Cu}_{41} \mathrm{Sn}_{11}$.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-51}
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Figure 42 XRD of printed Cu10Sn part with SLM parameter and Cu10Sn Powder

SEM on LPBF Cu10Sn Part and Dendrite Measurement

Secondary and backscatter electron micrographs shown in Figure 43 consisted of dark matrix, $\alpha$ $\mathrm{Cu}$ (FCC) and light inter-dendritic phase of mixture $\delta-\mathrm{Cu}_{41} \mathrm{Sn}_{11}$ and $\alpha-\mathrm{Cu}$ (FCC). Dendrite structure can be clearly observed Figure 43, and so the primary dendrite arm spacing (PDAS) was measured as schematically illustrated in Figure 44. The PDAS is expressed by:


\begin{equation*}
P D A S=\frac{L}{n-1} \tag{3}
\end{equation*}


where $\mathrm{L}$ is the total spacing from the first to the last arm, $\mathrm{n}$ is the number of existing dendrite arms in this area. PDAS determined for Cu10Sn sample shown in Figure 44 is $615.9 \pm 97 \mathrm{~nm}$. This value is extremely small for $\mathrm{Cu}-10 \mathrm{Sn}$ and demonstrates rapid cooling rate associated with LPBF and would be responsible for enhanced mechanical properties, i.e., tensile strength, yield strength and elongation.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-52}

Figure 43 Secondary and backscatter electron micrographs of etched Cu10-Sn sample made with recommended parameters $(350 \mathrm{w}, 750 \mathrm{~mm} / \mathrm{s}, 0.12 \mathrm{~mm}$ )

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_46ea9d70c5fdc95ea927g-53}
\end{center}

Figure 44 Primary dendrite arm spacing

Demonstrative Cu10Sn Component Manufactured by LPBF

In order to demonstrate the printability of the Cu10Sn powders by LPBF, a pipe-like component with complex internal features was manufactured following the recommended parameters: laser power of $350 \mathrm{~W}$, laser scan speed of $750 \mathrm{~mm} / \mathrm{s}$, hatch spacing of $120 \mu \mathrm{m}$, and layer thickness of $30 \mu \mathrm{m}$. This component had an outside diameter of $5 \mathrm{~cm}$ with the inner features having minimal thickness of $0.8 \mathrm{~mm}$ and is shown in Figure 45.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_46ea9d70c5fdc95ea927g-54}

Figure 45 Demonstrative Component Manufactured by LPBF of Cu10Sn10 (Power=350W, Scan Speed $=750 \mathrm{~mm} / \mathrm{s}$, Hatch Space=0.12 $\mathrm{mm}$ ) Double Layered Pipe ( $\sim 5 \mathrm{~cm}$ in Diameter)with Internal Cooling Channels and Grit-blasted Surface Finish

\section*{CHAPTER FOUR: CONCLUSION}
Laser powder bed fusion parametric study has been conducted using powders of Cu10Sn and pure $\mathrm{Cu}$. The Cu10Sn samples were in general very dense with relative density around $98 \%$ to $100 \%$ by Archimedes Principle and nearly $100 \%$ by image analysis when manufactured with the energy density range between 74 to $140 \mathrm{~J} / \mathrm{mm}^{3}$. This is indicative of a very good printability over a large window of processing. Phase constituents of the LPBF Cu10Sn were $\alpha-\mathrm{Cu}$ (FCC) phase and $\alpha$-Cu (FCC), $\delta$-Cu ${ }_{41} \mathrm{Sn}_{11}$ eutectoid phase. Laser powder bed fusion of pure $\mathrm{Cu}$ with the maximum laser power of $350 \mathrm{~W}$ was conducted, and the maximum relative density of pure $\mathrm{Cu}$ accomplished was $88 \%$ using the parameter set of laser power of $350 \mathrm{~W}$, laser scan speed of $200 \mathrm{~mm} / \mathrm{s}$, powder layer thickness of $0.03 \mathrm{~mm}$, hatch spacing of $0.12 \mathrm{~mm}$. Large irregular pores were observed in cross-sections due to the lack of fusion.

\section*{LIST OF REFERENCES}
[1] "Copper Alliance," \href{https://copperalliance.org.uk/about-copper/copper-alloys/}{https://copperalliance.org.uk/about-copper/copper-alloys/}.

[2] "Composition and Properties of Bronze," Bronze Metal Facts.

[3] "Standard Terminology for Additive Manufacturing Technologies".

[4] S. Lasers, \href{https://www.spilasers.com/whitepapers/metal-additive-manufacturing/}{https://www.spilasers.com/whitepapers/metal-additive-manufacturing/}.

[5] T. W. T. Caffrey, "Additive manufacturing state of the industry," Wohlers Report, 2015.

[6] G. N. L. K. W. Adriaan B. Spierings, "Designing Material Properties Locally with Additive Manufacturing technology SLM," in Solid Freeform Fabrication Symposium, Austin, TX, USA, 2012.

[7] F. V. F. V. Benjamin Vayre, "Metallic additive manufacturing: State-of-the-art review and prospects, Grenoble," Cambridge University Press, vol. 13, no. 2, pp. 89-96, 2012.

[8] T. A. ,. K. C. Xibing Gong, "Review on Powder-Based Electron Beam Additive Manufacturing Technology," in ASME/ISCIE 2012 International Symposium on Flexible Automation, St. Louis, Missouri, USA, June 18-20, 2012.

[9] J. HIEMENZ, "EBM Offers a New Alternative for Producing Titanium Parts and Prototypes," in Rapid Prototyping/Manufacturing, 2006.

[10] T. E. S. Z. F. J. K. S. A. P. F. L. Jianzhong Ruan, "A Review of Layer Based Manufacturing Processes for Metals," in Solid Freeform Fabrication Symposium, December 2005.

[11] E. M. K. A. S. M. G. J. H. D. A. R. P. W. S. F. M. R. B. W. Lawrence E. Murr, "Fabrication of Metal and Alloy Components by Additive Manufacturing: Examples of 3D Materials Science," Journal of Materials Research and Technology, vol. 1, no. 1, pp. 42-54, April-June 2012.

[12] F. V. F. V. B Vayre, "Identification on Some Design Key Parameters for Additive Manufacturing: Application on Electron Beam Melting," Procedia CIRP, vol. 7, pp. 264-269, 2013.

[13] K. M. L. G. G. A. C. R. K. T. O. Mari Koike, "Evaluation of titanium alloy fabricated using electron beam melting system for dental applications," Journal of Materials Processing Technology, vol. 211, no. 8, pp. 1400-1408, August 2011.

[14] S. B. U. A. S. S. P. E. P. F. J. E. L. Loeber, "Comparison of selective laser and electron beam melted titanium aluminides," in Solid Freeform Fabrication Symposium, June 2011.

[15] G. E. C. C. O. G. AVIATION, "An Overview of Ni Base Additive Fabrication Technologies for Aerospace Applications (Preprint)," Mar 2011.

[16] P. D. O. L. A. H. P. Timothy J. Horn, "Overview of Current Additive Manufacturing Technologies and Selected Applications," Science Progress, vol. 95, no. 3, pp. 255282, September 1, 2012.

[17] E. D. J. V. M. S. J. Geraedts, "Three Views On Additive Manufacturing: Business, Research, And Education," in Proceedings of TMCE, 2012.

[18] K. A. H. W. S. Max Hansen, "Constitution of Binary Alloys," Journal of The Electrochemical Society, vol. 105, 1958.

[19] B. Knapp, Copper, Silver and Gold, Australia: Reed Library, 1996.

[20] "Bronze Disease, Archaeologies of the Greek Past," the original, 26 February 2015.

[21] G. L. Trigg and E. H. Immergut, "Encyclopedia of Applied Physics, Encyclopedia of Applied Physics Volume 4," VCH Publishers, 1992, p. 267-272.

[22] C. Hammond, The Elements, in Handbook of Chemistry and Physics (81st ed.), CRC press, 2004.

[23] "Resistance Welding Manufacturing Alliance," in Resistance Welding Manual (4th ed.), 2003, p. 18-12.

[24] W. Chambers and R. Chambers, Chambers's Information for the People (5th ed.), 1884.

[25] Galvanic Corrosion, Corrosion Doctors, Retrieved 29 April 2011.

[26] C. U. K. G. P. H. A. N. E. V. U. J. E. Sergio Scudino, "Additive manufacturing of Cu-10Sn bronze," Materials Letters, vol. 156, pp. 202-204, 1 October 2015.

[27] D. Z. Z. J. J. G. F. P. Z. Zhongfa Mao, "Processing optimisation, mechanical properties and microstructural evolution during selective laser melting of Cu-15Sn high-tin bronze," Materials Science and Engineering: A, vol. 721, pp. 125-134, 4 April 2018.

[28] D. Z. Z. P. W. K. Z. Zhongfa Mao, "Manufacturing Feasibility and Forming Properties of Cu4Sn in Selective Laser Melting," Materials, 2017.

[29] E. V. S. A. M. A. P. A. Lykov, "Selective Laser Melting of Copper," Materials Science Forum, vol. 843, pp. 284-288, 2016.

[30] K. N. M. Y. K. I. H. K. Toshi-Taka Ikeshoji, "Selective Laser Melting of Pure Copper," JOM, vol. 70, p. pages396-400, 2018.

[31] L. C. A. G. D. B. P. Marzia Colopi, "Selective laser melting of pure Cu with a $1 \mathrm{~kW}$ single mode fiber laser," Procedia CIRP, vol. 74, pp. 59-63, 2018.

[32] P. Technologies, "\href{https://www.metallographic.com/MetallographicEtchants/Metallography-Copper-alloy-etchants.htm}{https://www.metallographic.com/MetallographicEtchants/Metallography-Copper-alloy-etchants.htm}".

[33] V. F. C. T. Thijs Lore, V. H. Jan and J.-P. Kruth, "A study of the microstructural evolution during selective laser melting of Ti-6AI-4V," Acta Materialia, vol. 58, no. 9, pp. 3303-3312, May 2020.

[34] Y. L. Q. B. Bi Zhang, "Defect Formation Mechanisms in Selective Laser Melting: A Review," Chinese Journal of Mechanical Engineering , vol. 30, p. 515-527, 21 April 2017.

[35] M. ALIAKBARI, "Additive Manufacturing: State-of-the-Art, Capabilities, and Sample Applications with Cost Analysis," 2012.


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\title{Machine Learning of Selective Laser Melting }

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LAWRENCE LIVERMORE NA TIONAL

B. Yuan, G. Guss, A. Wilson, S. Hau-Riege, P. Depond, S. McMains, M. Matthews, B. Giera

\section*{March 22, 2018}
Advanced Materials Technologies

This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.

\section*{WILEY-VCH}
DOI: $10.1002 /$ ((please add manuscript number))

Article type: Full paper

\section*{Machine Learning Based Monitoring of Laser Powder Bed Fusion}
Bodi Yuan, Gabriel M. Guss, Aaron C. Wilson, Stefan P. Hau-Riege, Phillip J. DePond, Sara McMains, Manyalibo J. Matthews, and Brian Giera*

Keywords: laser powder bed fusion, machine learning, additive manufacturing, selective laser melting

A two-step machine learning approach to monitoring Laser Powder Bed Fusion (LPBF) additive manufacturing is demonstrated that enables on-the-fly assessments of laser track welds. First, in situ video melt pool data acquired during LPBF is labeled according to the (1) average and (2) standard deviation of individual track width and also (3) whether or not the track is continuous, measured post-build through an ex situ height map analysis algorithm. This procedure generates three ground truth labeled datasets for supervised machine learning. Using a portion of the labeled 10-millisecond video clips, a single Convolutional Neural Network architecture is trained to generate three distinct networks. With the remaining in situ LPBF data, the trained neural networks are tested and evaluated and found to predict track width, standard deviation, and continuity without the need for ex situ measurements. This two-step approach should benefit any LPBF system - or any additive manufacturing technology - where height-map-derived properties can serve as useful labels for in situ sensor data.

\section*{1. Introduction}
Laser Powder Bed Fusion (LPBF, or equivalently Selective Laser Melting) is an additive manufacturing technology that produces metal parts, layer by layer, by melting powdered metals and alloys with a high-power laser ${ }^{[1]}$. Considering the beneficially large set of metallic powders available to LPBF for fabricating objects of virtually any shape, the technique is versatile and ideally suited for applications such as rapid prototyping and lightweighting ${ }^{[2]}$. The final material properties of parts made via LPBF are extremely sensitive to\\
the powder properties ${ }^{[3]}$ (e.g., powder shape, flow characteristics, porosity, laser absorptivity ${ }^{[4],[5]}$, etc.) and laser parameters (e.g., beam size, power, scan rate, etc. $)^{[6,7]}$. As such, it is a significant challenge to identify the optimal operating parameters to rapidly and reliably produce parts with the desired properties without defects ${ }^{[8]}$. Furthermore, many types of LPBF defects arise due to inherent variability in the powder properties ${ }^{[9]}$, bed thickness non-uniformity ${ }^{[10]}$, and laser parameters and scan paths that result in improper power melting $^{[11]}$. Thus, even after optimizing LPBF operating parameters and identifying suitable processing windows ${ }^{[12]}$, rapid build qualification, improved quality, and higher production yields require methods of monitoring the melt pool and/or powder bed in situ, i.e. during a build, that enable real-time process feedback and automated quality detection ${ }^{[13,14]}$.

The majority of LPBF process monitoring approaches rely on non-contact sensing ${ }^{[15]}$ from optical, thermal ${ }^{[16]}$ and/or acoustic ${ }^{[17,18]}$ sensors. These sensors provide assessments of spatial and spectral features of the melt pool ${ }^{[19,20]}$, process plume ${ }^{[21]}$, degree of spatter ${ }^{[22-25]}$, overhang layers ${ }^{[26]}$, or print bed. High-speed image sequences of the melting process ${ }^{[27]}$, scans of the powder bed ${ }^{[28],[10]}$, beam quality ${ }^{[29]}$, and/or thermal monitoring ${ }^{[30]}$ are all routinely collected forms of in situ monitoring data. Making use of this data requires methods that can extract relevant diagnostic information. For instance, before initiating laser melting, automated computer vision algorithms can characterize metal powder feedstocks ${ }^{[31]}$, and image analysis of newly spread powder can reveal non-uniformities in the powder bed thickness ${ }^{[32]}$. Aminzadeh et. al. demonstrated layer-by-layer detection of fusion defects from images using a Bayesian classifier ${ }^{[33]}$. Real-time events such as material ejecta are detectable by applying manually-set thresholds to high speed near-infrared images of the melt pool. Also, increasing the $\mu \mathrm{m} / \mathrm{pixel}$ image resolution relative to the standard deviation of measured track width, $\sigma_{\text {measured, }}$, may result in improved predictions of the final track width, $\delta_{\text {predicted, }}$, and topography ${ }^{[34]}$. Reducing laser power proportionally to an integrated signal from a photodiode calibrated against a CMOS camera results in smoother overhang structures ${ }^{[35]}$. Using images

\section*{WILEY-VCH}
of the print bed taken after laser melting, a level sets method can detect intentionally created defects, ${ }^{[36]}$ machine vision algorithms can identify pore defects, ${ }^{[37]}$ and multifractal image analysis can characterize layers with balling, cracks and pores, and no defects ${ }^{[38]}$. Visual imaging equipment is appealing to LPBF monitoring systems because it is relatively inexpensive and provides non-contact sensing ${ }^{[13]}$.

As with most additive manufacturing systems, analysis of LPBF sensor data currently occurs post-build, rendering process monitoring and rectification impossible. Machine learning offers a route to convert sensor data into real-time assessments; however, this requires a wealth of labeled sensor data that traditionally is too time-consuming and/or expensive to assemble. In this manuscript, this critical issue of generating labeled video data for machine learning is solved. An original multi-stage convolutional network is trained that processes in situ high speed video data to predict properties of track welds measured ex situ following an LPBF print. The in situ machine learning models rely on labeled time segments of high-speed video data generated from a separate height map analysis algorithm. The height map analysis algorithm presented here processes height map data of isolated track welds and extracts ground truth labels of the average and standard deviation of the width along each track and whether or not each track is continuous. A newly-developed single, general convolutional architecture is trained to predict ex situ measurements from as little as 10 video frames with a correlation coefficient of $R^{2}=0.93$ for track width, $R^{2}=0.70$ for standard deviation of track width, and prediction accuracy of $93.1 \%$ for track continutiy. The algorithm successfully generalizes across multiple tracks created with several combinations of the laser power and speed. In terms of broader impact, since this approach to generate labeled training sets for in situ machine learning-based detection algorithms does not rely on specific LPBF characteristics, is should be extensible to other additive manufacturing technologies ${ }^{[40]}$.

\section*{2. Methods}
In what follows, bead-on-plate LPBF experiments are performed wherein 870 isolated $5 \mathrm{~mm}$ track welds are created under a variety of randomly chosen laser speed and power settings while simultaneously recording video. After unwelded powder is removed, height maps of bare laser tracks are generated and analyzed with a novel height map analysis algorithm to determine the per-pixel average track width, $\delta_{\text {measured, }}$, standard deviation of the track width, $\sigma_{\text {measured, and give each track a Boolean "continuity label" that identifies whether }}$ or not a track is continuous. Each video is assigned three labels and assembled into training sets for our machine learning algorithm. A single supervised machine learning acrhitecture is used to predict these three ex situ measurements from in situ video data, as described below.

An Aconity LAB system from Aconity3D is used for welding single tracks of 316L stainless steel. The system uses a carbon fiber brush to spread metal powder evenly into a $\sim 50$ $\mu \mathrm{m}$ layer atop a $180 \mathrm{~mm}$ 316L stainless steel plate in an argon-purged environment. Galvanometer mirrors scan the high-power laser across evenly spaced track sites on the powder bed at 11 possible scan speeds and 11 possible laser powers in evenly-spaced increments between $100-400 \mathrm{~mm} / \mathrm{s}$ and $50-375 \mathrm{~W}$, respectively, with each set of laser conditions repeated up to seven times. In situ video data is recorded at frame rate of $1 \mathrm{kHz}$ and frame size of $256 \times 256$ pixels using a 10-bit Mikrotron EOsens MC1362 incorporated into the optical system diagrammed in Figure 1. The illumination laser and Mikrotron video camera are co-aligned with the high-power laser. These components share a common moving focal point, fixed at the melt pool while the laser scans each track site. In each video, the melt pool and spatter are visible for each frame. The total frames per video range from $12-50$ frames, depending on the laser scan speed. The camera pixel size is $14 \mu \mathrm{m} / \mathrm{pixel}$.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_123d7fb5db614938938fg-07}
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Figure 1. Schematic of video capture system. Adjustable mirrors trace the path of a focal point shared between the co-aligned high-speed camera, illumination laser, and high-power laser. The camera records in situ video taken during each welding event.

Upon completing the bead-on-plate experiment, unwelded powder is removed from the plate and a Keyence VR3000 3D macroscope is used to generate a height map of all laser tracks. Figure 2a shows the grayscale electro-optical image of an array of isolated track welds. Structured light scans from the Keyence VR3000 instrument measure the height at each pixel in order to produce a surface map as shown in Figure 2b. Our pixel-level classification algorithm distinguishes track from background as shown in Figure 2c. After applying our classification algorithm, any number of quality metrics can be calculated from a surface map, e.g. $\delta_{\text {measured, }} \sigma_{\text {measured, }}$ whether or not the track is continuous, surface roughness, etc., by de-noising the height data, distinguishing track from background, and analyzing the height values corresponding to the track. This paper focuses solely on the prediction of the mean and standard deviation of track widths and classification of track continuity with our proposed algorithm.

From the height maps, pixels are classified as one of three types: track weld, background, or etch (in which the height map gives values below the background). Since track locations are specified with pre-set spacing in both the horizontal and vertical directions, it is straightforward to analyze individual tracks in rectangular patches that encompass the

\section*{WILEY-VCH}
track and surrounding background. In each patch, background pixels are removed so that only weld and etch pixels remain via the following protocol:

\begin{enumerate}
  \item Calculate the mean pixel height in each patch, $h_{1}$.

  \item Identify pixels whose heights are within $h_{1}+l$, where $t$ is a small constant with default value $0.01 \mathrm{~mm}$. Pixels within this range are likely to belong to the track weld.

  \item Calculate the mean height for pixels outside of this range, $h_{2}$. Pixels whose heights are within $h_{2} \pm \iota$ belong to the background. The remaining pixels are given a preliminary classification of non-background.

\end{enumerate}

After executing the steps above, a binary \{background, non-background \} map is obtained that may contain mistakenly classified pixels due to the specified value of $\iota$ and inherent noise.

Such "noise" pixels appear as small isolated regions on the height map that do not manifest in the electro-optical images. To filter these noise pixels, suspected noise pixels per column of pixels are counted in a given patch and reclassified as background if that count, $n$, is below some threshold. Here $n=10$, which is $\sim 6 \%$ of the overall track length. Etch pixels correspond to negative height values that result from the laser etching into the plate. After de-noising, a post-processed height map identifies track, etch, and background, as shown in Figure 2c. From the post-processed height map, $\delta_{\text {measured }}$ and $\sigma_{\text {measured }}$ are computed for every track and these are used to assign ground truth labels for the corresponding in situ videos, thereby assembling a training set for two regression models. Each track is also assessed for continuity, i.e. a track is discontinuous if at least one gap of non-track pixels exists along its length, otherwise a track is continous. The continuity labels serve as a training set for a binary classification model. The entire plate is scanned in less than 4 hours the ex situ height map analysis runs in $<10$ seconds. Since a large training set of in situ LPBF data is amassed quickly, it is feasible to develop machine learning algorithms capable of assessing the in situ data.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_123d7fb5db614938938fg-09}
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Figure 2. Ex situ analysis of laser track height maps. (a) Electro-optical image of tracks weld on bare plate and corresponding height map (b). (c) results from applying the ex situ height map analysis algorithm that classifies each pixel as track, etch, or background, colored green, red, and white, respectively. From (c), per-pixel track width average, $\delta_{\text {measured, and }}$ standard deviation, $\sigma_{\text {measured, }}$, and continuity are determined.

The LPBF video dataset contains 870 individual videos, labeled according the ex situ height map analysis algorithm that provides each video a label of $\delta_{\text {measured }}$ and $\sigma_{\text {measured }}$ for regression, and track continuity for classification. To do this, 700 randomly selected videos are used to train candidate machine learning models and the remaining videos are used to test the fully-trained models. The standard mean squared error loss function is used for the regression predictions, while cross entropy loss is used for classification. The model architecture is developed using only the $\delta_{\text {measured }}$ labels, but is trained separately on all three labels, and the learning rate hyperparameter retuned. As described below, our convolutional neural network architecture requires videos to be a fixed frame length and resolution. For the fastest scan speed, there are only 12 frames of video and the first and last frames are omitted to ensure end-of-track artifacts did not affect the results. Thus, only the 10 middle frames are chosen from each video, i.e. middle $10 \mathrm{~ms}$ of video. Furthermore, the frames for each track are center-cropped into $64 \times 64$ pixel size images, eliminating a portion of the background from the videos so that the neural network trains on the most relevant region of the video that encompasses the laser spot. A convolutional neural network (CNN) ${ }^{[41],[42]}$ is used to address this regression or classification problem. The CNN model is configured and trained with the

\section*{WILEY-VCH}
TensorFlow ${ }^{[43]}$ library on an NVIDIA TITAN X GPU. A full description of the CNN model architecture and training hyperparameters is given in the Supporting Information; here, the most important features of our model are discussed.

To set the number of layers (the depth of the model), an initial architecture was configured with six convolutional layers, which contains sufficient capacity to learn $\delta_{\text {measured }}$ from the video data. Then the number of layers was reduced sequentially until the model did not exhibit overfitting. (Overfitted models provide excellent predictions for a training set, but do not generalize well to new datasets.) Based on several candidate model training sessions, three convolutional layers could generalize sufficiently to the test data, as discussed below. Although it is more common to use max-pooling to reduce dimensionality between convolutional layers, mean-pooling was found to outperforms max-pooling for learning to predict the track width. For this application, mean-pooling may help the CNN learn about the differences in melt pool size to generate predictions for the track width average, $\delta_{\text {predicted. If }}$ this is the case, the overall summation of the video pixel values would seem to be more relevant than the summation of max pixel values. Though the model architecture was not optimized based on track continuity or standard deviation of width measurements, reasonable results were obtained when retraining the same $\mathrm{CNN}$ model (developed with $\delta_{\text {measured) }}$ ) using $\sigma_{\text {measured }}$ and continuity labels as discussed below.

\section*{3. Results and Discussion}
After creating and scanning all tracks, the ex situ height map analysis algorithm is used to measure the tracks. Approximately $80 \%$ of all tracks are continous. Figure 3 shows measured track widths for all laser speed and power combinations studied, plotted as the average value of $\delta_{\text {measured }}$ with error bars corresponding to the standard deviation of repeat width measurements. Tracks are widest at high laser powers and slow scan speeds. The trends in Figure 3 agree with previous findings from experiments ${ }^{[44-47]}$ and simulation ${ }^{[48,49]}$\\
that show the melt pool width increases with increasing laser power-to-speed ratio, i.e. increasing volumetric energy density. Error bar values show no clear trend as a function of laser parameters throughout the dataset collected. Thus, an in situ detection technique based solely on empirical fits of these data mav not rolidoly captumonatural variances within the

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_123d7fb5db614938938fg-11(1)}
\end{center}

Figure 3. Measured track widths for every laser power and speed combination. The dataset exhibits an expected trend: lasers with slower speed (legend) and/or at higher power settings impart more energy into the powder bed to create wider tracks. Error bars represent the standard deviation of $\delta_{\text {measured }}$ from repeat measurements.

Track measurements are used as ground truth labels for each video taken during the welding process. Figure 4 shows the exact 10 middle center-cropped frames from the in situ videos and corresponding labels that are used to train the machine learning model for four different example laser conditions in our dataset. The bright area in the center of all video frames corresponds to incandescent light emitted from the melt pool. The video capture system alignment (Figure 1) ensures that the center of the melt pool appears in the same location of every frame. Figure 4 displays video segments in order of increasing $\delta_{\text {measured }}$ and

\includegraphics[max width=\textwidth, center]{2024_03_10_123d7fb5db614938938fg-11}\\
$310 \mathrm{~mm} / \mathrm{s}(\mathrm{a}, \mathrm{c})$ and $160 \mathrm{~mm} / \mathrm{s}(\mathrm{b}, \mathrm{d})$. Melt pool size and shape differences between videos at each distinct laser power setting are evident. At larger powers, the melt pool increases in size\\
and aspect ratio, as expected. Intuitively, the relative size of the melt pool appears to correlate with larger values of $\delta_{\text {measured. }}$. Frame-by-frame variations in the quantity of bright pixels also appear to correlate with increasing $\sigma_{\text {measured. }}$. For instance, there are more saturated pixels in the melt pools at high power in Figure 4(c,d) than at low power Figure 4(a,b). The track width may also correlate with the degree of spatter, which is more pronounced for smaller $\delta_{\text {measured. }}$.

It is hard to distinguish from visual inspection alone whether the melt pool is a better indicator of $\sigma_{\text {measured }}$ than the spatter. In addition to these features, temporal characteristics gathered from chronological series of frames may yield accurate predictors of resulting track properties. Moreover, there may be additional salient features besides characteristics of the melt pool spatter that correlate strongly with $\delta_{\text {measured }}$ and/or $\sigma_{\text {measured. It is unclear from }}$ inspection how one would identify track continuity from these video frames.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_123d7fb5db614938938fg-12}
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Figure 4. Machine learning training data examples: in situ Laser Powder Bed Fusion video sequences with labels of measured average track width and per pixel width standard deviation. The training process utilizes only 10 center-cropped frames from the midpoint of an LPBF video along with the measured track widths. The machine learning algorithm does not learn from the laser parameters of each video, which are $147.5 \mathrm{~W}$ at 310 $\mathrm{mm} / \mathrm{s} \mathrm{(a)}$ and $160 \mathrm{~mm} / \mathrm{s} \mathrm{(b)} \mathrm{and} 342.5 \mathrm{~W}$ at $310 \mathrm{~mm} / \mathrm{s}$ (c) and $160 \mathrm{~mm} / \mathrm{s}$ (d). (a) is a discontinuous track and (b-d) are continuous tracks. The entire videos are provided in the Supporting Information.

Since the relevant, visualized distinguishing features in the in situ video are not readily obvious, it is not straightforward to decipher the mapping between the video and track properties using only traditional video processing techniques. Rather than manually identifying relevant indicators within the entire in situ data set, machine learning is used to\\
train our neural network model to learn a suitable mapping between video segments and measured average track width and standard deviation and continuity. Once trained, the video regression CNN model generates predictions of the average track width, $\delta_{\text {predicted, }}$ standard deviation, $\sigma_{\text {predicted, and }}$, anack continuity. The accuracy of track continuity classification is $93.1 \%$. Regression model performance is assessed by comparing measured versus predicted values for both training and test sets in Figure 5. A narrow distribution of points around the line of equality (black line) indicates favorably robust model performance, while $\delta_{\text {predicted }}=\delta_{\text {measured }}$ or $\sigma_{\text {predicted }}=\sigma_{\text {measured }}$ for all predictions signifies problematic overfitting. The CNN exhibits variance, i.e. training set predictions outperform the test set, as indicated by the tighter distributions of predicted values along the equality line. Furthermore, the CNN model predictions of $\delta_{\text {predicted }}$ outperform those of $\sigma_{\text {predicted }}$ according to the respective coefficients of determination by $R_{\delta}{ }^{2}=0.93$ and $R_{\sigma}{ }^{2}=0.70$.

The discrepancy in model performance of predicting average track width versus standard deviation may be due only in part to the fact that the model architecture is developed using width data alone. Given the numerous available choices of model architectures and combinations of hyperparameters, different model configurations than chosen here may result in more accurate $\sigma_{\text {predicted. }}$. However, it seems likely that the standard deviation of width is inherently more difficult to predict than the width given the size and/or quality of our dataset. Outliers in Figure $5 \mathrm{~b}$ correspond to the slowest laser scan speeds, 130 and $100 \mathrm{~mm} / \mathrm{s}$. Thus, the 10 middle frames (of the 38-50 total frames per video collected at these conditions) the model uses do not contain information of the properties along the entire length of the track. This is a consequence of the CNN architecture, which requires a fixed frame number irrespective of laser operating parameters. Recurrent neural networks that generate predictions from input videos of variable length may help to alleviate this issue. Regardless, for any machine learning model that exhibits high variance, a larger dataset ensures higher quality\\
predictions ${ }^{[50,51]}$. Indeed, worse results (not shown) were obtained than in Figure 5 when the model was trained on a small subset of our data. Thus, by following the experimental procedure described here, additional videos can be collected, labeled via the rapid ex situ algorithm, and used to retrain the $\mathrm{CNN}$ to obtain more accurate $\delta_{\text {predicted }}, \sigma_{\text {predicted }}$, and continuity predictions. Nevertheless, using only $10 \mathrm{~ms}$ videos, the CNN predicts track LPBF widths and continuity and (to a lesser degree) width standard deviation without the need for time-consuming height map derived ex situ measurements.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_123d7fb5db614938938fg-14}

Figure 5. Predicted track widths (a) and standard deviation of track width (b) from 10frame LPBF video sequences versus ex situ measured value from height maps.

Predictions from the training and test sets (legend) that are close to the black line signify high accuracy. The fully-trained convolutional neural network predicts values from LPBF video

\section*{WILEY-VCH}
with coefficients of determination $R_{\delta}{ }^{2}=0.93$ and $R_{\sigma}{ }^{2}=0.70$ for average track width and standard deviation of the track width, respectively.

Going beyond this work, the training set can be expanded and/or the machine learning model can be modified to enable improved $\delta_{\text {predicted }}$ and $\sigma_{\text {predicted }}$ or possibly other height map derivable quality metrics, such as surface finish. In addition to detecting whether a track is defective, it is valuable to indicate where the defect occurs, which may be useful for potential rectification strategies. Moreover, it is worth pursuing whether other ex situ measurements (e.g., mechanical properties, microstructure, residual stress, part density, etc.) of LPBF printed objects are detectable from in situ data. An important requirement for in situ detection should involve predicting track properties in cases of multi-scan prints, e.g. parallel adjacent tracks, non-parallel tracks involved in complex strategies, etc. Semi-supervised or unsupervised machine learning may be necessary for cases where it is not desirable or possible to label all (or any) in situ data. Transfer learning techniques may help when ex situ measurements are difficult to obtain, e.g. x-ray computed tomography, and/or where complementary physicsbased simulations are available for only a subspace of the overall operating regime. While a deeper investigation into the model may reveal something about the features it uses to make predictions, it is unlikely to uncover important characteristics of the underlying physics of the LPBF process given the black box nature of CNNs at present. While our current model requires $10 \mathrm{~ms}$ video clips, faster detection rates may be possible without compromising prediction accuracy. Machine learning-based models generated with this approach can enable in situ quality detection and real-time process monitoring essential to rapid closed-loop control.

\section*{4. Conclusions}
A CNN model is developed, trained, and evaluated and shown to be capable of predicting LPBF track widths, width standard deviations, and track continuity from in situ video data alone. Here, video of LPBF tracks is collected using a variety of laser power and\\
scan speed settings; however, it is straightforward to incorporate additional forms of in situ data, e.g, pyrometer readings, acoustic sensing, etc., that may boost prediction quality.

Irrespective of the exact LPBF system configuration and/or chosen operating parameters, in situ data can be labeled using our ex situ height map analysis algorithm. After labeling in situ datasets with ex situ measurements, the model is then trained via supervised machine learning that can predict the final properties of LPBF track welds on-the-fly. With this approach, it should be possible to label in situ data via ex situ measurements for additive manufacturing technologies, e.g. extrusion-based and stereolithographic approaches, other than LPBF.

\section*{Supporting Information}
Supporting Information is available from the Wiley Online Library or from the author.

\section*{Acknowledgements}
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, LLNL-JRNL-748383. This work was also supported by a Berkeley Graduate Fellowship.

Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff)) Published online: ((will be filled in by the editorial staff))

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\section*{WILEY-VCH}
A procedure to label Laser Powder Bed Fusion video data and leverage it to train a convolutional neural network is demonstrated. Testing the neural network reveals it can predict track continuity and the average and standard deviations of track width from high speed video alone, reducing the need for post-build quality assessment.

\section*{Keywords}
laser powder bed fusion, machine learning, additive manufacturing, selective laser melting

B. Yuan, G. M. Guss, A. C. Wilson, S. P. Hau-Riege, P. J. DePond, S. McMains, M. J. Matthews, B. Giera*

Machine Learning Based Monitoring of Laser Powder Bed Fusion

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Copyright WILEY-VCH Verlag GmbH \& Co. KGaA, 69469 Weinheim, Germany, 2016.


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\title{Additive manufacturing of dense WE43 Mg alloy by laser powder bed fusion }


\author{Holden Hyer ${ }^{\mathrm{a}}$, Le Zhou ${ }^{\mathrm{a}, \mathrm{b}, *}$, George Benson ${ }^{\mathrm{a}}$, Brandon McWilliams ${ }^{\mathrm{c}}$, Kyu Cho ${ }^{\mathrm{c}}$, Yongho Sohn ${ }^{\mathrm{a}, \mathrm{b}, *}$\\
a Department of Materials Science and Engineering, University of Central Florida, Orlando, FL, 32816, USA\\
${ }^{\mathrm{b}}$ Advanced Materials Processing and Analysis Center, University of Central Florida, Orlando, FL, 32816, USA\\
${ }^{\mathrm{c}}$ Weapons and Materials Research Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA}
\date{}


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Full Length Article



\section*{A R T I C L E I N F O}
\section*{Keywords:}
WE43

Mg alloy

Laser powder bed fusion

Additive manufacturing

\begin{abstract}
A B S T R A C T WE43 is a high-strength, corrosion-resistant Mg-alloy containing rare earths such as Y and Nb, and has potential for many lightweight structural or bioresorbable prosthetic applications. In this study, additive manufacturing of dense WE43 alloy by laser powder bed fusion (LPBF) from gas atomized powders has been accomplished through studies involving single track scan of wrought WE43, parametric variation of LPBF, microstructural analysis and mechanical testing, both in compression and tension. The Archimedes method and image analyses from optical micrographs were employed to document the LPBF of dense ( $>99 \%$ relative density) WE43 using optimum parameters of $200 \mathrm{~W}$ laser power, $1100 \mathrm{~mm} / \mathrm{sec}$ scan speed, $0.13 \mathrm{~mm}$ hatch spacing, and $0.03 \mathrm{~mm}$ slice thickness. Moreover, the LPBF processing window for dense ( $>99 \%$ ) WE43 alloy was observed to exist for a range of power, $100 \sim 250 \mathrm{~W}$, using an energy density range of $32-37 \mathrm{~J} / \mathrm{mm}^{3}$. The as-built microstructure consisted of fine $(<10 \mu \mathrm{m}) \alpha-\mathrm{Mg}$ (hcp) grains with globular $\beta_{1}-\mathrm{Mg}_{3} \mathrm{Nd}$ precipitates and $(\mathrm{Y}, \mathrm{Zr})_{2} \mathrm{O}_{3}$ oxides. After the heat treatment, which consisted of solutionizing at $536{ }^{\circ} \mathrm{C}$ for $24 \mathrm{~h}$ and subsequent ageing at $205^{\circ} \mathrm{C}$ for $48 \mathrm{~h}$, the globular $\beta_{1}-\mathrm{Mg}_{3} \mathrm{Nd}$ precipitates were observed to have dissolved and re-precipitate into thin sheets. The $(\mathrm{Y}, \mathrm{Zr})_{2} \mathrm{O}_{3}$ oxides were not found to dissolve or coalesce, but were agglomerated within $\alpha$ - $\mathrm{Mg}$ (hcp) matrix. Under compression, the as-built LPBF WE43 had, on average, yield strength of $224 \mathrm{MPa}$, compressive strength of $417 \mathrm{MPa}$ and strain at failure of $9.5 \%$. In tension, the as-built LPBF WE43 had, on average, yield strength of $215 \mathrm{MPa}$, tensile strength of $251 \mathrm{MPa}$ and strain at failure of $2.6 \%$. After the heat treatment, the LPBF WE43 had yield strength of $219 \mathrm{MPa}$, tensile strength of $251 \mathrm{MPa}$ and strain at failure of $4.3 \%$. These values are comparable to those of WE43 design data specified by Magnesium Elektron.
\end{abstract}

\section*{1. Introduction}
Mg-alloys warrants interests in automotive, aerospace and biomedical applications because of its attractive properties such as strengthto-weight ratio, corrosion resistance, creep resistance, and bioresorbability (i.e., controlled corrosion and biocompatibility). Mg alloyed with rare earths such as $\mathrm{Y}, \mathrm{Nd}, \mathrm{Sc}, \mathrm{Yb}$ are known as the high strength ( $>160 \mathrm{MPa}$ tensile strength), high creep resistant alloys [1,2]. WE43 is a high strength ( $\sigma_{\mathrm{y}}=172 \mathrm{MPa}$ [3]) Mg-alloy with good creep resistance $[1,2]$ containing up to $4.3 \mathrm{wt} . \%$ yttrium ( $\mathrm{Y}$ ) and other rare earth elements such as Nd and Gd, up to $4.8 \mathrm{wt} . \%$ [3]. WE43 has been used in structural components for helicopters and automobiles as frames, gear boxes, casings, etc. [2,4,5]. Recently, it has been also considered for lightweight armors and protective helmets [4]. With increasing interests, WE43 has been also considered for bioresorbable prosthetic implants [6,7], because the high oxygen affinity of the rare earths can be utilized to control the corrosion behavior of the $\mathrm{Mg}$-alloy, i.e., dissolution rate, passivation mechanism, etc. [6,7].

Casting Mg-alloys demands technical attention due to $\mathrm{Mg}$ reactivity with $\mathrm{O}_{2}$, high flammability, and high vaporization pressure [8,9]. In addition, thermo-mechanical processing of $\mathrm{Mg}$-alloy remains challenging due to anisotropic hexagonal-closed-packed (hcp) crystal structure of $\mathrm{Mg}[10,11]$. Therefore, working of Mg-alloys is typically done at elevated temperatures and under an inert atmosphere, which increases the resources and time required for manufacturing of $\mathrm{Mg}$-alloys. To that end, additive manufacturing (AM), which can produce dense, complex shapes, could be an efficient route to manufacture Mg-alloy component.

Powder bed fusion (PBF) is an AM technology in which selected regions of a powder bed are melted, by either a laser or an electron beam, to build a component layer by layer [12-16]. Laser powder bed fusion (LPBF) has become popular in recent years as complex parts can be generated by computer aided design (CAD) and can be rapidly manufactured (e.g., $\sim 25 \mathrm{~cm}^{3}$ per hour for single laser unit) [17]. Moreover, alloys with high vapor pressures such as $\mathrm{Al}$ and $\mathrm{Mg}$ can be
\footnotetext{*Corresponding authors at: Department of Materials Science and Engineering, University of Central Florida, Orlando, FL, 32816, USA.

E-mail addresses: \href{mailto:le.zhou@ucf.edu}{le.zhou@ucf.edu} (L. Zhou), \href{mailto:yongho.sohn@ucf.edu}{yongho.sohn@ucf.edu} (Y. Sohn).
}
built with LPBF as the melting is local and performed in an inert atmosphere (i.e., does not require vacuum). However, many commercial alloys such as high strength $\mathrm{Al}$ alloy, e.g., AA7075, and high strength Ni based superalloy, e.g., CM247, cannot be built without large pores and/ or solidification cracks $[16,18,19]$. Therefore, there is a need to explore the processing behavior of existing commercial alloys, and to identify those that are suitable for LPBF.

Typically, in LPBF, there are four main, independent processing parameters: laser power $(\mathrm{W})$, the laser scan speed $(\mathrm{mm} / \mathrm{sec})$, the hatch spacing (distance between consecutive laser scans, $\mathrm{mm}$ ), and the powder bed layer thickness, commonly referred to as slice thickness (mm). These four parameters can be normalized with a term known as energy density $[12,15,16]$ :


\begin{equation*}
\text { EnergyDensity }=\frac{\text { LaserPower }}{\text { ScanSpeed } * \text { HatchSpacing } * \text { SliceThickness }} \tag{1}
\end{equation*}


Processing maps through optimization strategy for various metallic alloys can be determined by varying the four aforementioned parameters, frequently as a function of normalized value of energy density, until the right combination is identified where pores and/or solidification cracks are minimized, i.e., full density with structural integrity.

$\mathrm{AM}$ investigation on $\mathrm{Mg}$ and its alloys is scarce compared to that of Al- or Fe-alloys, but there exist various studies on a few different Mgalloys processed by different AM technologies [20-34]. Table 1 lists key parameters and results from LPBF studies of Mg-alloys. $\mathrm{Ng}$ et al. $[20,24,25]$ studied the interaction between pure Mg powder and single track laser scan, however, without printing any 3-D samples and/or components. Zhang et al. [32] examined LPBF build of a Mg - $9 \mathrm{wt} \% \mathrm{Al}$ (similar to $\mathrm{Mg}$ alloy, AZ91 which is composed of ( $\mathrm{Mg}-9 \mathrm{wt} . \% \mathrm{Al}-1 \mathrm{wt}$. $\% \mathrm{Zn})$ ) as functions of LPBF parameters, and reported build up to $82 \%$ relative density.

Wei et al. [29] also examined LPBF processing window for AZ91 and AZ31 ( $\mathrm{Mg}-3$ wt.\% Al - 1 wt.\% Zn), as well as for ZK60 (Mg - 5.2 wt.\% $\mathrm{Zn}-0.5 \mathrm{wt} \% \mathrm{Zr}$ ) [30] with detailed analyses of evaporation and microstructure. For AZ91 (Mg-9 wt\%Al-1 wt\%Zn) and AZ31 (Mg-3 wt\%Al$1 \mathrm{wt} \% \mathrm{Zn})$ alloys, energy density higher than $214 \mathrm{~J} / \mathrm{mm}^{3}$ yielded too much evaporation and excessive porosity, whereas that below $77 \mathrm{~J} /$ $\mathrm{mm}^{3}$ lead to excessive balling of the melt. The best parameters were found at an energy density of $166.7 \mathrm{~J} / \mathrm{mm}^{3}$, which had a corresponding laser power, scan speed, hatch spacing, and slice thickness of $200 \mathrm{~W}$, $333.33 \mathrm{~mm} / \mathrm{sec}, 0.09 \mathrm{~mm}$, and $0.04 \mathrm{~mm}$, respectively. For ZK60 alloy, the best processing parameters were identified at an energy density of $416.66 \mathrm{~J} / \mathrm{mm}^{3}$, which had a corresponding laser power, scan speed, hatching spacing, and slice thickness of $200 \mathrm{~W}, 300 \mathrm{~mm} / \mathrm{sec}, 0.08 \mathrm{~mm}$, and $0.02 \mathrm{~mm}$, respectively. Wei et al. [29] reported microhardness of these alloys comparable to traditionally manufactured Mg-alloys.

Recently, Jauer et al. [22] examined the feasibility of AZ91 and WE43 and reported that a set of optimum parameters (200 W laser power, $700 \mathrm{~mm} / \mathrm{sec}$ scan speed, $0.04 \mathrm{~mm}$ hatch spacing, and $0.03 \mathrm{~mm}$ slice thickness, corresponding to an energy density of $40.7 \mathrm{~J} / \mathrm{mm}^{3}$ ) produced a $99 \%$ dense part with a tensile strength of $\sim 300 \mathrm{MPa}$. The microstructure was investigated recently, which showed that there were possible $\mathrm{Mg}_{3} \mathrm{Gd}$ phases that could not be fully identified [34]. Given that the $\mathrm{Mg}_{3} \mathrm{Gd}$ phase is typically observed in conventionally produced WE43 alloy, the mechanism responsible for the extraordinary tensile strength of $300 \mathrm{MPa}$ still remains unclear. Gangireddy et al. [21] also released a recent study on LPBF of WE43 that reported optimum parameters of laser power, scan speed, hatch spacing, and slice thickness of $195 \mathrm{~W}, 800 \mathrm{~mm} / \mathrm{sec}, 0.2 \mathrm{~mm}$, and $0.03 \mathrm{~mm}$, respectively, corresponding to an energy density of $238.1 \mathrm{~J} / \mathrm{mm}^{3}$. These parameters, however, did not correspond to LPBF of fully dense WE43 alloy in their study. They reported the formation of Nd rich precipitates in the microstructure, but could not fully identify the phases formed. In addition, neither Jauer et al. [22] nor Gangireddy et al. [21] reported a systematic approach or results to understand the occurrence of pores and/ or solidification cracking as functions of LPBF. Moreover, neither study gave a detailed microstructural assessment as functions of LPBF for WE43, nor gave repeatable tensile and compressive properties of LPBF WE43.

Therefore, a systematic study for LPBF of WE43 was carried out, first by exploring the laser-WE43 interaction through single track scan study, and then by examining the development of solidification microstructure of LPBF WE43 samples as functions of LPBF parameters. Using the optimum parameters identified, mechanical behavior of LPBF WE43, before and after the heat treatment, was assessed to determine its strength and ductility, both in compression and tension. Finally, comprehensive microstructural analyses, including a detailed constituent phase analysis by transmission electron microscopy, were carried out to gain insights into LPBF solidification and mechanical behavior of LPBF WE43. Findings from this study would help establish AM capability for the existing WE43 alloy composition, and for newly designed Mg-alloys specific for AM technology such as LPBF.

\section*{2. Experimental details}
\subsection*{2.1. Single track scan}
To assess the processability of WE43 by LPBF, a feasibility study was performed with single track scan (STS) on wrought WE43 samples. A chill cast and cold rolled WE43 alloy was used for this study. Samples $25 \mathrm{~mm} \times 12 \mathrm{~mm} \times 12 \mathrm{~mm}$ in geometry were prepared by grinding with $\mathrm{SiC}$, polishing with diamond paste, and finishing with $0.05 \mu \mathrm{m}$ colloidal silica. Samples were then leveled with the build chamber floor so that the polished surface lay in the focus range of the laser. The sample was then laser scanned using a SLM $125 \mathrm{HL}$ LPBF system equipped with a continuous $\mathrm{Yb}$ fiber laser with a spot size of approximately $70 \mu \mathrm{m}$ and a

Table 1

Processing parameters of LPBF examined for Mg alloys in literature.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Alloy & Laser Power (W) & Scan Speed $(\mathrm{mm} / \mathrm{sec})$ & Hatch Spacing (mm) & Slice Thickness (mm) & Energy Density $\left(\mathrm{J} / \mathrm{mm}^{3}\right)$ & Reference \\
\hline
Pure Mg & None reported &  &  &  &  & $\mathrm{Ng}$ et al. [20,24,25] \\
\hline
Mg-9 wt.\% Al & $10-20$ & $10-40$ & 0.05 & 0.08 & $93.75-250$ & Zhang et al. [32] \\
\hline
AZ31, AZ91 & 200 & 333.3 & 0.09 & 0.04 & 167 & Wei et al. [29] \\
\hline
ZK60 & 200 & 300 & 0.08 & 0.02 & 416 & Wei et al. [30] \\
\hline
Mg-0, 1, 3, 5, 7 wt.\% Sn & 60 & 11.16 & Not reported & 0.05 & Not reported & Zhou et al. [33] \\
\hline
AZ91 & 90 & 700 & 0.03 & 0.035 & 122 & Schmid et al. [26] \\
\hline
AZ91 and WE43 & 100,200 & 800,700 & 0.03 & 0.04 & 104.16, 238.1 & Jauer et al. [22] \\
\hline
Mg-4Y-3Zr & $20-100$ & $200-10000$ & $0.015-0.12$ & 0.05 &  & Tandon et al. [28] \\
\hline
Mg-0, 1, 2, 3 wt.\% Mn & None reported &  &  &  &  & Yang et al. [31] \\
\hline
ZK60 & 50 & 600 & 0.1 & 0.1 & 8.33 & Shaui et al. [27] \\
\hline
Mg-3 wt.\% Zn-0, 1, 3, 5 wt.\% Dy & 60 & 3.33 & Not reported & 0.05 & Not reported & Long et al. [23] \\
\hline
WE43 & 195 & 800 & 0.2 & 0.03 & 40.7 & Gangireddy et al. [21] \\
\hline
WE43 & 200 & 700 & 0.04 & 0.03 & 238.1 & Zumdick et al. [34] \\
\hline
WE43 & 200 & 1100 & 0.13 & 0.04 & 35 & This Study \\
\hline
\end{tabular}
\end{center}

Table 2

Processing parameters examined and melt pool width and depth determined from single track scan investigation of WE43 using laser powder bed fusion.

\begin{center}
\begin{tabular}{llllll}
\hline
\begin{tabular}{l}
Speed \\
$(\mathrm{mm} / \mathrm{sec})$ \\
\end{tabular} & Power $(\mathrm{W})$ & Depth $(\mu \mathrm{m})$ & Width $(\mu \mathrm{m})$ & \begin{tabular}{l}
Depth-to- \\
width \\
Ratio \\
\end{tabular} & \begin{tabular}{l}
Linear Energy \\
Density $(\mathrm{J} /$ \\
$\mathrm{mm})$ \\
\end{tabular} \\
\hline
50 & 50 & 38.1 & 87.6 & 0.44 & 1.000 \\
50 & 75 & 346.3 & 206.7 & 1.68 & 1.500 \\
50 & 100 & 620.9 & 354.1 & 1.75 & 2.000 \\
50 & 125 & 919.9 & 387.8 & 2.37 & 2.500 \\
200 & 50 & 30.7 & 91.5 & 0.34 & 0.250 \\
200 & 75 & 227.4 & 232.1 & 0.98 & 0.375 \\
200 & 100 & 409.6 & 246.7 & 1.66 & 0.500 \\
200 & 125 & 575.5 & 278.3 & 2.07 & 0.625 \\
800 & 50 & 13.2 & 53.4 & 0.25 & 0.063 \\
800 & 100 & 140.1 & 165.1 & 0.85 & 0.125 \\
800 & 150 & 216.5 & 206.6 & 1.05 & 0.188 \\
800 & 200 & 326.1 & 169.8 & 1.92 & 0.250 \\
\hline
\end{tabular}
\end{center}

wavelength of $1070 \mathrm{~nm}$. Processing parameters examined during the STS are reported in Table 2. After STS, the samples were cross-sectioned, polished down to $0.05 \mu \mathrm{m}$, and etched with $1.0 \mathrm{vol}$. \% picric acid in distilled water for approximately $20 \mathrm{~s}$ for microstructural analysis.

\subsection*{2.2. Powder characterization}
WE43 powders were acquired from Magnesium-Elektron with a size distribution of $20 \sim 63 \mu \mathrm{m}$. The powder size distribution was refined by sieving the powders with finer mesh down to $4 \sim 40 \mu \mathrm{m}$ distribution in order to remove as many of the asymmetric powders as possible. Powder sampling was performed in accordance with ASTM B215 for sampling packaged powders. Powder particle morphology was analyzed with the FE-SEM, and the particle size distribution was determined by laser diffraction analyzer (Beckman Coulter LSTM 13 320).

\subsection*{2.3. Laser powder bed fusion parametric study}
STS provided insight into the development of melt pool, e.g., high power produced deep penetration and porosity, while low power produced smaller melt pools than the powder layer thickness. Based on results from STS investigation, the laser power for LPBF examined in this study ranged from 100 to $250 \mathrm{~W}$, while the scan speed was varied for each power as reported in Table 3. A hatch spacing of $0.13 \mathrm{~mm}$ was chosen as a constant to compensate for smaller melt pools and to reduce the impact of hatch spacing on the processing condition. WE43 has a high thermal conductivity ( $\sim 51 \mathrm{~W} / \mathrm{mK}[3,35]$ ), so a slice thicknesses $0.04 \mathrm{~mm}$ was chosen as a compromise as to reduce the impact of slice thickness on the processing condition. A $67^{\circ}$ scan rotation with a $10 \mathrm{~mm}$ striping pattern was employed to minimize texturing, if any, of the grains.

Using the LPBF parameters listed in Table 3, cubic samples with dimensions of $12 \mathrm{~mm} \times 12 \mathrm{~mm} \times 12 \mathrm{~mm}$ were built by SLM $125 \mathrm{HL}$. The cubes were built onto an AZ31 build plate for minimum thermal mismatch and good thermal conduction. Preheating of the build plate was set at $100^{\circ} \mathrm{C}$. The build was performed in an inert Ar atmosphere with an $\mathrm{O}_{2}$ content lower than $0.1 \%$. After the samples were removed from the build plate, relative density of each sample was measured via Archimedes method (in accordance with ASTM B962) 3 times by different ndividuals. The theoretical density used for the determination of reative density was $1.84 \mathrm{~g} / \mathrm{cm}^{3}$. Then, the samples were cross-sectioned and polished down to $0.05 \mu \mathrm{m}$ for optical microscopy. Percentage of flaws (e.g., porosity) was determined by image analyses of optical mirographs using ImageJ (National Institute of Health) for each of the ubic sample. At least 6 randomly selected locations at a magnification f $50 \mathrm{X}$ were analyzed for quantitative determination of porosity conent. The samples were then etched with 1.0 vol.\% picric acid in dislled water for approximately $20 \mathrm{~s}$ for microstructural analysis.

\subsection*{2.4. Heat treatment and mechanical testing}
From the parametric study described above, an optimum set of LPBF parameter, defined by the highest relative density and the lowest porosity, was found using a laser power of $200 \mathrm{~W}$ at a scan speed of $1100 \mathrm{~mm} / \mathrm{sec}$ while the hatch spacing of $0.13 \mathrm{~mm}$ and the slice thickness of $0.04 \mathrm{~mm}$ were held constant. Several samples for the assessment of mechanical behavior were built using the above parameters with $0^{\circ}$ tilt. In addition, subsequent $\mathrm{T} 6$ heat treatment, optimized by Jahedi et al. [10] for WE43, was employed, in which, the samples were solution heat treated (SHT) at $536{ }^{\circ} \mathrm{C}$ for $24 \mathrm{~h}$, and subsequently aged at $205^{\circ} \mathrm{C}$ for $48 \mathrm{~h}$. The sample that was SHT and aged is hereafter denoted as fully heat treated (FHT). During the heat treatment, the samples were encased in a quartz tube under an inert Ar atmosphere that was backfilled after a $10^{-6}$ torr vacuum.

For the assessment of mechanical behavior, both compression and tension testings were carried out. As shown by schematics in Fig. 1, cylindrical rods, $12 \mathrm{~mm}$ in diameter and $12 \mathrm{~mm}$ in height, were built by LPBF for compression testing, while the traditional dog-bone specimens with a gauge length of $25 \mathrm{~mm}$ were built for tensile testing according to ASTM E8M-3856. For consistency, 3 compressive specimens in as-built condition, and 3 tensile specimens in as-built and 3 in FHT conditions were tested using an MTS ${ }^{\mathrm{TM}}$ instrument. A quasi-static strain rate of $2 \times 10^{-4} / \mathrm{s}$ was employed, and the strain deformation was measured and recorded by a digital image correlation (DIC) camera positioned perpendicular to the loading direction. All samples were lightly ground with 1200 grit SiC paper so that optical measurement in tension and compression can be carried out by using DIC. Changes in sample dimension due to grinding were negligible, all less than $0.1 \mathrm{~mm}$ from those reported in Fig. 1. Care was taken to ensure the gauge length of $25 \mathrm{~mm}$ specified by ASTM E8M-3856. The DIC yielded the strain in tension, and failure in tension occurred within the gauge section for all samples. The DIC system consisted of a Tokina AT-X Pro macro $100 \mathrm{~mm}-\mathrm{f} / 2.8-\mathrm{d}$ lens with a resolution of $2448 \times 2048$ and VIC-2D 2009 software by Correlated Solutions, Inc. The capture frequency was $1 \mathrm{~Hz}$.

\subsection*{2.5. Microstructural characterization}
Microstructural features of starting powders, STS bulk samples, and the as-built, SHT, FHT samples were examined by a variety of characterization techniques including optical microscopy (OM), X-ray diffraction (XRD), field emission scanning electron microscopy (SEM) equipped with X-ray energy dispersive spectroscopy (XEDS), and

Table 3

Processing parameters examined during LPBF optimization study for WE43.

\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Power (W) & Scan Speed $(\mathrm{mm} / \mathrm{sec})$ & Hatch Spacing (mm) & Slice Thickness (mm) \\
\hline
100 & $100,200,300,400,500,600,700,800,900,1000$ & 0.13 & 0.04 \\
\hline
150 & $200,400,600,800,900,1000,1100,1200,1400,1600$ & 0.13 & 0.04 \\
\hline
200 & $400,600,800,1000,1100,1200,1300,1400,1600$ & 0.13 & 0.04 \\
\hline
250 & $800,1000,1100,1200,1300,1400,1600$ & 0.13 & 0.04 \\
\hline
\end{tabular}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_23039e81728c252f41ddg-04}
\end{center}

Fig. 1. WE43 alloy sample produced by LPBF for the assessment of mechanical behavior under (a) compression and (b) tension. All units are in mm.

transmission electron microscopy (TEM) equipped with XEDS and high angle annular dark field (HAADF) through scanning TEM (STEM). Nikon Metaphot optical microscope was employed to acquire optical micrographs that were used to determine the porosity content and melt pool dimension. Quantitative microscopy was carried out using ImageJ (National Institutes of Health). Constituent phase analyses were carried out for starting powders and LPBF samples, before and after the heat treatment using Panalytical Empyrean X-ray diffractometer set up with $\mathrm{Cu} \mathrm{K}_{\alpha}$ radiation operating at $45 \mathrm{kV}$ and $40 \mathrm{~mA}$. The $\theta-2 \theta \mathrm{XRD}$ scan was performed from $15-90^{\circ}$ with a $0.008^{\circ}$ step size and acquisition time of $0.4 \mathrm{~s}$ per step. A Zeiss Ultra-55 FE-SEM was used for microstructural analyses of starting powders, STS bulk samples, and the as-built, SHT, FHT samples. An accelerating voltage of $25 \mathrm{kV}$ was employed for yield $\mathrm{K}_{\alpha}$ radiation of $\mathrm{Mg}, \mathrm{Y}$, and $\mathrm{Zr}$, as well as $\mathrm{L}_{\alpha}$ radiation of $\mathrm{Nd}$ and $\mathrm{Gd}$, which were used for compositional analyses by XEDS. The Si-Drift XEDS detector employed was Thermo-Fisher-Noran System 7, coupled with Thermo Scientific NSS Version 3 analytical software. Detailed analyses for phase constituents and microstructure were carried out by using FEI/ Tecnai ${ }^{\text {TM }}$ F30 TEM operating with an accelerating voltage of $300 \mathrm{kV}$. Bright-field, dark-field, and selected area electron diffraction (SAED) along with HAADF-STEM and XEDS were utilized. In-situ liftout (INLO) technique was employed to obtain site-specific TEM thin foils by using a FEI TEM200 Focused Ion Beam (FIB).

\section*{3. Results}
\subsection*{3.1. Single track scan}
Fig. 2 presents selected optical micrographs of the melt pools observed from the STS study using the bulk sample of wrought WE43. The depth and width of the melt pool from the STS were measured as indicated in Fig. 2(c), and depth-to-width ratio was determined as reported in Table 2 as functions of processing parameters. As presented in Figs. 3(a) and 3(b), at constant scanning speed, 50, 200 or $800 \mathrm{~mm} / \mathrm{sec}$, an increase in laser power increased the depth and width, respectively, of the melt pool. Within the LPBF parameters examined, the depth varied linearly with power, while the width varied parabolically with power. The same measurements of the melt pool depth and width as a function of linear energy density (i.e., defined without slice thickness and hatch spacing) is presented in Figs. 3(c) and (d), respectively. At constant power, an increase in scanning speed decreased the depth and width of the melt pool as shown in Figs. 4(a) and (b), respectively. Correspondingly, an increase in energy density increased the depth and width of the melt pool as shown in Figs. 4(c) and 4(d), respectively. Variation of depth and width appear to be non-linear as a function of scan speed (or linear energy density) at constant power. Utilizing a combination of higher laser power and faster scan speed gave a more dramatic change in melt pool depth. Fig. 5 presents the depth-to-width ratio plotted against linear energy density, and demonstrates that a wide range of linear energy density can be employed to produce same depth-to-width ratio. For example, to produce depth-to-width ratio of 1.5 , a linear energy density can be varied approximately from 0.3 to $1.5 \mathrm{~J} / \mathrm{mm}$. This may suggest that linear energy density is not best way to normalize the data.

While STS may not be able to quantitatively determine LPBF parameters due to many differences in bulk and powder bed, for WE43 alloy, STS demonstrated that cracks were not observed in any of the solidified melt pools and melt-pool/bulk boundaries as shown in Fig. 6. Porosity was observed at the bottom of some of the deeper melt pools, i.e., high depth-to-width ratio. In wrought WE43 alloy away from the melt pool, $\alpha-\mathrm{Mg}$ (hcp) grains with $10-20 \mu \mathrm{m}$ in size, were observed, and their boundaries were decorated with segregated rare-earth additions (e.g., Y, Gd, Zr, Nd) as presented by the bright backscatter contrast in Fig. 6(a). However, within the melt pool, much finer structural features were observed, with grain size ranging from 1 to $3 \mu \mathrm{m}$ as shown in Fig. 6(b). Segregation of rare-earth addition, similar to that shown in Fig. 6(a) by the bright backscatter contrast was observed at this fine scale.

\subsection*{3.2. Powder characterization}
Fig. 7(a) presents secondary electron micrograph of the WE43 powders used for LPBF investigation. They were, in general, spherical in shape, free of satellites, and exhibited good flowability. Cross-sections of these powders were also examined as shown in Fig. 7(b) by backscatter electron micrograph. Typical powder alloy microstructure with inter-dendritic regions heavily segregated with alloying additions for WE43, such as Y, Gd, Zr, Nd, was observed, and this is somewhat similar to the microstructure observed within the melt pool from the STS study. The D10, D50, D90, and mean particle sizes were 4.4, 18.1, 38.7, and $20.1 \mu \mathrm{m}$ respectively, as presented by the particle size distribution in Fig. 7(c).

\subsection*{3.3. Laser powder bed fusion parametric investigation}
Parameters listed in Table 3 were employed to manufacture cube\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-05}

Fig. 2. Optical micrographs of selected melt pool geometry observed in single track study: (a) $150 \mathrm{~W}$ at $800 \mathrm{~mm} / \mathrm{sec}$; (b) $75 \mathrm{~W}$ at $200 \mathrm{~mm} / \mathrm{sec}$; (c) $75 \mathrm{~W}$ at $50 \mathrm{~mm} / \mathrm{sec}$; (d) $125 \mathrm{~W}$ at $200 \mathrm{~mm} / \mathrm{sec}$; (e) $125 \mathrm{~W}$ at $50 \mathrm{~mm} / \mathrm{sec}$.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-05(1)}

Fig. 3. Melt pool measurements from single track scan study: (a) depth as a function of power; (b) width as a function of power; (c) depth as a function of linear energy density; and (d) width as a function of linear energy density.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-06(1)}

Fig. 4. Melt pool measurements from single track scan study: (a) depth as a function of scan speed; (b) width as a function of scan speed; (c) depth as a function of linear energy density; and (d) width as a function of linear energy density.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_23039e81728c252f41ddg-06}
\end{center}

Fig. 5. Depth-to-width ratio of the melt pool as a function of linear energy density determined from the single track scan study. samples ( $12 \mathrm{~mm} \times 12 \mathrm{~mm} \times 12 \mathrm{~mm}$ ) for LPBF parametric examination and optimization investigation. Relative density of each cube sample was determined, first volumetrically by Archimedes method, and then by image analysis of cross-sectional optical micrographs. The theoretical density used in Archimedes determination of relative density was kept constant at $1.84 \mathrm{~g} / \mathrm{cm}^{3}$ for WE43. Fig. 8 presents the relative density of all the cube samples as a function of volumetric energy density, defined in Eq. (1). In general, relative density was observed to be low ( $\sim 90 \%)$ when the energy density was low $\left(\sim 20 \mathrm{~J} / \mathrm{mm}^{3}\right)$. With an increase in energy density up to $40 \mathrm{~J} / \mathrm{mm}^{3}$, a sharp increase in relative density was observed for all laser power used. However, inconsistency in change of relative density as a function of energy density was observed with a further increase above $50 \mathrm{~J} / \mathrm{mm}^{3}$. For example, samples produced using the laser power of $250 \mathrm{~W}$, a decrease in relatively density was observed above the energy density of $50 \mathrm{~J} / \mathrm{mm}^{3}$ as shown in Fig. 8(d). However, relative density of some above $100 \%$ was recorded for samples produced with very high energy density. To clarify this inconsistency, composition of all as-built samples was examined.

The inconsistency in density measurement by Archimedes method was found to be due to evaporation of $\mathrm{Mg}$ when excessive energy density was employed. The $\mathrm{Y}$ and $\mathrm{Nd}$ are the largest alloying addition in WE43. The nominal composition of WE43 has approximately $7 \mathrm{wt} \%$ rare earth. Fig. 9 presents the composition of rare earth, i.e., sum of Y and other rare earth, mostly $\mathrm{Nd}$, that was observed to vary with the\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-07}

Fig. 6. Cross-sectional backscatter electron micrographs from (a) a melt-pool/ bulk interface and (b) within a melt pool produced for WE43 with $125 \mathrm{~W}$ laser power and $200 \mathrm{~mm} / \mathrm{sec}$ scan speed.

energy density employed during LPBF. All four plots have the same limits for the y-axis ( $5 \sim 10 \mathrm{wt} . \%$ ). The sample built with the highest energy density using $100 \mathrm{~W}$ laser power yielded the highest relative density, however, had nearly $10 \mathrm{wt} \%$ rare earth content (i.e., lower Mg content). This change in composition produced relative density above $100 \%$ of standard density $1.84 \mathrm{~g} / \mathrm{cm}^{3}$. In other words, the samples built with low power and low scan speed (i.e., high energy density) yielded high density, including some above $100 \%$, because of Mg evaporation or rare earth enrichment. Cubic samples built with the laser power of $200 \mathrm{~W}$ and $250 \mathrm{~W}$ had a composition of $7 \sim 8 \mathrm{wt} . \%$ total rare earth, independent of energy density employed, because the scan rate was relatively higher at a fixed energy density.

Fig. 10 presents selected secondary electron micrographs from WE43 alloy samples built using various powers and scan speeds. There were no solidification cracks observed in any of the samples. Observation of porosity/flaws with the variation of power and scan speed can be qualitatively described as: (1) porosity formation due to vaporization at high energy density, (2) an optimum LPBF with minimal defects, and (3) flaws due to lack of fusion at low energy density. Fully dense WE43 alloy with a relative density of $99.7 \%$, was produced by LPBF using the laser power of $200 \mathrm{~W}$ and scan speed of $1100 \mathrm{~mm} / \mathrm{sec}$ as highlighted in Fig. 10. Therefore based on density measurement ( $>99.7$ $\%$ ) by Archimedes and image analyses, and with due consideration for compositional consistency in WE43 and build-rate (i.e., preference for higher scan speed), a laser power of $200 \mathrm{~W}$ and scan speed $1100 \mathrm{~mm} /$ sec were chosen as the optimum LPBF parameters for WE43 to be built in SLM125HL. Aforementioned, the hatch spacing and slice thickness remained constant at $0.13 \mathrm{~mm}$ and $0.04 \mathrm{~mm}$, respectively. This optimized parameter set corresponded to $35 \mathrm{~J} / \mathrm{mm}^{3}$.

\subsection*{3.4. Phase constituents and microstructure}
Fig. 11 presents XRD patterns from the LPBF WE43 that were asbuilt, after SHT (solution heat treated at $536{ }^{\circ} \mathrm{C}$ for $24 \mathrm{~h}$ ), and FHT (SHT at $536{ }^{\circ} \mathrm{C}$ for $24 \mathrm{~h}$, and subsequently aged at $205^{\circ} \mathrm{C}$ for $48 \mathrm{~h}$ ). For all samples, $\alpha-\mathrm{Mg}, \mathrm{Mg}_{3} \mathrm{Nb}$, and $\mathrm{Y}_{2} \mathrm{O}_{3}$ phases were identified in XRD patterns, although diffraction from the $\mathrm{Mg}_{3} \mathrm{Nb}$ was more evident in FTH sample. The $\alpha-\mathrm{Mg}$ phase had lattice parameters determined to be a $=3.21 \AA$ and $\mathrm{c}=5.21 \AA$, which are nearly identical to the reported\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-07(1)}

Fig. 7. Characterization of WE43 powders employed for LPBF: (a) powder morphology examined by secondary electron micrograph; (b) dendritic microstructure observed from the cross-sectional backscatter electron micrograph; and (c) particle size distribution analyzed by laser diffraction analysis.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-08}

Fig. 8. Relative density measured for LPBF WE43 samples by using Archimedes method and image analysis of optical micrographs as a function of volumetric energy density with laser power of (a) $100 \mathrm{~W}$, (b) $150 \mathrm{~W}$, (c) $200 \mathrm{~W}$ and (d) $250 \mathrm{~W}$.

value for $\mathrm{Mg}$ [11,36]. Lattice parameter determined for $\mathrm{Y}_{2} \mathrm{O}_{3}$ was a $=10.67 \AA$, which is slightly larger than the reported value [36]. The oxygen source for the formation of $\mathrm{Y}_{2} \mathrm{O}_{3}$ phase includes oxide scale on alloy powders and LPBF build chamber kept below $0.1 \%$ oxygen. Lattice parameter determined for $\mathrm{Mg}_{3} \mathrm{Nd}$ was $\mathrm{a}=7.36 \AA$, which closely match the value reported in literature [36,37].

A typical melt pool microstructure was observed parallel to the build direction as presented in Fig. 12(a) under optical microscopy after picric acid etch (with some etch pits). Within these melt pools, no discernable grain structure was readily observable using backscatter electrons, however, many spherical and flaky white particles $(1$ $5 \mu \mathrm{m}$ ) were observed with picric acid etch as labelled in Fig. 12(b). Based on XEDS, these white particles were all rich in rare earth, and some of the larger ones contained $\mathrm{O}$ along with rare earths, particularly the $\mathrm{Y}$.

Fig. 13(a) presents a high angle annular dark field (HAADF) TEM micrograph of as-built WE43 alloy. Similar to backscatter electron micrographs, white particles and particle-agglomerates due to larger average atomic number were observed. A selected region marked in Fig. 13(a), was analyzed further using XEDS mapping as presented in Figs. 13(b) for Mg, 13(c) for Nd, 13(d) for Y, 13(e) for O, 13(f) for Zr and $13(\mathrm{~g})$ for Al. They confirmed that small dispersed precipitates were rich in $\mathrm{Nd}$ corresponding to the $\mathrm{Mg}_{3} \mathrm{Nd}$ observed in XRD, some particles were rich in $\mathrm{Y}$ and $\mathrm{O}$ corresponding to the $\mathrm{Y}_{2} \mathrm{O}_{3}$ observed in XRD, and some contained $\mathrm{Al}$ and $\mathrm{Zr}$. The particles rich in $\mathrm{Al}$ and $\mathrm{Zr}$ are most likely $\mathrm{Al}_{3} \mathrm{Zr}$, which have been known to form, and can act as heterogenous nucleation sites in Al alloys modified with $\mathrm{Zr}[38,39]$. Selected area electron diffraction (SAED) presented in Fig. 13(h) confirmed that the matrix was hcp $\alpha-\mathrm{Mg}$. High resolution TEM micrograph in Fig. 13(i) and subsequent Fast Fourier Transform (FFT inset) confirmed that the small white precipitates were $\mathrm{Mg}_{3} \mathrm{Nd}$.

Fig. 14 shows backscatter electron micrographs of the FHT (i.e., SHT at $536{ }^{\circ} \mathrm{C}$ for $24 \mathrm{~h}$, then subsequently aged at $205^{\circ} \mathrm{C}$ for $\left.48 \mathrm{~h}\right)$ WE 43 sample. Microstructure appeared to be similar to that of the as-built sample, however, in general, with better definition: Mg matrix and white particles, some containing O. At higher magnification, the larger flake-like particles were resolved to consist of even smaller particles embedded in Mg matrix as shown in Fig. 14(b). The XEDS from larger particle-agglomerates consisted of $\mathrm{Y}, \mathrm{Zr}$ (minor) and $\mathrm{O}$, corresponding to the XRD observation of $\mathrm{Y}_{2} \mathrm{O}_{3}$ with a slightly larger lattice parameter, i.e., $(\mathrm{Y}, \mathrm{Zr})_{2} \mathrm{O}_{3}$ solution phase. Smaller particles that are dispersed evenly throughout contained Nd, but not O, in XEDS, therefore would correspond to the $\mathrm{Mg}_{3} \mathrm{Nd}$ intermetallic phase. Grain structure corresponding to the grain size of several micrometers was observed as presented in Fig. 14(b).

In LPBF WE43 alloy after FHT, many plate-like precipitate structures were observed as shown by the bright-field TEM micrograph in Fig. 15(a). The corresponding HAADF micrograph in Fig. 15(b) show a\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-09}

Fig. 9. Sum of rare earth $(\mathrm{Y}+\mathrm{Nd})$ content measured by XEDS as a function of relative density for WE43 samples produced by LPBF using the laser power of (a) $100 \mathrm{~W}$, (b) $150 \mathrm{~W}$, (c) $200 \mathrm{~W}$ and (d) $250 \mathrm{~W}$.

rather small grain structure (e.g., $2 \sim 5 \mu \mathrm{m}$ ) with well-defined platelike precipitates, and HAADF micrograph in Fig. 15(c) presents the microstructural arrangement of these plates. Fig. 15(d) presents high resolution TEM micrograph for $\mathrm{Mg}_{3} \mathrm{Nd}$ plates along with SAED pattern that yielded the lattice parameter of $7.40 \AA$, which has increased from the one determined for as-built sample ( $7.26 \AA$ ).

XEDS mapping of LPBF WE43 after FHT supported the phase constituent analyses: $\alpha-\mathrm{Mg}$ matrix, $\mathrm{Mg}_{3} \mathrm{Nd}$ plates, $\mathrm{Y}_{2} \mathrm{O}_{3}$ particles and possibly $\mathrm{Al}_{3} \mathrm{Zr}$ as presented in Fig. 16. In particular, after FHT, as observed in Fig. 15(b), particle-agglomerate region that contain $\mathrm{Y}$ and $\mathrm{O}$ were observed to consist of a mixture of $\alpha-\mathrm{Mg}$ and $\mathrm{Y}_{2} \mathrm{O}_{3}$ as shown by Figs. 16(b), 1(d) and 16(e). Therefore, the larger bright flake-like regions observed in Figs. 12(b), 13(a), 14, and 15(b) do not correspond to single, large $\mathrm{Y}_{2} \mathrm{O}_{3}$ particles.

\subsection*{3.5. Mechanical behavior under compression and tension}
Mechanical behavior of WE43 under compression for the as-built samples was examined using three samples. Results were repeatable for the three samples tested and they are reported in Table 4 and presented in Fig. 17(a). The as-built WE43 had an average compressive strength of $223.6 \mathrm{MPa}$, the maximum \% strain at failure was determined to be 9.5 $\%$, and the maximum compressive strength was recorded at $416.9 \mathrm{MPa}$ for the LPBF as-built WE43.\\
Mechanical behavior under tension for the as-built and FHT WE43 was examined using three samples for each. Results were repeatable for the 3 samples tested for each condition, and they are reported in Table 4 and presented in Fig. 17(b). The as-built WE43 had an average yield strength of $214.4 \mathrm{MPa}$, similar to $218.8 \mathrm{MPa}$ for the FHT WE43. However, the FHT WE43 had a larger \% strain with an average value of $4.3 \%$. The maximum $\%$ strain of for the as-built WE43 was determined to be $2.6 \%$. The average ultimate tensile strength (UTS) was about the same for both the as-built and FHT WE43 at 250.9 and $250.7 \mathrm{MPa}$, respectively. These values for both the as-built and FHT WE43 are comparable to WE43 design data (Magnesium Elektron Datasheet 467) [3] with yield strength, tensile strength, and strain at failure of $172 \mathrm{MPa}, 220 \mathrm{MPa}$, and $2 \%$, respectively.

\section*{4. Discussion}
\subsection*{4.1. Interaction of WE43 with laser}
WE43 microstructure was observed to develop favorably for the LPBF by (1) displaying the classical keyhole-mixed-conduction mode transition, (2) solidifying without cracking, and (3) solidifying with substantial grain refinement. As presented in Fig. 2, melt pool characteristic transition from conduction, to mixed mode, and to keyhole was observed as a function of energy input controlled by laser power\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-10(1)}

Fig. 10. Selected secondary electron micrographs from WE43 alloy samples produced with various power and scan speed of LPBF. An optimized parameter, $200 \mathrm{~W}$ in laser power and $1100 \mathrm{~mm} / \mathrm{sec}$ in scan speed, was found to yield nearly-fully-dense ( $>99.7 \%$ ) WE43 without any solidification cracking.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_23039e81728c252f41ddg-10}
\end{center}

Fig. 11. X-ray diffraction patterns from the as-built, solution heat treated (SHT), and fully-heat-treated (FHT) samples of WE43 produced by LPBF. and scan speed. As mentioned before, in this study, hatch spacing and slice thickness were held constant, although their variations may change the energy input slightly. Therefore, focus was placed on effects of laser power and scan speed. During STS investigation, higher energy input (laser power of $125 \mathrm{~W}$ and scan speed of $50 \mathrm{~mm} / \mathrm{sec}$ ) represented by a high linear energy density $(2.5 \mathrm{~J} / \mathrm{mm})$, was observed to produce deeper melt pool with a large depth-to-width ratio, and more importantly porosity due to entrapped gas (e.g., keyhole mode) [14]. At lower energy input (laser power of $150 \mathrm{~W}$ and scan speed of $800 \mathrm{~mm} /$ sec) corresponding to a low linear energy density $(0.188 \mathrm{~J} / \mathrm{mm})$, a shallow melt pool would develop, as the heat is readily conducted into the bulk, which would not be effective for LPBF (e.g., conduction mode) [14]. Therefore, a mix-mode would be favored for LPBF to allow for enough penetration of melt into the previous powder-solidified layer, but not enough to cause trapped gas porosity. Microstructural development and the measurement of melt pool geometry, as presented in Fig. 2-5, demonstrated that WE43 exhibits this transition gradually and therefore favorably for LPBF. As seen in Fig. 10 from LPBF parametric optimization study, this transition translates to porosity at higher energy density, flaws due to insufficient melting at lower density, and near-fully density at appropriate intermediate energy density.

In addition, during the STS study, WE43 melt pool was observed to solidify without cracking and with a substantial grain refinement as shown in Figs. 2 and 6, respectively. The nucleation and growth of large-and-columnar matrix grains (e.g., much larger than the melt pool\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-11(1)}

Fig. 12. Cross-sectional (a) optical and (b) backscatter electron micrographs of the LPBF as-built WE43 alloy.

size), at least for some aluminum alloys $[38,39]$ have been documented to be related to the intergranular solidification cracking. In this study, WE43 produced by LPBF had fine grains $(1 \sim 3 \mu \mathrm{m})$ after STS by laser.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-11}

Fig. 14. Cross-sectional backscatter electron micrographs of the fully heat treated LPBF WE43 alloy at (a) low and (b) high magnification.

Fine grain structure in WE43, associated with high nucleation rate and low growth rate, has been also reported by Dhahri et al. [5] who performed high laser power scans with a $\mathrm{CO}_{2}$ pulse laser on WE43.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-11(2)}

Fig. 13. (a) High angle annular dark field TEM micrograph from the LPBF as-built WE43 alloy, and corresponding XEDS mapping for (b) Mg, (c) Nd, (d) Y, (e) O, (f) $\mathrm{Zr}$, and (g) Al from the region marked in (a). Electron diffraction analyses via TEM confirmed the presence of (h) $\alpha-\mathrm{Mg}$ and (i) $\mathrm{Mg}_{3} \mathrm{Nd}$.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-12}

Fig. 15. (a) Bright field and (b) corresponding HAADF TEM micrograph from the fully heat treated LPBF WE43 sample; (c,d) Microstructure consisted of well-defined $\mathrm{Mg}_{3} \mathrm{Nd}$ plates in $\alpha$ - $\mathrm{Mg}$ matrix.

Furthermore, corresponding to the solidification into small grains, no solidification cracking was observed in any of the LPBF-produced WE43 samples as presented in Fig. 10. Similar to the STS study results, fine matrix grains $(2 \sim 5 \mu \mathrm{m})$ were observed in LPBF WE43 as presented Fig. 14(b) and 15(a). Therefore, for LPBF WE43, a systematic LPBF study is warranted to examine the presence of rare earth as heterogeneous nucleation agents and their role in mitigating solidification cracking (i.e., LPBF of Mg-alloys with and without rare earth).

\subsection*{4.2. LPBF processing behavior of WE43}
As presented in Figs. 8 and 10, nearly fully-dense WE43 alloy was produced with LPBF using an energy density of $32 \sim 37 \mathrm{~J} / \mathrm{mm}^{3}$ from all four laser powers, $100,150,200$, and $250 \mathrm{~W}$ with varying scan speed examined in study. This may suggest that WE43 can be built at low laser powers to conserve energy or at high speeds with high laser power to increase the build-rate. However, the composition of WE43 varied as a function of power-scan-speed employed. One of the main concerns with processing Mg alloys is the high vapor pressure of Mg. Fig. 18(a) shows the calculated vapor pressure for pure $\mathrm{Mg}, \mathrm{Y}, \mathrm{Zr}, \mathrm{Nd}$, and Gd. Overwhelmingly, $\mathrm{Mg}$ has the highest vapor pressure by almost 20 or more orders of magnitude difference. Understandably, it is concerning that $\mathrm{Mg}$ would vaporize faster than the rare earth elements, thus increasing the overall weight of the part and making the alloy more enriched with rare earth than the nominal composition.

As was discussed with Fig. 9, the relative content of rare earth was observed to increase with an increase in energy density for the cubic samples built with low laser powers, i.e., $100 \mathrm{~W}$ and $150 \mathrm{~W}$, using slow scan speed. This yielded an increase in relative density of WE43 as presented in Fig. 8, sometimes greater than $100 \%$ of its theoretical density at $1.84 \mathrm{~g} / \mathrm{cm}^{3}$, because of relative enrichment of rare earth. However, the relative content of the rare earths, at $7 \sim 8 \mathrm{wt} . \%$, did not change when laser power of 200 and $250 \mathrm{~W}$ were employed with appropriate scan speed. This observation proves rather useful as the composition of commercial WE43 does not need to be adjusted to compensate for the loss of $\mathrm{Mg}$, and optimum parameters for LPBF can be found at an energy density of $32 \sim 37 \mathrm{~J} / \mathrm{mm}^{3}$ as long as the laser power remains sufficiently high, at 200 and $250 \mathrm{~W}$, with appropriate scan speed. This observation also points to a needed study to understand the heat transfer kinetics as functions of power and scan speed, as the "static" quantity of energy density does not capture the dynamics of melting and solidification.

\subsection*{4.3. Precipitation behavior of WE43 built by LPBF}
WE43 is an age hardenable $\mathrm{Mg}$ alloy with an ageing sequence of $\beta^{\prime \prime} \rightarrow \beta^{\prime} \rightarrow \beta_{1} \rightarrow \beta[10,37]$. The $\beta^{\prime \prime}$ phase is a metastable hcp structure with the composition of $\mathrm{Mg}_{3}(\mathrm{Y}, \mathrm{Nd})[10,37,42,43]$. The $\beta^{\prime}$ phase develops during heat treatment between $200 \sim 250{ }^{\circ} \mathrm{C}$ [42]. There is still some debate as to the structure, and its stoichiometry can be either $\mathrm{Mg}_{24} \mathrm{Y}_{2} \mathrm{Nd}_{3}$, or the more common $\mathrm{Mg}_{12} \mathrm{NdY}$. Prior to the equilibrium phase, $\beta-\mathrm{Mg}_{14} \mathrm{Nd}_{2} \mathrm{Y}$, the $\beta_{1}$ phase, identified as $\mathrm{Mg}_{3} \mathrm{Nd}$, has been reported to form as well. The $\beta_{1}-\mathrm{Mg}_{3} \mathrm{Nd}$ has a face-centered-cubic (fcc) $\mathrm{BiF}_{3}$ (cF16) structure and its presence has been associated with enhanced creep resistance [1,2,44].

The precipitate phase identified in both the as-built and aged WE43 was confirmed to be $\beta_{1}-\mathrm{Mg}_{3} \mathrm{Nd}$ by XRD analysis and analytical TEM as presented in Figs. 11,13, and 15, respectively. The LPBF process that consists of initial laser energy input, solidification and subsequent heat-\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-13}

Fig. 16. (a) High angle annular dark field TEM micrograph from the LPBF WE43 alloy after full heat treatment, and corresponding XEDS mapping for (b) Mg, (c) Nd, (d) $\mathrm{Y}$, (e) $\mathrm{O}$, (f) $\mathrm{Zr}$, and (g) Al from the region marked in (a).

exposure (i.e., laser scan for layers above) allowed the formation of $\beta_{1}$ $\mathrm{Mg}_{3} \mathrm{Nd}$, bypassing the formation of $\beta$ " and $\beta$ ' phases. More importantly the $\beta_{1}-\mathrm{Mg}_{3} \mathrm{Nd}$ remained and only grew after solutionizing and aging, and did not transform to the equilibrium $\beta-\mathrm{Mg}_{14} \mathrm{Nd}_{2} \mathrm{Y}$ phase. The $\beta_{1^{-}}$ $\mathrm{Mg}_{3} \mathrm{Nd}$ phase was found to grow into plate-like structure after the solution heat treatment at $536{ }^{\circ} \mathrm{C}$ and subsequent age hardening at $205^{\circ} \mathrm{C}$. Under a certain orientation, the plate-like structures appear bright white in HAADF corresponding to the basal plane of hcp-Mg, as shown in Fig. 15(c). TEM observation with various tilt angles demonstrated that they are not needles.

Table 4

Tensile and compressive mechanical behavior of WE43 manufactured by laser powder bed fusion.

\begin{center}
\begin{tabular}{lllll}
\hline
Sample & Testing Type & $0.2 \%$ Yield Strength (MPa) & Ultimate Strength (MPa) & $\%$ Strain at Failure \\
\hline
As-built & Compression & 221.8 & 420.0 & 9.60 \\
 &  & 219.8 & 418.2 & 9.70 \\
 & 229.3 & 412.4 & 9.20 &  \\
 &  & Avg $=223.6 \pm 4.09$ & 249.5 & Avg $=9.5 \pm 0.20$ \\
 &  & 209.4 & 255.0 & 2.78 \\
 &  & 217.7 & 248.3 & 2.20 \\
Heat-treated $^{*}$ & 215.9 & Avg $=250.9 \pm 2.92$ & Avg $=2.62 \pm 0.29$ &  \\
 &  & Avg $=214.4 \pm 3.54$ & 258.4 & 4.78 \\
 &  & 225.5 & 247.1 & 3.53 \\
 &  & 214.7 & 246.6 & 4.63 \\
 &  & Avg $=250.7 \pm 5.47$ & Avg $=4.31 \pm 0.55$ &  \\
\hline
\end{tabular}
\end{center}

\footnotetext{" Note: solutionizing at $536{ }^{\circ} \mathrm{C}$ for $24 \mathrm{~h}$ and subsequent ageing at $205^{\circ} \mathrm{C}$ for $48 \mathrm{~h}$.
}
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-14}

Fig. 17. Engineering stress vs. engineering strain observed during (a) compressive and (b) tensile test for the WE43 alloy samples produced by LPBF.

The absence of $\beta-\mathrm{Mg}_{14} \mathrm{Nd}_{2} \mathrm{Y}$ may be related to the presence of fine $\mathrm{Y}_{2} \mathrm{O}_{3}$ dispersoids embedded in Mg matrix presented in Figs. 12-16. Although they appear as large particles, several micrometers in size in Fig. 12(b), 13(a), and 14(a), detailed observation demonstrated that they are dense agglomerates of nano-scale $\mathrm{Mg}+\mathrm{Y}_{2} \mathrm{O}_{3}$ embedded in $\mathrm{Mg}$ matrix as shown in Figs. 14(b), 15(b), 16(a), 16(d), and 16(e). The $\mathrm{Y}_{2} \mathrm{O}_{3}$ has the largest formation of energy (e.g., Ellingham diagram shown in Fig. 18(b)) among elemental constituents in WE43, and can perhaps act as a heterogenous nucleation site for the $\alpha-\mathrm{Mg}$ matrix. However, no such confirmation can be made in this study because they are distributed evenly throughout the alloy, and not necessarily located along the grain boundaries. The $\mathrm{Zr}$ alloying addition was also observed, mostly in $\mathrm{Al}_{3} \mathrm{Zr}$, given that $\mathrm{Zr}$ is immiscible with $\mathrm{Mg}$. The $\mathrm{Al}_{3} \mathrm{Zr}$ has shown to help nucleate the $\alpha$-Al matrix in many $\mathrm{Al}$ alloys, both wrought and AM'ed alloys [38,39]. However, it cannot be confirmed what type of role it plays in $\mathrm{Mg}$ solidification. Given the presence of $\mathrm{Y}$ in $\mathrm{Y}_{2} \mathrm{O}_{3}$, it may not have been possible for either the $\beta^{\prime \prime}$ or $\beta$ ' phases to develop during LPBF and subsequent heat treatment totaling at $72 \mathrm{~h}$.

\section*{5. Summary}
The following summarizes the findings from the investigation of\\
LPBF manufacturing of WE43 alloy:

1 Using single track scan as an assessment for determining printability of an alloy, no cracking was observed in any of the melt pools. Furthermore, limited porosity content was observed, mainly found at the bottom of melt pools due to trapping of gas from keyhole formation. Overall, a fine grain structure was observed in each of the melt pools.

2 Through process mapping, the best processing parameters to use for the LPBF of WE43 with a near-full density of $99.7 \%$ was found at a laser power, scan speed, hatch spacing, and slice thickness of $200 \mathrm{~W}$, $1100 \mathrm{~mm} / \mathrm{sec}, 0.13 \mathrm{~mm}$, and $0.04 \mathrm{~mm}$ respectively. Moreover, the mapping can be divided into three regions: lack of fusion due to low energy density, an optimized parameter set with > $99 \%$ density, and spherical pore formation due to high energy density. Overall, high density ( $>99 \%$ ) could be achieved with an energy density of $32 \sim 37 \mathrm{~J} / \mathrm{mm}^{3}$. However, laser power of $200 \mathrm{~W}$ and $250 \mathrm{~W}$ with correspondingly appropriate scan speed were observed to produce WE43 with proper compositions.

3 The $\beta_{1}-\mathrm{Mg}_{3} \mathrm{Nd}$ precipitates smaller than a micrometer were found distributed throughout the matrix of the as-built WE43. After heat treatment, the $\beta_{1}-\mathrm{Mg}_{3} \mathrm{Nd}$ phase was found to dissolve, and develop into plate like precipitates. The $\mathrm{Y}_{2} \mathrm{O}_{3}$ dispersoids was also found distributed uniformly throughout WE43 as a part of flake-like structure that consisted of dense nano-scale $\mathrm{Mg}+\mathrm{Y}_{2} \mathrm{O}_{3}$ agglomerate. The $\mathrm{Y}_{2} \mathrm{O}_{3}$ phase did not dissolve or coalesce after the heat treatment.

4 Compressive yield strength of $224 \mathrm{MPa}$ in the as-built condition was obtained for LPBF WE43. Maximum compressive strength and strain reached $417 \mathrm{MPa}$ and $9.5 \%$, respectively. Tensile yield strength of $214 \mathrm{MPa}$ in the as-built condition, and of $219 \mathrm{MPa}$ in the FHT condition were obtained from LPBF WE43. Moreover, the maximum tensile strain at fracture increased from 2.6 to $4.3 \%$ after the heat treatment. The tensile strength was similar for both the as-built and FHT WE43 at $251 \mathrm{MPa}$.

\section*{CRediT authorship contribution statement}
Holden Hyer: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing review \& editing, Visualization. Le Zhou: Validation, Formal analysis, Investigation, Data curation. George Benson: Validation, Formal analysis, Investigation, Data curation. Brandon McWilliams: Resources, Supervision, Project administration, Funding acquisition. Kyu Cho: Resources, Supervision, Project administration, Funding acquisition. Yongho Sohn: Conceptualization, Methodology, Resources, Writing review \& editing, Visualization, Supervision, Project administration, Funding acquisition.

\section*{Declaration of Competing Interest}
Authors of this manuscript do not have any financial and personal relationships with other people or organizations that could inappropriately influence (bias) our work. So we have no conflict of interests to declare.

\section*{Acknowledgements}
This research was sponsored by the U.S. Army Research Laboratory under a cooperate agreement contract, W911NF1720172. The views, opinions and conclusions made in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_23039e81728c252f41ddg-15}

Fig. 18. Calculated (a) Ellingham diagram and (b) vapor pressure for major elemental constituents of WE43, i.e., Mg, Y, Nd, Zr, and Gd [40,41].

\section*{Appendix A. Supplementary data}
Supplementary material related to this article can be found, in the online version, at doi:\href{https://doi.org/10.1016/j.addma.2020.101123}{https://doi.org/10.1016/j.addma.2020.101123}.

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[29] K. Wei, M. Gao, Z. Wang, X. Zeng, Effect of energy input on formability, microstructure and mechanical properties of selective laser melted AZ91D magnesium alloy, Mater. Sci. Eng. A 611 (2014) 212-222.

[30] K. Wei, Z. Wang, X. Zeng, Influence of element vaporization on formability, composition, microstructure, and mechanical performance of the selective laser melted Mg-Zn-Zr components, Mater. Lett. 156 (2015) 187-190.

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[34] N.A. Zumdick, L. Jauer, L.C. Kersting, T.N. Kutz, J.H. Schleifenbaum, D. Zander Additive manufactured WE43 magnesium: a comparative study of the microstructure and mechanical properties with those of powder extruded and as-cast WE43, Mater. Charact. 147 (2019) 384-397.

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\title{Effect of energy density on laser powder bed fusion built single tracks and thin wall structures with $100 \mu \mathrm{m}$ preplaced powder layer thickness }


\author{S.K. Nayak, S.K. Mishra, C.P. Paul*, A.N. Jinoop, K.S. Bindra\\
Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, Maharashtra, India\\
Laser Technology Division, Raja Ramanna Centre for Advanced Technology, Indore 452013, Madhya Pradesh, India}
\date{}


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\section*{H I G HL I G H T S}
\begin{itemize}
  \item Laser Powder Bed Fusion of single tracks and thin walls at $100 \mu \mathrm{m}$ layer thickness.
  \item Process window identified in terms of energy density for stable single tracks.
  \item Parametric investigation on track morphology, track geometry and wall geometry.
  \item Analytical and regression models developed for track and wall geometry.
  \item Geometrical variation from single track to thin walls investigated.
\end{itemize}

\section*{A R T I C L E I N F O}
\section*{Keywords:}
Laser additive manufacturing

Powder bed fusion

Thin walls

Single track

Geometry

\begin{abstract}
A B S T R A C T Laser Powder Bed Fusion (LPBF) is one of the advanced manufacturing technologies used for fabricating near net shaped components directly from CAD model data by selectively melting pre-placed layer of powder in layer by layer fashion. LPBF process is widely researched with layer thickness up to $60 \mu \mathrm{m}$ and is now commercially deployed for many metallic materials. However, very limited literature is available in public domain for LPBF with layer thickness $>60 \mu \mathrm{m}$ as the process in this window has many challenges in geometry control and reproducibility due to inherent process instability. However, higher layer thickness with larger beam diameter can bring better productivity and shorter built time with limited compromise on minimum feature size. The present work focuses on a systematic parametric study on single track and thin wall fabrication using LPBF at layer thickness of $100 \mu \mathrm{m}$ by varying laser power (150-450 W) and scan speed (0.02-0.08 m/s) using SS 316L powder. For the range of parameters under investigation, process window yielding stable tracks (regular and uniform) is obtained for energy density between 87.5 and $140 \mathrm{~J} / \mathrm{mm}^{3}$. An analytical model for predicting the width of the track and a regression model for the depth of re-melted zone in the substrate subsurface and track area during single track fabrication is developed in terms of energy density. The average difference in predicted and experimental values for width and area of the track are $3.18 \%$ and $7.61 \%$, respectively within the process window. Width of thin walls built at the same parameters is measured and the variation between width of thin wall and track is estimated in terms of energy density. The width of thin walls fabricated are observed to be larger than that of single track built at the same combinations of process parameters primarily due to preheating effect. For the range of parameters under investigation, the highest values of width of thin wall and its difference from corresponding width of track is observed at $112.5 \mathrm{~J} / \mathrm{mm}^{3}$ in the process window. The study paves a way in understanding the effect of higher layer thickness on the geometry of LPBF built components.
\end{abstract}

\section*{1. Introduction}
Laser Additive Manufacturing (LAM) is the process of fabricating components by adding materials in a layer-wise fashion using high energy laser as heat source [1,2]. Also previously known as Laser Rapid Manufacturing, the process provides feature based design and manufacturing approach that facilitates multi-functional and multimaterials fabrication of engineering and prosthetic components for customised applications [3]. Laser Powder Bed Fusion (LPBF) is one of the widely deployed LAM process for fabricating complex shaped metallic components by using the shape design freedom of LAM $[2,4]$. It involves laying a thin layer of metal powder on a substrate and selective
\footnotetext{\begin{itemize}
  \item Corresponding author at: Laser Technology Division, Raja Ramanna Centre for Advanced Technology, Indore 452013, Madhya Pradesh, India.
\end{itemize}

E-mail address: \href{mailto:paulcp@rrcat.gov.in}{paulcp@rrcat.gov.in} (C.P. Paul).
}
melting using a focused laser energy to fuse a region of the powder bed as per the geometry data obtained from solid model $[1,5,6]$. A number of such layers are laid one over the other and near net shaped components are obtained [7]. LPBF is widely known with different commercial names, such as Direct Metal Laser Sintering by EOS GmbH, Laser CUSING by Concept Laser, Direct Metal Printing by 3D System and Selective Laser Melting by SLM Solutions [2]. LPBF can fabricate components with unlimited complexity, light weight designs and porous geometry involving thin walls and solid structures, eliminating the many steps involved in conventional manufacturing routes resulting in reduced lead time. One of the exciting applications of LPBF is fabrication of thin wall structures for light weight applications. Thin wall structures are built by laying single tracks one over another and thus, single track is the basic building block for building thin wall structures.

Many researchers have investigated and reported LPBF of single track and thin walls in published literature. Ning et al. developed an analytical model by considering moving point heat source solution with stationary coordinate and origin at boundary of part. The model found close agreements with experimental values on LPBF of IN625 in previous literature [8]. Rosso et al. presented a complete strategy for process modelling that includes Finite Element Analysis (FEA) based model development with simplified assumptions like no melt pool fluid dynamics and homogenised bed. The model was validated from previous literature and in-house experiments involving in-situ melt pool thermal field measurements [4]. Verhaeghe et al. modelled LPBF process using enthalpy formulation by taking the penetration of laser and shrinkage into account. The influence of incorporating or neglecting evaporation effects in the model was studied. The model results were compared with the experimental results and it was concluded that evaporation in the process modelling of LPBF yielded results closer to experimental values [9]. Chen et al. derived a volumetric heat source model on LPBF of ceramics based on Beer-Lamberts law and used Newtonian constitutive law to consider the shrinkage due to consolidation from powder to liquid and a semi-implicit formulation is used to capture the liquid and gas interface. The final bead shape is well related to surface tension and viscosity [10]. Arisoy et al. presented a 3D nonlinear finite element based model that uses different energy density values to simulate LPBF process for both single and multi-tracks and used it to predict melt pool sizes of IN625 at $20 \mu \mathrm{m}$ layer thickness with reasonable accuracy [11]. Schwalbach et al. developed a discrete source model for thermal history prediction during LPBF and verified it against an analytical model for single track geometry. The model was calibrated successfully using single track deposits with $25 \mu \mathrm{m}$ layer thickness to match the melt pool depth and width for Ti-6Al-4V [12]. Keshavarzkermani et al. investigated the effect of laser energy density on Hastelloy-X single track during LPBF for maximum layer thickness of $60 \mu \mathrm{m}$. It was observed from parametric studies that, for a fixed value of laser energy density, laser power has greater influence than scan speed on the melt pool geometry [13]. Guo et al. investigated the effect of process parameters during LPBF of Tungsten single tracks at layer thickness of $80 \mu \mathrm{m}$. It was observed that, with increase in linear energy (ratio of laser power and scan speed) width and penetration depth of the tracks increases [14]. Yadroitsev et al. investigated the effect of layer thickness up to $400 \mu \mathrm{m}$ and reported that as the layer thickness is increased for a particular power, the scanning speeds can be varied within a smaller range for obtaining continuous tracks [15].

LPBF of thin walls was also investigated by several researchers. Calignano et al. investigated the effect on process parameters during LPBF of AlSi10Mg thin walls using a layer thickness of $25 \mu \mathrm{m}$ and found that the walls built perpendicular to the direction of scrapper movement were more prone to distortions or trace breaks due to frictional forces [16]. Lin et al. built Lobster eyed AlSi10Mg thin walled components by placing two groups of thin walls perpendicular to each other using LPBF at $30 \mu \mathrm{m}$ layer thickness. Systematic investigation was performed to obtain the effect of laser processing parameters on densification behaviour, dimensional accuracy, surface roughness and forming defects. It was found that with increase in laser power, outside surface roughness (surface roughness on the outer surface of the component) reduced and inside surface roughness (surface roughness on the inner surface of the component) increased for the built walls [17]. Li et al. systematically studied the heat losses to loose powder in LPBF of thin walls with $40 \mu \mathrm{m}$ layer thickness by using conductivity dependant and wall thickness dependant convection coefficients in FEM. It was found that the boundary conditions defined by the later coefficient yielded better peak temperature prediction accuracy than former by $36 \%$, while at the same time decreasing the computation time by $75 \%$ [18].

The above reported researches are mostly focused on LPBF of single track and thin wall with layer thickness less than $60 \mu \mathrm{m}$ primarily due to process instabilities issues at higher layer thickness [19]. Only few reports $[14,15]$ are available for higher layer thickness and they observed unstable molten pool yielding non-repeatable track geometry. Further, very limited parametric investigations supported by analytical and regression models are explored and reported in published literature to understand the geometry variation and geometry correlation between single track and thin wall structures at higher layer thickness [20]. It motivates us to investigate LPBF with higher layer thickness of $100 \mu \mathrm{m}$.

In the present work, a number of single tracks and thin walls are built at different process parameter combinations with the layer thickness of $100 \mu \mathrm{m}$ using an indigenously developed LPBF system. Track geometry, i.e., track width, track depth and track area (refer

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-02}
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Fig. 1. Typical cross-section of LPBF built single track.

Fig. 1) is systematically investigated. It may be noted in Fig. 1 that the layer thickness is the thickness of the preplaced powder on the bed in as-spread condition, which is derived from the displacement of buildplate. The pre-placed powder in as-spread condition is loosely packed, which gets densified due to laser melting and subsequent consolidation/solidification. Hence, track height is less than the layer thickness. Subsequently, in our work, the track geometry is analysed and the process window is identified in terms of energy density for stable tracks. The effect of process parameters including energy density on the track width, track depth and track area is investigated. A simplified model in terms of energy density is developed to predict the track width and regression models in terms of energy density are developed for track depth and track area. Further, effect of process parameters including energy density on width of the thin walls and the difference between width of thin walls and track widths are investigated. Corresponding regression models in terms of in terms of energy density are also developed for width of thin walls and the difference between width of thin wall and track width.

\section*{2. Materials and methods}
\subsection*{2.1. Materials}
SS 316L is a material with excellent corrosion resistance, high toughness, good ductility, moderate strength and high temperature oxidation resistance up to $870{ }^{\circ} \mathrm{C}$ [21]. The material possesses good oxidation resistance in intermittent and continuous service. The material also possess excellent weldability by all standard fusion and resistance welding methods [21]. It finds wide applications in the field of food preparation equipment, medical implants, medical equipment, structural applications, marine environment applications etc. due to its excellent corrosion resistance. Commercially available SS 316L powder with spherical shape and size ranging from 45 to $100 \mu \mathrm{m}$ is used. Fig. 2 shows the morphology of SS 316L powders obtained by Scanning Electron Microscope (SEM). Sandblasted SS 304L of $75 \mathrm{~mm}$ diameter and $10 \mathrm{~mm}$ thickness is used as the substrate material for building single track and thin walls. Tables 1 and 2 presents the composition of powder and properties of SS316L, respectively.

\subsection*{2.2. Experimental setup}
In the present work, a $500 \mathrm{~W}$ fibre laser based indigenously developed LPBF system at Raja Ramanna Centre for Advanced Technology (RRCAT), Indore, India is deployed. Fig. 3(a) and (b) presents the pictorial representation and schematic diagram of LPBF system, respectively. It essentially consists of a $500 \mathrm{~W}$ fibre laser, galvano scanner,

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-03}
\end{center}

Fig. 2. SEM image of SS 316L Powder.\\
Table 1

Composition of SS316L Powder used for present work.

\begin{center}
\begin{tabular}{lcccccccccl}
\hline
Element & Fe & $\mathrm{Cr}$ & $\mathrm{Ni}$ & $\mathrm{Mo}$ & $\mathrm{Mn}$ & $\mathrm{Si}$ & $\mathrm{P}$ & $\mathrm{S}$ & $\mathrm{C}$ \\
\hline
Percentage composition & Bal & 17.4 & 10.9 & 2.8 & 1.4 & 0.5 & 0.024 & 0.010 & 0.01 \\
\hline
\end{tabular}
\end{center}

Table 2

Properties of SS316L.

\begin{center}
\begin{tabular}{llll}
\hline
Property & Value & Unit & Reference \\
\hline
Density & $\sim 8$ & $\mathrm{~g} / \mathrm{cc}$ & $[22]$ \\
Specific Heat Capacity & 0.5 & $\mathrm{~J} / \mathrm{g}{ }^{\circ} \mathrm{C}$ & $[23]$ \\
Enthalpy of Fusion & 280 & $\mathrm{~J} / \mathrm{g}$ & $[23]$ \\
Melting Point & $\sim 1500$ & ${ }^{\circ} \mathrm{C}$ & $[24]$ \\
\hline
\end{tabular}
\end{center}

controller, powder hopper, powder spreading unit and build plate. Galvano-Scanner provides the $\mathrm{x}$ and $\mathrm{y}$ movement for laser beam as per the geometry of each layers. The build volume of the system is $250 \times 250 \times 250 \mathrm{~mm}^{3}$ with a laser spot diameter of about $500 \mu \mathrm{m}$. Full factorial experimental design is deployed for building single tracks and thin walls by varying laser power. Laser power is varied from $150 \mathrm{~W}$ to $450 \mathrm{~W}$ with four levels and scan speed is varied from 0.02 to $0.08 \mathrm{~m} / \mathrm{s}$ with three levels. A constant layer thickness of $100 \mu \mathrm{m}$ is used for the study. Each thin wall is built by laying 40 single tracks one over the other.

For characterizing track geometry, wire EDM is used to cut the built tracks along the transverse direction and the samples are extracted for analysing the cross-section. The samples are prepared using standard metallographic procedure. Subsequently, electrolytic etching is carried out in a solution of $10 \mathrm{~g}$ of oxalic acid in $100 \mathrm{ml}$ distilled water at $12 \mathrm{~V}$ for 10-15 s. These etched samples are studied under optical microscope (Make: Olympus). Quantimet-image analysis software is used to analyse the geometry of the track cross-section. The track area is measured using Quantimet image processing software from images obtained from optical-microscope. Further, 3D Laser scanner is used to obtain the 3D model geometry information in as-built condition of the wall structures. Inspect software is used to obtain transverse cross section profile of the built walls and analyse the wall width at different locations.

\section*{3. Results and discussion}
\subsection*{3.1. Track geometry}
Track geometry is one of the important features to be considered during LPBF process, as it is the basic building block for this layer-bylayer process. It directly affects the properties of built structure. Among the various process parameters in LPBF, layer thickness is one of the most dominating parameters and it governs the availability of material during LPBF process. A higher layer thickness makes the availability of more powder and yields higher build rate, but its value can be increased within certain limit. At one end, a higher layer thickness changes the dynamics of molten pool and may result in non-uniform and irregular tracks. On the other end, higher layer also results in a lower track aspect ratio (the ratio of track width to track height) that may cause lack of fusion zones along the tracks during multiple overlapped track deposition [25]. Our experimental observations about the effect of layer thickness on the track geometry is as follows: Though a lower layer thickness $(20-50 \mu \mathrm{m})$ results in a higher gradient of thermo-physical properties within the layer, the limited powder volume restricts the instability of molten material flow during LPBF. It is because the surface tension forces greatly overwhelm gravitational forces at these layer thickness. The higher layer thickness ( $>60 \mu \mathrm{m})$ results in the availability of larger volume of material and non-simultaneous melting of entire layer, which generates greater instability in the molten pool. For higher layer thickness, the laser energy is absorbed in top most layer

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\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-04(1)}
\end{center}

(a)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-04}
\end{center}

(b)

Fig. 3. LPBF system at RRCAT (a) Photographic view (b) Schematic diagram.

and it melts instantly. Thereafter, the melting of material is because of two competitive phenomena: melting due to heat conduction; and melting due to conglomeration of powder and molten metal within the layer. This results in larger gradient in thermo-physical properties and the presence of powder layer underneath the molten pool facilitating more fluid flow freedom and greater molten pool instability during the process. Further, the gravity and Marangoni effect also affect the shape of the molten pool. From processing parameter point of view, a larger dwell time at a particular spot is required for proper melting and consolidation, which results in lower thermal gradient and significantly affects the surface tension in the melt pool, which in turn affect the Marangoni convection. These observations are in agreement with the earlier report by King et al. [26].

The surface topography of the tracks and the values of track width, track depth and track cross-section area at various processing parameters are summarized in Table 3. The obtained result matrix is assessed using the combined parameter Energy Density (ED). ED is expressed mathematically in Eq. (1).

$\mathrm{ED}=\frac{\mathrm{P}}{\mathrm{v}_{\mathrm{s}} \times \mathrm{D} \times \mathrm{t}}$

where $\mathrm{P}, \mathrm{v}_{\mathrm{s}}, \mathrm{t}$ and $\mathrm{D}$ represent the laser power $(\mathrm{W})$, scan speed $(\mathrm{mm} / \mathrm{s})$, layer thickness ( $\mathrm{mm}$ ) and beam diameter ( $\mathrm{mm}$ ), respectively.

\subsection*{3.1.1. Overall track morphology}
A number of single tracks are laid at different laser power and scan speeds for parametric investigation and process window development. Fig. 4 presents the top view of the LPBF built single tracks at various processing parameters. Surface topography examination shows that the

Table 3

Track Geometry at different process conditions.

\begin{center}
\begin{tabular}{lllllll}
\hline
S.No. & \begin{tabular}{l}
Laser \\
Power \\
$(\mathrm{W})$ \\
\end{tabular} & \begin{tabular}{l}
Scan \\
Speed \\
$(\mathrm{m} / \mathrm{s})$ \\
\end{tabular} & \begin{tabular}{l}
Track \\
Width \\
$(\mu \mathrm{m})$ \\
\end{tabular} & \begin{tabular}{l}
Track Cross \\
Section \\
Area $\left(\mathrm{mm}^{2}\right)$ \\
\end{tabular} & \begin{tabular}{l}
Track \\
Depth \\
$(\mu \mathrm{m})$ \\
\end{tabular} & Remarks \\
\hline
1 & 150 & 0.02 & 423.3 & 0.04431 & 134.833 & Non-uniform \\
2 & 250 & 0.02 & 510.2 & 0.0534 & 187.59 & Non-uniform \\
3 & 350 & 0.02 & 549.2 & 0.05749 & 361.6 & Non-uniform \\
4 & 450 & 0.02 & 665.0 & 0.0696 & 422.7 & Non-uniform \\
5 & 150 & 0.05 & 340.2 & 0.03561 & 60.02 & Irregular \\
6 & 250 & 0.05 & 469.7 & 0.04916 & 132.19 & Stable \\
7 & 350 & 0.05 & 484.3 & 0.05069 & 226.37 & Stable \\
8 & 450 & 0.05 & 545.4 & 0.05373 & 247.32 & Non-uniform \\
9 & 150 & 0.08 & 282.1 & 0.02953 & 51.78 & Irregular \\
10 & 250 & 0.08 & 377.3 & 0.0395 & 124.5 & Irregular \\
11 & 350 & 0.08 & 431.2 & 0.04044 & 175.45 & Stable \\
12 & 450 & 0.08 & 497 & 0.04061 & 212.73 & Stable \\
\hline
\end{tabular}
\end{center}

tracks can be classified into stable and unstable tracks. Stable tracks show proper wetting with the substrate and minimal variation in the width along the track length. Unstable tracks display either improper wetting or significant width variation $(\geq 2 \%)$ along the track length. Unstable tracks can be further classified into irregular and non-uniform tracks. Irregular tracks are unstable tracks that show poor wetting with the substrate. While, non-uniform tracks are unstable tracks that show proper wetting with substrate, but with significant variation in the track width along the track length. The experimental result matrix (refer Table 3) is evaluated using combined parameter, ED and it is observed that for $\mathrm{ED}<87.5 \mathrm{~J} / \mathrm{mm}^{3}$, the tracks are irregular which can be attributed to the lack of sufficient ED preventing the flow of the melt over the substrate, resulting in poor wetting of the substrate by the melt pool. For ED between $87.5 \mathrm{~J} / \mathrm{mm}^{3}$ and $140 \mathrm{~J} / \mathrm{mm}^{3}$, the tracks are observed to be stable. In this case, ED is sufficient to cause the melt and flow of molten material over the substrate causing proper wetting and thereby, displaying uniform width along the track length. For ED > $140 \mathrm{~J} / \mathrm{mm}^{3}$, the tracks are observed to be non-uniform. In this case, very high value of ED causes significant turbulence inside the melt pool leading to melt instabilities. Further, excess ED causes powder adjacent to beam spot to melt due to heat conduction. This melting also creates a low pressure region around the melt pool that would pull the adjacent powder into the melt pool. This phenomenon is referred to as denudation [27]. Thus, significant turbulence, melting due to conduction and denudation effect are the reasons for non-uniformity along the track length for ED $>140 \mathrm{~J} / \mathrm{mm}^{3}$. Therefore, ED between $87.5 \mathrm{~J} / \mathrm{mm}^{3}$ and $140 \mathrm{~J} / \mathrm{mm}^{3}$ is selected as the process window for stable tracks at $100 \mu \mathrm{m}$ layer thickness.

\subsection*{3.1.2. Track width}
It is the distance between two extreme points on transverse cross section of the track in contact with the substrate surface (Refer Fig. 1). It is observed in Table 3 that track width increases with laser power and reduces with increase in scan speed. As the laser power increases from $150 \mathrm{~W}$ to $450 \mathrm{~W}$, an increase in track width is observed mainly due to the increase in the size of the melt pool. The increase in track width is $\sim 39 \mu \mathrm{m}, 15 \mu \mathrm{m}$ and $54 \mu \mathrm{m}$, when the laser power is increased from $250 \mathrm{~W}$ to $350 \mathrm{~W}$ at $0.02 \mathrm{~m} / \mathrm{s}, 0.05 \mathrm{~m} / \mathrm{s}$ and $0.08 \mathrm{~m} / \mathrm{s}$, respectively. Between $250 \mathrm{~W}$ and $350 \mathrm{~W}$, at $0.08 \mathrm{~m} / \mathrm{s}$ the increase in track width is due to direct melting under laser beam influence. At $0.05 \mathrm{~m} / \mathrm{s}$, the increase in track width is restricted as it approaches beam diameter. At $0.02 \mathrm{~m} / \mathrm{s}$, the powders neighbouring the laser beam spot also start melting due to conduction mode and it increases with increase in laser power. Further, increase in the laser power from $350 \mathrm{~W}$ to $450 \mathrm{~W}$ leads to significant variation in track width with maximum increase of $21 \%$ at $450 \mathrm{~W}$ and $0.02 \mathrm{~m} / \mathrm{s}$. The reason for this increment is the significant

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-05(1)}
\end{center}

Fig. 4. LPBF built track at different laser power and scan speed. The process window for desirable laser power and scan speed values inside the dotted line.

contribution of powder melting by both direct melting and heat conduction.

The results obtained for track width are compiled in terms of ED and presented in Fig. 5. It can be seen in Fig. 5 that the track width increases with increase in ED. Pearson correlation is used to co-relate the variation between ED and track width. Pearson correlation varies from -1 and 1 and shows the extent of linear relation between two variables. In the present work, Pearson correlation coefficient of 0.918 is observed between ED and track width with $\mathrm{P}$ value of 0.00 , which indicates strong and positive correlation between track width and ED. An increase in ED results in the increase in the amount of material melted which enhances the melt pool size and track width. It can be seen that the track width is more than the laser beam spot beam diameter for the value of $\mathrm{ED} \geq 180 \mathrm{~J} / \mathrm{mm}^{3}$. For the value of $\mathrm{ED}<180 \mathrm{~J} / \mathrm{mm}^{3}$, the track formation is primarily dominated by laser melting of the powder. For the value of ED $\geq 180 \mathrm{~J} / \mathrm{mm}^{3}$, the track formation is governed by both laser melting of the powder and melting of neighbouring powder particles (powder particles outside the laser beam incident zone) due to conduction. This results in track width wider than the laser beam spot diameter. Due to higher layer thickness $(100 \mu \mathrm{m})$ the effects of gravity forces become significant and melt pool viscosity is reduced due to decreased heat dissipation which, causes the melt pool to flow outwards entrapping neighbourhood powders and increasing the melt pool width.

Further, ANOVA is performed on track width to estimate the

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-05}
\end{center}

Fig. 5. Variation of track width with Energy Density.\\
Table 4

ANOVA for effect of laser power and scan speed on track width.

\begin{center}
\begin{tabular}{llllll}
\hline
Source & \begin{tabular}{l}
Degree of \\
Freedom \\
\end{tabular} & \begin{tabular}{l}
Sum of \\
Squares \\
\end{tabular} & \begin{tabular}{l}
Mean Sum of \\
Squares \\
\end{tabular} & F-value & P-value \\
\hline
Power & 3 & 75,318 & 25106.1 & 77.25 & 0.000 \\
Scan speed & 2 & 39,345 & 19672.6 & 60.53 & 0.000 \\
Error & 6 & 1950 & 325 &  &  \\
Total & 11 & 116,613 &  &  &  \\
\hline
\end{tabular}
\end{center}

contribution of laser power and scan speed on track width. Table 4 presents the Degree of Freedom, Sum of Squares, Mean Sum of Squares, F-values and P-value obtained from ANOVA studies of track width. It is seen that, both laser power and scan speed have significant effect on the track width. However, laser power is more significant with a contributing factor of $64.58 \%$ and the percentage contribution of scan speed towards track width is $33.73 \%$. During laser scanning, part of the incident energy is utilised for melting and the rest is dissipated. One of the determining factors of the melt-pool size is laser beam interaction time with the powder and conductivity of the powder. Since the conductivity of the powder is much less than that of the bulk, the beampowder interaction time that is determined by scan speed has lesser influence on the width of the melt pool as compared to laser power.

There has been many research efforts to predict the processing parameters for LPBF [4,9,28]. Most of these requires intensive calculations, while other requires domain expertise. To provide a simplified and quicker solution to predict the track width for single layer during LPBF, an analytical model is developed assuming that the (a) thermophysical properties are independent of temperature (b) heat losses due to conduction, convection and radiation is assumed to be $55 \%$ [29]. (c) absorptivity value is taken as same as in case of continuous flat surface material and it is assumed not to vary with beam angle of incidence with respect to melt pool surface. Laser absorptivity is taken as 0.3 [26].

The green density of the metal powder on pre-placed powder bed is experimentally determined and its value found to be $80 \%$ of solid metal.

Fig. 6 presents the schematic diagram for track width modelling. In this model, the track width is computed by comparing local laser energy available as per Gaussian laser beam profile with energy required to melt locally available mass of metal powder on the powder bed along the laser beam diameter. For all values of local laser energy more than energy required to melt local metal powder mass available, the metal powder is melted and deposited. The rapidity of LPBF process and poor

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-06}
\end{center}

Fig. 6. Schematic for Track Width Modelling.

thermal conductivity of pre-placed bed powder governs the instantaneous melting of powder by local energy balance. Therefore, the laser energy available after absorption should be just equal to the energy required for the melting of entire powder layer at that location. This energy balance in terms of Minimum Energy Density $\left(E D_{\min }\right)$ and local laser fluence ( $\mathrm{I}_{\text {edge }}$ ) can be written as:

$E D_{\text {min }} \times t=I_{\text {edge }} \times \frac{D}{v_{s}} \times \frac{(100-\eta)}{100}$

After rearrangement, it can be rewritten as

$\mathrm{W}=\mathrm{D} \sqrt{\frac{1}{2} \ln \left(\frac{8 \cdot \alpha \cdot \mathrm{ED}}{\pi \cdot \rho\left(\mathrm{c}_{\mathrm{p}}\left(\mathrm{T}_{\mathrm{m}}-\mathrm{T}_{0}\right)+\mathrm{L}\right)} \times \frac{(100-\eta)}{100}\right)}$

where $t, D, \alpha, \rho, \eta, T_{m}, L, c_{p}, T_{0}$ and $W$ are layer thickness, laser beam diameter, laser absorptivity, green density of the metal powder on prepowder bed, percentage of heat energy loss, melting temperature of SS316L, latent heat of fusion for SS316L, specific heat of SS316L, ambient temperature and track width respectively.

Fig. 5 also presents the comparison of model and experimental track width data for various value of ED. The mean difference between model and experimental results within the process window $\left(87.5-140 \mathrm{~J} / \mathrm{mm}^{3}\right.$ ) is found to be $14.73 \%$. At higher ED values, the maximum difference is found to be $20.51 \%$. Higher ED value causes increase in process instabilities due to Marangoni convection in melt pool and results in increased spatter in melt pool. A difference of $20.51 \%$ between model and experimental results is achieved for low value of process parameters $\left(\mathrm{P}=150 \mathrm{~W} \& \mathrm{v}_{\mathrm{s}}=0.02 \mathrm{~m} / \mathrm{s}\right)$. The low value of laser power has poor laser penetration that results in poor wetting of the substrate, while the low scan speed provides sufficient energy to create the melt pool. Both these factors contribute to the Plateau-Rayleigh instability in melt pool, resulting in balling effect [30] as shown in Fig. 4. The mean difference between computed and experimental results for the process window zone is found to be $3.18 \%$. The experimental observations show that the values of track width are lesser than the laser beam diameter for the ED below $180 \mathrm{~J} / \mathrm{mm}^{3}$, while it is lesser than the laser beam diameter for ED below $140 \mathrm{~J} / \mathrm{mm}^{3}$ as per the developed analytical model. This variation in experimental and analytical values in the range of ED between 140 and $180 \mathrm{~J} / \mathrm{mm}^{3}$ is primarily due to hunting phenomena between the two defined mechanism ("pure laser melting" and "laser melting and melting of neighbouring powder due to conduction") yielding unstable and non-uniform track formation. Hence, the limiting value of ED is chosen as $140 \mathrm{~J} / \mathrm{mm}^{3}$ for defining the process window.

\subsection*{3.1.3. Track depth}
Track depth is the vertical distance between the substrate's surface to the lowest point in the intermixing or remelting zone on the substrate subsurface created due to the moving laser spot. ED affects the extent of substrate melting and higher layer thickness decreases the energy

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-06(1)}
\end{center}

Fig. 7. Variation of track depth with ED.

reaching the substrate that affects the track depth.

Fig. 7 shows the variation of track depth with ED. Track depth shows a general increasing trend with ED. The calculated value of Pearson correlation is calculated to be 0.913 with P-value of 0.000 for relationship between track depth and ED, which indicates strong and positive correlation between track depth and ED. Thus, an increase in ED causes increased melting of the substrate. An increase in ED by increasing laser power at constant scan speed enhances the laser energy penetration into the substrate leading to increase in track depth. An increase in ED by decrease in scan speed at constant laser power increases the dwell time of the laser spot at a particular point which in turn increases the amount of energy incident at a point. Higher amount of energy at a point increases the size of the melt pool and eventually the track depth. It is observed that within the defined process window, the track depth values lie between 125 and $150 \mu \mathrm{m}$ that are in order of the layer thickness. This is in agreement with King et al. [24]. The track depth values are logarithmically fitted and Chi-square values (measure of how well do the observed data correspond to the fitted model) for sets of four consecutive track depth values are calculated. It is observed that the set of values within the defined process window yield Chisquare value of 0.022 confirming the goodness of fit. These observations are in-line with Beer-Lamberts law [31].

It is observed that at high values of process parameters (laser power: $350-450 \mathrm{~W}$ and scan speed: $0.05-0.08 \mathrm{~m} / \mathrm{s}$ ) and low values of process parameters (laser power: $150-250 \mathrm{~W}$ and scan speed: 0.02-0.05 m/s), the track depth variation with ED follows logarithmic fit with best $\mathrm{R}^{2}$ value ( $>0.9$ ). High laser power and low scan speed shows that track depth varies linearly with ED with $\mathrm{R}^{2}=0.9993$. At lower power and higher speed, poor $\mathrm{R}^{2}$ value $(<0.65)$ is observed for both linear and logarithmic fitting. Within ED range of $60-250 \mathrm{~J} / \mathrm{mm}^{3}$, total energy that is incident on the top most surface of the powder bed decreases exponentially due to heat dissipation across the $100 \mu \mathrm{m}$ powder layer thickness. Therefore, at high laser power-high scan speed and low laser power-low scan speed, logarithmic variation of track depth with ED is observed. This is in accordance with Beer-Lamberts law [31]. At high laser power and low scan speed (ED between $140 \mathrm{~J} / \mathrm{mm}^{3}$ and $450 \mathrm{~J} /$ $\mathrm{mm}^{3}$ ), heat penetration into substrate increases due to high ED. For high ED, excessive localised vaporisation leading to high spattering is observed implying transition towards keyhole mode. Any further increase in ED implies unrestricted increase of depth due to eventual formation of keyhole. At lower laser power and higher scan speed (ED between $37.5 \mathrm{~J} / \mathrm{mm}^{3}$ and $100 \mathrm{~J} / \mathrm{mm}^{3}$ ) i.e. at low $\mathrm{ED}$ values, it is observed that the tracks are irregular and show a tendency for balling implying poor wetting with the substrate and improper penetration of laser energy into the substrate. This results in poor $R^{2}$ value with logarithmic fit for track depth as a function of ED. It is also observed

Table 5

ANOVA for effect of laser power and scan speed on track depth.

\begin{center}
\begin{tabular}{llllll}
\hline
Source & \begin{tabular}{l}
Degree of \\
Freedom \\
\end{tabular} & \begin{tabular}{l}
Sum of \\
Squares \\
\end{tabular} & \begin{tabular}{l}
Mean Sum of \\
Squares \\
\end{tabular} & F-value & P-value \\
\hline
Power & 3 & 84,927 & 28309.0 & 19.17 & 0.002 \\
Scan speed & 2 & 41,555 & 20777.7 & 14.07 & 0.005 \\
Error & 6 & 8860 & 1476.6 &  &  \\
Total & 11 & 135,342 &  &  &  \\
\hline
\end{tabular}
\end{center}

that the combination of high laser power and high scan speed results in higher track depth values as compared to low laser power and low scan speed values. It can be reasoned that at low laser power and low scan speed, the diffusivity of incident laser energy is significantly reduced at higher powder layer thickness as the conductivity of metal in powder form can be 100 times lower than in bulk form [20].

Further, ANOVA is conducted on track depth to find the significant contribution of laser power and scan speed. Table 5 presents the Degree of Freedom, Sum of Squares, Mean Sum of Squares, F-values and Pvalue obtained from ANOVA studies of track depth. It is seen that laser power has a dominating effect on track depth with a percentage contribution of $62.74 \%$ and $30.7 \%$ for laser power and scan speed, respectively. Changing laser power instantly changes the depth of the melt pool, while changing the scan speed causes slower spread of melt pool due to poor conductivity and hence poorer penetration. This leads to higher significance for laser power over scan speed.

\subsection*{3.1.4. Track area}
Track area (TA) is the area of the cross-section of the track above the substrate surface. Track area is the combined parameter of both track width and track height (vertical distance from substrate surface to top most point on the track). The track area provides information about the amount of material consolidated at a place due to laser scanning. The track area also provides compiled information of track width and track height i.e. track geometry. Thus, considering these added advantages track area is measured in the present study.

Fig. 8 presents the variation of TA with ED. It is seen that the TA shows an increasing trend with ED. The Pearson's correlation coefficient between TA and ED and $\mathrm{P}$ value is 0.92 and 0 , respectively indicating a positive and strong correlation between TA and ED. This can be primarily due to melting of more amount of powder at higher values of ED. Higher ED increases the melting of powder adjacent to beam spot due to higher heat conduction. A higher ED also leads to low pressure region around the melt pool and subsequent convection currents pulling the nearby powder particles towards the melt pool. These powder particles are sucked by the melt pool through capillary action and contribute to the increase in volume and cross-section area of the track by denudation. This is just because the higher layer thickness yields

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-07}
\end{center}

Fig. 8. Variation of track area with ED.\\
Table 6

ANOVA for effect of laser power and scan speed on track area.

\begin{center}
\begin{tabular}{llllll}
\hline
Source & \begin{tabular}{l}
Degree of \\
Freedom \\
\end{tabular} & Sum of Squares & \begin{tabular}{l}
Mean Sum of \\
Squares \\
\end{tabular} & F-value & P-value \\
\hline
Power & 3 & 0.0005269 & 0.0001756 & 12.81 & 0.005 \\
Scan speed & 2 & 0.0006984 & 0.0003492 & 25.46 & 0.001 \\
Error & 6 & 0.0000823 & 0.0000137 &  &  \\
Total & 11 & 0.0013076 &  &  &  \\
\hline
\end{tabular}
\end{center}

poor heat dissipation due to lower thermal conductivity of powder in green density form. This makes the availability of higher laser energy and generates molten pool at higher temperature and lower viscosity. Low viscous molten metal along with density generates Marangoni flow and entrapment of neighbouring powder particles yielding larger TA. Further, it may be noted that the slope of TA with respect to ED decreases as ED value increases. This can be due to the fact that the track width is restricted as it approaches beam diameter, which in turn causes restriction in track area. The track area values for different ED are logarithmically fitted. It is observed that the regression model has mean and maximum difference of $7.61 \%$ and $11.89 \%$ respectively from the experimental data showing a good fit. The maximum and minimum difference in experimental and the regression model within the process window is $11.89 \%$ and $2.52 \%$ respectively.

Further, ANOVA is conducted on track area to find the significant contribution of laser power and scan speed. Table 6 presents the Degree of Freedom, Sum of Squares, Mean Sum of Squares, F-values and Pvalue obtained from ANOVA studies of TA. It is seen that scan speed is the most significant factor affecting the TA. The percentage contribution of laser power and scan speed towards track cross section area are $40.29 \%$ and $53.41 \%$, respectively. It means that that laser-powder interaction time plays a vital role in consolidating amount of material at a place. The extent of interaction determines the material melted due to conduction and denudation effects. Thus, scan speed is significant than laser power, as scan speed directly relates to interaction time.

Further, the build rate (BR) of the tracks are computed, which. BR is the volume of metal powder melted and consolidated by LPBF process per unit time. It determines the total time required for final component to be built by LPBF process. The BR is a function of cross section area and the scanning speed and presented in equation (4). The Pearson correlation factor between ED and BR is found to be -0.6 and P-value to be 0.039 . The greater significance of scan speed over laser power supports the negative correlation between BR and ED.

$\mathrm{BR}=\mathrm{TA} \times \mathrm{v}_{\mathrm{s}}$

Further, ANOVA is conducted on BR of tracks to find the significant contribution of laser power and scan speed. Table 7 presents the Degree of Freedom, Sum of Squares, Mean Sum of Squares, F-values and Pvalue obtained from ANOVA studies of track BR. It is seen that, both laser power and scan speed have significant effect on the BR with scan speed having more contribution. The percentage contribution of laser power and scan speed are $12.05 \%$ and $86.24 \%$, respectively i.e. scan speed has more effect on the BR as compared to laser power. The laser power positively influences the track width and the influence gets limited as the track width approaches beam diameter, while the scan speed positively influences rate of increase in track length without any

Table 7

ANOVA for effect of laser power and scan speed on BR.

\begin{center}
\begin{tabular}{llllll}
\hline
Source & \begin{tabular}{l}
Degree of \\
Freedom \\
\end{tabular} & \begin{tabular}{l}
Sum of \\
Squares \\
\end{tabular} & \begin{tabular}{l}
Mean Sum of \\
Squares \\
\end{tabular} & F-value & P-value \\
\hline
Power & 3 & 1.01965 & 0.33988 & 14.11 & 0.004 \\
Scan speed & 2 & 7.29420 & 3.64710 & 151.44 & 0.000 \\
Error & 6 & 0.14450 & 0.02408 &  &  \\
Total & 11 & 8.45835 &  &  &  \\
\hline
\end{tabular}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-08(1)}
\end{center}

(a)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-08}
\end{center}

(b)

Fig. 9. LPBF fabricated thin wall (a) typical cross-section (b) average geometrical profile.

limiting factor for the chosen range of parameters. Hence, the scan speed shows greater significance over laser power.

\subsection*{3.2. Wall structures}
Thin wall structures in LPBF can be built by layer-wise addition of single tracks. Wall structures are built using the parameters presented in Table 3 by laying 40 layers one over the other. Fig. 9 presents the typical transverse cross section and geometrical profile of thin walls built using LPBF obtained by Laser 3D scanning.

\subsection*{3.2.1. Wall width}
Wall width is defined as the horizontal distance between two sides of the cross section of the wall. It is obtained by taking the average of three width measurements along the wall cross section at $1.5 \mathrm{~mm}$ (Meas. 1), $2.5 \mathrm{~mm}$ (Meas. 2) and $3.5 \mathrm{~mm}$ (Meas. 3) from the base as indicated in Fig. 9(b). Fig. 10(a) presents the variation of wall width with laser power at different scan speeds. It is observed that the wall width shows a positive relation with laser power and inverse relation with scan speed. Fig. 10(b) presents the variation of wall width with ED. It is observed that the wall width shows an increasing trend with ED. Pearson correlation of 0.965 is observed between ED and wall width with $\mathrm{P}$-value of 0 , indicating strong and positive correlation between track width and ED. The primary reason for increase in wall width with increase in laser power and decrease in scan speed is due to improved melting of metal powders at higher values of ED. Preheating from previous layers also contributes to the width of the layer being built. A higher ED results in higher preheat and hence, an incremental effect is seen on the wall width. The energy provided by moving laser spot and the energy from previous layers would contribute to higher temperature in melt pool. This positively affects the melting of adjacent powder melting due to heat conduction and denudation of adjacent powders. A higher temperature of melt pool due to higher ED also decreases viscosity and surface tension, therefore assisting sideways spread of the melt pool. Due to higher layer thickness heat dissipation is poor which contributes to Marangoni flow of the melt pool due to reduced viscosity and significant gravity effects. An increment in the wall width at a particular layer can also be due to outward melt pool flow due to partial remelting occurring when the subsequent layers is being built. It is observed that the wall width increases with ED significantly for low values of ED. But, further increase in ED value leads to reduction in the slope of wall width values mainly because of relatively reduced influence of the laser outside the beam diameter. A logarithmic fit is applied to the wall width values at different ED. The logarithmic regression model shows a good fit with mean difference between experimental and modelled values equal to $4.8 \%$ within the process window. The highest value of wall width is found for $112.5 \mathrm{~J} / \mathrm{mm}^{3}$ within the process window.

ANOVA is conducted on wall width to find the significant contribution of laser power and scan speed. Table 8 presents the Degree of Freedom, Sum of Squares, Mean Sum of Squares, F-values and P-value obtained from ANOVA studies of wall width. It is seen that, both laser power and scan speed have significant effect on the wall width with scan speed having more contribution. The percentage contribution of laser power and scan speed are $37.12 \%$ and $61.37 \%$, respectively. This can be due to higher preheat energy leading to increase in thermal

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-08(3)}
\end{center}

(a)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-08(2)}
\end{center}

(b)

Fig. 10. Variation of wall width with (a) laser power at different scan speeds (b) ED.

Table 8

ANOVA studies on wall structures for effect of laser power and scan speed on wall width.

\begin{center}
\begin{tabular}{llllll}
\hline
Source & \begin{tabular}{l}
Degree of \\
Freedom \\
\end{tabular} & \begin{tabular}{l}
Sum of \\
Squares \\
\end{tabular} & \begin{tabular}{l}
Mean Sum of \\
Squares \\
\end{tabular} & F-value & P-value \\
\hline
Power & 3 & 0.125591 & 0.041864 & 49.79 & 0.000 \\
Scan speed & 2 & 0.207623 & 0.103812 & 123.46 & 0.000 \\
Error & 6 & 0.005025 & 0.000841 &  &  \\
Total & 11 & 0.338260 &  &  &  \\
\hline
\end{tabular}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_38cd4cb3d836d7daf3f5g-09}
\end{center}

Fig. 11. Variation of difference in wall and track widths with ED.

conductivity of the metal powder and substrate. Because of higher conductivity, the laser beam-powder interaction time governed by scan speed has significant effect on the width of the melt pool while the influence of laser power over melt pool size is limited by beam diameter.

\subsection*{3.2.2. Variation between track width and wall width}
Fig. 11 shows the variation of the difference between wall width and track width with ED. It is observed that the difference in width is positive for all values of ED and it increases with increase in ED. The Pearson correlation coefficient between the difference in width and ED is 0.917 and $\mathrm{P}$-value is 0 , showing a strong and positive correlation between ED and difference in wall and track widths. It can be said that the greater width of wall as compared to track built at same ED values is majorly due to excess pre-heat available in previous layers that leads to spreading of melt pool and melting of excess material from the vicinity. The excess preheat increases the temperature of previous layers yielding lower thermal gradient and slower cooling rate. The difference between wall width and track width is observed to increase with ED. The reason can be attributed to increase in the preheating of lower layers at higher ED. Other factors that contribute to the increase in the width are increased denudation and increased melting due to heat conduction which are caused by the increase in energy available due to increased pre-heat energy. The values of difference between wall width and track width are linearly fit. It is also observed that for ED $\leq 150 \mathrm{~J} /$ $\mathrm{mm}^{3}$ the experimental values show very high fluctuation from the linear regression model in the range of $6 \%$ to $34 \%$. It is just because the preheating effect at these values is much lower yielding random and unstable melting and deposition of material. For ED $\geq 150 \mathrm{~J} / \mathrm{mm}^{3}$ a lower difference in linear regression model in the range of $2 \%-6 \%$ is observed. It is because the preheat effect in this case is sufficiently higher which impedes heat dissipation due to lower thermal gradient and causes uniform and reproducible material deposition. Further, highest value of difference between wall width and track width is found for $\mathrm{ED}$ values of $112.5 \mathrm{~J} / \mathrm{mm}^{3}$.

\section*{4. Conclusions}
In the present work, an indigenously designed and developed LPBF system is used to build SS316L single tracks and thin wall structures at a layer thickness of $100 \mu \mathrm{m}$. Full factorial experiments are performed by varying the laser power from $150 \mathrm{~W}$ to $450 \mathrm{~W}$ at four levels and scanning speed from $0.02 \mathrm{~m} / \mathrm{s}$ to $0.08 \mathrm{~m} / \mathrm{s}$ at three levels. Analytical and regression models are suggested to predict the track width, track depth and track area and to correlate the track geometry and LPBF parameters. The following conclusions can be derived:

i. While LPBF of tracks it was experimentally found that stable tracks are obtained in the ED range of $87.5 \mathrm{~J} / \mathrm{mm}^{3}$ and $140 \mathrm{~J} / \mathrm{mm}^{3}$. Irregular tracks are formed for ED $<87.5 \mathrm{~J} / \mathrm{mm}^{3}$ because of poor wetting and non-uniform tracks are formed for ED $>140 \mathrm{~J} / \mathrm{mm}^{3}$ because of turbulence inside the melt pool leading to melt instabilities.

ii. Track width shows positive correlation with laser power and negative correlation with scan speed and an overall positive correlation with energy density. The track width values less than beam diameter are primarily attributed to pure melting and the track width values greater than beam diameter are attributed to both pure melting and melting due to heat conduction. Laser power and scan speed show significant effect on track width though the significance of laser power is higher. An analytical model is developed to predict the track width and the model shows good prediction $(<5 \%)$ for experimental values with mean difference of $3.18 \%$ within the process window.

iii. Track depth shows positive correlation with laser power and negative correlation with scan speed and positive correlation with energy density because the depth is positively affected by the extent of laser penetration and increase in melt pool size with dwell time. Both laser power and scan speed shows significant effect on track depth although significance of laser power is higher. The laser energy incident at a given spot gets distributed across the powder layer and the substrate following Beer-Lambert's law and therefore a logarithmic regression fit for track depth values at different ED show best fit within the process window with chisquare value 0.022 .

iv. Track area shows positive correlation with laser power and negative correlation with scan speed and a positive correlation with energy density because energy density positively affects the degree of melting occurring at a particular spot that in turn positively affects the track area. Track area is observed to vary logarithmically with ED and the mean difference between the experimental and logarithmically fit model is $7.61 \%$ within the process window. Both laser power and scan speed shows significant effect on track area although the significance of scan speed is higher. Track area is used to calculate build rate. The build rate shows negative correlation with ED. Scan speed shows nearly 7 times more significance effect on the build rate.

v. Wall width shows positive correlation with laser power and negative correlation with scan speed and a positive correlation with energy density because energy for melting at a particular layer is provided by both moving laser and preheat energy stored from previous layers which, positively affects the wall width. The wall width is observed to vary logarithmically with energy density with a mean difference of $4.8 \%$ within the process window. Both laser power and scan speed show significant effect on track width though the significance of scan speed is higher. Highest value of wall width is found to be at the value of $112.5 \mathrm{~J} / \mathrm{mm}^{3}$.

vi. The wall width is greater than the corresponding track width and the difference between the wall width and track width shows positive trend with energy density which can be attributed to preheat energy stored in previously built layers that increase with energy density. The difference values are linearly fitted and observed to\\
vary from $6 \%$ to $34 \%$ for energy density less than $150 \mathrm{~J} / \mathrm{mm}^{3}$ and from $2 \%$ to $6 \%$ for energy density greater than $150 \mathrm{~J} / \mathrm{mm}^{3}$. Highest value of difference between wall width and track width is found to be at the value of $112.5 \mathrm{~J} / \mathrm{mm}^{3}$.

vii. The present study involving LPBF of wall at $100 \mu \mathrm{m}$ thickness shows that it is possible to achieve reproducible continuous deposition with the maximum variation in track width, track depth, track area and wall width are $2 \%, 7 \%, 4.5 \%$ and $4 \%$, respectively for the process window of $87.5-140 \mathrm{~J} / \mathrm{mm}^{3}$.

viii. The study paves the way for LPBF of defect free thin walled engineering components with layer thickness of $100 \mu \mathrm{m}$. Material properties for these applications are being studied. Further, it is being planned to generate the process window for fabricating solid structures.

\section*{Declaration of Competing Interest}
None.

\section*{Acknowledgement}
S.K. Nayak and A.N. Jinoop acknowledge the financial support by Raja Ramanna Centre for Advanced Technology (RRCAT), Department of Atomic Energy, Government of India and Homi Bhabha National Institute, Mumbai. The authors thank Mr. C S Mandloi of LAM lab, RRCAT for their help during sample preparation. The authors thank the support of Mr. S. Raghavendra, Mr. Ganapati V. Kane and Mr. Anurag Chaturvedi of Proton Accelerator Group, RRCAT for providing Laser scanning facilities for 3D imaging of LPBF built thin wall samples. The authors thank Mr. S Yadav, Mr. A Sahu, Mr. K Dileep and other members of Laser Additive Manufacturing Lab at RRCAT, Indore, India.

\section*{Appendix A. Supplementary material}
Supplementary data to this article can be found online at https:// \href{http://doi.org/10.1016/j.optlastec.2019.106016}{doi.org/10.1016/j.optlastec.2019.106016}.

\section*{References}
[1] A.N. Jinoop, C.P. Paul, K.S. Bindra, Laser assisted direct energy deposition of Hastelloy-X, Opt. Laser Technol. 109 (2019) 14-19.

[2] C.P. Paul, A.N. Jinoop, K.S. Bindra, Metal additive manufacturing using lasers, in: R. Singh, J.P. Davim (First Eds.), Additive Manufacturing : applications and innovations, CRC Press, Boca Raton, 2018, pp. 37--88.

[3] A. Kumar, C.P. Paul, A.K. Pathak, P. Bhargava, L.M. Kukreja, Optics \& Laser Technology A finer modeling approach for numerically predicting single track geometry in two dimensions during Laser Rapid Manufacturing, Opt. Laser Technol. 44 (2012) 555-565.

[4] C. Bruna-rosso, A.G. Demir, B. Previtali, Selective laser melting finite element modeling: validation with high-speed imaging and lack of fusion defects prediction, Mater. Des. 156 (2018) 143-153.

[5] J. Zhuang, Y. Lee, W. Hsieh, A. Yang, Determination of melt pool dimensions using DOE-FEM and RSM with process window during SLM of Ti6Al4V powder, Opt. Laser Technol. 103 (2018) 59-76.

[6] Z. Yan, W. Liu, Z. Tang, X. Liu, N. Zhang, M. Li, Review on thermal analysis in laserbased additive manufacturing, Opt. Laser Technol. 106 (2018) 427-441.\\
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[12] E.J. Schwalbach, S.P. Donegan, M.G. Chapman, K.J. Chaput, M.A. Groeber, A discrete source model of powder bed fusion additive manufacturing thermal history, Addit. Manuf. 25 (2019) 485-498.

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[14] M. Guo, D. Gu, L. Xi, L. Du, H. Zhang, J. Zhang, Formation of scanning tracks during Selective Laser Melting (SLM) of pure tungsten powder : morphology, geometric features and forming mechanisms, Int. J. Refract. Metals Hard Mater. 79 (2019) 37-46.

[15] I. Yadroitsev, I. Smurov, Selective laser melting technology: from the single laser melted track stability to 3D parts of complex shape, Phys. Procedia. 5 (2010) 551-560.

[16] F. Calignano, G. Cattano, D. Manfredi, Manufacturing of thin wall structures in AlSi10Mg alloy by laser powder bed fusion through process parameters, J. Mater. Process. Tech. 255 (2018) 773-783.

[17] K. Lin, L. Yuan, D. Gu, Influence of laser parameters and complex structural features on the bio-inspired complex thin-wall structures fabricated by selective laser melting, J. Mater. Process. Tech. 267 (2019) 34-43.

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[19] H. Schleifenbaum, A. Diatlov, C. Hinke, Direct photonic production: towards high speed additive manufacturing of individualized goods, Prod. Eng. Res. Devel. 5 (2011) 359-371.

[20] A.V. Gusarov, I. Smurov, Modeling the interaction of laser radiation with powder bed at selective laser melting, Physics Procedia. 5 (2010) 381-394.

[21] Stainless Steel - Grade 316L - Properties, Fabrication and Applications (UNS S31603). < \href{https://www.azom.com/article.aspx?ArticleID}{https://www.azom.com/article.aspx?ArticleID} = $2382>$ (accessed 02 August 2019).

[22] W.E. King, et al., Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing, J. Mater. Process. Tech. 214 (2014) 2915-2925.

[23] Stainless Steel - Grade 316 (UNS S31600). < \href{https://www.azom.com/properties}{https://www.azom.com/properties}. aspx?ArticleID = $863>$, 2019 (accessed 2 August 2019).

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[29] P. Mishra, et al., Energy efficiency contributions and losses during selective laser melting, J. Laser Appl. 30 (2018) 032304-1-032304-9.

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\title{EBM-manufactured single tracks of Alloy 718: Influence of energy input and focus offset on geometrical and microstructural characteristics }


\author{Paria Karimi ${ }^{\text {a,* }}$, Esmaeil Sadeghi ${ }^{a}$, Joakim Ålgårdh ${ }^{a, b}$, Joel Andersson ${ }^{a}$\\
a Department of Engineering Science, University West, 46186 Trollhättan, Sweden\\
${ }^{\mathrm{b}}$ Powder Materials \& Additive Manufacturing, Swerea KIMAB AB, 16440 Kista, Sweden}
\date{}


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\maketitle


\section*{A R T I C L E I N F O}
\section*{Keywords:}
Powder bed fusion

Electron beam melting

Experimental design

Solidified microstructure

Single track

Geometrical characteristics

Alloy 718

\begin{abstract}
A B S T R A C T Electron beam melting-powder bed fusion (EBM-PBF) is an additive manufacturing process, which is able to produce parts in layer-by-layer fashion from a 3D model data. Currently application of this technology in parts manufacturing with high geometrical complexity has acquired growing interest in industry. To recommend the EBM process into industry for manufacturing parts, improved mechanical properties of final part must be obtained. Such properties highly depend on individual single melted track and single layer. In EBM, interactions between the electron beam, powder, and solid underlying layer affect the geometrical (e.g., re-melt depth, track width, contact angle, and track height) and microstructural (e.g., grain structure, and primary dendrite arm spacing) characteristics of the melted tracks. The core of the present research was to explore the influence of linear energy input parameters in terms of beam scanning speed, beam current as well as focus offset and their interactions on the geometry and microstructure of EBM-manufactured single tracks of Alloy 718. Increased scanning speed led to lower linear energy input values $(<0.9 \mathrm{~J} / \mathrm{mm})$ in an specific range of the focus offset $(0-10 \mathrm{~mA})$ which resulted in instability, and discontinuity of the single tracks as well as balling effect. Decreasing the scanning speed and increasing the beam current resulted in higher melt pool depth and width. By statistical evaluations, the most influencing parameters on the geometrical features were primarily the scanning speed, and secondly the beam current. Primary dendrite arm spacing (PDAS) slightly decreased by increasing the scanning speed using lower beam current values as the linear energy input decreased. By increasing the linear energy input, the chance of more equiaxed grain formation was high, however, at lower linear energy input, mainly columnar grains were observed. The lower focus offset values resulted in more uniform grains along the <001〉 crystallographic direction.
\end{abstract}

\section*{1. Introduction}
In recent years, the electron beam melting-powder bed fusion (EBMPBF) technique has shown a considerable progress in manufacturing geometrically complex and highly dense parts [1-5]. The essential operation in EBM is track-by-track and successive layer-by-layer melting of feedstock powder to form a final 3D part [6-10]. A necessary condition for obtaining a high quality additively manufactured part is stability of geometrical characteristics of individual single tracks and a good cohesion between each melted track.

In EBM, the interaction between the electron beam, powder, and solid underlying layer involves phenomena such as heat transfer (e.g. radiation, absorption, and conduction), phase transformations, fluid flow driven by surface tension gradients, mass transfer within the molten pool, as well as chemical reactions [8,11]. By modification of process parameters, it is possible to avoid various undesirable effects such as geometrical irregularity of the melted track or balling effect which could lead to poor mechanical bonding between tracks and layers $[12,13]$. This explains the essential need for developing a comprehensive scientific understanding of the EBM process related phenomena and its process parameters on the beam-powder-solid underlying layer interactions.

It has been found that energy input is the most significant process parameter in PBF processes in term of microstructural characteristics $[1,12,14,15]$. The energy input $\left(\mathrm{J} / \mathrm{m}^{3}\right)$ is a measure for the averaged applied energy per volume of material during the scanning of a single layer; see Eq. (1) [23]. For a single track, calculation of energy per unit length of track so-called "linear energy input" is the ratio between beam power and scanning speed, see Eq. (2) [16]. Variations in the linear energy input parameters (scanning speed and beam current) [17,18], as
\footnotetext{\begin{itemize}
  \item Corresponding author.
\end{itemize}

E-mail address: \href{mailto:paria.karimi@hv.se}{paria.karimi@hv.se} (P. Karimi).
}
well as the focus offset generate different geometrical features in the samples.

Energy input $\left(\mathrm{J} / \mathrm{mm}^{3}\right)$


\begin{equation*}
=\frac{\text { voltage }(\mathrm{kV}) \times \operatorname{current}(\mathrm{mA})}{\text { scanning speed }\left(\frac{\mathrm{mm}}{\mathrm{s}}\right) \times \text { layer thickness }(\mu \mathrm{m}) \times \text { Line offset }(\mu \mathrm{m})} \tag{1}
\end{equation*}


Linear energy input $(\mathrm{J} / \mathrm{mm})=\frac{\text { voltage }(\mathrm{kV}) \times \operatorname{current}(\mathrm{mA})}{\text { scanning speed }\left(\frac{\mathrm{mm}}{\mathrm{s}}\right)}$

The feedstock powder properties also has a significant effect on the formation of a sound and continuous single track with a low amount of irregularities [19]. The mechanism of distortion, irregularities and formation of drops may be associated with thermo-physical properties of the powder, peculiarities of its deposition and spreading, layer thickness, and linear energy input parameters of the beam [20]. The value of linear energy input strongly influences the interaction between beam, powder, and solid underlying layers and therefore has to be carefully controlled in EBM. Moreover, the focus offset is the value of current used by focusing coils located in the electron gun column to concentrate the beam, which significantly affects the geometry of melted tracks. Altering the track geometry is an approach to change the thermal gradient and solidification condition of the melt pool [21].

Furthermore, the formation of satellites particles typically occurs in EBM due to; molten material spattering, partial melting of powder in peripheral region of the beam spot [12,15], remolten drops surrounding and their metallurgical contacts with the track. This can eventually provoke the formation of pores in AM parts and influence surface roughness [22,23]. Its effect is serious for the internal surfaces of the parts, especially for fine channels and thin-walled structures. Therefore, there is an essential need to find out an appropriate process window for melting of a stable and continuous single track without those challenges.

In this study, the role of the main influencing linear energy input parameters (e.g., scanning speed and beam current) as well as focus offset on the formation of a single track were investigated. Microstructural (e.g., grain structure, and primary dendrite arm spacing) and geometrical (e.g., re-melted depth, track width, contact angle, and track height) characteristics were investigated in correlation to changes in these parameters. A statistical analysis of variance was performed using a design of experiments (DoE) approach in order to quantify statistical significance of these parameters on the track geometry and microstructure.

\section*{2. Material and Experimental Setup}
\subsection*{2.1. Material}
Plasma-atomized Alloy 718 powder supplied by Arcam AB (Mölndal, Sweden) was used as feedstock material in the EBM process. According to the specification from the supplier, the particle size distribution of the virgin powder was $+45-105 \mu \mathrm{m}$; however, the feedstock powder was a mixture of virgin and re-used powder and particle size distribution of the mixture was $+45-145 \mu \mathrm{m}$. The provided nominal chemical composition of the powder by the supplier is given in Table 1.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-02}
\end{center}

Fig. 1. Schematic of melted single track on the stand.

\subsection*{2.2. EBM Setup}
The experiments were carried out using an A2X EBM machine (Arcam AB, Mölndal, Sweden) with a constant gun-accelerating voltage $(60 \mathrm{kV})$. The machine uses the software version of 4.2.201. The sintering and melting process began once the preheat temperature of $1023^{\circ} \mathrm{C}$ was reached. The layer thickness and power calculation function were constantly held at $75 \mu \mathrm{m}$ and off-mode respectively during the entire building process.

Samples in the shape of single tracks were produced with $20 \mathrm{~mm}$ length according to Fig. 1, positioned on a stainless steel build plate. As shown in Fig. 1, an additional substrate (stand) was printed using standard Arcam process parameters as a base before the single tracks were laid out [6]. The main benefit of using the stand is to avoid dilution effects between the melted tracks and build plate, which contribute to changes in melting temperature of the powder. The distance between each stand was $5 \mathrm{~mm}$ and height of each stand was $8 \mathrm{~mm}$ from the build plate.

\subsection*{2.3. Experimental Design and Characterization of Microstructure}
A full factorial design of experiment (DoE) using MODDE 12 (Umetrics, Umea, Sweden) software in three levels was applied to screen the three parameters (scanning speed, beam current, and focus offset). The full factorial design considered all interactions between the selected parameters (e.g. scanning speed $\times$ beam current, scanning speed $\times$ focus offset, and focus offset $\times$ beam current). To cover the full range of the process parameters, three values of the main process parameters were selected, presented in Table 2. Based on the values in the table, the complete DoE parameter run is presented in Table 3. Each run in the DoE was repeated four times for each single track and in each single track; two cross sections (see Fig. 2a) were evaluated to have enough statistical analysis during the study. The responses to the DoE were both geometrical characteristics, such as melt pool width (w), track height (d1), re-melt depth/penetration depth (d2), and average of contact angle $\left(\Theta=\frac{\theta_{1}+\theta_{2}}{2}\right)$, shown in Fig. 2b, and microstructural characteristics, such as primary dendrite arm spacing (PDAS) and grain structure in the cross section of the single tracks.

The effectiveness of the three parameters on each studied response is shown with a plus or minus ( + and - ) sign as well as a number in percent. While the percentage gives the level of effectiveness, the plus and minus signs show the incremental and decreasing effects of the studied parameter on the pre-defined response, respectively.

All the samples were sectioned at a distance of $7 \mathrm{~mm}$ from the start and end of the single tracks (see Fig. 2a), perpendicular to the scanning direction and ground using SiC paper up to 1200 grit. The ground samples were then polished using a $0.05 \mu \mathrm{m} \mathrm{SiC}$ suspension. The

Table 1

Chemical composition of the Alloy 718 powder.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Element & $\mathrm{Ni}$ & Co & $\mathrm{Cr}$ & Mo & $\mathrm{Ti}$ & Mn & $\mathrm{Nb}$ & $\mathrm{P}$ & $\mathrm{Ta}$ & $\mathrm{Al}$ & $\mathrm{Fe}$ & $\mathrm{Si}$ & $\mathrm{S}$ & $\mathrm{C}$ \\
\hline
wt $\%$ & 54.11 & 0.04 & 19.0 & 2.99 & 1.02 & 0.12 & 4.97 & 0.004 & $<0.01$ & 0.52 & Bal. & 0.06 & $<0.001$ & 0.03 \\
\hline
\end{tabular}
\end{center}

Table 2

Levels of each investigated EBM process parameters.

\begin{center}
\begin{tabular}{lcccc}
\hline
\multirow{2}{*}{No.} & Parameter & \multicolumn{2}{l}{Level of each parameter} &  \\
\cline { 3 - 5 }
 &  & Minimum level & Center level & Maximum level \\
\hline
1 & Beam current (mA) & 7 & 11 & 15 \\
2 & \begin{tabular}{c}
Beam scanning speed \\
$(\mathrm{mm} / \mathrm{s})$ \\
\end{tabular} & 300 & 650 & 1000 \\
3 & Focus offset (mA) & 0 & 5 & 10 \\
\hline
\end{tabular}
\end{center}

Table 3

Full factorial screening design of each investigated EBM process parameter.

\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
\begin{tabular}{l}
Trail no \\
$\#$ \\
\end{tabular} & \begin{tabular}{l}
Scanning speed \\
$(\mathrm{mm} / \mathrm{s})$ \\
\end{tabular} & \begin{tabular}{l}
Beam current \\
$(\mathrm{mA})$ \\
\end{tabular} & \begin{tabular}{l}
Focus offset \\
$(\mathrm{mA})$ \\
\end{tabular} & \begin{tabular}{l}
Linear energy \\
input $(\mathrm{J} / \mathrm{mm})$ \\
\end{tabular} \\
\hline
1 & 300 & 15 & 0 & 3.00 \\
\hline
2 & 300 & 15 & 5 & 3.00 \\
\hline
3 & 300 & 15 & 10 & 3.00 \\
\hline
4 & 300 & 11 & 0 & 2.20 \\
\hline
5 & 300 & 11 & 5 & 2.20 \\
\hline
6 & 300 & 11 & 10 & 2.20 \\
\hline
7 & 300 & 7 & 0 & 1.40 \\
\hline
8 & 300 & 7 & 5 & 1.40 \\
\hline
9 & 300 & 7 & 10 & 1.40 \\
\hline
10 & 650 & 15 & 0 & 1.38 \\
\hline
11 & 650 & 15 & 5 & 1.38 \\
\hline
12 & 650 & 15 & 10 & 1.38 \\
\hline
13 & 650 & 11 & 0 & 1.02 \\
\hline
14 & 650 & 11 & 5 & 1.02 \\
\hline
15 & 650 & 11 & 10 & 1.02 \\
\hline
16 & 1000 & 15 & 0 & 0.90 \\
\hline
17 & 1000 & 15 & 5 & 0.90 \\
\hline
18 & 1000 & 15 & 10 & 0.90 \\
\hline
19 & 1000 & 11 & 0 & 0.66 \\
\hline
20 & 1000 & 11 & 5 & 0.66 \\
\hline
21 & 1000 & 11 & 10 & 0.66 \\
\hline
22 & 650 & 7 & 0 & 0.64 \\
\hline
23 & 650 & 7 & 5 & 0.64 \\
\hline
24 & 650 & 7 & 10 & 0.64 \\
\hline
25 & 1000 & 7 & 0 & 0.42 \\
\hline
26 & 1000 & 7 & 5 & 0.42 \\
\hline
27 & 1000 & 7 & 10 & 0.42 \\
\hline
\end{tabular}
\end{center}

polished cross sections were electrolytically etched with $10 \mathrm{wt} \%$ oxalic acid at room temperature and $3 \mathrm{~V}$ for 5 to $10 \mathrm{~s}$ to reveal the PDAS and grain structure.

At first, the examination of microstructural features was performed using light optical microscope (LOM) (Olympus-BX60M, Tokyo, Japan) to measure the above-mentioned geometrical features. In addition, LOM was used to analyze the type of defects present, such as powderinduced pores (round shape pores) and process-induced defects (e.g., solidification shrinkage pores). Scanning electron microscope (SEM) (ZEISS EVO 50, Cambridge, UK) equipped with energy dispersive spectrometry (EDS) was used to examine PDAS. Electron backscatter diffraction (EBSD) system (GAIA3-TESCAN, Cambridge, UK) operating at accelerating voltage of $15 \mathrm{kV}$ was employed to investigate the effect of linear energy input and focus offset on grain orientation. The EBSD mappings of 10 exemplary single tracks were obtained using a step size of $3 \mu \mathrm{m}$.

\section*{3. Results}
This research was aimed to find out the effect of the three main process parameters including beam scanning speed, beam current as well as focus offset on the geometrical and microstructural features of Alloy 718 during EBM. Therefore, the geometrical features of the samples is evaluated first, and the influence of the process parameters on the microstructure is studied afterwards.

\subsection*{3.1. Geometrical Features}
Owing to the large domain of the process parameters analyzed in DoE, the melted single tracks of various shapes, dimensional characteristics, and stabilities were examined, see Table 3. It is pertinent to mention that the conclusions from these results can be given only for a definite type of EBM machine and a certain type of feedstock powder. Thus, comparison of the results can be done only for similar machine systems or powders.

\subsection*{3.1.1. Continuity of Single Track}
As given in Table 3 and shown in Fig. 4, non-continuous samples were formed at linear energy input values lower than $0.9 \mathrm{~J} / \mathrm{mm}$ in the pre-defined range of focus offset. At linear energy input values range of $0.9-1.38 \mathrm{~J} / \mathrm{mm}$, the melted single tracks were continues. However, it should be mentioned that the adhesion between the solid and liquid was locally lower than the cohesive forces of the liquid in some areas of the tracks, so the tracks did partially spread on the stand, see Fig. 3.

Fig. 4(a-b) displays the preliminary observation of the top surface of the single tracks with different values of the scanning speed, beam current, and focus offset. According to Eq. (2), a high scanning speed and low beam current results in low values of linear energy input. Such low linear energy input values $(<0.9 \mathrm{~J} / \mathrm{mm}$ ) was indicated to be insufficient for achieving a complete and continuous melt. The parameter settings \# 25-27 from Table 3 had the lowest amount of the linear energy input values and as it is shown in Fig. 4a, a few droplets were only formed on the stand. By increasing the beam current for low scanning speeds $(<650 \mathrm{~mm} / \mathrm{s}$ ), continues single tracks with smooth surface were obtained (\# 1 and \# 4 as shown in Fig. 4a).

Fig. 4b shows the effect of focus offset for constant linear energy input values (e.g., 0.9 (\# 16-18), 1.02 (\# 13-15), and $1.38 \mathrm{~J} / \mathrm{mm}$ (\# $10-12)$ ). It was found that by increasing the focus offset in each linear energy input values, the stability of the single tracks increased which could be due to formation of the deeper melt pool, as illustrated in Table 4.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-03}
\end{center}

Fig. 2. LOM micrographs of a) top view of single track, process parameter \#1 from Table 3, and b) geometrical measurement from cross section of a single track.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-04}
\end{center}

Fig. 3. Topographical SEM image (BSE mode) of a part of sample \# 15

\subsection*{3.1.2. Melt Pool Dimension}
The LOM images from cross sections presented in Fig. 5 show the geometrical features such as; re-melt depth (d2), melt pool width (w), track height (d1), and contact angle ( $\theta$ ), see Fig. 2b. The statistical measurement reported in Table 4 were imported to the DoE model to estimate the effect of beam current and scanning speed for different focus offset values ( 0,5 , and $10 \mathrm{~mA}$ ) on the geometrical features using $4 \mathrm{D}$ contour graphs (4D: 3 process parameters plus one response parameter), see Fig. 6.

From Fig. 6(a1-a3), it can be noted that by increasing the beam current for lower values of the scanning speed (increased linear energy input), the width of melt pool increased in all three focus offset values. The maximum and minimum values of the melt pool width $(\mathrm{w})$ in the continuous tracks were $821 \pm 38$, and $443 \pm 42 \mu \mathrm{m}$ belonged to samples \#3 and 18, respectively. Based on the DoE analysis the main affecting factors on the melt pool width were the scanning speed, and beam current with affecting coefficients of $-56 \%$ and $+31 \%$, respectively. According to the DoE calculations, the effect of focus offset and the interaction among all the three parameters (scanning speed $\times$ beam current; scanning speed $\times$ focus offset; and beam current $\times$ focus offset) were insignificant.

The re-melt depth also increased in a similar manner as the melt pool width; see Fig. 6(b1-b3). Owing to the highest linear energy input values in each certain focus offset, samples $\# 1,2$, and 3 showed the highest re-melt depth, around $448 \pm 28, \quad 511 \pm 22$, and $478 \pm 30 \mu \mathrm{m}$, respectively. Thus, by considering consolidated layer thickness of $75 \mu \mathrm{m}, 7-8$ underlying layers were re-melted. The main influential parameters were scanning speed and beam current with $-158 \%$ and $+81 \%$ affecting coefficient, respectively. In addition, focus offset was also found to have a minimal effect on the re-melt depth. The effect of focus offset was estimated by DoE to be around $+14 \%$. The effect of interaction parameters was also insignificant. This is a clear indication that enhancing the linear energy input values resulted in a large melt pool geometry. In addition, by increasing the focus offset, the melt pool width decreased whereas the re-melt depth increased, see Fig. 6.

\subsection*{3.1.3. Track Height}
It was observed that for the focus offset value of $0 \mathrm{~mA}$, when the linear energy input value was increased, the track height increased. However, for the focus offset value of $5 \mathrm{~mA}$, the track height appears to\\
\includegraphics[max width=\textwidth, center]{2024_03_10_825bcba88c9715ece761g-04(1)}

Fig. 4. Top view of selected samples using different process parameter settings, a) effect of scanning speed and beam current on the morphology of the samples, and b) effect of focus offset on the morphology of the samples.

Table 4

Full factorial screening design with the geometrical responses.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Trail no \# & Continuity of track & Re-melt depth-d2 $(\mu \mathrm{m})$ & Track width-w $(\mu \mathrm{m})$ & Track height-d1 $(\mu \mathrm{m})$ & Contact angle- $\theta\left({ }^{\circ}\right)$ \\
\hline
1 & Continuous & $448 \pm 28$ & $800 \pm 47$ & $129 \pm 25$ & $44 \pm 15$ \\
\hline
2 & Continuous & $511 \pm 22$ & $821 \pm 43$ & $89 \pm 24$ & $33 \pm 11$ \\
\hline
3 & Continuous & $478 \pm 30$ & $822 \pm 38$ & $111 \pm 28$ & $49 \pm 14$ \\
\hline
4 & Continuous & $319 \pm 26$ & $732 \pm 50$ & $101 \pm 21$ & $37 \pm 13$ \\
\hline
5 & Continuous & $371 \pm 25$ & $706 \pm 26$ & $96 \pm 19$ & $49 \pm 10$ \\
\hline
6 & Continuous & $423 \pm 33$ & $705 \pm 35$ & $88 \pm 22$ & $43 \pm 14$ \\
\hline
7 & Continuous & $210 \pm 35$ & $603 \pm 49$ & $95 \pm 29$ & $33 \pm 11$ \\
\hline
8 & Continuous & $226 \pm 30$ & $580 \pm 18$ & $150 \pm 24$ & $62 \pm 19$ \\
\hline
9 & Continuous & $245 \pm 27$ & $566 \pm 25$ & $121 \pm 19$ & $55 \pm 18$ \\
\hline
10 & Continuous & $225 \pm 21$ & $590 \pm 32$ & $121 \pm 18$ & $45 \pm 8$ \\
\hline
11 & Continuous & $232 \pm 16$ & $554 \pm 41$ & $139 \pm 17$ & $58 \pm 5$ \\
\hline
12 & Continuous & $180 \pm 21$ & $529 \pm 42$ & $133 \pm 15$ & $49 \pm 10$ \\
\hline
13 & Non-continuous & - & - & - & - \\
\hline
14 & Continuous & $170 \pm 22$ & $453 \pm 43$ & $130 \pm 23$ & $63 \pm 14$ \\
\hline
15 & Continuous & $122 \pm 21$ & $445 \pm 22$ & $173 \pm 24$ & $69 \pm 12$ \\
\hline
16 & Non-continuous & - & - & - & - \\
\hline
17 & Non-continuous & - & - & - & - \\
\hline
18 & Continuous & $91 \pm 16$ & $444 \pm 42$ & $163 \pm 21$ & $68 \pm 16$ \\
\hline
19 & Non-continuous & - & - & - & - \\
\hline
20 & Non-continuous & - & - & - & - \\
\hline
21 & Non-continuous & - & - & - & - \\
\hline
22 & Non-continuous & - & - & - & - \\
\hline
23 & Non-continuous & - & - & - & - \\
\hline
24 & Non-continuous & - & - & - & - \\
\hline
25 & Non-continuous & - & - & - & - \\
\hline
26 & Non-continuous & - & - & - & - \\
\hline
27 & Non-continuous & - & - & - & - \\
\hline
\end{tabular}
\end{center}

be almost constant regardless of the total linear energy input, see Fig. 6(c1-c3). In contradiction for the final focus offset value of $10 \mathrm{~mA}$, a lower linear energy input value resulted in a taller track height. Based on the statistical measurements in this study, the range of the track height for stable and continuous tracks were about $88-173 \mu \mathrm{m}$ with a coefficient of variation (ratio of the standard deviation to the mean value) of the track height about $26 \%-37 \%$. It was found that none of the investigated parameters had an effective role on the track height in this pre-defined range.

\subsection*{3.1.4. Contact Angle}
According to Fig. 6(d1-d3), at all the three focus offset values, by decreasing the linear energy input (low beam current and higher scanning speed), the contact angle increased as well. Therefore, it was found by DoE that the main effective parameter on the contact angle was the scanning speed with an affecting factor of $+27 \%$, whereas the other parameters and interactions did not show any significant effect on the contact angle. The highest contact angle belonged to the sample \# 18 with $67 \pm 16^{\circ}$ and the lowest belonged to the sample \# 2 with $33 \pm 11^{\circ}$, which had the highest linear energy input value.

\subsection*{3.2. Solidified Microstructure of Single Tracks}
Fig. 7 shows that the microstructure of the melted single tracks with different process conditions consisted of an austenite dendritic structure with submicron-scale primary dendrite-cell spacing. Fig. 7a shows that the grains and direction of dendrites-cells was faced towards the center point of the melt pool which had a fine groove on the top surface due to the interaction of the beam and melt pool. The image contrast disclosed in the SEM images (Fig. 7(a-b)) shows dependence on the crystallographic orientation of the single grains and as such describes the orientation of grains in the polycrystalline domain. If crystal planes are parallel to the incident beam in SEM, the electrons penetrate deeper and the grains appear darker in the image. Fig. 7(a1) shows the melt pool at a higher magnification. The presence of extensive solidification shrinkage pores can be seen in interdendritic areas (both primary and secondary spacing) mainly in the top-center area of the melt pool which is reported as the last area to be solidified [24]. Fig. 7(a2) illustrates that the direction of the dendrites was altered from the stand to the new melt pool owing to the high thermal gradient in that direction. As a result of the higher cooling rate at the bottom of the melt pool rather than the top, very fine dendrites-cells were observed at the bottom of the melt pool with small secondary arms where the heat transfer to the stand was significant. Accordingly, observation of larger secondary arms can be explained at the top areas, see Fig. $7 \mathrm{~b}$.

\subsection*{3.2.1. Effect of Linear Energy Input and Focus Offset on Primary Dendrite Arm Spacing (PDAS)}
The dendrite-cell spacing was measured in the cross section of all the melted tracks. The maximum and minimum average values (obtained from 15 measurements in each sample) were $5.5 \pm 0.4$ and $2.8 \pm 0.5 \mu \mathrm{m}$ for samples \# 3 and 18 , respectively. As a general trend, the dendrite-cell spacing decreased by decreasing the linear energy input value. The scanning speed and beam current had statistically significant influence on the dendrite-cell spacing. According to DoE, the effect of the scanning speed factor was established to about $-32 \%$ for the dendrite-cell spacing in any place of the cross section of the tracks. The estimated size effect of the beam current factor on the dendrite-cell spacing in the cross section of the tracks was $+20 \%$. In addition, from the 4D contour response images, higher values of the focus offset caused coarser dendrite-cell spacing (Fig. 8).

\subsection*{3.2.2. Effect of Linear Energy Input on Grain Orientation}
The EBSD results in Fig. 9 showed that at the linear energy input value of $0.9 \mathrm{~J} / \mathrm{mm}$ in which the penetration depth was the lowest, mainly epitaxial growth was obtained from the partially melted grains from the stand. Increasing the linear energy input ( 2.2 and $3.0 \mathrm{~J} / \mathrm{mm}$ ) led to a larger melt pool, where the chance of crystallization and observation of new small grains became high. It can therefore be concluded that higher linear energy input led to more equiaxed microstructure whereas relatively lower linear energy input results in a more or less columnar microstructure.

\subsection*{3.2.3. Effect of Focus Offset on Grain Orientation}
The effect of the focus offset on the orientation of the grains was shown by the EBSD mapping in Fig. 10 for samples \#1, 2, 3 and for\\
a)

$$
\text { Focus offset }=0
$$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-06(1)}
\end{center}

b)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-06}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-06(2)}
\end{center}

Fig. 5. Cross section of each track, a) focus offset $=0 \mathrm{~mA}$, b) focus offset $=5 \mathrm{~mA}$, and c) focus offset $=10 \mathrm{~mA}$.

linear energy input of $3.0 \mathrm{~J} / \mathrm{mm}$ and samples \#4, 5, 6 for linear energy input of $2.2 \mathrm{~J} / \mathrm{mm}$. It was observed that for a focus offset of $0 \mathrm{~mA}$, the grain orientations were mainly sustained in $\langle 001\rangle$ direction and the misorientation was slightly lower than for the focus offset of $10 \mathrm{~mA}$. This result was confirmed in the second row of the EBSD mapping in Fig. 10.

\section*{4. Discussion}
\subsection*{4.1. Geometrical Characteristics}
As seen in Fig. 3, localized adherence of the single track on the stand is due to several complicated reasons. Firstly, it can be due to the beam fluctuations while scanning. During the melting process, beam has some fluctuations, which could affect the interaction between the beam and powders, and subsequently on the wettability of the melted material on the stand $[26,27]$. Secondly, the roughness of the underlying layer is also important [9,28]. At points like point (1) in Fig. 11, which has deeper valley compared to the points like point (2), the remelted depth is different which can lead to different Marangoni effects. These phenomena can cause different adherence along the single track. Thirdly, it can be due to powder particle levelling before melting [12]. As shown in Fig. 11, the powders were not perfectly distributed on the stand, so one reason can be the presence of the partially sintered powders. Thus, the thickness of powder along the single track also is not constant and has some deviations, which can affect the adherence of the melted track on the stand. In addition to these reasons, other phenomenon during melting of the powders like powder spattering due to the electrical charges of powder particles in some points along the track, can influence on the shape of the single track [1].

The consistency and continuity of the single tracks are attributed to many factors, such as powder particle distribution [29], melt pool dynamics [30], or surface tension of molten material. The variations in the linear energy input and focus offset generated different behavior of the single tracks as seen in Fig. 4. As shown in Fig. 4a, for the high linear energy input values, a continuous melt pool was formed, which was due to the sufficient linear energy input to be imported on the powders. In addition, higher linear energy input values can lead to capillary and thermo-capillary flows (Marangoni effect) which significantly affect the shape of the track and its continuity [25]. Fig. 4b also showed less chance of gap formation in higher focus offset values in a same amount of scanning speed and beam current. In order to rationalize this behavior, looking at the melt pool width and depth results at Fig. 6 showed that higher focus offset has sharper beam. A sharper beam increases the energy density, which increases energy absorption and leads to a reduction in the exposure area. A less focus beam reduces the energy density, i.e., energy absorption and increases the exposure area, which further leads to un-melted powder [31].\\
\includegraphics[max width=\textwidth, center]{2024_03_10_825bcba88c9715ece761g-07}\\
\includegraphics[max width=\textwidth, center]{2024_03_10_825bcba88c9715ece761g-08(1)}

Fig. 7. SEM images (BSE mode) of the solidified microstructure in the cross section of the melt pool in the melted track \# 1.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-08}
\end{center}

Fig. 8. 4D contour response process parameters on primary dendrite-cell spacing.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-09(1)}
\end{center}

Linear energy input: $1.4 \mathrm{~J} / \mathrm{mm} \quad$ Linear energy input: $2.2 \mathrm{~J} / \mathrm{mm} \quad$ Linear energy: $3.0 \mathrm{~J} / \mathrm{mm}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-09(2)}
\end{center}

Sample coordinate system\\
\includegraphics[max width=\textwidth, center]{2024_03_10_825bcba88c9715ece761g-09}

Fig. 9. EBSD mapping of the grain orientations in the melt pools produced by different linear energy input values $(0.9-3.0 \mathrm{~J} / \mathrm{mm})$.

\subsection*{4.1.1. Melt Pool Dimension}
The corresponding measurements of the melt pool dimension including melt width and remelted depth were shown in Table 4 and the estimated analysis from the DoE were presented in Fig. 6. In order to rationalize the melt pool width and re-melt depth changes at different process conditions, it is known that at high values of linear energy input (low scanning speed and high beam current), a large volume of powder is involved in the track formation, and form a large melt pool size. In addition, the beam-powder-underlying solid layer interaction time increases at low scanning speed and high beam current, and consequently increases the width and re-melted depth of the melt pool [32].

\subsection*{4.1.2. Track Height}
Another geometrical feature investigated was the height of a track which is primarily determined by powder layer thickness and most likely varies depending on the stand roughness, particularities of powder raking, levelling and spreading, and geometrical characteristics of the powder [12]. As shown in Fig. 6(c1-c3), different results was obtained in the various focus offset values which shows not clear relationship between the process parameters and track height.

\subsection*{4.1.3. Contact Angle}
From the literature [16], it has been found that the contact angle track height is a function of track height and melt pool width. For instance, with an increase in the track height, the contact angle also increases, see Eq. (3);

$\Theta=2 \times \tan ^{-1}\left(\frac{2 \times d 1}{w}\right)$

where $\theta$ is contact angle $\left({ }^{\circ}\right), \mathrm{d} 1$ is track height $(\mu \mathrm{m})$ and $\mathrm{w}$ is melt pool width $(\mu \mathrm{m})$. Additionally, the contact angle is a function of the wetting phenomenon in EBM as well, and it implies that the molten powder spreads on the stand or previously melted layer, instead of balling up on its surface [33], see Fig. 3. It is also known that wetting ridges can affect the fluid behavior and spreading process during the PBF processing [34]. By increasing the beam current, the temperature in the melt pool also increases [12]. High temperature can lead to the thermo-capillary phenomena known as the Marangoni effect and can expand the melt pool [35]. This leads to the enlargement in the curvature of the liquid surface, and increase in the contact angle. However, the liquid-surface tension generally decreases at higher temperatures where wettability and subsequent reduction in the contact angle are promoted [12,34].

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-10(1)}
\end{center}

Fig. 10. EBSD mapping of the grain orientations in melt pools using different linear energy input ( 2.2 and $3.0 \mathrm{~J} / \mathrm{mm}$ ) values by altering focus offset ( 0,5 , and $10 \mathrm{~mA}$ ).

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_825bcba88c9715ece761g-10}
\end{center}

Fig. 11. Schematic view of the powders on the stand showing the roughness of the stand surface.

Thus, the contact angle is a result of several phenomenon such as surface tension, and Marangoni effect, etc. In addition, as seen in Fig. 6(d1-d3), by decreasing the focus offset, the melt pool became wider and shallower, which implied lower contact angle in low predefined focus offset.

\subsection*{4.2. Solidified Microstructure of Single Tracks}
In EBM, the beam spot size is about several hundreds of microns (compared to a few millimeters in some other AM processes such as laser metal deposition or laser cladding) resulting in that the melt pool is significantly small $[36,37]$. This leads to a very rapid solidification process, and as a result a fine dendrite/cell spacing [6,12,23,38]. The dendrite-cellular microstructure apparent in the material is illustrated in Fig. 7 and usually occurs as a consequence of constitutional supercooling $[35,39,40]$. The degree of constitutional supercooling depends on the actual temperature gradient into the liquid as well as the solute enrichment of the liquid in front of the solid-liquid interface [35]. For a given solute concentration profile, the highest temperature gradient corresponds to planar growth. As the gradient decreases, the crystallization mode changes from planar to cellular, cellular to dendritic and, finally, to dendritic solidification mode [35]. Characteristic length of the microstructure is governed by the cooling rate values, i.e., $\mathrm{R}$ (solidification rate) $\times \mathrm{G}$ (thermal gradient). The increase in the cooling rate results in the finer microstructural features (i.e. smaller dendritecell spacing, and finer dendrites) [35].

As seen in Fig. 8, PDAS was increased in higher linear energy input values which could be due to a resulted big melt pool and slower heat dissipation compared to a small melt pool which can be cool down faster [9]. The reason for slightly coarser PDAS at higher focus offset can be owing to deeper melt pool as showed in Fig. 6.

\subsection*{4.2.1. Effect of Linear Energy Input on Grain Structure}
The beam parameters not only change the grain size and orientation, but also alter some important process properties such as the highest temperature inside melt pool, the dimension of melt pool and even the melt pool mode (conductive and keyhole). The general grain structure for all AM-processed materials is a directional columnar grain structure [4,14,25]. In fact, during the solidification, the melt pool boundary acts as a nucleation site for new grains, where the new grains start to grow towards the beam incidence point.

As showed in Fig. 9, the nucleation of the new grains occurred at the bottom of the melt pool as clarified by the white dashed lines. Grains with the most favorably orientation with respect to the temperature gradient at the liquid-solid interface grow further where less favorably grains were terminated after a short growth close to the melt pool boundary. This means that if the favorite orientation of a grain is more parallel to the thermal gradient vectors at the melt pool boundary, the chance of extensive grain growth is higher. As a result of this competitive grain growth, many small grains can be observed near the melt pool boundary. The large temperature gradient inside the melt pool leads to a high growth rate of elongated grains and thus little chance for new sites for grains to nucleate in the bulk melt during the solidification $[23,33]$. A closer look at the melt pool boundary in Fig. 9 revealed that there was an intense competitive grain growth at the initial stage of solidification.

Heat transfer from the superheated melt into the bottom cooled solid part is one of the most important phenomena during EBM. As shown in Fig. 7(a-b), by increasing line energy, the melt pool size was\\
extended and resulted in a high re-melted depth and melt pool width. The EBSD results in Fig. 9 showed that at the linear energy input value of $0.9 \mathrm{~J} / \mathrm{mm}$ in which the penetration depth was the lowest, mainly epitaxial growth was obtained from the partially melted grains from the stand. The primary reason is that most heat leaves the melt pool mainly by heat conduction via the bottom of the melt pool. Thus, due to the high thermal gradient at bottom of the melt pool and its decrease in the upper surface of the melt pool, the epitaxial growth of the columnar grains is promoted [25].

Increasing the linear energy input values, $(2.2$ and $3.0 \mathrm{~J} / \mathrm{mm})$ led to a larger melt pool, where the chance of crystallization and observation of new small grains became high. The heat flux towards the stand is the source of solidification and the crystallization is mainly governed by that condition [25]. It can therefore be concluded that higher energies promotes nucleation of new equiaxed grains whereas relatively lower energies results in a more or less columnar microstructure.

\subsection*{4.2.2. Effect of Focus Offset on Grain Orientation}
For the lowest focus offset values $(0 \mathrm{~mA})$, sample \#1 in the first row and sample \#4 in the second row revealed the lowest re-melt depth. For a low re-melt depth, the degree of the thermal gradient became higher in the direction perpendicular to the layers, which resulted in less misorientation degree of the grains in the microstructure. By increasing the temperature gradient along the build direction inside the melt pool, more uniform grains formed inside the melt due to an improved condition for competitive grain growth [41,42].

\section*{5. Conclusions}
The effect of three main process parameters (scanning speed, beam current, and focus offset) on EBM-manufactured single tracks of Alloy 718 was investigated and further analyzed by the use of an experimental design approach. The approach aimed to identify the impact of the three parameters on the geometrical features of the single tracks, such as melt pool width (w), height of a track (d1), re-melt depth (d2), and contact angle $(\theta)$. In addition, the effect of these parameters on grain orientation and primary dendrite arm spacing (PDAS) were also addressed.

\begin{itemize}
  \item The DoE permitted an establishment of a hierarchy of the process parameters.
  \item Lower linear energy input ( ${ }^{<} 0.9 \mathrm{~J} / \mathrm{mm}$ ) led to a high risk in formation of non-continuous tracks, instability and balls.
  \item The most influencing parameter on the geometrical features was the scanning speed, followed by the beam current.
  \item Compared to the other two parameters, the focus offset was found to have quantitatively less effect on the geometrical features.
  \item Coarser primary dendrite arm spacing (PDAS) was obtained at higher linear energy input values.
  \item By increasing the linear energy input, more small equiaxed grains structure were formed, however, at lower linear energy input, more columnar grains were observed.
  \item Lower focus offset resulted in a less misorientation within the grains.
  \item The proposed approach can be applied for further development of the manufacturing strategy and optimization of the EBM process.
\end{itemize}

\section*{Acknowledgments}
The authors would like to thank Dr. Anders Snis from Arcam AB and Mr. Jonas Olsson from University West for sharing their knowledge in running the EBM machine. The authors would also like to thank Dr. Stefan Gustafsson from Chalmers University of Technology for training in EBSD mapping. Funding from the "European Regional Development Fund", the "Simulation and Control of Material affecting Processes" (SiCoMap) and the "Sustainable Manufacturing Through NextGeneration Additive Process" (SUMAN-Next) projects with funding from the KK foundation, are highly acknowledged.

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[39] C.T. Sims, Norman S. Stoloff, William C. Hagel, Chester T. Sims, Norman S. Stoloff, William C. Hagel (Eds.), Superalloys II: High-Temperature Materials for Aerospace and Industrial Power, Wiley, 1987.

[40] M.M. Kirka, K.A. Unocic, N. Raghavan, F. Medina, R.R. Dehoff, S.S. Babu, Microstructure development in Electron beam-melted Inconel 718 and associated tensile properties, JOM 68 (3) (Mar. 2016) 1012-1020.

[41] W.-C. Huang, K.-P. Chang, P.-H. Wu, C.-H. Wu, Lin, 3D printing optical engine for controlling material microstructure, Phys. Procedia 83 (Jan. 2016) 847-853.

[42] L. Liu, T. Huang, M. Qu, G. Liu, J. Zhang, H. Fu, High thermal gradient directional solidification and its application in the processing of nickel-based superalloys, J. Mater. Process. Technol. 210 (1) (Jan. 2010) 159-165.

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\title{Effect of processing parameters during the laser beam melting of Inconel 738: Comparison between simulated and experimental melt pool shape }


\author{D. Grange ${ }^{a, c, *}$, A. Queva ${ }^{\text {b,c }}$, G. Guillemot ${ }^{b}$, M. Bellet ${ }^{b}$, J.-D. Bartout ${ }^{a}$, C. Colin ${ }^{a}$\\
a MINES ParisTech, PSL Research University, MAT - Centre des matériaux, CNRS UMR 7633, BP 87, 91003, Evry, France\\
b MINES ParisTech, PSL Research University, CEMEF - Centre de Mise en Forme des Matériaux, CNRS UMR 7635, CS10207 Rue Claude Daunesse, 06904, Sophia\\
Antipolis Cedex, France\\
${ }^{\mathrm{c}}$ Safran Additive Manufacturing, a Technology Platform of Safran Tech, Rue des Jeunes Bois, Châteaufort, 78114, Magny-Les-Hameaux, France}
\date{}


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\section*{A R T I C L E I N F O}
Associate Editor: A Clare

\section*{Keywords:}
Laser beam melting

Melt pool shape

Finite element simulation

Convection

Nickel-based alloy

\begin{abstract}
A B S T R A C T Numerical simulation is a powerful tool to understand the link between processing parameters and solidification conditions during the laser beam melting (LBM) process. To be able to use this tool for microstructural control, numerical models need to be validated on a large set of experimental conditions, to ensure that the model describes the predominant physical phenomena. In this study, an experimental set of twenty tracks was produced in an Inconel 738 alloy, with a wide range of energy input and scanning speed. Experimental melt pool shapes were compared to the predictions of a multiphysics numerical model. In this model, the powder bed is considered as a continuum. The laser source is modeled with a Beer-Lambert absorption law, and surface tension, Marangoni force and recoil pressure are the driving forces for melt pool dynamics. This kind of model offers an efficient computational time, but requires a calibration of the absorption coefficient and a representative description of laser-matter interaction. In order to represent correctly heat and mass transfer during laser-matter interaction, the model needs to account for the loss of matter caused by the ejection of powder particles and spatters. A novel calibration method was proposed to calculate the absorption coefficient. This method uses the experimental cross sections of the melt pools and a simplified analytical expression of energy balance. The use of this calibration method enabled a good agreement between experiments and calculations on a large process window. The values obtained by the calibrations resulted in a phenomenological expression of absorptivity coefficient with process parameters. Based on this expression, a comparison was made with another numerical model from literature using a time-consuming ray-tracing method in order to calculate the absorptivity coefficient. Similar results have been obtained, demonstrating the potential of the proposed approach to predict the melt pool shape and thus better understand the combined effect of laser-matter interaction and solidification in LBM process.
\end{abstract}

\section*{1. Introduction}
Inconel 738 (IN738 LC) is a Nickel-based superalloy of great interest in aerospace industry, because of its excellent mechanical properties in high temperature environment, such as in aircraft engines, where parts undergo service temperatures higher than $900^{\circ} \mathrm{C}$. As a consequence, the mastering of additive manufacturing (AM) of Inconel 738 parts by laser beam melting (LBM) is a real challenge. Indeed, the high sensitivity of Inconel 738 to solidification cracking as known from the welding community makes its manufacturing by LBM process critical. This alloy is difficult to weld, and hence it is also difficult to process additively. The challenge is then to identify appropriate LBM "process window" (set of process parameters) adapted to a fabrication without any defect.\\
In the context of AM-LBM, solidification cracking of Inconel 738 has been experimentally investigated in several studies, some of which focus on the influence of processing parameters. Cloots et al. (2016) have shown that the number of microcracks tends to decrease when the scanning velocity is increased while the beam power is maintained constant. Grange et al. (2020) have shown that the cracking is minimal when the material is processed with small melt pools with a strong overlap. They mentioned four contributing factors for solidification cracking: the extent of the mushy zone, the intensity of stresses in the mushy zone, a positive role of a fine grain structure and a positive effect of material remelting to avoid crack propagation.

Beside experiments, numerical simulation is a powerful tool to understand and control materials processing. The development of numerical simulation, assessed and validated by experimental observations
\footnotetext{\begin{itemize}
  \item Corresponding author at: MINES ParisTech, PSL Research University, MAT - Centre des matériaux, CNRS UMR 7633, BP 87, 91003, Evry, France.
\end{itemize}

E-mail address: \href{mailto:david.grange@mines-paristech.fr}{david.grange@mines-paristech.fr} (D. Grange).
}

\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
\multicolumn{2}{|c|}{Nomenclature} & \multicolumn{2}{|l|}{Thermal} \\
\hline
\multicolumn{2}{|c|}{Acronyms} & $C_{p}$ & Heat capacity $\left(\mathrm{J}^{\left.\mathrm{kg}^{-1} \cdot \mathrm{K}^{-1}\right)}\right.$ \\
\hline
LBM & Laser beam melting & $D$ & Thermal diffusivity $\left(\mathrm{m}^{2} . \mathrm{s}^{-1}\right)$ \\
\hline
LPBF & Laser powder bed fusion & $\Delta H$ & Equivalent enthalpy corresponding to the absorbed energy \\
\hline
LS & Level set &  & \begin{tabular}{l}
divided by the mass of the characteristic diffusion volume \\
$\left(\mathrm{J} . \mathrm{kg}^{-1}\right)$ \\
\end{tabular} \\
\hline
\multicolumn{2}{|c|}{\multirow{2}{*}}{}\{\begin{tabular}{l}
Experimental \\
$E_{l}=P_{L} / v_{L} \quad$ Linear incident energy $\left(\mathrm{J} \cdot \mathrm{mm}^{-1}\right)$ \\
\end{tabular}\} & $h$ & \includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-02}
 \\
\hline
 &  & $h_{s}$ & Enthalpy at solidus temperature $\left(\mathrm{J} . \mathrm{kg}^{-1}\right)$ \\
\hline
\multicolumn{2}{|c|}{\multirow{2}{*}}{$H_{M P}=H_{R Z}+H_{a p p} \quad$ Height of the track $(\mu \mathrm{m})$} & $\dot{q}_{L}$ & Heat source input $\left(\mathrm{W} \cdot \mathrm{m}^{-3}\right)$ \\
\hline
 &  & \begin{tabular}{l}
$\dot{q}_{v}$ \\
$\dot{q}_{v}$ \\
\end{tabular} & Vaporization heat loss $\left(\mathrm{W} \cdot \mathrm{m}^{-3}\right)$ \\
\hline
$H_{R Z}$ & Height of the remelted zone $(\mu \mathrm{m})$ & $T$ & Temperature $\left({ }^{\circ} \mathrm{C}\right)$ \\
\hline
$p$ & Porosity of the powder bed & $T_{0}$ & Room temperature $\left({ }^{\circ} \mathrm{C}\right)$ \\
\hline
$P_{L}$ & Laser power (W) & $T_{l}$ & Liquidus temperature $\left({ }^{\circ} \mathrm{C}\right)$ \\
\hline
$\phi_{L}$ & Laser beam $1 / \mathrm{e}^{2}$ diameter $(\mu \mathrm{m})$ & $T_{\text {peak }}$ & Peak temperature at the center of the beam $\left({ }^{\circ} \mathrm{C}\right)$ \\
\hline
$r_{L}$ & Laser beam radius $(\mu \mathrm{m})$ & $T_{s}$ & Solidus temperature $\left({ }^{\circ} \mathrm{C}\right)$ \\
\hline
$S_{a p p}$ & \begin{tabular}{l}
Volume of the apparent part of the track per unit of track \\
length $\left(\mu \mathrm{m}^{2}\right)$ \\
\end{tabular} & $T_{v}$ & Boiling temperature $\left({ }^{\circ} \mathrm{C}\right)$ \\
\hline
$S_{\text {ejected }}$ & \begin{tabular}{l}
Volume per unit of track length in which powder particles \\
are ejected without being melted $\left(\mu \mathrm{m}^{2}\right)$ \\
\end{tabular} & \begin{tabular}{l}
$\alpha$ \\
$\rho$ \\
$\lambda$ \\
\end{tabular} & \begin{tabular}{l}
Density $\left(\mathrm{kg} \cdot \mathrm{m}^{-3}\right)$ \\
Thermal conductivity $\left(\mathrm{W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}\right)$ \\
\end{tabular} \\
\hline
\multirow[t]{2}{*}{$S_{\text {free }}$} & \begin{tabular}{l}
Volume per unit of track length of powder which is free \\
after the interaction with the laser beam, due the collapse \\
\end{tabular} & $\lambda_{d}$ & \begin{tabular}{l}
Thermal conductivity of the dense phase (solid and liquid) \\
$\left(\mathrm{W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}\right)$ \\
\end{tabular} \\
\hline
 & of the powder bed on both sides of the track $\left(\mu \mathrm{m}^{2}\right)$ & $\lambda_{p}$ & Thermal conductivity of the powder bed $\left(\mathrm{W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}\right)$ \\
\hline
$S_{\text {interaction }}$ & \begin{tabular}{l}
Interaction volume per unit of track length, in which \\
particles can be either ejected of melted $\left(\mu \mathrm{m}^{2}\right)$ \\
\end{tabular} & \multicolumn{2}{|c|}{Hydrodynamics} \\
\hline
$S_{\text {melted }}$ & \begin{tabular}{l}
Volume per unit of track length of melted powder bed \\
$\left(\mu \mathrm{m}^{2}\right)$ \\
\end{tabular} & \begin{tabular}{l}
$f_{V}$ \\
$g$ \\
\end{tabular} & \begin{tabular}{l}
Total volume forces $\left(\mathrm{N} . \mathrm{m}^{-3}\right)$ \\
Acceleration due to gravity $(9.81)\left(\mathrm{m} . \mathrm{s}^{-2}\right)$ \\
\end{tabular} \\
\hline
\multirow{2}{*}{}\begin{tabular}{l}
$S_{M P}=S_{C}$ \\
$S_{\text {spatter }}$ \\
\end{tabular} & $p p+S_{R Z} \quad$ Volume of the track per unit of track length $\left(\mu \mathrm{m}^{2}\right)$ & $n$ & Normal vector \\
\hline
 & \begin{tabular}{l}
Volume of material per unit of track length and then \\
ejected as spatters $\left(\mu \mathrm{m}^{2}\right)$ \\
\end{tabular} & \begin{tabular}{l}
$\gamma$ \\
$\frac{\partial \gamma}{\partial T}$ \\
\end{tabular} & \begin{tabular}{l}
Surface tension $\left(\mathrm{N} \cdot \mathrm{m}^{-1}\right)$ \\
Marangoni coefficient $\left(\mathrm{N} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}\right)$ \\
\end{tabular} \\
\hline
\multirow[t]{2}{*}{$\tau_{\text {app }}$} & Fraction of material interacting with the laser beam which & $\mu$ & Dynamic viscosity (Pa.s) \\
\hline
 & \begin{tabular}{l}
participates in the apparent part of the track (-) \\
Scanning speed of the laser beam $\left(\mathrm{mm} \cdot \mathrm{s}^{-1}\right)$ \\
\end{tabular} & $\mu_{d}$ & \begin{tabular}{l}
Dynamic viscosity of the dense metallic material (solid and \\
liquid) (Pa.s) \\
\end{tabular} \\
\hline
\multirow{3}{*}{}\begin{tabular}{l}
$v_{L}$ \\
$W_{M P}$ \\
$\Delta Z_{\text {powder }}$ \\
\end{tabular} & Width of the melt pool $(\mu \mathrm{m})$ & $\mu_{p}$ & Dynamic viscosity of the powder bed (Pa.s) \\
\hline
 & Powder bed height $(\mu \mathrm{m})$ & Level-Set &  \\
\hline
 &  & $\psi$ & Distance function $(\mu \mathrm{m})$ \\
\hline
\end{tabular}
\end{center}

and measurements, allows engineers to develop strategies to identify adequate process windows. However, it should be observed in LBM context that a very complex physics is at stake. Therefore, addressing directly the prediction of solidification cracking through numerical simulation might be a too ambitious objective, as this would require predictive models in laser/metal interaction, fluid flow, solidification, formation of microstructure, and thermo-mechanics in the semi-solid state. It appears then that a more progressive approach in numerical simulation development should be preferred, with a first assigned objective: a thermo-fluid numerical model capable of calculating a reliable description of LBM solidification conditions. Indeed, predicting the melt pool shape, the extension of the mushy zone, as well as the temperature gradients and cooling rates locally in the vicinity of the melt pool and in the mushy zone, is an obvious prerequisite before addressing thermo-mechanics. This is precisely the objective of the present paper: the evaluation of a multiphysics thermo-fluid simulation model by reference to experimental measurements, for LBM of Inconel 738.

Numerous experimental studies highlighted the complexity and the multiplicity of the physical phenomena at stake and show which ones are essential to consider in numerical models. Experimentally, Yadroitsev and Smurov (2010) demonstrated the influence of process parameters such as scanning speed and laser power on single track formation for different alloys, including IN625. They demonstrated that melt pool penetration into the substrate is required to stabilize the track building and avoid track irregularities of balling. Furthermore, the tracks shape and dimensions are largely influenced by surface tension and Marangoni forces. Bidare et al. (2018) used fast camera equipment to develop observations of tracks development and vaporization stage during LBM process for stainless steel. They demonstrated that this latter phenomenon highly influences the melt pool and particles dynamics. Wang et al. (2017) suggested that the observed liquid spattering is a consequence of the recoil pressure induced by vaporization combined with Marangoni effect using $\mathrm{CoCr}$ powder. Furthermore, as shown by Matthews et al. (2016), the recoil pressure is also partly responsible for the denudation on track sides. From this short literature review, it appears that a predictive numerical model should at least take into account the following physical phenomena: heat transfer, fluid flow, surface tension including Marangoni effect, and laser/matter interaction including vaporization effect.

The numerical simulation community has worked for several years to develop computational codes matching the previous requirements. Complex models have been developed to predict the melt pool and final track shape. Most of them consider the scale of powder particles, with an explicit description of every particle of the powder bed. Khairallah et al. (2016) presented an arbitrary Lagrangian-Eulerian (ALE) multiphysics code to simulate laser-matter interaction and fluid flow with an application to Ti-6Al-4 V. The Marangoni effect and the recoil pressure are considered in order to predict denudation during the heating stage. Martin et al. (2019) used this model to provide better understanding of

Table 1

Process parameters investigated in present study. Cases are ordered by increasing linear energy.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
$\#$ & $v_{L}\left[\mathrm{~mm} . \mathrm{s}^{-1}\right]$ & $P_{L}[\mathrm{~W}]$ & \includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-03}
 & $\#$ & $v_{L}\left[\mathrm{~mm} . \mathrm{s}^{-1}\right]$ & $P_{L}[\mathrm{~W}]$ & $E_{l}\left[\mathrm{~J} . \mathrm{mm}^{-1}\right]$ \\
\hline
1 & 1350 & 280 & 0.21 & 11 & 315 & 115 & 0.37 \\
\hline
2 & 570 & 120 & 0.21 & 12 & 1000 & 370 & 0.37 \\
\hline
3 & 380 & 85 & 0.22 & 13 & 225 & 96 & 0.43 \\
\hline
4 & 960 & 230 & 0.24 & 14 & 730 & 340 & 0.47 \\
\hline
5 & 750 & 180 & 0.24 & 15 & 300 & 140 & 0.47 \\
\hline
6 & 1075 & 275 & 0.26 & 16 & 500 & 310 & 0.62 \\
\hline
7 & 1100 & 320 & 0.29 & 17 & 360 & 230 & 0.64 \\
\hline
8 & 430 & 125 & 0.29 & 18 & 385 & 265 & 0.69 \\
\hline
9 & 685 & 210 & 0.31 & 19 & 455 & 385 & 0.85 \\
\hline
10 & 800 & 260 & 0.33 & 20 & 245 & 215 & 0.88 \\
\hline
\end{tabular}
\end{center}

the occurrence of porosities during the transition from a track to another one. Bayat et al. (2019) developed a similar multiphysics model and applied it to Ti-6Al-4 V. They were able to get an accurate prediction of the melted zone dimensions compared to experimental observations. Aggarwal et al. (2019) used a similar model on $316 \mathrm{~L}$ stainless steel. They used the simulation to understand the influence of the distance between the powder bed position and the focal plane of the laser beam on the resulting melting mode (conduction or keyhole). However, being based on an explicit discretization of the powder bed particles, and possibly ray-tracing for laser/metal interaction, all these approaches are still excessively time consuming to model track evolution. This limits length of simulation domains even more when the formation of multiple tracks and layers is considered, as in effective AM. In view of an efficient search for process windows, a reasonable computational time is required as well as the development of a reliable model. Consequently, the simulation model previously proposed in Queva et al. (2020) is considered in the present study. In this approach the powder bed is modelled as a continuum and a Beer-Lambert absorption law is assumed to consider the progressive absorption of laser energy in matter, which generates lower computational time than previous ones. Queva et al. (2020) reported that the CPU time required to simulate a single track is approximately 3.5 times smaller than with other approaches. However, as a counterpart, the laser absorptivity is a variable parameter which has to be calibrated. In this article, a novel method was proposed to calibrate the absorptivity coefficient, with a combination of semi-analytical reasoning and numerical simulations in order to investigate the effect of processing parameters on experimental melt pool cross sections.

The study reported here was structured as follows:

\begin{itemize}
  \item The evolution of the melt pool shape of IN738 was studied, for a wide range of LBM processing parameters. A set of twenty experiments was carried out under different laser power and scanning speed to provide a process window delimiting parameters where the track is stable from those associated to keyhole or capillary instabilities. A study of mass transfer during the interaction between the laser beam and the powder bed was conducted, based on optical profilometry measurements, and revealed the necessity to account for metal ejections. This is reported in Section 2.
  \item Experimental observations were compared with the predictions of the numerical model developed by Queva et al. (2020). A novel calibration method for the absorptivity coefficient of the numerical simulation was proposed, based on the experimental cross sections of the melt pool and a simplified analytical expression of energy conservation. This is reported in Section 3.
  \item After calibration, numerical simulation results and experimental observations were compared for the whole process window, demonstrating the capabilities of the present numerical approach to provide an efficient prediction of the melted zone dimensions, in a wide range of process parameters, and with an efficient computational time. The transition from very low keyhole melt pool morphology to deep keyhole is presented. An investigation of the absorptivity coefficient evolution with processing parameters is proposed and compared with in-situ measurements from literature, showing a good agreement. This is reported in Section 4.
\end{itemize}

\section*{2. Experiments}
\subsection*{2.1. Experimental protocol}
All the experiments reported here were undertaken with a gas atomized powder of Inconel $738 \mathrm{LC}$, and a Concept Laser M2 machine. The particle size distribution is Gaussian, with diameter percentiles $D_{10}=17 \mu \mathrm{m}, D_{50}=28 \mu \mathrm{m}$ and $D_{90}=45 \mu \mathrm{m}$. The substrate is a cylinder of $30 \mathrm{~mm}$ diameter and $10 \mathrm{~mm}$ height, previously fabricated with the same printer and the same material. The upper surface was then polished with 1200-grit paper and sandblasted to prevent the powder from sliding on the substrate. A powder layer was deposited with a rigid coater. The laser beam had a Gaussian power distribution, with a $1 / e^{2}$ diameter set to $\phi_{L}=100 \mu \mathrm{m}$ while the laser power $P_{L}$ and the scanning speed $v_{L}$ varied respectively in the range $85-384 \mathrm{~W}$ and $225-1350$ $\mathrm{mm} \cdot \mathrm{s}^{-1}$. Twenty tracks were built with a length of $20 \mathrm{~mm}$ and a gap of 1 $\mathrm{mm}$ between the centers of two adjacent tracks. The $1 \mathrm{~mm}$ gap guarantees that the melting of the different tracks are thermally\\
\includegraphics[max width=\textwidth, center]{2024_03_10_fc82295ca80e2636ba5dg-03(1)}

Fig. 1. (a) Geometrical features of the tracks; (b) Top view of the tracks on the substrate after powder removal.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-04}
\end{center}

Fig. 2. Process window defined with the results obtained on a representative cross section for each processing parameters investigated.

independent, with no waiting time between the melting of two adjacent tracks. The process parameters are indicated in Table 1.

After irradiation, the substrate was scanned with an optical profilometer AltiSurf 500, before and after removal of the powder bed. The substrate was carefully moved from the building plate to the plate of the profilometer, to prevent any movement in the powder bed. A first scanning of the surface was done with the powder bed. Then, the powder bed was removed with a fine brush, before a second scanning. Measurements assessed a good uniformity of the powder bed thickness, with a height of powder $\Delta Z_{\text {powder }}$ between 105 and $120 \mu \mathrm{m}$. To measure the dimensions of the single tracks, the substrate was cut transversally to the scanning direction. Four cuts were distributed regularly along the track length, excluding $1.5 \mathrm{~mm}$ at both extremities to avoid the initial and final transient regime of the melt pool. After a polishing down to $1 \mu \mathrm{m}$, the shape of the melt pools was revealed with a glyceregia etching (15 $\mathrm{ml} \mathrm{HCl}+10 \mathrm{ml}$ glycerol $+5 \mathrm{ml} \mathrm{HNO}_{3}, 20 \mathrm{~s}$ by swabbing) and observed with an optical microscope. The following geometrical features are measured (Fig. 1): the melt pool width $W_{M P}$, the height of the remelted zone $H_{R Z}$, the height of the upper (or apparent) part of the track $H_{a p p}$, the total melt pool height $H_{M P}=H_{a p p}+H_{R Z}$ and the areas of the upper part of the track and of the remelted zone $S_{a p p}$ and $S_{R Z}$.

\subsection*{2.2. Melt pool shapes and process windows}
A transversal cut of every track is displayed on a $\left(v_{L}, P_{L}\right)$ diagram in Fig. 2. Firstly, a small angle of about $6^{\circ}$ exists between the centerline of the tracks and the vertical. This is due to the inclination between the laser beam and the vertical, linked to the position of the substrate on the building plate. Secondly, solidification cracks are often visible within the melt pools and in the substrate. This is actually not surprising, as Inconel 738 LC is known to be prone to solidification cracking (Cloots et al., 2016). Most importantly, a variety of melt pool morphologies are visible on the diagram. These morphologies can be firstly described as a function of the incident linear energy $E_{l}=P_{L} / v_{L}$ (in $\mathrm{J} . \mathrm{mm}^{-1}$ ), whose isovalues are represented with oblique dotted lines.

For intermediate linear energies $\left(0.22<E_{l}<0.5 \mathrm{~J} . \mathrm{mm}^{-1}\right)$, the tracks have a reasonable penetration in the substrate, showing a ratio $H_{R Z} / H_{\text {app }}$ between 1 and 3 . A sufficient remelting is indeed important to avoid a lack of fusion and for the repair of defects. For high linear energies $\left(E_{l}>0.5 \mathrm{~J} . \mathrm{mm}^{-1}\right)$, the tracks have a keyhole shape and a deep penetration with a ratio $H_{R Z} / H_{a p p}>3$. As visible on the figure, pores are particularly frequent in that domain, making it inadequate for fabrication. At low linear energies, when $E_{l}<0.22 \mathrm{~J} . \mathrm{mm}^{-1}$, the tracks have a low penetration in the substrate and a high wetting angle $\theta>90$ $\left.{ }^{\circ}\right)$. Due to the surface tension, single tracks with a high wetting angle can be subjected to instabilities and therefore show an increased variability of their dimensions along their length. An estimation of the variability of the dimensions with several cuts is particularly necessary in that domain. Note that at a low laser power $\left(P_{L}<120 \mathrm{~W}\right)$, a region is observed where the tracks both have a low wettability and a keyhole shape. This region was arbitrarily included in the domain of low wettability, in grey.

The mean dimensions of the melt pools are presented in Fig. 3(a), whereas their dispersion, defined as the ratio of the standard deviation to the mean, are displayed in Fig. 3(b). As expected, the dispersion is the highest in the low wettability domain. Both the apparent part and the remelting zones have highly varying shapes, with a dispersion of $H_{\text {app }}$ up to $30 \%$ and a dispersion of $H_{R Z}$ sometimes over $60 \%$ (around $45 \%$ for $\left.H_{M P}=H_{\text {app }}+H_{R Z}\right)$. On the contrary, the melt pool width remains quite stable in that region, with a dispersion under $15 \%$. Qualitatively, all dimensions increase with the incident linear energy $E_{l}=P_{L} / v_{L}$, although the increase is limited for $H_{a p p}$. The limits of the domain defined above are reported on the graphs with dotted lines. It can be seen that the green domain of Fig. 2 corresponds to the region with a good stability of the melt pool and still a limited penetration.

The objective of the article is to discuss the effect of the processing parameters on the melt pool shape. First, experimental data were investigated using approximate analytical models, enabling a first evidence of prevailing phenomena and a discussion on energy and mass conservation. Second, relevant multiphysics numerical simulation was used to provide a quantitative prediction of the melt pool shapes. This second part focuses particularly on the green region in Fig. 2.

Several analytical models - actually applied to dense material - aim to represent the melt pool dimensions. Hann et al. (2011) demonstrated that the melt pool depth with different materials and processing parameters collapse to one curve when plotted as a function of a normalized enthalpy:

$\frac{\Delta H}{h_{s}}$, with $\Delta H=\frac{A P_{L}}{\pi \rho \sqrt{D v_{L}\left(\phi_{L} / 2\right)^{3}}}$

The specific enthalpy at melting (solidus) temperature is noted $h_{s}=$ $h\left(T=T_{s}\right)$ and $\Delta H$ corresponds to the absorbed energy divided by the mass of the characteristic diffusion volume, where $A$ is the absorptivity and $D$ the thermal diffusivity. A description of the melt pool depth with\\
(a)\\
\includegraphics[max width=\textwidth, center]{2024_03_10_fc82295ca80e2636ba5dg-05}

(b)\\
\includegraphics[max width=\textwidth, center]{2024_03_10_fc82295ca80e2636ba5dg-05(1)}

Fig. 3. (a) Melt pool dimensions and (b) their variability as a function of processing parameters (cubic interpolation).\\
(a)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-06(1)}
\end{center}

(c)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-06}
\end{center}

(b)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-06(2)}
\end{center}

(d)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-06(3)}
\end{center}

Fig. 4. Evolution of a-b) the height of the remelted zone $H_{R Z}$ and c-d) the melt pool width $W_{M P}$ as a function of the incident linear energy $P_{L} / v_{L}$ and of $P_{L} / v_{L}^{0.5}$. Red dots belong to the keyhole domain and grey dots to the low wettability domain. Blue dots are associated to the stability domain The error bars correspond to the standard deviation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

this model may seem surprising at first sight, because it only considers conductive thermal transfers, whereas the melt pool depth is known to depend significantly on other phenomena, as recoil pressure. In a study by King et al. (2014), the depth of melt pools produced by LBM was also found to be a function of the normalized enthalpy. Normalized enthalpy was also successful in describing keyhole transition, which highly depends on recoil pressure. They showed with an analytical thermal model that the normalized enthalpy was proportional to the peak temperature $T_{\text {peak }}$ at the center of the beam:

$\frac{\Delta H}{h_{s}}=\pi \frac{T_{p e a k}}{T_{s}}$

For that reason, the effect of saturated vapor pressure on the melt pool shape becomes significant when the peak temperature exceeds the boiling temperature, i.e. when the normalized enthalpy exceeds a certain value. In our experiments, only $P_{L}$ and $v_{L}$ are variable, the melt pool depth should be then, according to Eq. (1), a function of $P_{L} / \sqrt{v_{L}}$. On the contrary, Moniz et al. (2019), in a study of LBM process applied to ceramic materials, proposed a model in which the melt pool dimensions do not depend on the peak temperature, but rather on the linear density of energy absorbed by the material, $A P_{L} / v_{L}$. However, it should be noted for ceramic material that the incident energy of the laser beam accumulates in the material due to low thermal diffusion. The melt pool corresponds to the area where the local energy absorbed reaches the melting enthalpy. According to that model, melt pool dimensions should not depend on $P_{L} / \sqrt{v_{L}}$, but rather on $E_{l}=P_{L} / v_{L}$.

Considering the present experimental results, the width of the melt pool $W_{M P}$ and the height of the remelted zone are plotted both as a function of $E_{l}=P_{L} / v_{L}$ and $P_{L} / \sqrt{v_{L}}$ (Fig. 4). Different marker colors and types are used for the melt pool, depending on the domain presented in Fig. 2. As in the studies previously cited, the values of $H_{R Z}$ globally collapse to one curve when plotted as a function of $P_{L} / \sqrt{v_{L}}$, whereas they are much dispersed when plotted as a function of the incident linear energy. This could imply that due to the recoil pressure, the melt pool depth is much more affected by the peak temperature of the melt pool than by the total amount of incident energy. The impact of the recoil pressure on the melt pool shape will be further investigated in section 3. Due to an evolution as a function of $P_{L} / \sqrt{v_{L}}, H_{R Z}$ increases with an increase of the scanning velocity while the linear energy is kept constant, see for example the melt pools with $E_{l} \approx 0.3 \mathrm{~J} . \mathrm{mm}^{-1}$ on Fig. 2. On the contrary, the melt pool width does not seem to evolve as a function of $P_{L} / \sqrt{v_{L}}$ but is better described by the incident linear energy $E_{l}=P_{L} / v_{L}$. This dimension seems to be less linked to the peak temperature than to the amount of incident energy.\\
(a)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-07(2)}
\end{center}

(b)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-07(3)}
\end{center}

Fig. 5. Melt pool transverse area $S_{M P}$ vs two functions of process parameters, for the whole experimental tests.

\subsection*{2.3. Energy and mass transfer}
The two characteristic sections $S_{a p p}$ and $S_{M P}=S_{a p p}+S_{R Z}$ are related to energy and mass transfer and their conservation during the laser beam interaction. Indeed, $S_{M P}$ is the volume of molten metal per unit length of the single track and is therefore a consequence of the amount of energy absorbed by the melt pool. The section $S_{\text {app }}$ is the volume of consolidated powder per unit length of the track. A good understanding of the energy and mass transfers during the irradiation is necessary to model accurately the process. In the following section, we discuss the experimental values of $S_{M P}$ and $S_{a p p}$ and the consequences regarding process numerical simulation.

\section*{- Energy conservation}
Let us consider a melt pool with a section $S_{M P}$ that reaches a mean temperature $T_{M P}$. The enthalpy increase per unit of track length is then $S_{M P}\left(\rho h\left(T_{M P}\right)-\rho h\left(T_{0}\right)\right)$, where $\rho h$ is the specific enthalpy and $T_{0}$ the room temperature. Under the approximation that most of the beam energy is absorbed by the melt pool, the energy balance can be written:

$A\left(E_{l}-E_{l, m i n}\right)=S_{M P}\left(\rho h\left(T_{M P}\right)-\rho h\left(T_{0}\right)\right)$

where $E_{l, \min }$ is the minimal linear energy to create a melt pool. Such a first order relationship can be assessed by plotting $S_{M P}$ (experimental values) as a function of $E_{l}$ in Fig. 5(a). It is visible that $E_{l, \text { min }}$ is close to $0.05 \mathrm{~J} . \mathrm{mm}^{-1}$. However, the alignment of the dots is not perfect and a significant difference of melt pool transverse section is observed for tracks having similar values of incident linear energy. A possible explanation is that the absorptivity $A$ varies significantly with the processing parameters, as it was observed for example by Cunningham et al. (2019). As absorptivity increases with the laser beam power and decreases with scanning velocity and considering the evolution measured by Trapp et al. (2017), we propose the following expression in the range of processing parameters: $A=C_{1} \cdot\left(P_{L}^{a} v_{L}^{b}-C_{2}\right)^{1 / 2}$. Moreover, we propose a further approximation that the mean temperature of the melt is constant in first order. Under these assumptions, $S_{M P}$ should be proportional to $\left(P_{L}^{a} \nu_{L}^{b}-C_{2}\right)^{1 / 2} \cdot\left(E_{l}-E_{l, \min }\right)$. Interestingly, Fig. 5(b) shows that with $a=0.2, b=-0.06, C_{2}=1.4$ and $E_{l}=0.05 \mathrm{~J} \mathrm{~mm}^{-1}$, the points obtained for very different regimes almost perfectly align. The evolution of absorptivity suggested here will be discussed later in the article, thanks to numerical simulation.

\section*{- Mass conservation}
During the interaction between the laser beam and the powder bed, particle dynamics is complex. Bidare et al. (2018) employed high speed imaging to observe the vapor plume, the argon gas flow and their effect on powder particles movements. They highlighted that numerous particles are entrained by the gas flow, some of which are drawn in towards the melt pool, while others are blown away. Moreover, some metal is ejected during fusion, as spatters. As the objective is to predict the dimensions of the consolidated tracks, experimental evidence of the extent of such mass transfers is required. Particularly, ejections of matter affect the amount of metal consolidated in the track.

We based an analysis detailed hereafter on profilometry measurements on a single track, with $P_{L}=230 \mathrm{~W}$ and $v_{L}=960 \mathrm{~W}$ (referred as (a)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-07}
\end{center}

(b)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-07(1)}
\end{center}

Fig. 6. Height of material around the track $P_{L} 230 v_{L} 960$ before and after removal of the powder: (a) transverse profiles at four different locations on the track, (b) identification of the transverse sections $S_{a p p}$ and $S_{\text {free }}$ on the mean profile.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-08}
\end{center}

(a)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-08(1)}
\end{center}

(b)

Fig. 7. Schematic representation of mass transfers: (a) during the interaction between the laser beam and the powder bed; (b) powder bed after particles displacement and rearrangement.

$\left.P_{L} 230 v_{L} 960\right)$. The surroundings of the track are scanned before and after removal of the powder. Fig. 6(a) displays the transverse profile of material height at four different locations along the track, before and after removal of powder. For each location, the profile was averaged on a length of $3 \mathrm{~mm}$ in the scanning direction, to reduce dispersion.

It is visible that the original powder bed thickness of $120 \mu \mathrm{m}$ was modified during the interaction with the beam, as a result of powder consolidation by melting and ejections. No complete denudation is observed on both sides of the track as this latter is still covered with powder. This is in line with the observations of Bidare et al. (2018). They noted that denudation decreases with an increase of the powder bed height. For a powder bed thickness around $120 \mu \mathrm{m}$, they noticed that powder particles roll towards the track without leaving a completely denudated area. In the present case, the powder has a good ability to flow and the powder bed thickness is significantly higher than the track height. Consequently, the single track is covered with powder after the interaction with the beam.

The area of powder bed left empty after the beam interaction is called $S_{\text {free }}$ (Fig. 6(b)). We propose to discuss the significance of material ejection with a comparison between $S_{a p p}$ and $S_{\text {free }}$. The mean values measured on the four transverse profiles are $S_{a p p}=4600 \mu \mathrm{m}^{2}$ and $S_{\text {free }}=$ $20300 \mu \mathrm{m}^{2}$. Let us suppose first that there is no material ejection (i.e. no ejected powder particles and no spatters). In permanent regime, these two sections are linked by the porosity of the powder bed $p: S_{a p p}=$ $S_{\text {free }}(1-p) / p$ (cf. Eq. (6) in development below). This leads to a porosity of $p=0.82$, which is not possible, as this value is significantly higher than the porosity of poured powder $(p=0.55)$. As consequence, there is obviously a significant matter loss. To estimate the loss of matter, a powder bed porosity of 0.5 was assumed. In fact, it should be noted that the density is difficult to estimate as it depends on several parameters as the coater or the fluidity of the powder, etc. Nevertheless, the reasoning is still valid with a value of the porosity value $p=0.4$ and $p=0.6$ and the sensitivity of the result to that parameter will be calculated. Fig. 7(a) represents the volume of interaction $S_{\text {interaction }}=W \Delta Z_{\text {powder }}$, defined as the volume in which powder particles are likely to be ejected or molten. The volumes of ejected and molten powder are respectively noted as $S_{\text {ejected }}$ and $S_{\text {molten }}$ as shown on Fig. 7(a). The consolidation transforms the porous volume of powder $S_{\text {molten }}$ into a volume of dense matter $S_{\text {molten }}(1-p)$, which is either blown away as spatters $\left(S_{\text {spatter }}\right)$ or participates in the creation of the apparent part of the track $\left(S_{a p p}\right)$ : $S_{\text {molten }}(1-p)=S_{\text {app }}+S_{\text {spatter }}$. After scanning by the laser beam, a volume $S_{\text {free }}$ of the powder bed is left empty. The rearrangement of the powder bed by rolling of particles is considered isovolumic without modification of $S_{\text {free }}$, as shown in Fig. 7(b). The expression of $S_{\text {free }}$ is then:

$S_{\text {free }}=S_{\text {ejected }}+p \mathrm{~S}_{\text {molten }}+\mathrm{S}_{\text {spatter }}=S_{\text {ejected }}+S_{\text {molten }}-S_{\text {app }}$\\
The fraction $\tau_{\text {app }}$ of useful material can then be calculated. This parameter is defined as the ratio of the quantity of matter which is consolidated, $S_{a p p}$, per the quantity of matter which is either consolidated or lost as powder ejections, $(1-p) S_{\text {ejected }}$, or lost as spatter, $S_{\text {spatter }}$ :

$\tau_{a p p}=\frac{S_{a p p}}{S_{a p p}+S_{\text {spatter }}+(1-p) S_{\text {ejected }}}=\frac{S_{\text {app }}}{(1-p)\left(S_{\text {molten }}+S_{\text {ejected }}\right)}$

The value of $\tau_{a p p}$ is comprised between zero and one: zero corresponds to a situation where no track forms and one to a situation with no matter loss by particle ejections or spatters. Using (4), we obtain:

$\tau_{a p p}=\frac{S_{a p p}}{(1-p)\left(S_{a p p}+S_{\text {free }}\right)}$

A porosity of powder bed $p=0.5$ gives a fraction of useful material $\tau_{a p p}=0.37$. The fraction of metal consolidated in the track after interacting with the laser beam is rather small. Moreover, this conclusion is not affected by the uncertainties about $p$, as values of the porosity $p=0.4$ and $p=0.6$ give respectively $\tau_{\text {app }}=0.30$ and $\tau_{a p p}=0.46$. For this track, a significant amount of metal is either ejected as powder particles or as spatters. This result is not surprising, considering the extent of ejected material observed by Bidare et al. (2018).

The analytical models demonstrate their interest to interpret the experimental result and understand some of the physical phenomena at stake. Nevertheless, these models are not fully satisfactory to describe the melt pool dimensions in the whole domain. Indeed, both the complete melt pool shape evolution and the thermal gradients responsible for the occurrence of defects such as hot cracking cannot be predicted with analytical models. Consequently, in the following section, a multiphysical model was used to predict quantitatively the dimensions of the melt pools.

\section*{3. Simulation of the melt pool shapes}
\subsection*{3.1. Numerical model}
A continuous-mesoscale finite element model thereafter applied to simulate the development of the set of single tracks was previously proposed for the investigation of melt pool development on metallic alloys during LBM process (Queva et al., 2020). This model relies on a level set (LS) formulation of conservation equations. Basically, the simulation domain is shared into two parts associated with the metallic material and the protective atmosphere. The metallic material includes the substrate, the powder bed, the melt pool and the solidified bead. The use of a continuous-mesoscale approach aims at considering the powder bed as a continuum with homogenized properties in order to limit high computation costs (Chen et al., 2017).

The LS method is relevant to follow the spatial and temporal

Table 2

Material properties for IN738LC and gas.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
 & Property & Symbol & Value & Unit & Reference \\
\hline
\multirow{10}{*}{IN738LC} & Solidus, liquidus, boiling temperature & $T_{s}, T_{l}, T_{v}$ & 1216, 1341, 3062 & ${ }^{\circ} \mathrm{C}$ & Thermo-Calc (2020) - lever rule \\
\hline
 & Absorption coefficient of powder, liquid & $\alpha_{p}, \alpha_{l}$ & 25,100 & $\mathrm{~mm}^{-1}$ & - \\
\hline
 & Density solid/liquid & $\rho_{s}, \rho_{l}$ & 7659, 7118 & $\mathrm{~kg} \cdot \mathrm{m}^{-3}$ & Thermo-Calc (2020) \\
\hline
 & Heat capacity of solid/liquid phase & $C_{p, s}, C_{p, l}$ & 643,754 & J. $\mathrm{kg}^{-1} \cdot \mathrm{K}^{-1}$ & Thermo-Calc (2020) \\
\hline
 & Latent heat of fusion & $L_{f}$ & $266 \cdot 10^{6}$ & $\mathrm{~J} . \mathrm{kg}^{-1} \cdot \mathrm{K}^{-1}$ & Thermo-Calc (2020) \\
\hline
 & Latent heat of vaporization & $L_{v}$ & $6690 \cdot 10^{6}$ & $\mathrm{~J} . \mathrm{kg}^{-1}$ & Thermo-Calc (2020) \\
\hline
 & Thermal conductivity of bulk & $\lambda_{d}$ & \begin{tabular}{l}
$0.014 \cdot T+6.7\left[0, T_{l}\right]$ \\
$0.0136 \cdot T+6.7\left[T_{l}, 3500\right]$ \\
\end{tabular} & $\mathrm{W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}$ & JMatPro (2020) \\
\hline
 & Surface tension coefficient at melting & $\gamma_{l}$ & 1.8 & N. $\mathrm{m}^{-1}$ & Quested et al. (2009) \\
\hline
 & Marangoni coefficient & $\partial \gamma / \partial T$ & $-1 \cdot 10^{-4}$ & $\mathrm{~N} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}$ &  \\
\hline
 & Liquid dynamic viscosity & $\mu_{l}$ & $7 \cdot 10^{-3}$ & Pa.s & Mills et al. (2006) \\
\hline
\multirow{4}{*}{Gas} & Density & $\rho_{g}$ & 1.3 & $\mathrm{~kg} \mathrm{~m}^{-3}$ & Dry air properties (2020) \\
\hline
 & Heat capacity & $C_{p, g}$ & 1000 & $\mathrm{~J} . \mathrm{kg}^{-1}$ &  \\
\hline
 & Thermal conductivity & $\lambda_{g}$ & 0.024 & $\mathrm{~W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}$ &  \\
\hline
 & Dynamic viscosity & $\mu_{g}$ & $2.4 \cdot 10^{-4}$ & P a.s &  \\
\hline
\end{tabular}
\end{center}

evolution of the metal/gas interface caused by the fusion/solidification steps endured by metallic material during building, also considering capillary and vaporization effects along the melt pool surface. Since the powder bed is assumed as continuous, the apparent density, thermal conductivity and dynamic viscosity have to be evaluated depending from local temperature and material state. This approach aims at simulating the thermo-mechanical evolution of material during process to follow track development. Heat transfer and fluid flow are consequently computed in the entire domain. For the present paper, only the relevant features are mentioned and described hereunder. More details are provided in Queva et al. (2020) for interested readers.

\section*{- Thermal evolution}
Heat transfer is obtained as the solution of the non-steady equation for energy conservation:

$\frac{\partial\{\rho h\}}{\partial t}+\nabla \cdot(\{\rho h\} \boldsymbol{u})-\nabla \cdot(\{\lambda\} \nabla T)=\dot{q}_{L}-\dot{q}_{v}$

where $\rho$ is the density, $h$ is the specific enthalpy, $\boldsymbol{u}$ is the velocity field obtained after the resolution of Navier-Stokes equations. $\lambda$ is the thermal conductivity and $T$ is the temperature field. The right hand side terms $\dot{q}_{L}$ and $\dot{q}_{v}$ represent respectively the heat source input induced by the laser and the heat loss due to vaporization. The brackets correspond to the mixture of quantities associated to metal and gas domains as developed in a LS approach. Both fusion and solidification phase changes are coupled with the resolution of this non-linear equation. The accurate modelling of the laser power input $\dot{q}_{L}$, is crucial to compute relevant melt pool evolution and final shape since phenomena such as capillary effect and recoil pressure, which are highly temperature dependent, govern melt pool dynamics. However, laser interaction should be distinguished between surfaces associated to powder material and liquid metal. For the laser/powder interaction, multiple reflections occur due to the interactions between powder particles and radiation when the laser beam penetrates the powder bed. Consequently, a volume heat source following the Beer-Lambert law was used to model the volume source:

$\dot{q}_{L}=A \frac{2 P_{L}}{\pi r_{L}^{2}} \exp \left(-\frac{2 r^{2}}{r_{L}^{2}}\right) \alpha \exp \left(-\int_{0}^{z} \alpha d l\right)$

where $A$ and $\alpha$ are respectively the absorptivity and the local absorption coefficient, and $z$ is the distance below the gas/metal interface. For the laser/liquid metal interaction, high and local absorption of laser energy should impose to use an expression restricted to the metal surface. However, in practice, Eq. (8) is used with a high value of absorption coefficient for the liquid phase $\alpha_{l}$ to ensure consistency with the surface expression provided in literature.

\section*{- Hydrodynamic evolution}
The melt pool dynamics is modeled by the momentum conservation equation (Navier-Stokes equation):

$\{\rho\}\left(\frac{\partial \boldsymbol{u}}{\partial t}+(\boldsymbol{u} \cdot \nabla) \boldsymbol{u}\right)-\nabla \cdot\{\underline{\underline{\boldsymbol{\sigma}}}\}=\boldsymbol{f}_{v}$

where $\underline{\sigma}$ is the stress tensor and $f_{v}$ is the total volumetric force, including surface tension, Marangoni force, recoil pressure and gravity. The stress tensor is directly related to the strain-rate tensor and consequently to the velocity field $u$ by a Newtonian behavior law with the dynamic viscosity $\mu$. Eq. (3) is coupled with the mass conservation equation:

$\nabla \cdot \boldsymbol{u}=\dot{\theta}$

where $\dot{\theta}$ represents the negative volume expansion rate associated with the transition from powder to dense material, which is supposed to occur in a certain temperature range. The velocity $\boldsymbol{u}$ is evaluated to follow the gas/metal interface when updating the LS function, by solving the transport equation:

$\frac{\partial \psi}{\partial t}+\boldsymbol{u} \cdot \nabla \psi=0$

However, after the transportation stage, the eikonal property $(\|\psi\|=1)$ is not respected anymore. A geometric reinitialization method is used (Shakoor et al., 2015) to recalculate the distance function with respect to the position $\psi=0$ obtained after the resolution of Eq. (5). Furthermore, the LS method involves mass conservation issues. Therefore, a method reported in literature (Zhang et al., 2019) has been applied presently to overcome this drawback. Anisotropic mesh adaptation techniques, based on error estimation, are used to optimize the CPU time cost.

\subsection*{3.2. Material properties}
The material properties of IN738LC and the gas are described in Table 2. The properties related to enthalpy evolution and phase changes are evaluated with Thermocalc software and NI25 database (Thermo-Calc, 2020). Thermal conductivity of the bulk material is calculated with

Table 3

Laser parameters $\left(P_{L}, v_{L}\right)$ in the process window delimited in Fig. 2 providing track stability as shown in Fig. 3.b and chosen for comparisons between numerical simulations and experiments.

\begin{center}
\begin{tabular}{lllllllll}
\hline
\begin{tabular}{l}
Case number \\
$\#$ \\
\end{tabular} & 4 & 5 & 6 & 7 & 9 & 10 & 12 & 14 \\
\hline
$v_{L}\left(\mathrm{~mm} \cdot \mathrm{s}^{-1}\right)$ & 960 & 750 & 1075 & 1100 & 685 & 800 & 1000 & 730 \\
$P_{L}(\mathrm{~W})$ & 230 & 180 & 275 & 320 & 210 & 260 & 370 & 340 \\
$E_{l}\left(\mathrm{~J} \cdot \mathrm{mm}^{-1}\right)$ & 0.24 & 0.24 & 0.26 & 0.29 & 0.31 & 0.325 & 0.37 & 0.47 \\
\hline
\end{tabular}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-10(2)}
\end{center}

Fig. 8. Simulation domain with temperature field and melt pool shape obtained for $P_{L} 230 v_{L} 960$.

JMatPro (JMatPro, 2020) software and properties of the material in liquid state are taken from experimental studies. To evaluate the thermal conductivity of the powder bed $\lambda_{p}$, the model developed by Zehner and Schlünder (1970) is used which considers the thermal conductivity of bulk and gas, thermal contacts and radiations:

$\frac{\lambda_{p}}{\lambda_{g}}=1-\sqrt{1-p}+\frac{2 \sqrt{1-p}}{1-\beta B}\left[\frac{(1-\beta) B}{(1-\beta B)^{2}} \ln \left(\frac{1}{\beta B}\right)-\frac{B+1}{2}-\frac{B-1}{1-\beta B}\right]$

where $\beta=\lambda_{g} / \lambda_{d}$ and $B=1.25((1-p) / p)^{10 / 9}$.

As illustrated in the study of Queva et al. (2020), below solidus temperature, the dynamic viscosity for powder and dense phase is

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-10}
\end{center}

(a) Conduction mode\\
Table 4

Differences on the melted zone morphology between experimental and numerical results before calibration for case \#4 $\left(P_{L} 230 v_{L} 960\right) . \mathrm{DIFF}=(\mathrm{NUM}-\mathrm{EXP}) / \mathrm{EXP}$ represents the relative error between experiments and simulation in percent.

\begin{center}
\begin{tabular}{lllll}
\hline
Case \#4 & Unit & EXP & NUM & DIFF (\%) \\
\hline
$H_{a p p}$ & $\mu \mathrm{m}$ & 45 & 43.7 & -2.9 \\
$H_{R Z}$ & $\mu \mathrm{m}$ & 70 & 8.9 & -87.3 \\
$H_{M P}$ & $\mu \mathrm{m}$ & 115 & 52.6 & -54.3 \\
$W_{M P}$ & $\mu \mathrm{m}$ & 125 & 88.6 & -29.1 \\
$S_{M P}$ & $\mu \mathrm{m}^{2}$ & 9252 & 3772 & -59.2 \\
\hline
\end{tabular}
\end{center}

assumed constant (10 Pa.s and 1000 Pa.s respectively). During the phase change, the dynamic viscosity decreases exponentially with temperature. Finally, when the temperature exceeds the liquidus temperature, the dynamic viscosity remains constant at $7.0 \cdot 10^{-3}$ Pa.s.

The absorption coefficient $\alpha_{p}$ of the powder bed has little influence in steady state, as most of the incident energy then irradiates the liquid surface of the melt pool. However, this absorption coefficient has an importance when the laser beam starts to irradiate the powder bed, at the very beginning of scanning. The value of $\alpha_{p}$ is chosen so that a significant proportion of the energy reaches the substrate. The absorption coefficient in the liquid corresponds to a very low characteristic distance of energy penetration $\left(1 / \alpha_{l}=10 \mu \mathrm{m}\right)$. The interaction is indeed close to a surface interaction, as the dense material is opaque at the wavelength of the laser beam.

\subsection*{3.3. Simulation of case $P_{L} 230 v_{L} 960$}
The scope of this paper is to validate simulation on processing parameters interesting for fabrication. For that reason, the comparison is focused on cases with a good track stability and without a deep keyhole shape (selection of cases located in the green region on Fig. 2). The laser parameters are resumed in Table 3.

The configuration case \#4 was firstly investigated with $P_{L}=230 \mathrm{~W}$ and $v_{L}=960 \mathrm{~mm} . \mathrm{s}^{-1}$ noted $P_{L} 230 v_{L} 960$. The whole simulated domain is shown in Fig. 8 with overall dimensions $2 \times 0.5 \times 1.1 \mathrm{~mm}^{3}$. The previous section highlighted the significance of ejections during laser beam interaction. The present model treats the powder bed as a uniform medium and thus does not account for entrained particles due to gas flow. Therefore, the chosen value of the powder bed thickness is significantly lower than the experimental one, to account for the metal ejections outside the simulated domain. A layer of powder with thickness of $55 \mu \mathrm{m}$ and porosity of $50 \%$ is deposited on the substrate. The laser beam develops linear scanning with constant velocity. The trajectory evolves from initial position $(x, y)=(0.25,0.25) \mathrm{mm}$ to final position $(1.75$, $0.25) \mathrm{mm}$.

The initial temperature is set to $20^{\circ} \mathrm{C}$. For the thermal resolution, adiabatic boundary conditions are applied on each face of the total

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-10(1)}
\end{center}

(b) Keyhole mode

Fig. 9. Schematic of laser multiple reflections for (a) conduction mode and (b) keyhole mode leading to an enhancement of laser matter interaction.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-11(1)}
\end{center}

Fig. 10. Influence of absorptivity on the predicted melted area for $P_{L} 230 v_{L} 960$.

domain. For the resolution of melt pool dynamics, a pure sliding condition is considered along the four lateral faces; a sticking condition is imposed along the lower face; and the upper face is free, allowing gas input or output. The total number of elements evolves from $\approx 1750000$ at the start to 2000000 at the end of the simulation in order to keep a good track morphology representation.

Regarding data reported in previous studies (Mayi et al., 2020), a first value of absorptivity $A$ is set at 0.3 . The comparison between the numerical simulation and the experiments is shown in Fig. 11(a) and Table 4.

Significant differences in the melted zone shape are observed between simulation and experiment. Indeed, the various dimensions predicted by the numerical simulation underestimate results experimentally achieved. The heat input is clearly insufficient to melt enough matter to reach the expected dimensions. Furthermore, the\\
Table 5

Differences on the melted zone morphology between experimental and numerical results before and after calibration for case $\# 4\left(P_{L} 230 v_{L} 960\right)$.

\begin{center}
\begin{tabular}{lllll}
\hline
Case \#4 & Unit & EXP & NUM (after calibration) & DIFF (\%) \\
\hline
$H_{a p p}$ & $\mu \mathrm{m}$ & 45 & 43.6 & -3.1 \\
$H_{R Z}$ & $\mu \mathrm{m}$ & 70 & 67 & -4.3 \\
$H_{M P}$ & $\mu \mathrm{m}$ & 115 & 110.6 & -3.8 \\
$W_{M P}$ & $\mu \mathrm{m}$ & 125 & 116 & -7.2 \\
$S_{M P}$ & $\mu \mathrm{m}^{2}$ & 9252 & 9038 & -2.3 \\
\hline
\end{tabular}
\end{center}

deviations are too large to assume that differences are related to an error in estimation of material properties.

\subsection*{3.4. Calibration of absorptivity coefficient}
The absorptivity value of 0.3 previously proposed corresponds to the case of a laser interacting perpendicularly with a perfectly plane metal surface (Trapp et al., 2017). As illustrated in Fig. 9(a), this case is encountered in conduction mode, where vaporization weakly occurs or is negligible. Due to surface tension forces, the melt pool shape is globally smooth and consequently, as shown in Fig. 9(a), the laser energy is reflected after striking the melt pool back to the gas. However, vaporization phenomenon is usually observed in SLM process, as reported in the introduction. Consequently, the recoil pressure induced by vaporization generates a keyhole where the laser beam penetrates deeply the melt pool.

Consequently, its morphology cannot anymore be assumed as planar. Considering the melt pool morphology as shown in Fig. 9(b), multiple reflections take place in the capillary. Therefore, the fraction of laser energy reflected back to the gas and definitely lost in conduction mode, returns to the melt pool in keyhole mode and increases the amount of absorbed energy. Consequently, the apparent absorptivity of the material is increased. Furthermore, Trapp et al. (2017) have measured for

\includegraphics[max width=\textwidth, center]{2024_03_10_fc82295ca80e2636ba5dg-11}\\
\includegraphics[max width=\textwidth, center]{2024_03_10_fc82295ca80e2636ba5dg-11(2)}

Fig. 11. Comparison between numerical results (red) and experimental observations on optical micrograph on cross-sectional view (blue) for case \#4 (a) before and (b) after calibration. The scale bar is common for each image.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-12(4)}
\end{center}

Fig. 12. Comparison between numerical and experimental results in the process window. The blue and red contours represent respectively the boundary of the experimental and simulated melted zones in a cross section of the track, after solidification.

(a)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-12(2)}
\end{center}

(c)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-12(3)}
\end{center}

(b)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-12(1)}
\end{center}

(d)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-12}
\end{center}

Fig. 13. Evolution of (a) the apparent height $H_{a p p}$, (b) the melt pool depth $H_{R Z}$, (c) the apparent width $W_{M P}$ and (d) the melted melt pool area $S_{M P}$ as a function of the linear energy $\left(E_{l}\right)$.\\
stainless steel $316 \mathrm{~L}$ the evolution of absorptivity with respect to laser power for a fixed laser scan velocity. They demonstrated that the capillary topology is responsible for an increase of the apparent absorptivity, associated with increasing laser power energy absorption.

Different approaches have been proposed in the literature to model and simulate multiple reflections of laser wave. Generally, the raytracing method is used to provide a precise repartition of the energy introduced into the material (Khairallah et al., 2016). This method uses Fresnel's laws to deduce the light ray paths also considering the transmittance and the absorbance of the material depending on the light ray incidence angle. However, this method is generally costly in a 3D simulation context. In the present paper, a calibration methodology is used to provide an estimation of the absorptivity coefficient and efficiently compare experimental measurements and numerical simulation. An increase in the absorptivity value leads to a larger amount of energy delivered to the material. Consequently, the melted zone enlarges. Moreover, as shown in Fig. 10, an affine relationship is observed in the study range between the transverse area of the melt pool $\left(S_{M P}\right.$, perpendicular to the laser scan direction) obtained in numerical simulation and the absorptivity input value. This affine relationship is also consistent with the simplified energy conservation model, discussed in section 3 (cf. Eq. (4)). For the present configuration, this leads to a proposed value of 0.72 for the absorptivity, to match the experimental value of $S_{M P}$

Consequently, according to this linear dependence, two numerical simulations with different values of the absorptivity coefficient are sufficient to determine the absorptivity coefficient providing relevant comparisons with experimental observations.

\subsection*{3.5. Comparison of the experimental/simulated melt pool shape}
After calibration of absorptivity as described above, Fig. 11(b) and Table 5 illustrate the comparison of the predicted melt pool shape and the experimental observation with a calibrated value for absorptivity of 0.72 .

Contrary to the previous simulation (for which $A=0.3$ ), the model predicts more accurately both the track shape and the associated dimensions. Indeed, an increase in input energy is observed when increasing absorptivity coefficient. More energy is available to melt matter and larger dimensions in melted domain are achieved. In addition, since more energy is provided, higher temperatures are observed in the melt pool.

As a result, the recoil pressure induced by vaporization is more intense, leading also to an increase of the melt pool depth and the global track dimension as explained previously by Queva et al. (2020). This result demonstrates the importance of accounting for the multiple reflections phenomena into the keyhole to obtain a good agreement with experimental observations. Consequently, the calibration of absorptivity was repeated for every simulated case in Table 3, leading to different values of absorptivity.\\
3.6. Application to the whole experimental plan: comparison with observations

Fig. 12 compares on cross-section views the results given by the numerical simulation with the experimental observations in the process window. A good agreement is obtained between numerical and experimental results in the whole process window. Indeed, from a configuration with a low linear energy $(0.24 \mathrm{~J} / \mathrm{mm})$ to a configuration considering a significant linear energy value $(0.47 \mathrm{~J} / \mathrm{mm})$, the model is able to predict both the melt pool dimensions and morphology. Fig. 13 presents quantitatively the comparison of the results obtained by the present model with experiment. As shown in Table 6, a good agreement is obtained between numerical simulation and experiments for $H_{a p p}, H_{R Z}$, $W_{M P}$ and $S_{M P}$. Indeed, for $H_{R Z}, W_{M P}$ and $S_{M P}$ the maximum of deviation between numerical and experimental results are lower than 8\%. Moreover, the mean value of the deviation of each dimension does not exceed $6.6 \%$. It has to be noted for case \#14 that the powder bed height has been raised from 55 to $70 \mu \mathrm{m}$. This will be discussed in the next section.

Comparisons are obtained between experimental observations and numerical results on cross-section views on the left side in Fig. 14. On the right side of the same figure, the keyhole mode transition as linear energy increases is illustrated in longitudinal section snapshots. These comparisons are obtained for cases of interest from Table 3. The model demonstrates the capacity to simulate melt pool dynamics from low keyhole geometry to deep ones. As explained in the last part, stronger recoil force is applied to the gas/melt pool interface due to higher temperatures encountered as linear energy increases. Furthermore, it can be observed that the velocity magnitude reaches $5 \mathrm{~m} . \mathrm{s}^{-1}$, which is consistent with the maximum values reported by Ly et al. (2017) for Ti-6Al-4 V. It is also consistent with the values found by Bayat et al. (2019) for IN718.

\section*{4. Discussion}
\subsection*{4.1. Melt pool dimensions}
Even if the present model is able to predict correctly the melt pool dimension, it tends to slightly underestimate the apparent height $H_{\text {app }}$. One of the possible explanations is that some particles are drawn from both sides of the track toward the melt pool, as observed by Bidare et al. (2018). Here, because the powder bed is modelled as a continuum, this effect is not considered in the simulation, leading to an underestimation of $H_{a p p}$. Particles dynamics with movements towards the melt pool and away from the melt pool could be an impacting phenomenon and should be consider to provide accurate estimation of $H_{a p p}$ on the whole process window.

Moreover, for the numerical case with the highest linear energy (case \#14- $P_{L} 340 v_{L} 730$ ), as explained in the previous section, since the apparent height measured experimentally is much higher than the other cases investigated in the process window, a slight modification has been brought to the model by modifying the powder bed thickness for the

Table 6

Differences on the melted zone morphology between experimental (average of the different measures, noted M(EXP)) and numerical results for cases from Table 3 . DIFF is still calculated in percent.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\multirow{2}{*}{Case} & \multicolumn{2}{|c|}{$\boldsymbol{H}_{a p p}[\mu \mathrm{m}]$} & \multirow[b]{2}{*}{DIFF} & \multicolumn{2}{|c|}{$\boldsymbol{H}_{R Z}[\mu \mathrm{m}]$} & \multirow[b]{2}{*}{DIFF} & \multicolumn{2}{|c|}{$W_{M P}[\mu \mathrm{m}]$} & \multirow[b]{2}{*}{DIFF} & \multicolumn{2}{|c|}{$S_{M P}\left[\mu \mathrm{m}^{2}\right]$} & \multirow[b]{2}{*}{DIFF} \\
\hline
 & $\mathrm{M}(\mathrm{EXP})$ & NUM &  & M(EXP) & NUM &  & M(EXP) & NUM &  & M(EXP) & NUM &  \\
\hline
$\# 4$ & 53.75 & 43.6 & -18.8 & 70 & 67 & -4.3 & 125.3 & 116 & -7.7 & 10530 & 9038 & -14.2 \\
\hline
$\# 5$ & 57 & 44.2 & -13.7 & 61 & 57 & -6.6 & 123.5 & 115 & -6.9 & 9791 & 11290 & 5.1 \\
\hline
$\# 6$ & 55 & 49.5 & -10 & 87 & 82 & -5.7 & 132 & 121.5 & -8.0 & 12218 & 10676 & -12.6 \\
\hline
$\# 7$ & 60 & 50.3 & -16.2 & 97 & 100 & 3.1 & 133 & 132 & -0.8 & 14277 & 12956 & -9.3 \\
\hline
$\# 9$ & 61.25 & 51.2 & -16.4 & 85 & 80 & -5.9 & 147.8 & 150 & 1.5 & 14501 & 14698 & 1.4 \\
\hline
\#10 & 59.75 & 50.7 & -15.1 & 106 & 108 & 1.9 & 143.3 & 144 & 0.5 & 15477 & 15435 & -0.3 \\
\hline
\#12 & 60 & 52.6 & -12.3 & 153 & 149 & -2.6 & 149 & 151 & 1.3 & 21318 & 20027 & -6.1 \\
\hline
\#14 & 77 & 74.7 & -3.0 & 191 & 184 & -3.7 & 148 & 150 & 1.4 & 25867 & 23768 & -8.1 \\
\hline
\end{tabular}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-14}
\end{center}

Fig. 14. Comparison between numerical simulation and experiments on cross-sections and snapshots of the melt pool morphology transition as linear energy increases. The red and blue contours represent respectively numerical and experimental results. The black contour represents the melt pool shape. The scale bar is the same for each comparison case.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_fc82295ca80e2636ba5dg-15}

Fig. 14. (continued).

simulation (from $55 \mu \mathrm{m}$ to $70 \mu \mathrm{m}$ ) to enhance the calibration of the numerical simulation. Some assumptions can be advanced in order to discuss this observation and explain this choice. Matthews et al. (2016) consider that the denudation zone enlarges as laser power increases. Consequently, the proportion of ejected powder due to depression, of spatters generated from the melt pool and of powder entrained into the

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-16(1)}
\end{center}

(a)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-16(2)}
\end{center}

(b)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_fc82295ca80e2636ba5dg-16}
\end{center}

(c)

Fig. 15. Comparison between numerical absorptivity coefficient obtained after calibration by the present numerical simulation, and experimental measurements made by Trapp et al. (2017).

melt pool may evolve as laser power increases. However, despite that consideration, the constant powder bed thickness ( $55 \mu \mathrm{m}$ ) allows to predict accurately the melt pool dimensions of most cases.

The present model helps in understanding the influence of the laser power or the laser scan speed on laser-matter interaction, melt pool dynamics and finally the final bead shape obtained. For instance, for couples with similar linear energy $\left(0.24 \mathrm{~J} \cdot \mathrm{mm}^{-1}\right.$ for cases $\#\{1,2\}$ and $0.46 \mathrm{~J} \cdot \mathrm{mm}^{-1}$ for case $\#\{14,15\}$ ) a larger melted area and a higher melt pool depth $H_{R Z}$ are obtained. Indeed, for the case with the higher value of laser power and more importantly velocity, the keyhole wall angle tends to increase and modify the keyhole morphology as demonstrated by Cunningham et al. (2019). Therefore, it enhances the laser rays due to multiple reflections to merge to the center of the keyhole, increasing the global absorptivity of laser energy and finally the melt pool depth as explained in the last paragraph.

\subsection*{4.2. Evolution of absorptivity coefficient}
Fig. 15 illustrates the absorptivity values used after calibration compared to experimental measurements obtained by Trapp et al. (2017) with a $316 \mathrm{~L}$ steel. It is important to note that for all the measurements reported by Trapp et al., the laser scan speed was fixed at $1500 \mathrm{~mm} / \mathrm{s}$. A first comparison is done in Fig. 15(a), consisting in simply plotting $A$ as a function of $P_{L}$, despite the fact that the eight calibrated values of the present study are obtained for different scan velocities. It can be seen on this first chart that the present calibrated values are somewhat higher than the experimental ones. However, when plotting now $A$ as a function of the linear energy $E_{l}$, in Fig. 15(b), we observe a better coherence between the different values: the $A$ values of the present study - generally obtained for higher $E_{l}$ - tend to align in continuity with the measurements of Trapp et al.

Nevertheless, dots are not well aligned on Fig. 15(b), showing that absorptivity is probably not a function of the linear energy, but of more complex function of $P_{L}$ and $v_{L}$. In section 2.3, it is shown that a good description of the evolution of $S_{M P}$ is achieved with an absorptivity having the following expression: $A=C_{1} \cdot\left(P_{L}^{a} v_{L}^{b}-C_{2}\right)^{1 / 2}$. Therefore, Fig. 15(c) shows a chart in which $A$ is plotted against $P_{L}^{a} v_{L}^{b}$ with $a=0.2$ and $b=-0.06$, for both Trapp et al. and present calibrated values. It is remarkable that, excepting the domain of lower energy, for which keyhole does not appear, the whole set of values is now almost perfectly aligned, demonstrating the relevance of proposed expression for $A$ :

$A=0.95\left(P_{L}^{a} v_{L}^{b}-1.4\right)^{1 / 2}$

This suggests that the laser power has probably a stronger effect on the absorptivity than the scanning velocity. This is consistent with the fact that absorptivity is affected by the recoil pressure and thus by the peak temperature.

\subsection*{4.3. Comparison with another numerical simulation}
The configuration investigated by Bayat et al. (2019) was considered. The process parameters used by Bayat et al. such as laser power $(285 \mathrm{~W})$, velocity scan $\left(960 \mathrm{~mm} . \mathrm{s}^{-1}\right)$ or deposited powder height $(40 \mu \mathrm{m})$ are used also for this comparison. It is first underlined that this configuration is addressed by numerical simulation for the alloy IN718, and not IN738LC as in the present study. However, the thermophysical properties of the two alloys are sufficiently close to make this comparison relevant. An interesting point is that the approach of Bayat et al. differs from the present one essentially by two points: i) an explicit description of the particles of the powder bed, and ii) a ray-tracing approach to model the multi-reflections of the laser beam.

Fig. 16(a) illustrates the results of Bayat et al., as extracted from their article: melt pool shape at time $0.7 \mathrm{~ms}$ and three cross-section views showing the formation of the track. Fig. 16(b) shows the results from the present model. A good agreement was obtained both on the temperature distribution in the melt pool and on its dimensions in the different crosssections. First, from the capillary front to the tail of the melt pool, the temperature distribution between the two simulations is substantially the same, with temperature exceeding $3000^{\circ} \mathrm{C}$ where the laser is heating. Second, on the different cross-section views, more precisely at $X=$ $[300,400,500] \mu \mathrm{m}$ from the beginning of the track as shown in the right part of Fig. 16, the maximum of relative deviation between the two models for the total melt pool height $H$ is $12.1 \%$. For the melt pool width $\mathrm{W}$ (considering Bayat et al. notations), the maximum of deviation is 4.9 $\%$.

However, there are some differences, first in the diffusion of heat through the powder bed around the melt pool. Diffusion is more rapid in the simulation of Bayat et al. than with the present approach. Looking at the right part of Fig. 16, it can be noticed that the powder bed generated by the DEM method in Bayat et al. seems to show an average porosity larger than the value used in the simulation with the present approach $(50 \%)$. Note that a higher porosity should favor a slower diffusion, instead of a faster one. The reason for a faster diffusion could be found in possible differences regarding the model for the homogenized conductivity of the powder bed. Finally, another difference lies in the effect of surface tension, which seems somewhat different in the two simulations, the trend to spheroidization being more marked in the present simulation.

Finally, an interesting point to underline is that the absorptivity coefficient ( 0.76 ) has been obtained by using Fig. 15(a) where a quasilinear relationship is obtained between the laser power and the\\
\includegraphics[max width=\textwidth, center]{2024_03_10_fc82295ca80e2636ba5dg-17}

Fig. 16. Comparison between numerical results obtained by a) Bayat et al. (2019), and b) the present numerical model. Part a) of the Figure is directly replicated from the article of Bayat et al. (2019). Color coding for temperature distribution is the same for parts a) and b).

absorptivity for the laser power range investigated. This absorptivity coefficient also matches with the phenomenological expression given by Eq. (13). In other terms, this means that no calibration is necessary to get a good agreement with another numerical result considering a more accurate absorptivity calculation. Consequently, this demonstrates that numerical simulation can help also to provide averaged absorptivity estimation evolution maps according to different parameters such as laser power, scan speed or linear energy. These numerical evolution maps are interesting, because the experimental estimation of absorptivity is time and energy consuming.

\section*{5. Conclusion}
In this study, a set of tracks were fabricated in an Inconel 738 LC nickel-base superalloy using LBM process with a large set of processing parameters. The dimensions of tracks were precisely measured and cross sections of melted domains observed. Processing parameters with a linear incident energy between 0.22 and $0.5 \mathrm{~J} \cdot \mathrm{mm}^{-1}$ lead to tracks with stable dimensions and a penetration ratio $H_{R Z} / H_{a p p}$ between 1 and 3 . The use of analytical models allowed to describe the melt pool cross section, but was found insufficient to estimate quantitatively the different melt pool dimensions. For quantitative prediction, an advanced thermo-fluid finite element model was used. A novel method was proposed to calibrate the model, which then successfully predicted the melt pools dimensions on a large processing window. The calibration required first to take into consideration the significant amount of particle ejection during the interaction between the laser beam and the powder bed. This was done by a precise analysis of track and powder bed topography measurements. Because in the present model such ejections are not explicitly modeled, it was necessary to reduce the powder bed thickness in the simulation. This adjustment being done, the main results of the study are the followings:

\begin{enumerate}
  \item It was demonstrated that this numerical model, which considers the powder bed as a continuum, has an excellent capability to describe the melt pool shapes on the whole process window, from low energy conditions up to the keyhole mode and from low to high scanning velocities.

  \item The study proved the importance to consider absorptivity as a variable parameter. A novel method was proposed to determine the value of absorptivity, with a combination of semi-analytical reasoning and numerical simulation. This method allowed expressing absorptivity as a function of the laser power and the scanning velocity. It was shown that such a correlation is fully consistent with separate in-situ measurements from the literature.

  \item Using this phenomenological expression of absorptivity, the predictive character of the simulation code was successfully tested by comparison with another simulation code from the literature, which - at the cost of higher computational times - addresses more directly the physics (ray tracing, particle motion).

\end{enumerate}

This work also allows defining some progress orientations:

\begin{enumerate}
  \item The above-mentioned correlation and validation with respect to experimental observations essentially lies on the measurement of transverse sections of tracks and remelted zones. It would be highly appreciated to consolidate this with an advanced instrumentation. Two axes can be mentioned: thermal imaging to measure surface temperature fields, and high-speed imaging to observe and quantify ejection and denudation phenomena.

  \item Nonetheless, considering the numerical model as it is, its capability to describe track formation on a wide process window is very promising for its future use to control the microstructure of nickel based superalloys processed by LBM, and more particularly solidification defects, such as hot cracking. This could be done first by a direct use of this thermo-fluid code, providing then critical quantities at the rear of the melt pool, such as temperature gradients and temperature rates, from which it is known that relevant cracking indicators can be produced. This could also be done by adding a solid mechanics solver to the code in order to predict stress and strainrates, and possibly directly simulate cracking.

\end{enumerate}

\section*{CRediT authorship contribution statement}
D. Grange: Conceptualization, Methodology, Investigation, Formal analysis, Writing - original draft. A. Queva: Methodology, Software, Investigation, Writing - original draft. G. Guillemot: Methodology, Validation, Writing - review \& editing. M. Bellet: Methodology, Writing - review \& editing, Supervision. J.-D. Bartout: Methodology, Resources. C. Colin: Methodology, Validation, Supervision.

\section*{Declaration of Competing Interest}
The authors report no declarations of interest.

\section*{Acknowledgements}
Safran Tech (Châteaufort, France) funded this study. The authors would like to thank Clara Moriconi and Bruno Macquaire for their constructive remarks.

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Thermo-Calc, 2020. Thermo-Calc Software Company, Solna, Sweden. www.thermocalc. com.

Trapp, J., Rubenchik, A.M., Guss, G., Matthews, M.J., 2017. In situ absorptivity measurements of metallic powders during laser powder-bed fusion additive manufacturing. Appl. Mater. Today 9, 341-349. \href{https://doi.org/10.1016/j}{https://doi.org/10.1016/j}. apmt.2017.08.006.

Yadroitsev, I., Smurov, I., 2010. Selective laser melting technology: from the single laser melted track stability to 3D parts of complex shape. Physics Procedia, Laser Assisted

Net Shape Engineering 6, Proceedings of the LANE 2010, Part 2 5, 551-560. https:// \href{http://doi.org/10.1016/j.phpro.2010.08.083}{doi.org/10.1016/j.phpro.2010.08.083}.

Zehner, P., Schlünder, E.U., 1970. Wärmeleitfähigkeit von Schüttungen bei mäßigen Temperaturen. Chem. Ingenieur Tech. 42, 933-941. \href{https://doi.org/10.1002/}{https://doi.org/10.1002/} cite. 330421408 .\\
Zhang, S., Guillemot, G., Gandin, C.-A., Bellet, M., 2019. A partitioned two-step solution algorithm for concurrent fluid flow and stress-strain numerical simulation in solidification processes. Comput. Methods Appl. Mech. Eng. 356, 294-324. https:// \href{http://doi.org/10.1016/j.cma.2019.07.006}{doi.org/10.1016/j.cma.2019.07.006}.

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\title{Mitigation of lack of fusion defects in powder bed fusion additive manufacturing }


\author{T. Mukherjee, T. DebRoy*\\
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, 16802, USA}
\date{}


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\section*{A R T I C L E I N F O}
\section*{Keywords:}
Powder bed fusion

Lack of fusion defect

Heat transfer and fluid flow

Marangoni convection

Non-dimensional temperature

\begin{abstract}
A B S T R A C T Components manufactured by additive manufacturing often exhibit improper fusion among layers and hatches. Currently, there is no practical way to select process parameters and alloy systems based on scientific principles to mitigate these defects. Here, we develop, test and demonstrate a methodology to predict and prevent these defects based on a numerical heat transfer and fluid flow model for the laser powder bed fusion (PBF) additive manufacturing (AM). These defects are avoidable by adjusting laser power, scanning speed, layer thickness and hatch spacing. An easy to use parameter is proposed for practical use in shop floors. Relative susceptibilities of three widely used AM alloys are demonstrated using this parameter.
\end{abstract}

\section*{1. Introduction}
In laser-assisted powder bed fusion (L-PBF) additive manufacturing (AM), components are made of multiple thin layers and hatches. The soundness of the component depends on the fusion bonding among successive layers and hatches [1,2]. Lack of fusion is detrimental to the mechanical properties of the component, and in extreme cases leads to part rejection [1,3]. Improper selection of laser power, scanning speed, laser spot radius, layer thickness, hatch spacing and alloy affect the formation of this defect [4]. Because of the involvement of many process parameters and alloys, currently there is no generally available methodology to guide engineers to avoid this defect.

Several attempts have been made to understand the effects of different process parameters on the lack of fusion defect for different alloy systems and significant volume of experimental data have been reported in the literature. Experimentally, lack of fusion defect was found to be reduced with increasing laser power for stainless steel [5], titanium alloys [4,6,7], aluminum alloys [8-10] and CoCrMo alloy [11]. Slower scanning speed was also found to reduce lack of fusion defect for titanium alloys [4,6,7,12,13] and aluminum alloys [8-10]. Thinner layer and small hatch spacing were proved to reduce this defect for stainless steel [5], titanium alloys [14] and aluminum alloys [8-10]. However, in these experiments, one process variable was varied while other parameters were kept constant. The brute force approach to evaluate a parameter space for avoiding such defects through empirical testing needs to be repeated for every alloy. Because of the involvement of many process parameters, experimental evaluation of the roles of process parameters on the prevalence of defects by trial and error is time consuming and expensive.

A recourse is to develop, test and validate a science based, easy to use methodology of avoiding these defects using heat transfer considerations. Heat conduction models $[15,16]$ were used to calculate the molten pool shape and size based on which the extent of lack of fusion voids were estimated. However, these models neglect the effect of molten metal convection that is often the main mechanism of heat transfer inside the pool [1]. Neglecting molten metal convection results in inaccurate molten pool shape and size [17] and thus introduces uncertainty in the lack of fusion defects. In short, the existing powder bed fusion literature does not provide any rigorous methodology for selecting process parameters and alloy system to minimize lack of fusion defect. A quantitative understanding of the effects of process parameters and alloy properties on lack of fusion defect and a practical means to mitigate this problem based on scientific principles are needed but not currently available.

Here, we show, for the first time, how the lack of fusion defects during PBF can be minimized by using heat transfer and fluid flow calculations. To quantify the lack of fusion defect, we propose a dimensionless number that involves common process parameters such as laser power, scanning speed, spot radius, layer thickness and hatch spacing and different alloy properties such as density, thermal conductivity, specific heat and latent heat of fusion. The dimensionless number also includes molten pool dimensions calculated using a welltested, three dimensional, transient heat transfer and fluid flow model of L-PBF process. This non-dimensional number provides a relative
\footnotetext{\begin{itemize}
  \item Corresponding author.
\end{itemize}

E-mail address: \href{mailto:rtd1@psu.edu}{rtd1@psu.edu} (T. DebRoy).
}

Table 1

Thermo-physical properties of SS 316, Ti-6Al-4 V and AlSi10Mg [23]. Here 'T' represents temperature in $\mathrm{K}$ ranging from ambient to the solidus temperature.

\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Properties & SS 316 & Ti-6Al-4V & AlSi10Mg \\
\hline
Liquidus temperature $(\mathrm{K})$ & 1733 & 1928 & 867 \\
\hline
Solidus temperature $(\mathrm{K})$ & 1693 & 1878 & 831 \\
\hline
Thermal conductivity (W/m K) & $11.82+1.06 \times 10^{-2} \mathrm{~T}$ & $1.57+1.6 \times 10^{-2} \mathrm{~T}-1 \times 10^{-6} \mathrm{~T}^{2}$ & $113+1.06 \times 10^{-5} \mathrm{~T}$ \\
\hline
Specific heat (J/kg K) & $330.9+0.563 \mathrm{~T}-4.015 \times 10^{-4} \mathrm{~T}^{2}+9.465 \times 10^{-8} \mathrm{~T}^{3}$ & $492.4+0.025 \mathrm{~T}-4.18 \times 10^{-6} \mathrm{~T}^{2}$ & $536.2+0.035 \mathrm{~T}$ \\
\hline
Density $\left(\mathrm{kg} / \mathrm{m}^{3}\right)$ & 7800 & 4000 & 2670 \\
\hline
Latent heat of fusion $(\mathrm{J} / \mathrm{kg})$ & $272 \times 10^{3}$ & $284 \times 10^{3}$ & $423 \times 10^{3}$ \\
\hline
Viscosity $(\mathrm{kg} / \mathrm{m} \mathrm{s})$ & $7 \times 10^{-3}$ & $4 \times 10^{-3}$ & $1.3 \times 10^{-3}$ \\
\hline
$\mathrm{d} \gamma / \mathrm{dT}(\mathrm{N} / \mathrm{m} \mathrm{K})$ & $-0.40 \times 10^{-3}$ & $-0.26 \times 10^{-3}$ & $-0.35 \times 10^{-3}$ \\
\hline
Absorption coefficient in liquid $\left(\eta_{1}\right)$ & 0.3 & 0.3 & 0.3 \\
\hline
Absorption coefficient in powder $\left(\eta_{\mathrm{P}}\right)$ & 0.7 & 0.7 & 0.7 \\
\hline
Volumetric expansion coefficient $(/ \mathrm{K})$ & $5.85 \times 10^{-5}$ & $2.5 \times 10^{-5}$ & $2.4 \times 10^{-5}$ \\
\hline
Young's modulus (GPa) & 206 & 110 & 68 \\
\hline
\end{tabular}
\end{center}

scale to compare different alloys based on their susceptibility to the lack of fusion defect over a wide range of process parameters. The effects of all thermophysical properties of the alloys are considered during heat transfer and fluid flow calculations which is required for the lack of fusion number. Since the volume of the fusion zone depends on the processing parameters, thermophysical properties of the alloy and the geometry of the component, all of these factors have to be taken into account in the modeling to estimate the lack of fusion defect. In addition, the important non-dimensional numbers that are important in LPBF such as Marangoni number and non-dimensional temperature are correlated with the occurrence of lack of fusion defect. Based on these findings we provide recommendations to mitigate lack of fusion defects in components. Although, the results presented here are for L-PBF process, the proposed lack of fusion number is applicable to all AM processes since it is formulated based on the underlying principles of the lack of fusion void formation that are similar in all AM processes.

\section*{2. Heat transfer and fluid flow model of PBF}
A well-tested, three-dimensional, transient heat transfer and fluid flow model of L-PBF is used to calculate the temperature field and molten pool dimensions. The model solves the following equations of conservation of mass, momentum and energy [18-20]:

$\frac{\partial u_{i}}{\partial x_{i}}=0$

$\rho \frac{\partial u_{j}}{\partial t}+\rho \frac{\partial\left(u_{i} u_{j}\right)}{\partial x_{i}}=\frac{\partial}{\partial x_{i}}\left(\mu \frac{\partial u_{j}}{\partial x_{i}}\right)+S_{j}$

where $\rho$ and $\mu$ are the density and the viscosity of the alloy, respectively, $u_{i}$ and $u_{j}$ are the velocity components along the $i$ and $j$ directions, respectively, $x_{i}$ is the distance along the $i$ direction and $S_{j}$ is the source term for $j$ th momentum conservation equation. The energy conservation equation is written as [18-20]:

$\frac{\partial h}{\partial t}+\frac{\partial\left(u_{i} h\right)}{\partial x_{i}}=\frac{\partial}{\partial x_{i}}\left(\alpha \frac{\partial h}{\partial x_{i}}\right)-\frac{\partial \Delta H}{\partial t}-\frac{\partial\left(u_{i} \Delta H\right)}{\partial x_{i}}+S_{v}$

where $h$ denotes the sensible heat, $t$ is the time, $\alpha$ and $\Delta H$ are the thermal diffusivity and the latent heat of fusion of the alloy, respectively, $u_{i}$ is the velocity components along the $i$ direction and $S_{v}$ is the source term for the volumetric heat source and is represented as [1]:

$S_{v}=\frac{\xi \eta P}{\pi r^{2} t} \exp \left[-\frac{\xi\left(x_{b}^{2}+y_{b}^{2}\right)}{r^{2}}\right]$

where $P$ is laser power, $r$ is laser beam radius, $\xi$ is power distribution factor varies between 1 and 3 [1], $x_{b}$ and $y_{b}$ are the distances from the laser beam axis along $\mathrm{X}$ and $\mathrm{Y}$ directions, respectively and $t$ is the powder layer thickness.

The solution domain consists of substrate, deposited layers and hatches, powder bed, and shielding gas. The substrate material is same as the alloy powder. Convective and radiative boundary conditions are applied to all surfaces of the solution domain as [1]:

$-k \frac{\partial T}{\partial z}=\sigma \varepsilon\left(T^{4}-T_{A}^{4}\right)+h_{c}\left(T-T_{A}\right)$

where $k$ is the thermal conductivity of alloy, $\sigma$ is the Stefan-Boltzmann constant $\left(5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}\right), \varepsilon$ is the emissivity, $T_{A}$ is the ambient temperature and $h_{c}$ is the convective heat transfer coefficient.

The convective flow of the molten metal is primarily driven by the surface tension variation on the top surface of the molten pool resulting from the spatial gradient of temperature. The resulting stress on the top surface of the molten pool, called Marangoni shear stress [20-22] along $\mathrm{X}$ and $\mathrm{Y}$ directions can be written as,

$\tau_{x}=\mu \frac{d u}{d z}=-\frac{d \gamma}{d T} G_{x}$

$\tau_{y}=\mu \frac{d v}{d z}=-\frac{d \gamma}{d T} G_{y}$

where $\mu$ is the viscosity of the liquid metal, $G_{x}$ and $G_{y}$ are the two components of temperature gradient along $\mathrm{X}$ and $\mathrm{Y}$ directions and $d \gamma / d T$ represents the surface tension gradient with respect to temperature that has a negative value for most commonly used alloys that do not contain any surface active element [1]. Temperature dependent thermo-physical properties of the alloy powders [23] are provided in Table 1.

More details about the implementation of this model for L-PBF are described in our previous publication [24] and are not repeated here. Only the salient features are indicated here. The conservation equations of mass, momentum and energy are discretized in the 3D Cartesian coordinate using the control volume method. All discretized equations are solved simultaneously to obtain enthalpy, velocity and pressure fields using the tri-diagonal matrix algorithm (TDMA) [25]. The temperature field is obtained from the enthalpy field by using temperature dependent specific heat of the alloy. The calculation procedure continues until all the hatches and layers are completed. These calculations are performed using an in-house Fortran code compiled using an Intel Fortran compiler. The process parameters used for the calculations are given in Table 2. The calculation time is approximately $5 \mathrm{~h}$ for a $20 \mathrm{~mm}$ long, 5 layers, 5 hatches build in a personal computer with a $3.40 \mathrm{GHz}$ i7 processor and 8 GB RAM.

\section*{3. Results and discussions}
Fig. 1(a) shows the three-dimensional temperature and velocity fields calculated using the heat transfer and fluid flow model during the building of first layer first hatch of a SS 316 build. The temperature and velocity fields on top (XY), transverse (YZ) and longitudinal (XZ) planes are shown in Fig. 1(b)-(d) respectively. The region bounded by the liquidus temperature isotherm ( $1733 \mathrm{~K}$ ) of SS 316 represents the fusion

Table 2

Process parameters used for calculations. Packing efficiency is a measure of extent of voids in the powder bed and is adapted from the literature [24].

\begin{center}
\begin{tabular}{ll}
\hline
Laser power, $\mathrm{W}$ & 60 \\
\hline
Scanning speed, $\mathrm{mm} / \mathrm{s}$ & $250-1000$ \\
Laser spot radius, $\mathrm{mm}$ & 0.050 \\
Layer thickness, $\mathrm{mm}$ & 0.030 \\
Hatch spacing, $\mathrm{mm}$ & 0.035 \\
Build length, $\mathrm{mm}$ & 20 \\
Substrate dimensions, $\mathrm{mm} \times \mathrm{mm} \times \mathrm{mm}$ & $22 \times 5 \times 2$ \\
Packing efficiency & 0.5 \\
\end{tabular}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-3(3)}
\end{center}

(c)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-3}
\end{center}

(d)

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-3(1)}
\end{center}

Fig. 1. Temperature and velocity distributions for 1 st hatch and 1 st layer of a $20 \mathrm{~mm}$ long SS 316 build on a $24 \mathrm{~mm}$ long SS 316 substrate using $60 \mathrm{~W}$ laser power and $500 \mathrm{~mm} / \mathrm{s}$ scanning speed on (a) 3D isometric section (b) top (c) longitudinal and (c) transverse planes. The length of the build is from $x=2.0 \mathrm{~mm}$ to $22.0 \mathrm{~mm}$. Other process conditions are mentioned in Table 2. Scanning direction of the laser beam is along the positive $\mathrm{x}$-axis.

zone of the molten pool. The light blue region within the liquidus and the solidus temperature ( $1693 \mathrm{~K}$ ) isotherms represents the mushy zone. Therefore, the $1693 \mathrm{~K}$ isotherm represents the molten pool boundary. The velocity vectors are represented by the black arrows whose magnitude can be found by comparing their length with the reference\\
\includegraphics[max width=\textwidth, center]{2024_03_10_2939f98f4c531399bef9g-3(2)}

Fig. 2. Comparison between the calculated and experimentally observed (a) width and (b) depth of the molten pool of a single layer single hatch builds of SS 316, Ti-6Al-4 V and AlSi10Mg at different linear heat inputs. The experimentally measured width and depth for SS 316 are adapted from Di et al. [5] and Li et al. [27], respectively. The experimental results for Ti-6Al-4 V and AlSi10Mg are taken from Gong et al. [12] and Kempen et al. [26], respectively. Gong et al. [12] and Kempen et al. [26] provided the macrograph from which Tang et al. [15] measured the dimensions.

vector provided. The velocity vectors are radially outwards because molten metal flows from the high temperature to the low temperature. The laser beam travels in the direction of positive X-axis. Therefore, the molten pool is elongated in the opposite direction (negative X-axis). The molten pool exhibits a teardrop shape that is attributed to rapid scanning speed of the PBF process [1]. The track width is determined from the solidus isotherms on the transverse sections as shown in Fig. 1(d).

Fig. 2(a) and (b) compare the calculated molten pool width and depth, respectively, and their variations with linear heat input (laser power/scanning speed) with independent experimental observations $[5,12,15,26,27]$ for single layer single hatch builds of SS 316, Ti-6Al$4 \mathrm{~V}$ and AlSi10Mg. For all three alloys, track width and depth increase with heat input as expected. Fair agreements between calculated and experimental results for all three alloys considered here provide us the confidence to use the model to predict the molten pool dimensions to

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-4}
\end{center}

Lack of fusion voids\\
\includegraphics[max width=\textwidth, center]{2024_03_10_2939f98f4c531399bef9g-4(1)}

Fig. 3. Transverse sectional view of the molten pools for 3 layers 5 hatches builds of (a) SS 316 (b) Ti-6Al-4 V and (c) AlSi10Mg using $60 \mathrm{~W}$ laser power, $1000 \mathrm{~mm} / \mathrm{s}$ scanning speed and $90 \mu \mathrm{m}$ hatch spacing. Other process conditions are mentioned in Table 2.

evaluate lack of fusion defect.

Figs. 3(a-c) show the computed shapes and sizes of the molten pool transverse sections (YZ plane) for different hatches and layers of five hatches, three layers, builds of SS 316, Ti-6Al-4 V and AlSi10Mg, respectively. For the SS 316 and Ti-6Al-4 V builds, unmelted regions between the molten pools indicating improper fusional bonding among layers and hatches represent the lack of fusion voids. For the same processing conditions, molten pools in AlSi10Mg build are the largest due to its lowest density. Therefore, AlSi10Mg does not exhibit any lack of fusion voids at the processing condition considered. Figs. 4 (a-c) show the computed shapes and sizes of the molten pool transverse sections (YZ plane) for different hatches and layers of five hatches, three layers, builds of SS 316 at different heat inputs. Lack of fusion voids observed in Fig. 4 (a) are eliminated by increasing laser power and decreasing scanning speed, as shown in Fig. 4 (b) and (c), respectively.

From Fig. 4 it is clear that the lack of fusion defect depends on both laser power and scanning speed. Figs. 5 (a) and (b) show the relation of experimentally measured [5,11] lack of fusion void fraction with laser power and scanning speed, respectively. In these plots the experimental data are taken from the independent literature [5,11]. It has been found that the amount of lack of fusion voids is inversely proportional to the laser power and directly proportional to the scanning speed. Apart from these two process conditions, layer thickness and hatch spacing also play important role in determining lack of fusion defect. Figs. 6 (a) and (b) show the relation of experimentally measured [14,28] lack of fusion void fraction with layer thickness and hatch spacing, respectively. In these plots the experimental data are taken from the independent literature [14,28]. It has been found that amount of the lack of fusion voids is directly proportional to both the layer thickness and hatch spacing.

From Figures (3-6) it is clear that the lack of fusion defect depends on alloy properties and process parameters such as laser power, scanning speed, layer thickness and hatch spacing. However, other process parameters such as laser spot radius, absorptivity of the laser beam at the powder bed, molten pool width and depth and rate of heat transfer also govern lack of fusion defect in PBF [4,15]. Therefore, to quantify and provide better understanding of the effects of these governing factors on the lack of fusion defect in PBF, a non-dimensional lack of fusion number $\left(L_{F}\right)$ is proposed and used here. This number, $L_{F}$ consists of all important process parameters and alloy properties and is represented as:

$L_{F}=\frac{\rho\left(C_{P} \Delta T+L\right)}{\frac{\eta P}{\pi r^{2} v}} F \frac{t}{d}\left(\frac{h}{w}\right)^{2}$

All the symbols used in this equation are described along with their units and dimensions in Table 3. Eq. (8) clearly indicates that the lack of fusion defect is proportional directly to scanning speed, layer thickness and hatch spacing and inversely to laser power as shown in Fig. 5 and 6. Molten pool width and depth and Fourier number used in this equation are calculated using the heat transfer and fluid flow model. Recently,

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-5}
\end{center}

\section*{Lack of fusion voids}
\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-5(1)}
\end{center}

Fig. 4. Transverse sectional view of the molten pools for 3 layers 5 hatches SS 316 builds using (a) $60 \mathrm{~W}$ power and $1000 \mathrm{~mm} / \mathrm{s}$ speed (b) $100 \mathrm{~W}$ power and $1000 \mathrm{~mm} / \mathrm{s}$ speed and (c) $60 \mathrm{~W}$ power and $250 \mathrm{~mm} / \mathrm{s}$ speed. All three results are using $90 \mu \mathrm{m}$ hatch spacing. Other process conditions are mentioned in Table 2.

we have shown how the molten pool dimensions vary with layers and hatches $[24,29]$. The dimensions do not change significantly after the $2^{\text {nd }}$ hatch and the layer where the temperature field reaches steady state $[24,29,30]$. Therefore, molten pool dimensions used in Eq. (8) are taken at $2^{\text {nd }}$ hatch after they reach the steady state. Since wider and deeper molten pool ensures proper fusional bonding among successive layers and hatches, both pool width and depth are in the denominator of Eq. (8). Other important material properties that affect pool dimensions and thus the lack of fusion defect such as viscosity and coefficient of surface tension are considered by including their effects during pool depth and width predictions. Fourier number indicates faster diffusive heat transfer relative to heat accumulation [31]. A high rate of heat transfer reduces the pool size and thus increases the lack of fusion defect. The term $\rho\left(C_{P} \Delta T+L\right)$ denotes the amount of heat needed to melt per unit volume of material. For a given heat input, an alloy with high energy required for melting exhibits smaller molten pool that increases the susceptibility of lack of fusion defect.

Fig. 7 shows that the experimentally measured $[5,15,28,13]$ lack of fusion void fraction $\left(V_{E}\right)$ for three commonly used alloys follows a linear relationship with corresponding $L_{F}$, which is estimated using Eq. (8). A sample calculation for the estimation of the $L_{F}$ for SS 316 is shown in the Supplementary document. Based on the trend of the data points presented in Fig. 7, the lack of fusion void fraction $\left(V_{E}\right)$ can be expressed as:

$V_{E}=15.3 L_{F}$\\
All statistical data to qualify this linear fit are summarized in Table 4. Eq. (9) is valid for the heat input range of $0.05-1.00 \mathrm{~J} / \mathrm{mm}$, which is widely used for major L-PBF applications [1]. In this equation, when $L_{F}$ is zero there are no lack of fusion voids observed. To include a new alloy, the correlation in Eq. (9) needs to be updated by including new experimental data for that alloy in Fig. 7. However, the lack of fusion number is applicable for any alloy for a wide range of processing conditions.

The lack of fusion number, $L_{F}$, provides a usable scale to estimate and compare the amount of lack of fusion void in L-PBF of different alloys. Fig. 8 compares three commonly used alloys based on their vulnerability to the lack of fusion defect at three different scanning speeds. SS 316 is the most susceptible to lack of fusion defect because of its smallest molten pool attributed to its relatively high density. Since rapid scanning reduces the pool size, amount of lack of fusion voids enhances with increasing scanning speed as shown in Fig. 8.

Lack of fusion defect depends largely on the molten pool shape and size governed by the flow of liquid metal driven primarily by the spatial gradient of interfacial tension, also known as the Marangoni stress [20-22]. Effects of Marangoni stress is quantified by the Marangoni number $[31,32]$ :

$M a=-\frac{d \gamma}{d T} \frac{\delta \Delta T}{\mu \alpha}$

where $\mu$ is the dynamic viscosity, $\alpha$ is the thermal diffusivity of the\\
\includegraphics[max width=\textwidth, center]{2024_03_10_2939f98f4c531399bef9g-6(1)}

Fig. 5. Relation of experimentally measured void fraction with (a) laser power and (b) scanning speed. The data to plot the figures (a) and (b) are taken from Darvish et al. [11] and Di et al. [5], respectively. The results at the figures (a) and (b) are for CoCrMo alloy and SS 316, respectively. The linearity of the plots is indicated by the correlation coefficients of 0.95 and 0.99 for figures (a) and (b), respectively.

alloy, $\delta$ is the characteristic length of the molten pool, which is taken as the width of the molten pool, $\Delta T$ is the difference between the peak temperature inside the pool and the solidus temperature of an alloy, and $\frac{d \gamma}{d T}$ is the surface tension gradient with respect to temperature. For most alloys that do not contain any surface active elements, this quantity is negative [1]. The peak temperature and pool width required for the calculations are estimated using the heat transfer and fluid flow model. Higher Marangoni number indicates vigorous flow of liquid metal inside the pool that increases the molten pool width and ensures proper fusional bonding among successive layers and hatches. Therefore, lack of fusion defect decreases when hatch spacing and layer thickness are constant for processes with higher Marangoni number as shown in Fig. 9.

Assuming a constant cross section, hatch spacing, and layer thickness, higher molten pool peak temperature may indicate heat accumulation and consequentially a larger molten pool which facilitates better bonding of the depositing metal with the previously deposited metal. Therefore, monitoring of peak temperature during AM can be used as an indicator of the extent of lack of fusion defect. A non-dimensional temperature $\mathrm{T}^{*}$ can reveal the change in the amount of lack of fusion voids due to rise in peak temperature [32]:\\
\includegraphics[max width=\textwidth, center]{2024_03_10_2939f98f4c531399bef9g-6}

Fig. 6. Relation of experimentally measured void fraction with (a) layer thickness and (b) hatch spacing. The data to plot the figures (a) and (b) are taken from Qiu et al. [14] and Aboulkhair et al. [28], respectively. The results at the figures (a) and (b) are for Ti-6Al-4 V and AlSi10Mg, respectively. The linearity of the plots is indicated by the correlation coefficients of 1.00 and 0.94 for figures (a) and (b), respectively.

Table 3

Variables used in the lack of fusion number $\left(L_{F}\right)$ in the MLT $\theta$ system.

\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Variable & S.I. unit & Dimension \\
\hline
Density of alloy, $\rho$ & $\mathrm{kg} / \mathrm{m}^{3}$ & $\mathrm{ML}^{-3}$ \\
\hline
Specific heat of alloy, $C_{P}$ & $\mathrm{~J} / \mathrm{kg} \mathrm{K}$ & $\mathrm{L}^{2} \mathrm{~T}^{-2} \theta^{-1}$ \\
\hline
\begin{tabular}{l}
Temperature gradient, $\Delta T=T_{L}-T_{S}$, where $T_{L}$ and $T_{S}$ \\
refer respectively to liquidus and solidus temperature \\
\end{tabular} & K & $\theta$ \\
\hline
Latent heat of fusion of alloy, $L$ & $\mathrm{~J} / \mathrm{kg}$ & $\mathrm{L}^{2} \mathrm{~T}^{-2}$ \\
\hline
Absorptivity of laser beam, $\eta$ & - & $\mathrm{M}^{\circ} \mathrm{L}^{\circ} \mathrm{T}^{0} \theta^{0}$ \\
\hline
Laser beam power, $P$ & $\mathrm{~W}$ & $\mathrm{ML}^{2} \mathrm{~T}^{-3}$ \\
\hline
Laser scanning speed, $v$ & $\mathrm{~m} / \mathrm{s}$ & $\mathrm{LT}^{-1}$ \\
\hline
Laser beam radius, $r$ & $\mathrm{~m}$ & $\mathrm{~L}$ \\
\hline
\begin{tabular}{l}
Fourier number, $F$ denoted by $F=\alpha / v l$ where $\alpha$ is the \\
thermal diffusivity of alloy and $l$ is the molten pool \\
length \\
\end{tabular} & - & $\mathrm{M}^{\circ} \mathrm{L}^{\circ} \mathrm{T}^{0} \theta^{0}$ \\
\hline
Layer thickness, $t$ & $\mathrm{~m}$ & $\mathrm{~L}$ \\
\hline
Hatch spacing, $h$ & $\mathrm{~m}$ & $\mathrm{~L}$ \\
\hline
Molten pool depth, $d$ & $\mathrm{~m}$ & $\mathrm{~L}$ \\
\hline
Molten pool half-width, $w$ & $\mathrm{~m}$ & $\mathrm{~L}$ \\
\hline
\end{tabular}
\end{center}

$T^{*}=\frac{T_{P}}{T_{L}}$

where $T_{P}$ and $T_{L}$ are the peak temperature and liquidus temperature of

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-7(2)}
\end{center}

Fig. 7. Values of experimental void fraction $\left(\mathrm{V}_{\mathrm{E}}\right)$ as a function of the lack of fusion number $\left(L_{F}\right)$ for AlSi10Mg [28], Ti-6Al-4 V [15,13] and SS 316 [15,5] showing a linear relationship. Experimentally measured void fraction values are directly taken from the literature. $L_{F}$ values are calculated using corresponding process parameters and alloy properties.

Table 4

Statistical data about the linear fit presented in Fig. 7.

\begin{center}
\begin{tabular}{ll}
\hline
Coefficient of determination & 0.82 \\
\hline
Standard deviation & 0.025 \\
p-value & Negligible (in the order of $10^{-8}$ ) \\
\hline
\end{tabular}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-7(1)}
\end{center}

Fig. 8. Values of the calculated lack of fusion number $\left(L_{F}\right)$ calculated for SS 316, Ti6Al4V and AlSi10Mg builds. The symbol (a), (b) and (c) denote the scanning speed of $500 \mathrm{~mm} / \mathrm{s}, 750 \mathrm{~mm} / \mathrm{s}$ and $1000 \mathrm{~mm} / \mathrm{s}$ scanning speed, respectively. All calculations are done at $60 \mathrm{~W}$ laser power and other processing conditions are provided in Table 2.

the alloy, respectively. The peak temperature required for the calculations may be either estimated from the heat transfer and fluid flow model or determined with a thermo-camera. Fig. 10 shows that the lack of fusion defect decreases with an increase in peak temperature. The peak temperatures for the parameter range considered here are below the boiling point of the alloys and keyholes do not form during the process. However, instabilities in the keyholes formed at very high power density may result in porosity that are different from the lack of fusion voids described here [1,33]. Fig. 9 and 10 show that the lack of fusion voids can be effectively minimized by enhancing Marangoni number and non-dimensional temperature during the process by

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-7}
\end{center}

Fig. 9. Variation of the calculated lack of fusion number $\left(L_{F}\right)$ as a function of Marangoni number for different heat inputs per unit length. The processing conditions for these results are provided in Table 2. The coefficient of determination of this quadratic fit is 0.82 .

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_2939f98f4c531399bef9g-7(3)}
\end{center}

Fig. 10. Variation of the calculated lack of fusion number $\left(L_{F}\right)$ as a function of non-dimensional temperature for different heat inputs per unit length. The processing conditions for these results are provided in Table 2.

adjusting different processing conditions.

\section*{4. Summary and conclusions}
A well-tested, three-dimensional, transient heat transfer and fluid flow model is used to calculate the temperature and pool dimensions used for the dimensionless calculations. The results presented here provide, for the first time, a quantitative basis for minimizing lack of fusion defect in components made by L-PBF based on scientific principles. Below are the specific findings.

\begin{enumerate}
  \item A non-dimensional number that considers $A M$ process parameters and alloy properties is developed and tested for preventing lack of fusion defects for a wide range of process conditions and three commonly used alloys.

  \item Among the three commonly used AM alloys considered, the biggest molten pool of AlSi10Mg for a given set of AM process parameters minimizes lack of fusion defect. Under the same processing conditions, AlSi10Mg and SS 316 are the least and most vulnerable to the\\
lack of fusion defect.

  \item A larger heat input per unit length obtained by reduction of scanning speed or an increase in laser power or both results is larger liquid pool and lower occurrence of lack of fusion defect.

  \item A high value of Marangoni number that indicates vigorous circulation of the liquid metal inside the molten pool correlated well with the reduction of the lack of fusion defects.

  \item High values of peak temperature also correlated well with the reduction of the occurrence of lack of fusion defects. Since the temperature can be monitored during deposition, this correlation can be used to reduce lack of fusion defects.

\end{enumerate}

\section*{Acknowledgements}
One of the authors (T.M.) acknowledges support of an American Welding Society research fellowship, grant number 179466. We also acknowledge helpful discussions with J.S. Zuback and G.L. Knapp of Penn State University and Prof. A. De from IIT Bombay and Prof. H.L. Wei from Nanjing University of Science and Technology for their interest in this research.

\section*{Appendix A. Supplementary data}
Supplementary material related to this article can be found, in the online version, at doi:\href{https://doi.org/10.1016/j.jmapro.2018.10.028}{https://doi.org/10.1016/j.jmapro.2018.10.028}.

\section*{References}
[1] DebRoy T, Wei HL, Zuback JS, Mukherjee T, Elmer JW, Milewski JO, et al. Additive manufacturing of metallic components - process, structure and properties. Prog Mater Sci 2018;92:112-224.

[2] El-Desouky A, Michael C, Mohamad M, Alaa E, Saniya L. Influences of energy density on microstructure and consolidation of selective laser melted bismuth telluride thermoelectric powder. J Manuf Process 2017;25:411-7.

[3] Mukherjee T, Zuback JS, De A, DebRoy T. Printability of alloys for additive manufacturing. Sci Rep 2016;6:19717.

[4] Thijs L, Verhaeghe F, Craeghs T, Van Humbeeck J, Kruth JP. A study of the mi crostructural evolution during selective laser melting of Ti-6Al-4V. Acta Mater 2010;58(9):3303-12.

[5] Di W, Yang Y, Su X, Chen Y. Study on energy input and its influences on singletrack, multi-track, and multi-layer in SLM. Int J Adv Manuf Technol 2012;58(9-12). 1189-99.

[6] Cunningham R, Narra SP, Montgomery C, Beuth J, Rollett AD. Synchrotron-based Xray microtomography characterization of the effect of processing variables on porosity formation in laser power-bed additive manufacturing of Ti-6Al-4V. JOM 2017;69(3):479-84.

[7] Tammas-Williams S, Zhao H, Léonard F, Derguti F, Todd I, et al. XCT analysis of the influence of melt strategies on defect population in Ti-6Al-4V components manufactured by Selective Electron Beam Melting. J Miner Mater Charact Eng 2015;102:47-61

[8] Buchbinder D, Schleifenbaum HB, Heidrich S, Meiners W, Bültmann J. High power selective laser melting (HP SLM) of aluminum parts. Phys Proced 2011;12:271-8.

[9] Olakanmi EO, Cochrane RF, Dalgarno KW. Densification mechanism and microstructural evolution in selective laser sintering of Al-12Si powders. J Mater Process Technol 2011;211(1):113-21.

[10] Olakanmi EO. Selective laser sintering/melting (SLS/SLM) of pure $\mathrm{Al}, \mathrm{Al}-\mathrm{Mg}$, and Al-Si powders: effect of processing conditions and powder properties. J Mater Process Technol 2013;213(8):1387-405.

[11] Darvish K, Chen ZW, Pasang T. Reducing lack of fusion during selective laser melting of CoCrMo alloy: Effect of laser power on geometrical features of tracks. Mater Des 2016;112:357-66.

[12] Gong H, Gu H, Zeng K, Dilip JJS, Pal D, Stucker B, et al. Melt pool characterization for selective laser melting of Ti-6Al-4V pre-alloyed powder. In Solid Freeform\\
Fabrication Symposium. 2014. p. 256-67.

[13] Gong H, Rafi K, Gu H, Starr T, Stucker B. Analysis of defect generation in Ti-6Al-4V parts made using powder bed fusion additive manufacturing processes. Additive Manuf 2014;1:87-98.

[14] Qiu C, Panwisawas C, Ward M, Basoalto HC, Brooks JW, Attallah MM. On the role of melt flow into the surface structure and porosity development during selective laser melting. Acta Mater 2015;96:72-9.

[15] Tang M, Pistorius PC, Beuth JL. Prediction of lack-of-fusion porosity for powder bed fusion. Additive Manuf 2017;14:39-48.

[16] Teng C, Gong H, Szabo A, Dilip JJS, Ashby K, Zhang S, et al. Simulating melt pool shape and lack of fusion porosity for selective laser melting of cobalt chromium components. J Manuf Sci Eng 2017;139(1):011009.

[17] Arrizubieta JI, Lamikiz A, Klocke F, Silvia M, Kristian A, Eneko U. Evaluation of the relevance of melt pool dynamics in Laser Material Deposition process modeling. Int J Heat Mass Transf - Theory Appl 2017;115:80-91.

[18] Mukherjee T, Zhang W, DebRoy T. An improved prediction of residual stresses and distortion in additive manufacturing. Comput Mater Sci 2017;126:360-72.

[19] Manvatkar V, De A, DebRoy T. Spatial variation of melt pool geometry, peak temperature and solidification parameters during laser assisted additive manufacturing process. Mater Sci Technol 2015;31(8):924-30.

[20] Knapp GL, Mukherjee T, Zuback JS, Wei HL, Palmer TA, De A, et al. Building blocks for a digital twin of additive manufacturing. Acta Mater 2017;135:390-9.

[21] Mukherjee T, Zuback JS, Zhang W, DebRoy T. Residual stresses and distortion in additively manufactured compositionally graded and dissimilar joints. Comput Mater Sci 2018;143:325-37.

[22] Manvatkar V, De A, DebRoy T. Heat transfer and material flow during laser assisted multi-layer additive manufacturing. J Appl Phys 2014;116(12):124905.

[23] Mills KC. Recommended values of thermo-physical properties for selected commercial alloys. Cambridge: Woodhead Publishing; 2002.

[24] Mukherjee T, Wei HL, De A, DebRoy T. Heat and fluid flow in additive manufacturing — part I: modeling of powder bed fusion. Comput Mater Sci 2018;150:304-13.

[25] Patankar SV, Heat Numerical. Transfer and fluid flow. New York: McGraw-Hill; 1982.

[26] Kempen K, Thijs L, Van Humbeeck J, Kruth JP. Processing AlSi10Mg by selective laser melting: parameter optimisation and material characterisation. Mater Sci Technol 2015;31(8):917-23,

[27] Li R, Shi Y, Wang Z, Wang L, Liu J, Jiang W. Densification behavior of gas and water atomized 316L stainless steel powder during selective laser melting. Appl Surf Sci 2010;256(13):4350-6.

[28] Aboulkhair NT, Everitt NM, Ashcroft I, Tuck C. Reducing porosity in AlSi10Mg parts processed by selective laser melting. Additive Manuf 2014;1:77-86.

[29] Mukherjee T, Wei HL, De A, DebRoy T. Heat and fluid flow in additive manufacturing - part II: powder bed fusion of stainless steel, and titanium, nickel and aluminum base alloys. Comput Mater Sci 2018;150:369-80.

[30] Craeghs T, Clijsters S, Yasa E, Bechmann F, Berumen S, Kruth JP. Determination of geometrical factors in Layerwise Laser Melting using optical process monitoring. Opt Laser Eng 2011;49(12):1440-6.

[31] Mukherjee T, Manvatkar V, De A, DebRoy T. Dimensionless numbers in additive manufacturing. J Appl Phys 2017;121(6):064904.

[32] Mukherjee T, Manvatkar V, De A, DebRoy T. Mitigation of thermal distortion during additive manufacturing. Scripta Mater 2017;127:79-83.

[33] King WE, Barth HD, Castillo VM, Gallegos GF, Gibbs JW, Hahn DE, et al. Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J Mater Process Technol 2014;214(12):2915-25.

Mr. T. Mukherjee is a doctoral student of Materials Science and Engineering at The Pennsylvania State University. His research interests include additive manufacturing, welding, numerical modeling, heat and mass transfer. He was awarded by American Welding Society Graduate Research fellowship and Robert E. Newnham Research Excellence Award by Penn State University.

Dr. T. DebRoy is Professor of Materials Science and Engineering at The Pennsylvania State University. His publications at the cross roads of metallurgy, welding, additive manufacturing and numerical heat transfer have been cited more than 15,000 times in the literature (Google scholar). His awards include the UK Royal Academy of Engineering's Distinguished Visiting Fellowship, a Fulbright Distinguished Chair in Brazil, The Arata Award of the International Institute of Welding (IIW), France, Easterling Award of the University of Graz, Austria, and Penn State's Faculty Scholar Medal. He serves as a Founding Editor of "Science and Technology of Welding and Joining."

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\title{Heterogeneous sensing and scientific machine learning for quality assurance in laser powder bed fusion - A single-track study }


\author{See Table C1.}
\date{}


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\begin{document}
\maketitle
Research Paper



\section*{A R T I C L E I N F O}
\section*{Keywords:}
Laser powder bed fusion

In-Situ quality monitoring

Process-mapping

Scientific machine learning

Sensor fusion

\begin{abstract}
A B S T R A C T Laser Powder Bed Fusion (LPBF) is the predominant metal additive manufacturing technique that benefits from a significant body of academic study and industrial investment given its ability to create complex geometry parts. Despite LPBF's widespread use, there still exists a need for process monitoring to ensure reliable part production and reduce post-build quality assessments. Towards this end, we develop and evaluate machine learning-based predictive models using height map-derived quality metrics for single tracks and the accompanying pyrometer and high-speed video camera data collected under a wide range of laser power and laser velocity settings. We extract physically intuitive low-level features representative of the meltpool dynamics from these sensing modalities and explore how these vary with the linear energy density. We find our Sequential Decision Analysis Neural Network (SeDANN) model - a scientific machine learning model that incorporates physical process insights - outperforms other purely data-driven black box models in both accuracy and speed. The general approach to data curation and adaptable nature of SeDANN's scientifically informed architecture should benefit LPBF systems with an evolving suite of sensing modalities and post-build quality measurements.
\end{abstract}

\section*{1. Introduction}
Despite the demonstrated potential of additive manufacturing (AM) to transcend the design and processing barriers of traditional manufacturing, the use of additively manufactured parts in missioncritical components is currently limited due to the tendency of the process to create flaws, owing to complex multi-scale physics governing the process [1]. Therefore, to ensure the functional integrity of additively manufactured parts, a critical need is to continually monitor the process using sensors built into the machine, and subsequently detect flaws through real-time analysis of the streaming in-process sensor signatures before these flaws are sealed in by later layers [2-5]. Accordingly, a reliable approach for sensor-based in-situ detection of flaws is vital towards establishing a smart additive manufacturing paradigm for the quality assurance of additively manufactured parts in which the functional properties of the part are assessed during the process, thus limiting expensive offline characterization of parts using X-ray computed tomography and post-process materials characterization $[6,7]$.\\
The goal of this work is to detect flaw formation in a specific type of AM process called laser powder bed fusion (LPBF) through data acquired from heterogenous in-process sensors in a manner that leverages physical insights from the process. In LPBF, metal in the form of powder is spread over a bed, and the material is selectively fused layer-by-layer through the energy supplied by a laser. The laser scans a (typically) rectilinear path through the rapid movement of a pair of galvanometric mirrors, and the resulting interaction between the laser and the powder material creates a pool of molten material, called the meltpool. The material solidifies in the wake of the meltpool along the path scanned by the laser. This locus of solidified material along the laser path is called single-track or hatch. A layer of the part consists of several overlapping single tracks. Once a layer is fused, the powder bed moves down by 50-100 $\mu \mathrm{m}$ (layer height), a new powder layer is raked on top, and the process continues until the part is completely built.

Fig. 1 shows quality differences via optical microscopy images of two stainless steel single tracks deposited at different laser power and laser velocity settings. Fig. 1(a) shows a single-track with uniform edges, no discontinuities, and no satellite artifacts. These single-track
\footnotetext{\begin{itemize}
  \item Corresponding author.
\end{itemize}

E-mail address: \href{mailto:giera1@1lnl.gov}{giera1@1lnl.gov} (B. Giera).
}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-02}
\end{center}

Fig. 1. Optical microscopy images of single tracks deposited at different laser power and laser velocity. (a) a single-track with uniform edges and no discernable faults - characteristics that are desirable while building LPBF AM parts. (b) a single-track with inconsistent width, discontinuities, and surface damage.

characteristics are desirable while building LPBF additively manufactured parts. In contrast, Fig. 1(b) shows a single-track with inconsistent consolidation - the width of the single-track is not only less (compared to the single-track in Fig. 1(a)), but also shows prominent discontinuity and damage.

We note that, the LPBF process falls under the general class of AM processes called powder bed fusion (PBF). In PBF various types of energy sources can be used to fuse the powder material. Apart from using a laser, energy sources include an electron beam (EPBF, with both thermionic and plasma beam), and infrared heating [8]. To increase processing speeds, LPBF systems with multiple lasers have been recently introduced by manufacturers [9]. Rapid whole-layer scans are possible by shaping an infrared beam with an array of optically addressable light valves akin to a photomask [10].

The fast and accurate in-situ identification of LPBF flaws, such as those demarcated in Fig. 1(b), from in-process sensor data is predicated on fusing heterogeneous sensor data $[2,11]$. Here we predict the integrity (build quality) of a single-track using a pyrometer and a high-speed optical video camera located coaxially to the laser path to capture meltpool-level phenomena. The rationale for emphasizing flaw detection at the single-track-level is that, since the single tracks form the basic building block of LPBF parts, identifying and correcting flaws at the single-track level is the key to prevent anomalies from being sealed in by subsequent layers, and cascading to the larger part-level.\\
At present, process monitoring in additive manufacturing is largely based on analysis of in-process sensor data with machine learning for detecting the occurrence of specific types of flaws. For instance, machine learning is used - in unsupervised [12-14], semi-supervised [15,16] and supervised [17-20] modes - to recognize patterns from in-situ sensors, such as meltpool shape and size. Subsequently, these patterns are correlated with a defect, such as porosity.

The prediction of the model is verified through on offline characterization of the part quality, typically with X-ray computed tomography [21-26]. Machine learning in the context of flaw detection in LPBF can be stratified into three-levels, focused on meltpool-, powder bed-, and part-level sensing [27-30]. For instance, in previous works optical and thermal cameras, and spectrometers have been instrumented in both offaxis (staring) and coaxial to the laser arrangements to obtain meltpool images and spectral emissions in the meltpool plume region [31,32]. The shape and spatter signatures subsequently derived from these sensors are analyzed and used to detect meltpool-level defects, e.g., lack-offusion porosity with machine learning techniques.

In what follows, we evaluate several data-driven models for singletrack quality prediction and find the scientific machine learning concept, which leverages physical process insights, performs better in terms of both prediction fidelity and computational efficiency than purely data-driven (black-box) models [4]. Furthermore, given the physically motivated model development process, this approach can

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-02(1)}
\end{center}

Fig. 2. Schematic of the experimental setup with the two in-situ sensors used in this work: pyrometer and high-speed video camera.

Table 1

Number of single tracks deposited at each of the 121 laser power and laser velocity combinations, summing to a total of 1009 single tracks.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 & \multicolumn{12}{|c|}{Laser Power P [W]} \\
\hline
 &  & 50 & 82.5 & 115 & 147.5 & 180 & 212.5 & 245 & 277.5 & 310 & 342.5 & 375 \\
\hline
\multirow[t]{11}{*}{Laser Velocity V $\left[\mathrm{mm} \cdot \mathrm{s}^{-1}\right]$} & 100 & 10 & 7 & 8 & 7 & 9 & 9 & 7 & 10 & 7 & 6 & 10 \\
\hline
 & 130 & 10 & 10 & 9 & 10 & 7 & 9 & 9 & 7 & 8 & 7 & 9 \\
\hline
 & 160 & 8 & 5 & 7 & 8 & 9 & 8 & 9 & 8 & 8 & 9 & 10 \\
\hline
 & 190 & 9 & 7 & 9 & 8 & 7 & 8 & 8 & 10 & 8 & 8 & 10 \\
\hline
 & 220 & 6 & 8 & 7 & 8 & 10 & 8 & 10 & 8 & 10 & 8 & 10 \\
\hline
 & 250 & 10 & 9 & 6 & 9 & 7 & 9 & 7 & 10 & 9 & 7 & 9 \\
\hline
 & 280 & 9 & 8 & 9 & 8 & 10 & 9 & 8 & 6 & 8 & 8 & 7 \\
\hline
 & 310 & 8 & 7 & 9 & 8 & 8 & 9 & 8 & 8 & 8 & 7 & 7 \\
\hline
 & 340 & 9 & 9 & 7 & 7 & 9 & 9 & 10 & 9 & 10 & 9 & 8 \\
\hline
 & 370 & 8 & 8 & 8 & 8 & 8 & 9 & 8 & 6 & 8 & 8 & 10 \\
\hline
 & 400 & 9 & 8 & 10 & 8 & 6 & 8 & 9 & 10 & 9 & 10 & 9 \\
\hline
\end{tabular}
\end{center}

extend beyond our specific LPBF embodiment to other AM process, such as directed energy deposition and electron beam powder bed fusion.

\section*{2. Methods}
Here we describe methodological details of data collection, labeling of single-track quality, feature extraction from sensor data and machine learning model development. While we execute these steps on our LPBF hardware, our approach is not limited to the sensing modalities we collect (e.g. high-speed video and pyrometry data) and our strategies can be implemented on other metal AM systems [5]. Similarly, the labeling methodology and model development and validation approaches described in this work are generalizable. We label the quality of a singletrack in terms of three quantitative metrics, namely the mean and standard deviation of the width (across its length) and percent continuity.

\subsection*{2.1. Experimental setup and in-process sensing}
We use an open architecture LPBF system for this study, shown in Fig. 2, and described in numerous previously published works [18, 33-39]. The laser source is an Ytterbium fiber continuous wave laser with single-mode propagation, $1070 \mathrm{~nm}$ wavelength, $20 \mu$ s rise time, and spot size adjusted to $206 \mu \mathrm{m}$ (1/e $e^{2}$ width). We perform in-situ monitoring of single-track quality via two sensors in the laser path (co-axial), namely a high-speed video camera and a pyrometer.

The high-speed video camera (10-bit Mikroton EOsens MC1362) acquires optical images of the meltpool at a rate of 1000 frames per second $(1 \mathrm{kHz})$ to capture the fast-changing shape and intensity of the meltpool. Appropriate calibration of the camera ensured that there were no saturated meltpool images in the data set. A $60 \mathrm{~W}$, continuous wave, $808 \mathrm{~nm}$ diode laser illuminates the high-speed video camera.

The camera saves $256 \times 256$ pixels $^{2}$ video frames with $14 \mu \mathrm{m} /$ pixel resolution. Additionally, due to the varying laser velocity settings and constant single-track length of $5 \mathrm{~mm}$, the number of images acquired for a single-track varies from 12 to 50 , e.g. videos collected at the fastest laser velocity of $400 \mathrm{~mm} \mathrm{~s}^{-1}$ have 12 frames and the slowest laser velocity of $100 \mathrm{~mm} \mathrm{~s}^{-1}$ have 50 frames.

The infrared pyrometer operates at a wavelength range of $1600-1800 \mathrm{~nm}$ with a sampling rate of $100 \mathrm{kHz}$. The pyrometer captures signatures of the energy that is radiated during single-track deposition at the laser-material interaction zone (meltpool) in the form of a temporal trace. While the pyrometer is not calibrated to the meltpool emissivity (and hence not converted to a temperature scale), it does provide an independent pathway to monitor the energy density $\left(E_{L}\right)$ at the meltpool for fusion. This is important because while the laser power and laser velocity may remain constant, the energy density may change due to change in laser focus height of the LPBF system [40,41].

\subsection*{2.2. Design of experiments}
A carbon fiber brush spreads stainless steel $316 \mathrm{~L}$ powder with particle size ranging from $15 \mu \mathrm{m}$ to $45 \mu \mathrm{m}$, forming a $\sim 50 \mu \mathrm{m}$ layer on a $180 \mathrm{~mm}$ stainless steel $316 \mathrm{~L}$ build plate. The experimental schema entails a full-factor design of experiments of 11 laser power $(\mathrm{P},[\mathrm{W}])$ and 11 laser velocity $\left(\mathrm{V},\left[\mathrm{mm} \cdot \mathrm{s}^{-1}\right]\right.$ ) settings [18]. Table 1 reports the 121 distinct ( $\mathrm{P}, \mathrm{V}$ ) combinations of laser power ranging 50-375 W in increments of $32.5 \mathrm{~W}$ and laser velocity ranging from 100 to $400 \mathrm{~mm} \mathrm{~s}^{-1}$ in increments of $30 \mathrm{~mm} \mathrm{~s}^{-1}$, along with the number of replicates. The numbers reported in Table 1 are the number of single tracks produced under each combination of $\mathrm{P}$ and $\mathrm{V}$.

We chose these two laser parameters because when taken together they result in a linear energy density applied to melt powder material, $\mathrm{E}_{\mathrm{L}}$ $=\mathrm{P} \cdot \mathrm{V}^{-1}\left[\mathrm{~J} \cdot \mathrm{mm}^{-1}\right]$. The energy density values studied in this work range from $E_{\mathrm{L}}=0.25-3.75 \mathrm{~J} \mathrm{~mm}^{-1}$. While previous works have studied the effect of process parameters on single tracks, the studies were conducted over a narrower parameter range followed by qualitative observations $[42,43]$.

In commercial LPBF systems, the laser velocity can often exceed $1000 \mathrm{~mm} \mathrm{~s}^{-1}$ [32]. Although, the open architecture system used in this work can sustain such large laser velocity ranges, we have restricted the maximum laser velocity to $400 \mathrm{~mm} \mathrm{~s}^{-1}$ due to the following two reasons.

First, apart from the power and velocity of the laser, its spot size also effects the input energy density. The spot size of the laser used in a commercial system is typically in the range of $50-100 \mu \mathrm{m}$. The spot size of the laser used in this work is much larger at $206 \mu \mathrm{m}$. Due to the bigger spot size, the laser energy is spread over a larger area, therefore, using higher laser velocity values would reduce the input energy density in our system. Furthermore, our offline studies with the open architecture system inform us that setting the laser velocity beyond the selected range would lead to highly discontinuous single tracks because of the extremely low energy density.

Second, there are sensing-related constraints under high laser velocity conditions. The number of images acquired by the high-speed video camera is inversely proportional to the laser velocity. For example, at 1000 frames per second ( $1 \mathrm{kHz}$ frame rate) of the high-speed video camera used in this work, 12 meltpool images are acquired for the single tracks deposited at $400 \mathrm{~mm} \mathrm{~s}^{-1}$. Hence, the high-speed video camera would be able to acquire two to three meltpool images at the most when single tracks are deposited at $1000 \mathrm{~mm} \mathrm{~s}^{-1}$ leading to severe data deficiency.

\subsection*{2.3. Extracting quality metrics from height maps}
Deposited single tracks were scanned with Keyence VR3000 noncontact optical profilometer to characterize their morphology. This rapid measurement produces a height map with a resolution of $29.5 \mu \mathrm{m}$ per pixel (in the X-Y plane) that we analyze to extract the following

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-04(1)}
\end{center}

Height from

powder bed $(\mathrm{mm}$ )

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-04}
\end{center}

Fig. 3. Representative height maps of single tracks deposited at different printing conditions. (a) Single-track deposited at $P=342.5 \mathrm{~W}$ and $\mathrm{V}=130 \mathrm{~mm} / \mathrm{s}$ shows the indices $\left(F_{i}\right.$ and $L_{i}$ ) used to extract single-track quality features, such as mean and standard deviation of the width (b) Single-track deposited at $\mathrm{P}=115 \mathrm{~W}$ and $\mathrm{V}=370 \mathrm{~mm} / \mathrm{s}$ highlights the length of discontinuity in the single-track (blue dotted line). Color bar depicts the height of single tracks from the powder bed. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) quality metrics: the mean of the width of the single-track $\left(\mu_{w}\right)$, the standard deviation of the width of the single-track over its length $\left(\sigma_{w}\right)$, and percent continuity (к) that ranges from $100 \%$ for fully continuous single tracks to $0 \%$ for unformed single tracks. Thus, the combination of these three metrics derived from the height map images encompass important quality-related aspects of the single tracks. Our aim is to predict these quality metrics as a function of process signatures derived from in-situ sensor data.

We acknowledge that including other materials characterizationrelated metrics, such as inclusion population, compositional variation, grain size, texture, precipitation and dislocation density will provide a fundamental insight into the microstructural evolution of single tracks $[42,43]$. This insight is indeed critical for understanding the causal thermal and fluid-flow phenomena that govern part quality in LPBF [1]. However, the focus of this work is on using in-process sensor data to detect flaw formation related to the macro-scale consolidation characteristics of single tracks in terms of their geometric integrity, such as width and continuity. In the same vein, we recognize other rigorous destructive and non-destructive measurement techniques, such as X-ray computed tomography, offer subsurface insights into LPBF process quality [44-46].

Fig. 3 demonstrates our approach to obtain the pixel-level quality metrics of single tracks from the height map image. Fig. 3(a) shows how we obtain pixel-level widths by computing the difference in the index values of the first and last non-zero pixels: $F_{i}$ and $L_{i}$, respectively at height map coordinate $i$. We then convert the pixel-level width to micrometers from the $29.5 \mu \mathrm{m} /$ pixel height map resolution using Eq. (1).

$\alpha_{w}^{i}=\left(L_{i}-F_{i}\right) \times 29.5 \quad \mu \mathrm{m}$

where, $i$ ranges from 1 to $N$, with $N$ as the number $\left(F_{i}, L_{i}\right)$ pairs along each single-track. During this pixel-level evaluation, we exclude any potential height map artifacts (shown in Fig. 3(a)) from our measurements. From the set of $\alpha_{w}^{i}$ corresponding to each single-track, we compute the mean width

$\mu_{w}=\frac{1}{N} \sum_{i=1}^{N} \alpha_{w}^{i}$

and standard deviation

$\sigma_{w}=\sqrt{\frac{\sum_{i=1}^{N}\left(\alpha_{w}^{i}-\mu_{w}\right)^{2}}{N}}$

Percent continuity is computed via,

$\kappa=\frac{N-\operatorname{count}\left(\alpha_{w}^{i}=0\right)}{N}$

where count $\left(\alpha_{w}^{i}=0\right)$ is the number of pixels (zero and non-zero) belonging to all discontinuities, as depicted by the blue dotted-line in Fig. 3(b).

We clarify that a discontinuity in this context is intended to convey separation of a single-track into discrete droplets, which results from a phenomenon called balling or droplet formation [1]. The single-track fails to fuse due to excessive laser velocity in relation to the laser power (explained in Section 3.1). The severity of the discontinuity is captured in Eq. (4), which quantifies the extent of continuity of a singletrack. A value of $\kappa=100 \%$ means there are no discontinuities in the single track, and $\kappa \rightarrow 0 \%$ for highly discontinuous single track; $\kappa=0 \%$ indicates a complete absence of a single-track (no single-track is printed). In Section 3.1 we link the variation in these quality metrics to four distinctive processing regimes of the LPBF process.

\subsection*{2.4. Extracting features from sensor data}
We leverage readily interpretable statistics-based features from pyrometer and high-speed video camera data of the meltpool as opposed to more complex signal processing techniques. An intuitive and simple feature set facilitates the ease of monitoring the meltpool dynamics with varying process parameters. This in turn promotes a deeper understanding of the complex process physics involved in LPBF AM. Consequently, this feature set helps integrate knowledge of the process physics into our machine learning-based model, consistent with the scientific machine learning paradigm.

We acknowledge that indeed complex signal processing techniques, such as wavelet-based signal decomposition and deep learning convolutional neural networks, are capable of extracting multifaceted process dynamics that are not readily apparent to the human intuition $[47,48]$. In this work, we endeavor to integrate the pattern recognition and correlation ability of machine learning while retaining interpretability of the underlying physical phenomena through accessible input feature sets.

\subsection*{2.4.1. Pyrometry signatures}
The pyrometer measures meltpool radiance that is proportional to the temperature. Accordingly, we posit that the temporal characteristics of the pyrometer signature offers an indirect measurement of the energy expended for melting the single-track. Taking this a step further, the pyrometer signature can be used to characterize the meltpool into different processing regimes. Using the 1D time series pyrometer signal for each single-track, we derive process signatures from the moments of its probability distribution, i.e. mean $\left(\mu_{p}\right)$, standard deviation $\left(\sigma_{p}\right)$, skewness $\left(\mu_{3, p}\right)$ and kurtosis $\left(\mu_{4, p}\right)$. We note that no a priori probability distribution has been assumed nor has any distribution been fitted to the data; we merely extract the statistical descriptors of the empirical sensor data. In our results (Section 3.2), we evaluate the change in statistical features of the pyrometer readings with respect to the four process LPBF regimes identified, viz. balling, lack-of-fusion, conduction, keyholing.

\subsection*{2.4.2. High-speed video signatures}
We hypothesize that the meltpool area and intensity correlate with the width of the single-track since these relate to the temperature of the meltpool and ultimately the processing regime. Similarly, the shape of\\
\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-05(2)}

Fig. 4. Co-axial high-speed video camera frames captured while depositing a single-track ( $\mathrm{P}=245 \mathrm{~W}, \mathrm{~V}=100 \mathrm{~mm} / \mathrm{s}$ ). (a) We fit an ellipse using adjustable parameters for the major and minor axis, respectively. (b) We use the set of center-to-edge distance ( $\mathrm{d}_{\mathrm{y}}$ ) to define the circularity of a meltpool.

the meltpool is linked to stability. This is supported by experiments and simulations that show that the length-to-width ratio of the meltpool is indicative of meltpool instability [49-51]. Typically, when the length of the meltpool is exceedingly large, it tends to segregate into discrete droplets - a phenomenon characterized by the balling regime. Hence, variation in the shape of the meltpool is intuitively correlated with the consistency of the single-track edge, which is given by the standard deviation of single-track width $\left(\sigma_{w}\right)[38,52-54]$.

Using the high-speed video of the meltpool, we extract the meltpool area $\left(A^{i}\right)$, meltpool intensity $\left(I^{i}\right)$, and circularity (shape) of the meltpool as a function of the mean $\left(\mu_{c}^{i}\right)$ and standard deviation $\left(\sigma_{c}^{i}\right)$ of its diameter.\\
However, as discussed through a representative example in Appendix B, we first eliminate spatter and other artifacts surrounding the meltpool in the high-speed video camera frames. Subsequently, we implement kmeans image segmentation followed by adaptive thresholding-based binarization and edge detection for demarcating the meltpool from the background. These steps were implemented by executing scripts available in the image processing libraries in MATLAB 2019a.

After performing these steps, we extract the four aforementioned features exclusively from the meltpool, as shown in Fig. 4. From every frame $j$, we determine the meltpool area\\
\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-05}

Output predicted laser parameters

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-05(1)}
\end{center}

Output predicted mean and standard deviation of width\\
Output predicted percent continuity\\
Fig. 5. A schematic of the sequential decision analysis neural network (SeDANN). The sensor data and height map shown above belong to a singletrack deposited at linear energy density $\left(E_{L}\right)$ of 0.33 , i.e. balling regime. The statistical probability distribution features extracted from the pyrometer are used in the first echelon artificial neural network (ANN) to predict the laser process parameters ( $\mathrm{P}$ and $\mathrm{V}$ ) followed by meltpool features derived from the high-speed video camera to predict the mean width and standard deviation and single-track continuity at higher echelons.\\
$A^{i}=\pi L_{\text {major }}^{j} L_{\text {minor }}^{j}$

from an elliptical fit (using MATLAB 2019a) to the meltpool circumference with adjustable parameters for the major $\left(L_{\text {major }}^{j}\right)$ and minor axes $\left(L_{\text {minor }}^{j}\right)$ as shown in Fig. 4(a). The fitting parameters are adjusted once and remain fixed throughout the analysis process. Moreover, since the analysis is done for a single-track of fused material, the laser direction does not change, and therefore the orientation of the meltpool does not vary (i.e., fitting parameters are not influenced by the position of the laser).

Fig. 4(b) demonstrates the manner in which we use the center point of the fitted ellipse to determine the meltpool circularity. We compute the Euclidean distance between the center of the meltpool, $d_{y}$, for the total number of pixels that comprise the meltpool's edge, $N_{e}$. For each high-speed video frame $j$, we use the set of $d_{y}$ to calculate the mean $\left(\mu_{c}^{j}\right)$ and standard deviation $\left(\sigma_{c}^{j}\right)$ values that account for the size and shape of the meltpool, respectively per Eq. (6). Smaller $\sigma_{c}^{i}$ correspond to meltpool shapes that are more circular.

$\mu_{c}^{j}=\frac{1}{N_{e}} \sum_{y=1}^{N_{e}} d_{y}$

$\sigma_{c}^{j}=\sqrt{\frac{\sum_{y=1}^{N_{e}}\left(d_{y}-\mu_{c}^{i}\right)^{2}}{N_{e}}}$

Meltpool intensity is calculated by summing the non-zero-pixel values belonging to the meltpool as shown in Eq. (7).

$I^{j}=\sum_{(x=1)}^{M} I_{x}$,

where, $I_{x}$ is the intensity of a pixel in the meltpool and $M$ is the number of pixels in the meltpool.

We use these sensor data features along with the single-track quality metrics as labels to evaluate the performance of various machine learning models (Section 3.3). The single tracks are split in the 80/20 manner, i.e. $80 \%$ of the single tracks are used for training a given machine learning model and $20 \%$ of the single tracks are used to test it. We discuss the architectural details of some of the models in Appendix A. The next section talks about development of the proposed SeDANN machine learning model.

\subsection*{2.5. Sequential decision analysis neural network (SeDANN)}
\subsection*{2.5.1. Model architecture}
The machine learning model that is hallmark of this work is our sequential decision analysis neural network (SeDANN), which is motivated by the idea of scientific machine learning and grey-box modeling, wherein we incorporate the knowledge of the complex process physics in a machine learning framework. Here we leverage the versatility and adaptability of shallow artificial neural networks (ANNs) and arrange their inputs/outputs in a sequential manner as depicted in Fig. 5. SeDANN is comprised of three echelons in which each echelon predicts a certain process regime or quality metric and passes it to subsequent echelons to boost their predictive accuracy.

This model architecture of the SeDANN relies on a statistical factor analysis (see Section 3.1 for detailed ANOVA table), which shows that single-track width is predicted with a higher degree of accuracy as a function of only the process parameters laser power and laser velocity, unlike percent continuity. The pyrometer is linked to the deposition energy $\mathrm{E}_{\mathrm{L}}$, and therefore captures the process regime, thus is placed in the first echelon. The meltpool features encapsulate the shape and intensity of the meltpool, and hence are intuitively linked to the morphology of the single-track width. In essence, this statistically informed approach to machine learning model design ensures sensors are used efficiently for single-track quality classification, i.e. quality metric(s) are identified using the appropriate sensor(s).

In Fig. 5, the first echelon ANN in the SeDANN is trained to predict the deposition laser power and laser velocity of a single-track segment as a function of the first four statistical moments of the pyrometer signal, i. e. mean $\left(\mu_{p}\right)$, standard deviation $\left(\sigma_{p}\right)$, skewness $\left(\mu_{3, p}\right)$ and kurtosis $\left(\mu_{4, p}\right)$ of the pyrometer signature. In the second echelon, the $\mathrm{P}$ and $\mathrm{V}$ values for a single-track segment, predicted from the first echelon, are used alongside meltpool image features extracted from the high-speed video camera images as inputs to a shallow ANN trained to predict the width of the single-track segment $\left(\mu_{w}\right)$. Additionally, in the second echelon, the standard deviation of the single-track width $\left(\sigma_{w}\right)$ is derived by estimating the mean width over three segments of the single-track. The third echelon predicts percentage continuity ( $\kappa$ ), as a function of meltpool features, and mean and standard deviation of single-track width predicted in the second echelon.

\subsection*{2.5.2. Training and testing}
We train and test the SeDANN (and other machine learning models) using 914 single tracks out of the total 1009 single tracks; sensor data from 95 single tracks were omitted due to inconsistencies in data acquisition. All the machine learning models studied in this work were implemented using scripts from the MATLAB 2019a machine learning library. The models were executed on a desktop computer with 16 GB RAM and threaded through a single core processor (Intel Core i7-7700HQ CPU @ $2.80 \mathrm{GHz}$ ). The training and validation dataset comprised of 657 and 73 tracks, respectively for a total of 730 single tracks, viz. $\sim 80 \%$ of the entire dataset.

The remaining 184 single tracks (20\%) are reserved exclusively for testing the trained and validated models. The training data does not change and remains static for the entire study, and network performance results are reported on the separate testing data. The testing data set and input features is therefore uniform and identical for all models bar the convolutional neural network tested in this work.

The training processes proceeds as follows. Each $5 \mathrm{~mm}$ track is divided into three segments of the length of $\approx 1.7 \mathrm{~mm}$. To ensure synchronization, the sensor data is also divided into three segments to correspond to the three sections. The division of every single-track into three segments results in a total of 2190 segmented single tracks for training. Ten-fold cross-validation was performed for training the shallow ANNs, i.e. the data was randomly divided into 10 equal parts, out of which 1/10th of it was used for validation and the rest for training. This strategy of randomized training-and-validation is repeated 10 times to obtain an unbiased estimate of the network efficiency over the entire dataset. The evaluation of SeDANN along with other machine learning algorithms is given in Section 3.3. The advantage of the sequential process monitoring approach embodied by the SeDANN are three-fold:

\begin{enumerate}
  \item Encapsulates the physical insight from the process to make predictions. Compared to deep learning techniques which use multiresolution filters at the expense of interpretability, the SeDANN approach uses rudimentary statistical features derived based on the physical reasoning of the process regimes, which in turn facilitates interpretability.

  \item Can accommodate heterogenous data sources, such as 1D time series from a pyrometer, and 2D streaming images from the high-speed video camera in a physically intuitive manner taking advantage of the capabilities of each type of sensor.

  \item Chaining shallow ANNs to make sequential decisions with a sparse set of features in each input layer is more computationally efficient and resistant to overfitting than using one large network with several features in the input layer.\\
\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-07}

\end{enumerate}

Fig. 6. Micrographs of cross-sectioned single tracks reveals subsurface information useful for demarcating the process regime. This data is adapted from the following reference [5].

\section*{3. Results and discussions}
This section establishes the vital link between process parameters, insitu sensor signatures and build quality. In Section 3.1, we quantify the variation in single tracks' quality metrics (mean and standard deviation of single-track widths, and percent continuity) as a function of the four $\mathrm{E}_{\mathrm{L}}$ regimes commonly used to characterize LPBF, viz. balling, lack-offusion, conduction, and keyholing. In Section 3.2, we demonstrate the transitional behavior of the high-speed video camera data and pyrometer signals with respect to these $\mathrm{E}_{\mathrm{L}}$ regimes. We evaluate the SeDANN and compare it against several other machine learning models for accuracy and computational efficiency in Section 3.3.

\subsection*{3.1. Effect of process parameters on single-track quality}
\subsection*{3.1.1. Destructive characterization}
In this section we show that the range of energy density values, $E_{L}$ $=0.25-3.75 \mathrm{~J} \mathrm{~mm}^{-1}$, encompassed by our dataset spans four key regimes for single-track formation: balling, lack-of-fusion, conduction, and keyholing. We cross-sectioned and conducted an offline metallographic analysis of a few single tracks created in each $\mathrm{E}_{\mathrm{L}}$ regime. Fig. 6 is adapted from previous work and shows the cross-sectioned single tracks produced at a decreased beam width of $100 \mu \mathrm{m}$ [5].

The cross-sectioning and metallographic analysis has three critical functions:

(1) The cross-sectional images provide deeper understanding and physical rationale for demarcating the four proposed energy density regimes, viz. keyhole, conduction, lack-of-fusion, and balling. In the absence of the cross-sectional data, these process regime demarcations would lack a clear physical justification.

(2) The cross-sectional images show that single tracks deposited under the four energy density regimes have distinctive weld bead characteristics which is indicative of their morphological quality.

(3) Cross-sectional images corroborate the veracity of the optical height map-derived energy density regimes. In other words, the cross-sectional images provide valuable cross-validation of the optical height map measurements used in this work.

Fig. 6(a) shows the cross-section of a single-track deposited in the keyholing regime under the following conditions: $(\mathrm{P}, \mathrm{V})=(375 \mathrm{~W}, \mathrm{~V}$ $=130 \mathrm{~mm} \mathrm{~s}^{-1}$ ) with $\mathrm{E}_{\mathrm{L}}=2.88 \mathrm{~J} \mathrm{~mm}^{-1}$. The cross-section shows high depth of penetration (reinforcement depth) and height above the substrate (reinforcement height) relative to the width, which is attributable to high $\mathrm{E}_{\mathrm{L}}$. The single-track has pores trapped deep inside the cavity made by the meltpool characteristic of keyhole formation. King et al. made similar single-track cross-section observations when depositing under the keyholing regime of process parameters [49].

Fig. 6(c), (d), and (g) shows the cross-section of single tracks that exhibit the lack-of-fusion phenomenon. Compared to Fig. 6(a), these single tracks are characterized by lower depth of penetration relative to their width, smaller reinforcement height, and have insufficiently fused material. Single tracks in Fig. 6(e), (h), (i) and (j) depict the balling effect due to low laser power relative its velocity, i.e., low energy density $\left(\mathrm{E}_{\mathrm{L}}<\right.$ $0.5 \mathrm{~J} \mathrm{~mm}^{-1}$ ). The balling effect observed in these single tracks results in high reinforcement height of the single-track relative to its depth of penetration and width. Indeed, in Fig. 6(h) the single-track depicts negligible penetration into the substrate, characteristic of discontinuity.

Lastly, Fig. 6(b) and (f) show the cross-section of a single-track deposited in the conduction regime deposited in the conduction zone, i.e. $1<\mathrm{E}_{L}<2$. The reinforcement height and depth of penetration are almost equal in these weld beads, and the bead width is approximately equal to the laser beam width. These cross-sectional micrographs of single tracks help to categorize them according to the four process parameter regimes. They inform of the presence of keyhole porosity and the degree to which a single-track is fused to the preceding layer (substrate in this case).

We exclusively use the height map data, as detailed in the next section, as it provides us with information regarding the overall thickness of a single-track and its edge uniformity. Furthermore, the height maps tell us about the presence of discontinuities in a single-track. These vital morphological traits of a single-track are not conveyed by the crosssectional micrographs. Additionally, the cross-sectional evaluation of numerous single tracks is expensive, laborious, and time-consuming. This makes it far more difficult to amass large labeled datasets required for machine learning when compared to surface-based height maps. Nevertheless, we can employ the physical insights gained from these detailed measurements (prior published work [5]) for analyzing sensing data and designing suitable machine learning architectures.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-08}
\end{center}

Fig. 7. Examples of height maps for single tracks deposited at various laser power and laser velocity settings colored-coded according to four distinct processing linear energy density $\left(\mathrm{E}_{\mathrm{L}}\right)$ regimes: balling, lack-of-fusion, conduction, and keyholing. Single tracks formed in the balling regime (blue) are highly discontinuous and relatively thinner. Single tracks within the lack-of-fusion regime (pink) exhibit uneven (high standard deviation) widths with a low mean width and few discontinuities. The ideal conduction regime (green) produces uniform single tracks with mean width within $\pm 20 \%$ of the laser spot size and no discernable discontinuity. In the keyholing regime (red), single tracks exhibit continuous widths that are over $20 \%$ larger than the laser spot size and relatively high standard deviation and may also contain porosity that cannot be verified with surface measurements alone. The color bar shown represents the height of single tracks from the powder bed. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

\subsection*{3.1.2. Demarcation of process regimes from height maps}
Fig. 7 shows top view examples of single-track height maps arranged according to laser power ( $\mathrm{P}$ ) and laser velocity (V) set points and grouped by the linear energy density $\left(\mathrm{E}_{\mathrm{L}}\right.$ ) regimes. The single-track morphology varies distinctly with $\mathrm{E}_{\mathrm{L}}$. Single tracks in the balling (metal droplet formation) regime have low widths and variable continuity. Under the low $\mathrm{P}$, high $\mathrm{V}\left(\mathrm{E}_{\mathrm{L}}<0.5 \mathrm{~J} \mathrm{~mm}^{-1}\right)$ these single tracks exhibit prominent discontinuities because the meltpool segregates into separate droplets, prohibiting long segments of continuous single tracks. We measure typical values for the percent continuity to range from $\sim 8 \%$ to $\sim 100 \%$. These observations are consistent with other works that characterize the consistency of single tracks at low energy densities with experiments and simulation $[34,50,54,55]$.

A second LPBF phenomena termed lack-of-fusion falls within $0.5<\mathrm{E}_{\mathrm{L}}<1 \mathrm{~J} \cdot \mathrm{mm}^{-1}$. Although these single tracks appear to be continuous, their edges are not uniform, i.e. the standard deviation of the width is high (measured typically in the range of $20-40 \mu \mathrm{m}$ ). The single tracks poorly fuse to the substrate (or prior layers in multilayer fabrication) because the energy supplied by the laser is insufficient leading to formation of lack-of-fusion porosity [56,57]. Single tracks deposited at the upper threshold of this regime $\left(\mathrm{E}_{\mathrm{L}} \rightarrow 1 \mathrm{~J} \cdot \mathrm{mm}^{-1}\right.$ at the magenta-green boundary in Fig. 7) exhibit high single-track continuity and low standard deviation of width, as opposed to those deposited at lower $\mathrm{E}_{\mathrm{L}}$.

Conduction mode of single tracks is observed in a third regime ranging from 1 to $2 \mathrm{~J} \cdot \mathrm{mm}^{-1}$. In the conduction regime, continuous single tracks fully fuse to the substrate and exhibit single-track mean width ranging from $160 \mu \mathrm{m}$ to $240 \mu \mathrm{m}$. Fig. 7 shows that single tracks in the conduction regime are characterized by high percent continuity and low standard deviation of width (or high edge uniformity). Given these single-track quality attributes, this operating regime produces fewer defects in overall part build quality. However, the quality of single tracks may decline at higher energy densities $\left(\mathrm{E}_{\mathrm{L}} \rightarrow 2 \mathrm{~J} \mathrm{~mm}^{-1}\right.$ at greenred boundary in Fig. 7).

The keyholing regime characterizes single tracks formed at the highest energy of the regimes, i.e. $\mathrm{E}_{\mathrm{L}}>2 \mathrm{~J} \cdot \mathrm{mm}^{-1}$. In the keyholing regime, the combination of high laser power and the low laser velocity results in large energy deposition. This high energy density causes the laser to penetrate deeper into the layers (substrate in the case of a singletrack), hence, the depth of the meltpool is substantially longer compared to its width [58]. The collapse of the material in the deep cavity made by the laser, followed by rapid solidification of the meltpool often leaves behind pores, which is called keyhole porosity [49,54] . These pores are detrimental to the mechanical properties of finished LPBF AM parts as they are initiation sites for crack formation [59].

\subsection*{3.1.3. Statistical analysis quantifying effect of process parameters}
We analyze the height maps of single tracks at every $(\mathrm{P}, \mathrm{V})$ combination to measure three quality metrics of the single-track, namely, mean $\left(\mu_{w},[\mu \mathrm{m}]\right)$, standard deviation $\left(\sigma_{w},[\mu \mathrm{m}]\right)$ of single-track width and percent continuity ( $\kappa$ ) (representative values provided in Appendix C). We perform statistical analysis (ANOVA) to relate P and V to these quality metrics as reported in Table 2 .

A key result is that $\mathrm{P}$ and $\mathrm{V}$ and their interaction term $\mathrm{P} \cdot \mathrm{V}$ have a

\section*{Table 2}
Results of analysis of variance (ANOVA) performed on the mean of single-track width, the standard deviation of single-track width, and the percent continuity of 914 single tracks. Highlighted values depict the most significant variables (p-value $<10 \%$ ).

\begin{center}
\begin{tabular}{|l|c|c|c|}
\hline
\begin{tabular}{l}
Percentage of the total \\
sum of squares variation \\
\end{tabular} & \begin{tabular}{c}
Mean of single- \\
track width $\left(\boldsymbol{\mu}_{\boldsymbol{w}}\right)$ \\
\end{tabular} & \begin{tabular}{c}
Standard deviation of \\
single-track width $\left(\boldsymbol{\sigma}_{\boldsymbol{w}}\right)$ \\
\end{tabular} & \begin{tabular}{c}
Percent continuity of \\
single-track $(\boldsymbol{\kappa})$ \\
\end{tabular} \\
\hline
Laser power $(\mathrm{P})$ & $59.86 \%$ & $19.97 \%$ & $61.62 \%$ \\
\hline
Laser velocity $(\mathrm{V})$ & $26.01 \%$ & $22.34 \%$ & $2.77 \%$ \\
\hline
Interaction $(\mathrm{P} \times \mathrm{V})$ & $3.01 \%$ & $9.05 \%$ & $4.05 \%$ \\
\hline
Regression $R^{2}$ & 0.8853 & 0.5420 & 0.6444 \\
\hline
\end{tabular}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-09}
\end{center}

Fig. 8. Contour (left) and scatter (right) plots of the effect of laser parameters on single-track width (a), standard deviation of width (b), and percent continuity (c) with demarcated boundaries of the four LPBF regimes.

statistically significant influence (p-value $<1 \%$ ) on the three singletrack quality metrics. This is an intuitive result that we expect for LPBF. In Table 2 , the $R^{2}$ value - which typically ranges from 0 to 1 represents the prediction fidelity for each of the output variables as a function of $\mathrm{P}$ and $\mathrm{V}$, and their statistical interaction $\mathrm{P} \times \mathrm{V}$. The percentage contribution of $\mathrm{P}$ and $\mathrm{V}$ is estimated as a ratio of the sum of squares of the factor (signal) to the total sum of squares (noise). Thus, the $\mathrm{R}^{2}$ is akin to the signal-to-noise ratio and represents the uncertainty in explaining the behavior of given single-track quality metric using the two process parameters and their interaction. A relatively low $\mathrm{R}^{2}$ signifies the inability of the process parameters and their interaction to explain the variation in the given quality metric. Although the process parameters $\mathrm{P}$ and $\mathrm{V}$ are statistically significant determinants of the single-track quality, the low $\mathrm{R}^{2}(<65 \%)$ for the standard deviation and percent continuity reinforce that process parameters are not sufficient to monitor single-track quality.

Fig. 8 maps these quality metrics using complementary plots in $(\mathrm{P}, \mathrm{V})$ contours (column 1) and along linear energy density ( $E_{L}$ ) (column 2). All plots highlight each of the four regimes with regions and markers, per the legends. Fig. 8 reiterates the ANOVA analysis in Table 2 in that considering only the process parameters $(\mathrm{P}, \mathrm{V})$ will yield insufficient predictions of the single-track quality metrics $\mu_{w}, \sigma_{w}$, and $\kappa$. Thus, this motivates the need to derive process signatures from in-situ sensors to understand and encapsulate the complex process phenomena in LPBF AM (Section 3.2).

Consistent with our analysis so far, we group our findings according to the four LPBF regimes to highlight the dependency of the single-track quality metrices on $\mathrm{E}_{\mathrm{L}}$. The contour plots map each quality metric onto the $(\mathrm{P}, \mathrm{V})$ plane with regimes denoted by shaded regions. The corresponding scatter plots show these single-track quality metrics as a function of $E_{L}$. Collectively, these plots map out the relationship between the process parameters and build quality in LPBF AM. We discuss the pairs of plots in each row in to give a quantitative overview of each metric within our labeled dataset.

The mean width of the single tracks is most significantly influenced by the laser power with approximately $60 \%$ of the variation in the mean of single-track width attributable to a change in laser power. This result is consistent with the work by Yadroistev et al., wherein the authors study the effect of various process parameters on geometric characteristics of stainless steel SAE 904 L single tracks [60].

The $\mathrm{R}^{2}$ value indicates that $\sim 88 \%$ of the variation in mean of singletrack width is explained by the process parameters alone. Conversely,\\
\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-10(2)}

\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-10}\\
\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-10(1)}

Fig. 9. Sensor data for single tracks representing the four regimes (all single tracks deposited at $\mathrm{V}=130 \mathrm{~mm} / \mathrm{s}$ : (a) Keyholing: $\mathrm{P}=375 \mathrm{~W}$; (b) Conduction: $\mathrm{P}=180 \mathrm{~W}$; (c) Lack-of-fusion: $\mathrm{P}=115 \mathrm{~W}$; (d) Balling: $\mathrm{P}=50 \mathrm{~W}$. The scanning direction is left to right in the plane of the page. Refer to Fig. 7 for color bar of singletrack height maps.

ANOVA suggests that only $\sim 54 \%$ of the variation observed in the standard deviation of single-track width is explained by the process parameters and their interaction. In other words, the process parameters alone are insufficient to predict the standard deviation of the single tracks. In case of the percent continuity of single tracks, the ANOVA analysis indicates that laser power has a high influence on variability. Furthermore, the relatively low $R^{2}$ value suggests that process parameters and their interaction do not wholly explain the variability in percent continuity of single tracks.

Fig. 8 (a1) and (a2) show the measured thickness using (P, V) contours and scatter plots, respectively. Single tracks characterized by the balling regime fall within $\sim 42-119 \mu \mathrm{m}$, with an average value of $75 \mu \mathrm{m}$. The widths of these single tracks are $\sim 40 \%$ of the nominal laser spot size of $206 \mu \mathrm{m}$. The significant deviation from the nominal beam diameter results in the balling phenomena which may lead to poor mechanical properties of the overall part. The mean width of single tracks in the lack-of-fusion regime is $138 \mu \mathrm{m}$ and all data falls within $93-181 \mu \mathrm{m}$. By contrast, single tracks in the conduction regime have an average mean width of $188 \mu \mathrm{m}$ and overall range of $130-255 \mu \mathrm{m}$ that lies within $\pm 20 \%$ of the nominal laser spot size. Since the width and nominal beam diameter are comparable in the conduction regime, this set of conduction process parameters (P, V) in Fig. 9(a1) produce desirable single tracks.

In the keyholing regime, the mean width of single tracks is $210 \mu \mathrm{m}$ with bounds of $130-323 \mu \mathrm{m}$. Here, the single-track widths are $20-50 \%$ larger than the nominal beam diameter. Laohapropanon et al. have observed similar over melting of single-tracks made using stainless steel $316 \mathrm{~L}$ when deposited at similar conditions [61]. The increase in width is attributable to the higher energy density, which can also cause keyhole collapse porosity. As with pores resulting from lack-of-fusion, pores from keyhole-melting are detrimental to the functional quality of LPBF parts. The (P, V) process mapping in Fig. 8 (a1) reveals the ideal process parameter range. Fig. 8 (a2) confirms the mean of single-track width increases linearly with the $\mathrm{E}_{\mathrm{L}}$ with a clear distinction observed between the four regimes.

Fig. 8 (b1 and b2) represent the effect of laser parameters on the standard deviation $\left(\sigma_{w}\right)$ of the single-track width. Unlike the mean, the standard deviation of single-track width does not exhibit a clear trend across the process parameters. This is shown in the Fig. 8 (b1) where non-uniform trends in data produce contours with data clusters and also non-distinct boundaries that poorly map onto the four regimes. Similarly, a prominent trend in the standard deviation of single-track width as a function of $\mathrm{E}_{\mathrm{L}}$ is not perceivable in the scatter plot in Fig. 8 (b2). Hence, to accurately predict the standard deviation in width of a singletrack, the process parameters must be supplemented with signatures derived from the in-process sensor data. For example, the high-speed video camera captures the variation in the meltpool shape and spatter which are indicative of the process stability. Also, the meltpool shape captured by the high-speed video camera can be intuitively related to the single tracks' morphological characteristics. Further, the pyrometer helps capture the energy density distribution over the entire length of the single-track, which is valuable in determining the process regime under which a single-track was deposited.

The contour plot of percent continuity shown in Fig. 8 (c1) suggest that laser power has a substantial effect on the percent continuity of single tracks. Thus, for any given laser velocity setting, the entire range of $\kappa$ is similar across all power settings. Most of the single tracks deposited in this work are observed to be continuous, apart from the portion of discontinuous single tracks deposited at low laser power and high laser velocity in the balling regime. As such, Fig. 8 (c2) shows that the range of $\kappa$ is widest in balling regime, with most of the data exhibiting low percent continuity. We observed that about $59 \%$ of the single tracks in this regime had percent continuity less than $80 \%$. Hence, we can conclude that the presence of discontinuities decreases with the increasing energy density.

This inference is reflected in the work done by Childs et al. on continuity of single tracks built under varying laser power and laser velocity [62]. They conclude that single tracks made of materials with narrow melting temperature range (e.g. stainless steel 314S and 316L) display high continuity when built at relatively low laser velocity and high laser power. This statistical analysis motivates our use of sensorderived signatures to better represent the intricacies of the process physics and consequently facilitate the estimation of hard-to-predict single-track qualities like standard deviation of width and percent continuity. Additionally, ANOVA results play a vital role in the design of the proposed SeDANN architecture.

\subsection*{3.2. Correlation of single-track quality, process regimes, and sensor signatures}
Having presented the single-track quality metrics measured via height maps, we now discuss sensor data, e.g. high-speed video camera and pyrometer readings, collected during fabrication. We systematically register the sensor data to these quality metrics, again using the same four processing regimes of LPBF to guide the discussion. This approach reveals the underlying physics and the efficacy of various process signatures to relate to $\mu_{w}, \sigma_{w}$, and $\kappa$. In this way, we incorporate these physical insights while constructing the SeDANN architecture that we compare against other purely data-driven black box machine learning methods.

\subsection*{3.2.1. Correlating single-track quality with sensor data}
Fig. 9 shows spatiotemporal high-speed video camera frames and spatial pyrometer readings for a characteristic single-track from each of the four regimes. It is observed that the mean amplitude of the pyrometer signal and meltpool size (extracted from high-speed video camera frames) are directly proportional to the linear energy density ( $\mathrm{E}_{\mathrm{L}}$ ).

We subdivide the single-track height map images and corresponding heterogenous sensor data into three segments of equal length that indicate the start, middle, and end of melting. Since single-track are $5 \mathrm{~mm}$ long, each segment length is $\sim 1.7 \mathrm{~mm}$. For each segment, the first, second and last high-speed video camera frame is shown. This is done to maintain consistency in the number of high-speed video camera frames shown per height map image, since the number of video frames vary according to the laser velocity the single-track setting.

We start by comparing single tracks in two regimes: keyholing ( $\mathrm{E}_{\mathrm{L}}$ $=2.8 \mathrm{~J} \cdot \mathrm{mm}^{-1}$ ) and conduction ( $\mathrm{E}_{\mathrm{L}}=1.3 \mathrm{~J} \cdot \mathrm{mm}^{-1}$ ) in Fig. 9(a) and (b), respectively. The conduction single-track has a smaller meltpool for every high-speed video camera frame, and correspondingly less prominent width along the entire single-track. Also, the amplitude of the pyrometer signals is generally higher at the higher energy density setting, which is confirmed in a subsequent histogram analysis of these pyrometer readings. Further, high-speed video camera frames in Fig. 9(a) display trailing intensity, i.e. behind the meltpool, in the keyholing regime that is consequent of high laser power $(\mathrm{P})$, low laser velocity $(\mathrm{V})$, and thus high $\mathrm{E}_{\mathrm{L}}$ at which the single-track is deposited. This phenomenon is less prominent in high-speed video camera frames for the other regimes.

Comparing single tracks deposited in the lack-of-fusion (Fig. 9(c), $\mathrm{E}_{\mathrm{L}}$ $=0.88 \mathrm{~J} / \mathrm{mm}$ ) against the conduction regime reveals that there is a slight decrease in the meltpool size as shown in the high-speed camera video frames and amplitude of the pyrometer reading. High-speed video camera frames in the lack-of-fusion regime show more spatter formation that the conduction region. These differences in the sensor data are evident in the morphology of the two single tracks, i.e. the single-track deposited at lower lack-of-fusion $\mathrm{E}_{\mathrm{L}}$ is thinner that in the conduction regime, which is consistent with Fig. 9(a2).

The trends in the pyrometer signal and illuminated meltpool in the high-speed camera continue in the balling (Fig. 9(d), $\mathrm{E}_{\mathrm{L}}=0.38$ ) regime. The lowest $\mathrm{E}_{\mathrm{L}}$ that corresponds to the balling single-track that produced the smallest meltpool size and correspondingly the lowest pyrometer signal amplitude. The high-speed video camera frames of the single-\\
\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-12}

Fig. 10. Histogram of pyrometer readings of single tracks deposited under the four process parameter regimes using the same example single tracks as in Fig. 9: all deposited at $\mathrm{V}=130 \mathrm{~mm} / \mathrm{s}$ with (a) Keyholing at $\mathrm{P}=375 \mathrm{~W}$; (b) Conduction at $\mathrm{P}=180 \mathrm{~W}$; (c) Lack-of-fusion at $\mathrm{P}=115 \mathrm{~W}$; (d) Balling at $\mathrm{P}=50 \mathrm{~W}$.

track deposited under the balling regime display a drastic increase in the spatter formation, thus highlighting the instability of the LPBF process under those process parameters. Further, it is evident that the pyrometer signal drops to nearly zero amplitude at the locations where discontinuities appear in the height map. The low amplitude, and absence of a signal corresponding to discontinuities in the single-track skews the probability distribution of the pyrometer data to the right.

The meltpool in the high-speed video camera frames in has an irregular shape, which is indicative of Plateau-Rayleigh instability and manifests substantial spatter compared to the rest of the regimes. Spatter formation and smaller meltpool size in the high-speed video camera data are also more noticeable with the largest number of discontinuities that appear in the balling regime. The contrast in meltpool characteristics, i. e. shape, size, intensity, is most apparent when comparing $\mathrm{E}_{\mathrm{L}}$ from the keyholing through balling regimes. Also, the pyrometer signals for the range of single-track morphologies suggests the variable thermal distribution expected for the $\mathrm{E}_{\mathrm{L}}$ regimes.

These observations justify the utility in estimating the meltpool circularity (shape), area (size) and intensity features from the highspeed camera frames and that they should serve as meaningful indicators of single-track quality. Similarly, we hypothesize shape parameters of the pyrometer signal distribution are representative of the single-track's thermal distribution, and thus also should yield enhanced predictions of the single-track quality. We use these observations to develop the architecture of SeDANN, i.e. the input and output for each artificial neural network in the echelons leverages these insights from the sensor signatures, e.g. predicting ( $\mathrm{P}, \mathrm{V})$ settings from pyrometer signals, under different process parameter regimes. For these reasons, we explore these process signatures in greater detail in Fig. 10 and Fig. 11.

\subsection*{3.2.2. Correlation of process regime with pyrometer data}
Fig. 10 show histograms of pyrometer (frequency versus intensity) readings for representative single tracks from each of the four processing regimes. The pyrometer readings along the $\mathrm{x}$-axis indicate the radiance of the meltpool. It is evident that the distribution of the pyrometer signatures become increasingly positively (right) skewed and taller with decreasing energy density. In other words, the number of readings with low amplitude increase as $\mathrm{E}_{\mathrm{L}}$ decreases, highlighting the first four moments of the pyrometer signature can indicate the process regime. The amplitude decreases from the highest values in keyholing to the lowest values in the balling regime. These observations are in close agreement with recently published results in Ref [5].

\subsection*{3.2.3. Correlation of process regime with high-speed video camera data}
Fig. 11 displays a single representative high-speed video camera frame for each set of laser conditions $(P, V)$ and indicates the $E_{L}$ regime. For demonstration purposes, we center-cropped and foreground enhanced each frame. In the lowest energy balling regime, the spatter surrounding the meltpool is pronounced, and the meltpool shape is irregular and smaller than regimes with $\mathrm{E}_{\mathrm{L}}>0.5 \mathrm{~J} \cdot \mathrm{mm}^{-1}$. These highspeed camera frames are most noticeable at the lowest laser power setting $(\mathrm{P}=50 \mathrm{~W})$, irrespective of the laser velocity.

At higher P, the meltpool shape irregularity decreases and size increases, but the spatter formation is always present. In the lack-of-fusion regime $\left(0.5 \leq \mathrm{E}_{\mathrm{L}}<1 \mathrm{Jmm}^{-1}\right)$, the meltpool shape becomes more regular, meltpool size increases, and the spatter formation reduces relative to frames collected in the balling regime. As the V increases in this regime, the meltpool develops a tail of trailing intensity. The undesirable meltpool characteristics observed in these regimes translates to insufficient fusion of single tracks that instigates the formation of irregular-shaped lack-of-fusion pores that are detrimental to the overall part quality.

At the two higher $\mathrm{E}_{\mathrm{L}}$ regimes, the meltpool is highly circular and there is minimal-to-no spatter as opposed to frames collected under $E_{L}$ $<1 \mathrm{~J} \mathrm{~mm}^{-1}$. The meltpools exhibit tails of trailing intensity, but they are not as pronounced as in the case of lack-of-fusion regime. Across the top row (lowest $\mathrm{V}$, increasing $\mathrm{P}$ ), these trends hold as $\mathrm{E}_{\mathrm{L}}$ increases. In the keyholing regime, the intensity of the trailing tail and overall size of the meltpool increases. Overly large meltpools under these conditions

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-13}
\end{center}

Fig. 11. Effect of processing parameters on the meltpool. In the balling region, meltpool shape is highly variable and the amount of spatter increases with the laser velocity. The radius of the meltpool is approximately $113.63 \mu \mathrm{m}$. Similar behavior arises in the lack-offusion regime, but the meltpool size is larger than in balling, i.e. average meltpool radius is $127.25 \mu \mathrm{m}$. At $\mathrm{E}_{\mathrm{L}}$ $>1 \mathrm{~J} / \mathrm{mm}$, in the conduction zone the meltpool characteristics are less variable and exhibit minimal spatter. The radius of the meltpool in this regime is approximately $148.57 \mu \mathrm{m}$. In keyholing $\mathrm{E}_{\mathrm{L}}>2 \mathrm{~J} / \mathrm{mm}$, the meltpool is largest with the average radius being approximately $173.63 \mu \mathrm{m}$. produce thick single tracks and uneven edges and underlying keyhole collapse-related pores that cannot be observed with this sensing modality.

The conclusions we draw from Fig. 8 - Fig. 11 are consistent in that the that the observable behavior of the meltpool changes with varying process parameters $(\mathrm{P}, \mathrm{V})$ as the sensor signatures change correspondingly. Therefore, it is crucial to extract information in the form of features from the sensor signatures to completely understand and capture the process physics.

\subsection*{3.2.4. Correlation between sensor signatures and process regimes}
Fig. 12 depicts the correlations between the different features extracted from sensors and their capacity to differentiate between the four process regimes. Fig. 12 (a1) shows a prominent correlation between the intensity $(I)$ and area (A) of the meltpool. Moreover, the data segregates into four clusters per the processing regimes. The area and intensity of the meltpool are the highest in the keyhole regime, albeit overlapping with the conduction region. The overlap is highest in the balling and lack-of-fusion regime. The correlation between the two feature representing the meltpool circularity $\left(\mu_{c}, \sigma_{c}\right)$ is shown in Fig. 12 (a2); whilst less prominent than the correlation between intensity and area of the meltpool, it shows pronounced clustering concerning the four process regimes.

In contrast to the meltpool signatures, the relationships between the pyrometer signal features in Fig. 12 (b1) and (b2) is a complex trend, and a considerable overlap is evident between the four process regimes. Fig. 12 (b1) portrays the relationship between mean $\left(\mu_{p}\right)$ and standard deviation $\left(\sigma_{p}\right)$ of pyrometer readings of single tracks deposited under various process parameter regimes. The curve flattens in the conduction and keyholing regimes. Fig. 12 (b2) describes the correlation between the skewness $\left(\mu_{3, p}\right)$ and kurtosis $\left(\mu_{4, p}\right)$ of pyrometer readings belonging to single tracks deposited at varying process parameters.

The pyrometer readings of single tracks deposited under the balling regime are positively skewed and leptokurtic. In the conduction regime, the pyrometer readings have a skewness of about zero and kurtosis approximately around 3 which points towards normal distribution of the pyrometer readings. Lastly, the pyrometer readings in the keyholing regime and partly the conduction regime are negatively skewed and platykurtic. The overlap between clusters and complex interaction between features induces the need for machine learning algorithms that capture the nonlinear relationship between the features to predict the single-track quality. These observations from Fig. 12 thus demonstrate the efficacy of the meltpool shape features and statistical moments of the meltpool and pyrometer sensor, respectively in capturing the change in the quality of the single tracks under varying process regimes.

It is evident that the process parameter $\mathrm{E}_{\mathrm{L}}$ regime, as determined by $(\mathrm{P}, \mathrm{V})$, dictate the single-track morphology via to $\mu_{w}, \sigma_{w}$, and $\kappa$. Secondly, an ANOVA (Table 2) study of process parameters alone is insufficient to understand the change in single-track morphology. As a supplement, we propose the use of sensor signatures to understand and encapsulate the process intricacies inherent to LPBF AM. We establish that machine learning models are essential to coalesce the process parameters and sensor derived features to predict single-track morphology with good statistical fidelity. For this purpose, we propose the SeDANN machine\\
\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-14}

(b1) Mean of pyrometer reading $\left(\mu_{\mathrm{p}}\right)$

O Balling $\times$ Lack-of-fusion

\begin{itemize}
  \item Conduction + Keyholing
\end{itemize}

Fig. 12. Correlations between features extracted from high-speed video camera frames and the pyrometer signals denoted by parameter regimes (legend). The four regimes can be demarcated based on these features, but some overlap and nonlinearity are evident necessitating the use of machine learning models.

Table 3

Performance matrix of the various machine learning approaches used in this work. The performance metric provided in each column header with error computed from the standard deviation of repeating the training and testing procedure 10 times $(n=10)$. Best performing approach is shown in bold. Except for SeDANN, the other approaches do not use the physical knowledge of the process regimes.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Machine learning approach & \begin{tabular}{l}
Energy density \\
$\left[\boldsymbol{R}^{2} \pm \sigma_{R^{2}}\right]$ \\
\end{tabular} & \begin{tabular}{l}
Mean of single-track \\
width $\left[R^{2} \pm \sigma_{R^{2}}\right]$ \\
\end{tabular} & \begin{tabular}{l}
Standard deviation of \\
single-track width \\
$\left[\boldsymbol{R}^{2} \pm \sigma_{R^{2}}\right]$ \\
\end{tabular} & \begin{tabular}{l}
Percentage \\
Continuity $\left[R^{2} \pm \sigma_{R^{2}}\right]$ \\
\end{tabular} & \begin{tabular}{l}
Binary Continuity Classification \\
(Continuous vs Discontinuous) \\
$\left[F 1 \pm \sigma_{F 1}\right]$ \\
\end{tabular} \\
\hline
SeDANN & $0.95 \pm 0.0006$ & $\mathbf{0 . 8 7} \pm \mathbf{0 . 0 2 3}$ & $\mathbf{0 . 8 1} \pm \mathbf{0 . 0 1 6}$ & $\mathbf{0 . 7 3} \pm \mathbf{0 . 1 1 0}$ & $0.82 \pm 0.026$ \\
\hline
\begin{tabular}{l}
Convolutional Neural Network \\
(CNN) \\
\end{tabular} & $0.90 \pm 0.021$ & $0.82 \pm 0.033$ & $0.33 \pm 0.023$ & $0.4688 \pm 0.090$ & $0.71 \pm 0.103$ \\
\hline
\begin{tabular}{l}
Long short-term memory (LSTM) \\
Recurrent neural network \\
(RNN) \\
\end{tabular} & $0.96 \pm 0.022$ & $0.86 \pm 0.017$ & $0.74 \pm 0.083$ & $0.4048 \pm 0.035$ & $0.56 \pm 0.028$ \\
\hline
Support Vector Machine (SVM) & $0.94 \pm 0.009$ & $0.81 \pm 0.018$ & $0.48 \pm 0.081$ & $0.4652 \pm 0.050$ & $0.83 \pm 0.029$ \\
\hline
K-nearest Neighbor (KNN) & $0.93 \pm 0.013$ & $0.75 \pm 0.041$ & $0.16 \pm 0.360$ & $0.5406 \pm 0.208$ & $0.77 \pm 0.048$ \\
\hline
\begin{tabular}{l}
Ensemble of regression trees \\
(CART) \\
\end{tabular} & $0.91 \pm 0.029$ & $0.77 \pm 0.009$ & $0.37 \pm 0.142$ & $0.66 \pm 0.088$ & $0.89 \pm 0.034$ \\
\hline
General Linear Model (GLM) & 0.9349 & 0.8242 & 0.3844 & 0.4967 & N/A \\
\hline
\end{tabular}
\end{center}

learning model (Section 2.5) to predict hitherto discussed single-track morphological characteristics.

\subsection*{3.3. Evaluation of machine learning algorithms}
Here we implement and evaluate a variety of data-driven modeling approaches in terms of performance accuracy - quantified in terms of regression $\mathrm{R}^{2}$ and F1-score metrics, and computation time (seconds) [22, 31, 32]. We compare the prediction fidelity of the SeDANN with six approaches, namely, Convolutional Neural Network (CNN), Recurrent Neural Network (RNN), Support Vector Machine (SVM), K-nearest Neighbor (KNN), Regression Trees (CART), and General Linear Model (GLM).\\
The results, reported Table 3, are based on the $20 \%$ of the testing data consisting of 184 single tracks. We evaluate in terms of the $R^{2}$ for each of the three single-track quality-related metrics: mean $\left(\mu_{w}\right)$ and standard deviation $\left(\sigma_{w}\right)$ of single-track width and the percent continuity of the single-track ( $\kappa$ ). Additionally, we performed binary classification on single-track continuity, i.e. perfectly continuous $\kappa=100 \%$ versus discontinuous $\kappa<100 \%$, where discontinuous single tracks represent defective quality. Since most single tracks are discontinuous in our imbalanced dataset, we compare binary classification via the F1-score (or harmonic mean of precision and recall). Also reported are the standard deviation of the prediction $\mathrm{R}^{2}\left(\sigma_{R^{2}}\right)$ and F1-score $\left(\sigma_{F 1}\right)$ over 10 replications of the training and testing process.

The CNN and long short-term memory (LSTM) RNN represent

Table 4

Time taken to predict/classify each quality metric of a single-track in milliseconds. Standard deviation of single-track width is omitted for all algorithms (except CNN) as it derived from the mean width of segments of a single-track.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Machine learning approach & \begin{tabular}{l}
Energy density of \\
single-track [ms] \\
\end{tabular} & \begin{tabular}{l}
Mean of single-track \\
width [ms] \\
\end{tabular} & \begin{tabular}{l}
Standard deviation of single- \\
track width [ms] \\
\end{tabular} & \begin{tabular}{l}
Binary Continuity \\
Classification [ms] \\
\end{tabular} & \begin{tabular}{l}
Percentage \\
Continuity [ms] \\
\end{tabular} \\
\hline
SeDANN & 0.02 & 0.04 &  & 0.12 & 0.06 \\
\hline
Convolutional Neural Network (CNN) & 12.2 & 186 & 8.4 & 7.8 & 6.2 \\
\hline
\begin{tabular}{l}
Long short-term memory (LSTM) \\
Recurrent neural network (RNN) \\
\end{tabular} & 5.5 & 9.8 &  & 7.9 & 6.0 \\
\hline
Support vector machine (SVM) & 0.05 & 0.08 &  & 0.038 & 0.012 \\
\hline
K-nearest neighbor (KNN) & 0.01 & 0.41 &  & 0.021 & 0.019 \\
\hline
Ensemble of regression trees (CART) & 0.12 & 0.03 &  & 0.11 & 0.18 \\
\hline
\end{tabular}
\end{center}

backpropagation based neural network machine learning approaches. Unlike the CNN and LSTM methods, SVM are not backpropagationbased and use hand-crafted features that use supervised and unsupervised learning. The KNN, GLM and CART models represent white-box linear models with no active learning component, and operate with and without hierarchical prediction, respectively. Due to its simplicity, we take GLM as the baseline model. In Table 3, Apart from the CNN, the input feature vectors for all the machine learning algorithms are identical. In other words, we use the same features extracted from both the high-speed video camera and the pyrometer raw sensor data as input vectors for the SeDANN, as well as all machine learning models (except the CNN).

In the context of the CNN, some of its embodiments, such as ResNet [63], VGGNet [64] and AlexNet [65], are relatively complex. We acknowledge that an optimized CNN model that leverages the computational efficacy of a graphical processing unit (GPU) may outperform the modeling approaches tested in this work. Indeed, testing our data with all the state-of-the-art CNN models would be out of the scope this work. Accordingly, we used only one type of CNN architecture, that was employed in our prior work in the context of process monitoring in LPBF $[27,30]$. We proceeded to optimize the hyperparameters of this CNN network through extensive offline studies using a manual grid search method. We present the optimized hyperparameters achieved from the manual grid search method in Appendix A. Our intent was to show that the SeDANN approach compared well with such a general CNN model used in our prior work in LPBF. Additionally, the CNN model tested in this work was compiled in MATLAB 2019a, and does not leverage GPU processing to maintain equitable comparison with all ML approaches.

While the CNN uses multi-resolution filters to process the input data, the SeDANN has a rudimentary ANN architecture with only one hidden layer and uses features derived based on the physical reasoning of the process regimes. The simple architecture and tractable features used by the SeDANN preserves physical interpretability - a key rationale for the scientific machine learning aspect of this work. While a CNN or RNN can be coupled with a sequential decision-making schema of the SeDANN, the essential novelty of the work is a sequential decision-making approach to scientific machine learning in the context of LPBF additive manufacturing process.

Also, the SeDANN approach can accommodate heterogeneous data sources, such as 1D time series from a pyrometer, and 2D streaming images from the high-speed video camera in a physically intuitive manner taking advantage of the capabilities of each type of sensor. Lastly, chaining shallow ANNs to make sequential decisions with a sparse set of features in a shallow neural network is computationally more efficient in comparison to using dense input data arrayed in multiple layers, such as image-based deep neural networks.

The network architectures for SeDANN, CNN, and LSTM are described in Appendix A. In Table 3, nearly all these approaches perform well for prediction of the mean of single-width, i.e. $R^{2}>0.75$. The prediction fidelity of machine learning improves for continuity (classification and prediction) and standard deviation of single-track width in comparison to the linear regression analysis. Particularly, for prediction of standard deviation, majority of the machine learning approaches\\
\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-15(1)}

(b) Actual standard deviation of single-track width ( $\mu \mathrm{m}$ )

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-15}
\end{center}

(c) Actual percent continuity of single-track width (\%)

Fig. 13. Predicted values of single-track quality using fifty randomly selected data points from different machine learning techniques. (a) All machine learning techniques perform well while predicting the mean of single-track width, which is depicted by the close of fit of predicted values to the straight line. (b) The statistical fidelity of predicting standard deviation of single-track width is low in comparison to the mean for all techniques as seen in Table 3. SeDANN has a better performance as well as limited bias in comparison to the other two deep learning techniques. Similarly, (c) SeDANN shows better percent continuity prediction fidelity in comparison to the other techniques.

(other than KNN) significantly outperform linear statistical analysis, with the SeDANN having the highest $\mathrm{R}^{2}$.

We also used machine learning models for prediction of the energy density values ( $\mathrm{E}_{\mathrm{L}}=\mathrm{P} \cdot \mathrm{V}^{-1}\left[\mathrm{~J} \cdot \mathrm{mm}^{-1}\right]$ ). The rationale is to compare and verify the efficacy of the SeDANN with other machine learning approaches in the context of the energy density. As shown in Table 3, all\\
the approaches tested in this work have similar prediction fidelity $\left(\mathrm{R}^{2}\right)$ in the context of the energy density. However, machine learning models, except the SeDANN, deteriorates when predicting the single-track quality metrics. This result has an important implication - being able to predict the energy density, i.e., process regime alone is not a robust indicator of predictive performance of a machine learning model.

The conventional machine learning approaches represented by SVM, KNN, ensemble of regression trees, have $\mathrm{R}^{2}$ less than $50 \%$ in predicting the standard deviation of the single-track width. Models that use the backpropagation learning techniques with derived process signatures, viz. SeDANN and RNN perform significantly better in capturing the standard deviation of single-track width with $\mathrm{R}^{2}$ approaching $60 \%$ and higher. However, of all algorithms tested, the SeDANN has prediction accuracy exceeding $80 \%$ for all the quality metrics tested.

Further, the prediction time for the various approaches is given in Table 4. Not only does the SeDANN outperform the CNN and LSTM models in predicting the single-track quality metrics, once trained, the prediction time is also a fraction of both the time taken by trained CNN and LSTM models. We reiterate that none of these data-driven models used GPU computing, and all, except the CNN, use identical input features. The relatively high prediction time observed in CNN and LSTM is undesirable as high latency in the in-situ monitoring of single tracks will cause a cascading delay for actuating a corrective control action within the right time frame during the LPBF AM process.

In Fig. 13, we compare top three performing models (SeDANN, CNN, LSTM) graphically via predicted versus measured plots of $\mu_{w}, \sigma_{w}$, and $\kappa$. In these plots, the distribution of datapoints for a given model indicates strength of correlation between predicted and measured values. Thus, a high performing model, i.e. $\mathrm{R}^{2} \rightarrow 1$, yields distribution of datapoints that cluster along the equality line (along the diagonal). Thus, as indicated quantitatively in Table 3, width predictions for all three models are similarly impressive in Fig. 13 (a).

The distribution of $\sigma_{w}$ predictions in Fig. 13 (b) shows SeDANN $\left(\mathrm{R}^{2} \sim\right.$ 0.81 ) outperforms the other two deep learning techniques. The CNN which does not use the signatures selected through rigorous correlation of sensor data and single-track quality, but directly uses the meltpool features, has poor prediction ability, approaching $R^{2} \sim 0.35$. Furthermore, Fig. 13 (c) demonstrates the superior performance of SeDANN $\left(R^{2}\right.$ $\sim 0.73$ ) in comparison to CNN and LSTM while predicting percent continuity of single tracks. Although the percent continuity predictions made by SeDANN do not have high accuracy, they have a good distribution around the regression line. On the contrary, both CNN and LSTM incorrectly predict high percent continuity for majority of single tracks.

A purely data-driven black-box approach, such as CNN despite its ability to accommodate complex nonlinear patterns, does not outperform rudimentary linear modeling approaches (GLM) that use features chosen based on understanding of the process physics. SeDANN combines the efficiency of these process physics-based features and shallow ANNs to invoke a grey-box model that outperforms white and black-box models. The simplicity, flexibility, and intuitiveness of the SeDANN can prove to be useful in expanding the current in-situ monitoring system by incorporating data from more sensors to predict more LPBF AM process characteristics.

\section*{4. Conclusion and future work}
This work investigates the causal relationship encompassing process parameters, in-process sensor signatures, and part quality in laser powder bed fusion (LPBF). The key finding of this work is that in-process quality assurance improves significantly when machine learning models incorporate process signatures that are based on fundamental knowledge of the process regime, as opposed to purely data-driven machine learning algorithms, such as deep learning convolutional neural networks.

We study the effect of varying common LPBF process parameters, i.e. laser power ( $\mathrm{P}$ ) and laser velocity $(\mathrm{V})$, on the quality of single tracks while collecting pyrometer and high-speed video data during fabrication. We generate quality labels of single-track morphology efficiently via analysis of height map measurements that extract the mean and standard deviation of their width and percent continuity. We then characterize these morphology labels in the four process parameter regimes based on linear energy density $\left(\mathrm{E}_{\mathrm{L}}=\mathrm{P} \cdot \mathrm{V}^{-1}\right)$ : keyholing, conduction, lack-of-fusion, and balling.

Furthermore, we identify how process signatures from our sensing modalities map onto the four $\mathrm{E}_{\mathrm{L}}$ regimes. Collectively, these insights motivate the design of our scientific machine learning model that predicts single-track quality by fusing sensing modalities in a physically intuitive way. Our Sequential Decision Analysis Neural Network (SeDANN) model thus utilizes specific sensor data-derived feature sets in a physically intuitive and effective manner, leveraging sequences of shallow and computationally tractable neural networks to correlate process signature(s) with quality metric(s).

We evaluate and compare the performance of SeDANN against several well-established machine learning approaches, such as convolutional neural network (CNN), long short-term memory (LSTM), recurrent neural network (RNN), among others. We find SeDANN outperforms purely data-driven (black-box) models. The SeDANN approach thus facilitates the inclusion of the knowledge of the process physics into machine learning, in keeping with the scientific machine learning paradigm. This makes the SeDANN highly interpretable, intuitive, computationally tractable, and less prone to overfitting compared to conventional black-box machine learning models. For instance, compared to the CNN tested in this work, for predicting the standard deviation of single tracks the incorporation of the physical knowledge of the process regimes improves the prediction fidelity $\left(\mathrm{R}^{2}\right)$ by as much as $40 \%$ within $1 / 10$ th of the computation time. However, the SeDANN approach remains to be extended for multi-layer builds, complex geometries, and additional functional quality metric than reported here. The extension of the SeDANN to multi-layer builds would necessitate synchronization of spatiotemporal information, such as the laser position with the sensor data.

The current work can be taken forward by the AM community in numerous directions. To have a concise and effectual process parameter space, we focused our attention solely to the effect of variations in laser power and laser velocity (in terms of $\mathrm{E}_{\mathrm{L}}$ ) on the LPBF process. This can be expanded by adding more process parameters, such as hatch spacing, laser spot size, etc., and studying variations in resulting quantities like volumetric energy density and enthalpy. Next, given the flexible nature of SeDANN, different types of sensor data over multiple layers readily can be added to the model to improve the prediction fidelity. For example, an acoustic emission sensor can be employed to detect process deviations that may affect the single-track quality [47]. Further, the SeDANN can be modified to incorporate multiple sensors, monitor multiple process phenomenon, thereby creating an integrated in-situ monitoring system for LPBF and other AM processes, e.g. electron beam powder bed fusion, in a way that accommodates the evolving sensing capabilities and quality specifications common to AM.

In a similar vein, addition of dimensionless quantities, such as bead statistics as a percentage of laser spot size will enable the transferability of the SeDANN model to other AM systems and sensing modalities. Furthermore, the current single-track characterization done by height map analysis, can be strengthened by performing additional diagnostics, such as X-ray computed tomography, to incorporate surface and subsurface information of the single tracks which may prove beneficial in improving process monitoring capabilities. Lastly, the height maps of single tracks can be used to perform bead height analysis along with single-track width and continuity.

\section*{CRediT authorship contribution statement}
Brian Giera: Supervision, Writing- reviewing \& editing, conceptualization. Gabriel Guss: Investigation, data curation. Jean Baptiste:

Investigation, Data curation. Manyalibo Matthews: Resources, Project administration, Funding acquisition. Prahalada Rao: Supervision, Writing- reviewing \& editing, Conceptualization, Funding acquisition. Aniruddha Gaikwad: Methodology, Software, Formal analysis, Data curation, Writing- original draft.

\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*{Acknowledgements}
This work was performed in part under the auspices of the U.S.\\
Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07-NA27344, LLNL-JRNL-808643. One of the authors (PR) thanks the National Science Foundation (NSF) for funding his research through the following grants CMMI-1719388, CMMI1739696, CMMI-1752069, and OIA-1929172 at University of NebraskaLincoln. Specifically, the concept of using machine learning for quality assurnace in metal additive manufacturing is funded through CMMI1752069 (Program Officer: Dr. Kevin Chou). This grant also provided supplemental funding through the NSF and CMMI Data Science Activities (Program Officer: Dr. Martha Dodson) and NSF INTERN Program (Program Officer: Dr. Prakash Balan). The NSF INTERN Program provided funding for the first author (AG) to spend 6-months at Lawrence Livermore National Laboratory under the aegis of Dr. Brian Giera.

\section*{Appendix A. Neural network architecture and optimization}
Sequential decision analysis neural network (SeDANN)

SeDANN leverages the knowledge of the process physics crucial to the single-track quality prediction. Three independent shallow artificial neural networks (ANN) are trained and tested for the SeDANN, per Fig. 5 in the main text. The ANN in the first echelon predicts the process parameter regime of a single-track segment using 1D signals of a pyrometer. These process parameter predictions are used for subsequent prediction of the width and percent continuity of a single-track. The second echelon's ANN predicts the segment width and is translated to mean and standard deviation of width of the entire single-track via echelon 1's predictions and meltpool characteristics extracted from the high-speed video camera frames. Lastly, in echelon 3, an ANN predicts the percent continuity, i.e. lack of discontinuity, via previously predicted parameters (echelon 1), meltpool characteristics, mean and standard deviation of the single-track width (echelon 2).

The three shallow ANNs have a similar architecture. Each ANN has three layers, viz. an input, an output, and a hidden layer. As the input feature space has a low dimensionality with respect to the sample size, the hidden layer has 12 neurons to ensure computational efficiency and mitigate overfitting. Instead of the commonly used logistic function, a hyperbolic tangent activation function is used for these neurons since its gradient facilitates in faster approach towards global minima of the error function, viz., mean squared error.

Regularization is used while training the ANNs to avoid overfitting of the approximated function to the training data. Regularization is performed by adding a penalty to the error function when the weights are too high. This penalty of high weights ensures the slopes of the ANN's approximated function are not too high and thus yields a good fit with the underlying function of the training data. Bayesian analysis is used to estimate the two regularization parameters that are applied to the error function and the weights of the neural network, as detailed elsewhere [66,67]. Additionally, the number of effective parameters, i.e. weights and biases that influence the function approximation, is calculated and the non-essential parameters are neglected. This reduces the model complexity, computational cost, and likelihood of overfitting.

The hyperparameters of the ANNs were optimized to reduce the error function. The sparse nature of the ANN architecture, and correspondingly low computation time, motivated a naïve grid search approach for the hyperparameter space optimization. It was observed that the ANN predictive capability was hampered when the complexity of the architecture was increased, i.e. the number of hidden layers and number neurons were increased. Therefore, abiding to the Occam's razor problem-solving principle, a modest neural network architecture was adopted.

\section*{Convolutional neural network (CNN)}
A convolutional neural network (CNN) was used to predict the quality metrics of the entire single-track with the help of high-speed video camera frames (while excluding pyrometer data). Fig. A1 shows how high-speed video camera frames of single tracks were concatenated. Single tracks that were deposited at high laser velocity have a smaller number of high-speed video camera frames (Fig. A1 (b)) in comparison to single tracks deposited at low laser velocity (Fig. A1 (a)). Thus, to maintain uniformity in the data (concatenated frames) size, the standard practice of zero padding was implemented (Fig. A1 (b)).

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-17(1)}
\end{center}

(a) Laser power= $115 \mathrm{~W}$; Laser velocity $=100 \mathrm{~mm} / \mathrm{s}$

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-17}
\end{center}

Fig. A1. Representative high-speed video camera frames of two single tracks (frame number is shown in the upper left corner of each image). Concatenated highspeed video camera frames of a single-track deposited at laser power $=115 \mathrm{~W}$, (a) laser velocity $=100 \mathrm{~mm} / \mathrm{s}$ and (b) laser velocity $=400 \mathrm{~mm} / \mathrm{s}$. Concatenated highspeed video camera frames of single tracks deposited at high laser velocity are padded with zeros to maintain a uniform image size.

A schematic representation of the CNN architecture is shown in Fig. A2. As seen in the figure, first layer is the input layer which takes the concatenated image of the high-speed video camera frames. The concatenated images were scaled down to $70 \%$ of their original size $(105 \times 6600$ pixels) to reduce the input data density. Consequently, the overall time required for hyperparameter optimization was significantly decreased.

Apart from the input and output layers, the CNN architecture has four blocks as shown in Fig. A2. Each block has a convolutional layer with a $3 \times 3$ kernel size and varying number of feature maps (channels), viz. 8, 16, and 32. After each convolution layer, batch normalization was performed followed by introduction of non-linearity to the neural network with the rectified linear unit (ReLU) activation function. Subsequently, in Block 1 and Block 2, a $2 \times 2$ mean-pooling layer is used to reduce the dimensionality of the output obtained from the activation function. In the last block, a

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-18}
\end{center}

Fig. A2. Schematic of the CNN architecture.

dropout layer with a rate of 0.4 was used. The dropout layer randomly ignores a fraction of the nodes in the network to avoid overfitting of the model (CNN) to the training data. This is followed by a dense layer with 10 hidden units. The output layer is made up of single unit which uses the crossentropy cost function for classification and the mean-squared error cost function for prediction.

An adaptive learning optimization technique was applied during training with the help of the Adam solver [68]. This yielded better classification/ prediction results on the test data set in comparison to the widely used stochastic gradient descent training method. A naïve grid search method was used for hyperparameter optimization. Table A1 shows the optimum hyperparameter values for this CNN architecture.

\section*{Long short-term memory recurrent neural network (LSTM-RNN)}
A long short-term memory (LSTM) neural network is a type of recurrent neural network (RNN), which was used to predict the quality metrics of single tracks. The mean and standard deviation of single-track width was derived from the widths of the three segments of the single tracks. In other words, width of each segment of a single-track was predicted, and the mean and standard deviation of these segment widths was calculated from the aggregate. A similar strategy was followed to predict the percent continuity of the single-tracks and to perform binary classification on single-track continuity. Features extracted from the pyrometer and high-speed video camera of single-track segments were concatenated and used in the LSTM-

Table A1

Optimum hyperparameter values of the CNN obtained from naïve grid search optimization.

\begin{center}
\begin{tabular}{lllll}
\hline
Batch-size & Initial learning rate & Input size & Dropout rate & Hidden units in dense layer \\
\hline
6 & 0.0001 & $[78,4804]$ & 0.4 & 10 \\
\hline
\end{tabular}
\end{center}

RNN for single-track quality metric prediction.

The first layer of the LSTM-RNN is the sequence input layer that can take $n$ elements in a sequence. For this work, $n=3$ which is the feature set (pyrometer and high-speed video camera) of three segments of a single-track. This is followed by a unidirectional LSTM layer with 300 hidden units which outputs a sequence. The output of the LSTM layer is fed into a dense layer with 100 hidden units. A dropout layer performs the dropout operation at a rate of 0.4 on the output of the dense layer. Next, a dense layer with 3 hidden units (corresponding to the number of segments) was used followed by a regression or classification layer which depended on the single-track quality metric being predicted. (Fig. A3).

As with the SeDANN and CNN, a naïve grid search technique was used for hyperparameter optimization. Table A2 shows the hyperparameter values that yielded the best regression and classification results.

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-19(3)}
\end{center}

Fig. A3. Schematic of the LSTM-RNN architecture.

Table A2

Optimum hyperparameter values of the LSTM-RNN obtained from naïve grid search optimization.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\begin{tabular}{l}
Batch- \\
size \\
\end{tabular} & \begin{tabular}{l}
Batch- \\
size \\
\end{tabular} & \begin{tabular}{l}
Initial \\
learning \\
rate \\
\end{tabular} & \begin{tabular}{l}
Initial \\
learning \\
rate \\
\end{tabular} & \begin{tabular}{l}
Number of \\
LSTM \\
layers \\
\end{tabular} & \begin{tabular}{l}
Number of \\
LSTM \\
layers \\
\end{tabular} & \begin{tabular}{l}
Dropout \\
rate \\
\end{tabular} & \begin{tabular}{l}
Dropout \\
rate \\
\end{tabular} & \begin{tabular}{l}
Hidden \\
units in first \\
dense layer \\
\end{tabular} & \begin{tabular}{l}
Hidden \\
units in first \\
dense layer \\
\end{tabular} & \begin{tabular}{l}
Maximum \\
number of \\
training epochs \\
\end{tabular} & \begin{tabular}{l}
Maximum \\
number of \\
training epochs \\
\end{tabular} \\
\hline
7 & 7 & 0.0001 & 0.0001 & 1 & 1 & 0.4 & 0.4 & 100 & 100 & 30 & 30 \\
\hline
\end{tabular}
\end{center}

\section*{Appendix B. Meltpool extraction from high-speed video camera frames }
In Fig. B1 we show the methodology adopted to extract meltpool from high-speed video camera frames (henceforth called images). Fig. B1 (a) shows a representative high-speed video camera images of a single-track deposited at laser power $(\mathrm{P})=115 \mathrm{~W}$ and laser velocity $(\mathrm{V})=100 \mathrm{~mm} \cdot \mathrm{s}^{-1}$. Given the noisy nature of the high-speed video camera frames, the conventional thresholding technique to segment images prove ineffective. Therefore, we implemented the unsupervised learning-based k-means technique to segment the high-speed video camera images. To account for the meltpool, spatter, and illuminated background, we segment the image into 4 clusters as shown in Fig. B1 (b). An extensive visual analysis of the kmeans segmented images reveal that the said technique performs quite well in the segmentation task.

Next, a binary mask of the meltpool is created as shown in Fig. B1 (c). This mask is used to extract the meltpool intensity (I) values from the original high-speed video camera image (Fig. B1 (a)) and to determine the meltpool area (A). Subsequently, the binarized meltpool image is used to determine the meltpool edge with the help of the Canny edge detector as shown in Fig. B1 (d) [69]. The distance from center of the meltpool to the edge pixels $\left(d_{y}\right)$, as shown in Figure $B(d)$, is used to compute the meltpool circularity $\left(\mu_{c}, \sigma_{c}\right)$.

(a) Original image

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-19(4)}
\end{center}

(b) K-means segmented image

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-19(1)}
\end{center}

Image segmented in 4 clusters (c) Binary meltpool image\\
\includegraphics[max width=\textwidth, center]{2024_03_10_cc3981078ca442cb949eg-19}

Meltpool circularity is determined by edge pixels

\begin{center}
\includegraphics[max width=\textwidth]{2024_03_10_cc3981078ca442cb949eg-19(2)}
\end{center}

$$
\text { xels }
$$

Fig. B1. A representative example of meltpool extraction from high-speed video camera frames. The above shown high-speed video camera frames belongs to a single-track deposited at $115 \mathrm{~W}$ laser power and $100 \mathrm{~mm} / \mathrm{s}$ laser velocity. The image size before and after segmentation is 256 pixels $\times 256$ pixels.

\section*{Appendix C. Single-track quality metrics under varying process parameters}
Table C1

Representative values of mean width ( $\mu_{\mathrm{w}}[\mu \mathrm{m}]$ ), standard deviation of the width ( $\sigma_{\mathrm{w}}[\mu \mathrm{m}]$ and) and percentage continuity ( $\kappa$ ) of single tracks, appear in the top, middle, and bottom positions, respectively, in each cell that indicate the laser power and velocity settings. The values have been color-coded according to the four process parameter regimes introduced in Section 1.

Laser power (W)

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
 & 50 & 82.5 & 115 & 147.5 & 180 & 212.5 & 245 & 277.5 & 310 & 342.5 & 375 \\
\hline
\multirow{3}{*}{100} & $\mu_{w}=87.58$ & 158.01 & 150.51 & 152.85 & 176.78 & 190.63 & 253.03 & 257.05 & 289.39 & 320.39 & 323.51 \\
\hline
 & $\sigma_{w}=34.18$ & 50.45 & 30.62 & 42.04 & 38.62 & 50.27 & 62.44 & 53.54 & 63.25 & 49.59 & 56.11 \\
\hline
 & $K=62.07$ & 96.55 & 97.13 & 95.4 & 95.98 & 86.78 & 94.83 & 88.51 & 98.85 & 93.68 & 87.36 \\
\hline
\multirow{3}{*}{130} & 60.46 & 101.39 & 125.94 & 153.77 & 195.17 & 194.13 & 231.26 & 255.79 & 265.19 & 248.37 & 267.63 \\
\hline
 & 24.18 & 22.58 & 28.24 & 31.54 & 38.92 & 29.15 & 51.03 & 53.24 & 39.99 & 51.99 & 80.82 \\
\hline
 & 36.21 & 94.83 & 95.4 & 94.83 & 94.83 & 89.66 & 91.38 & 90.8 & 88.51 & 89.66 & 89.66 \\
\hline
\multirow{3}{*}{160} & 79.97 & 104.69 & 93.33 & 134.96 & 159.61 & 205.97 & 202.26 & 226.32 & 249.37 & 241.41 & 262.09 \\
\hline
 & 34.66 & 27.45 & 25.13 & 24.96 & 30.09 & 80.42 & 41.47 & 44.9 & 45.5 & 51.97 & 36.77 \\
\hline
 & 61.49 & 93.1 & 93.1 & 93.1 & 94.83 & 95.4 & 91.38 & 96.55 & 93.1 & 93.68 & 86.78 \\
\hline
\multirow{3}{*}{190} & 77.48 & 66.22 & 111.61 & 155.81 & 159.39 & 180.88 & 189.96 & 198.82 & 236.03 & 226.42 & 255.72 \\
\hline
 & 45.17 & 23.21 & 26.9 & 35.05 & 34.8 & 24.15 & 30.75 & 29.65 & 55.93 & 38.26 & 50.98 \\
\hline
 & 45.98 & 63.22 & 94.25 & 93.68 & 93.68 & 93.68 & 87.36 & 91.95 & 90.23 & 87.36 & 88.51 \\
\hline
\multirow{3}{*}{220} & 55.26 & 119.45 & 128.63 & 135.54 & 126.04 & 157.36 & 171.94 & 181.18 & 195.84 & 212.98 & 240.54 \\
\hline
 & 24.14 & 31.93 & 40.07 & 34.97 & 53.8 & 23.51 & 44.32 & 40.34 & 30.67 & 34.88 & 30.05 \\
\hline
 & 43.1 & 94.25 & 96.55 & 94.83 & 91.95 & 94.25 & 90.8 & 90.8 & 86.78 & 90.23 & 85.06 \\
\hline
\multirow{3}{*}{250} & 49.43 & 80.26 & 85.71 & 107.26 & 144.87 & 141.39 & 164.23 & 178.21 & 185.33 & 208.71 & 187.72 \\
\hline
 & 21.32 & 18.06 & 27.24 & 24.84 & 36.77 & 31.35 & 26.69 & 34.81 & 33.75 & 34.5 & 53.82 \\
\hline
 & 30.46 & 87.93 & 85.63 & 91.95 & 93.1 & 89.66 & 88.51 & 92.53 & 91.95 & 90.23 & 78.74 \\
\hline
\multirow{3}{*}{280} & 69.47 & 84.27 & 91.73 & 142.13 & 118.93 & 140.41 & 163.34 & 168.11 & 185.34 & 190.39 & 212.68 \\
\hline
 & 23.36 & 25.13 & 20.67 & 48.2 & 29.17 & 29.62 & 35.1 & 35.19 & 47.71 & 33.1 & 33.65 \\
\hline
 & 31.61 & 91.95 & 92.53 & 92.53 & 92.53 & 93.68 & 92.53 & 93.1 & 89.66 & 89.66 & 83.33 \\
\hline
\multirow{3}{*}{310} & 42.36 & 61.75 & 92.14 & 98.68 & 107.37 & 133.25 & 126.97 & 162.34 & 154.47 & 190.45 & 193.45 \\
\hline
 & 16.79 & 21.27 & 30.71 & 23.19 & 27.18 & 25.51 & 36.45 & 27.41 & 39.04 & 28 & 30.63 \\
\hline
 & 16.09 & 75.86 & 91.38 & 93.68 & 91.38 & 90.23 & 87.93 & 91.95 & 87.36 & 87.93 & 91.38 \\
\hline
\multirow{3}{*}{340} & 42.8 & 62.17 & 89.01 & 88.65 & 119.48 & 135.06 & 129.75 & 155.73 & 171.35 & 158.32 & 173.74 \\
\hline
 & 18.67 & 24.56 & 25.61 & 26.19 & 23.6 & 23.67 & 28.4 & 30.46 & 30.66 & 39.84 & 34.69 \\
\hline
 & 15.52 & 70.69 & 94.25 & 93.1 & 91.95 & 92.53 & 88.51 & 92.53 & 87.36 & 85.63 & 79.89 \\
\hline
\multirow{3}{*}{370} & 51.04 & 54.83 & 80.64 & 63.06 & 93.82 & 132.08 & 124.93 & 142.58 & 170.71 & 180.97 & 185.74 \\
\hline
 & 22.67 & 20.09 & 23.41 & 27.2 & 25.57 & 28.49 & 29.81 & 27.04 & 25.17 & 30.19 & 36.27 \\
\hline
 & 11.49 & 50.57 & 87.93 & 71.84 & 90.8 & 94.25 & 89.66 & 90.8 & 89.08 & 86.78 & 83.33 \\
\hline
\multirow{3}{*}{400} & 57.87 & 57.54 & 87.73 & 84.64 & 112.18 & 117.13 & 115.19 & 130.09 & 137.46 & 139.11 & 166 \\
\hline
 & 26.05 & 25.63 & 28.31 & 22.94 & 38.31 & 30.42 & 28.43 & 22.13 & 26.46 & 30.39 & 31.03 \\
\hline
 & 54.02 & 53.45 & 91.38 & 91.95 & 94.83 & 93.68 & 89.08 & 93.1 & 89.66 & 83.33 & 84.48 \\
\hline
\end{tabular}
\end{center}

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