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| \title{Towards 3-D texture control in a $\beta$ titanium alloy via laser powder bed fusion and its implications on mechanical properties } | |
| \author{Sravya Tekumalla ${ }^{\mathrm{a},{ }^{*}}$, Jian Eng Chew ${ }^{\mathrm{b}}$, Sui Wei Tan ${ }^{\text {c }}$, Manickavasagam Krishnan ${ }^{\text {c }}$,\\ | |
| Matteo Seita ${ }^{\mathrm{a}, \mathrm{b}, \mathrm{d}}$\\ | |
| a School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore\\ | |
| ${ }^{\mathrm{b}}$ School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore\\ | |
| ${ }^{c}$ Advanced Remanufacturing Technology Centre (ARTC), Agency for Science, Technology and Research (A*STAR), Singapore 637143, Singapore\\ | |
| ${ }^{\mathrm{d}}$ Singapore Centre for 3D Printing, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore} | |
| \date{} | |
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| \begin{document} | |
| \maketitle | |
| Research paper | |
| \section*{A R T I C L E I N F O} | |
| \section*{Keywords:} | |
| Crystallographic texture control | |
| Beta Ti alloy | |
| Elastic modulus | |
| Mechanical properties | |
| Deformation behavio | |
| \begin{abstract} | |
| A B S T R A C T Fusion-based additive manufacturing (AM) offers a new opportunity to design metallic materials with complex, direction-dependent mechanical properties by controlling the orientation distribution of the constituent grains-also known as texture. Texture control may be achieved site-specifically by varying the processing variables and tailoring the local melt pool geometry and solidification kinetics. However, the type and direction of textures currently achievable in AM alloys are limited by the melt pool geometry itself. In this work, we advance the capabilities of controlling crystallographic texture in laser powder bed fusion (LPBF) by producing specimens of $\beta$ titanium-niobium alloy with textures aligned along three different directions: the laser scan direction (SD), the build direction (BD), and-for the first time-the direction perpendicular to both BD and SD (i, e., PD). We achieve this three-dimensional (3-D) texture control by fine tuning the keyhole melt pool geometry and amount of overlap throughout the build. We test the tensile properties of the three different specimens along their respective texture axes and elucidate the relationships between crystallographic orientation, mesostructure, and mechanical behavior. We find that the novel PD texture exhibits the best combination of strength, strain hardenability, and ductility. We ascribe these results to the unique mesostructure of this specimen. This work opens new opportunities for designing novel materials with directional properties by achieving threedimensional (3-D) texture control during fusion-based AM. | |
| \end{abstract} | |
| \section*{1. Introduction} | |
| The combined freedom of design and ability to control the microstructure of materials site-specifically [1,2] make additive manufacturing (AM) a promising technology to produce metal parts with complex geometries [3,4] and tailored properties [5,6]. Several studies have demonstrated the possibility of tuning features such as porosity [7], grain structure and morphology [1,8,9], composition [10-13], and residual stresses [14] using different AM processes, and the beneficial effects that these features may have on part properties. Another promising strategy that has raised a lot of interest across the academic community relies on controlling the crystallographic texture of metal alloys produced via fusion-based AM processes [15-19]. Notable examples are previous works focused on face centered cubic (FCC) alloys-including stainless steel 316 L [17,18] and Inconel 718 [15]-and body-centered cubic (BCC) alloys-such as titanium-based alloys [19]—produced by laser powder bed fusion (LPBF). The interest behind controlling the crystallographic texture is motivated by the additional opportunities to impart directional mechanical properties to the build by aligning the resulting textures along specific directions [5, $16,19,20]$. This capability offers the opportunity to design and produce materials that combine microstructures with largely different mechanical behaviors, which may unlock novel deformation mechanisms $[5,21$, 22]. It may also be useful to site-specifically tailor materials properties that are indirectly related to texture, such as those governed by grain boundaries $[23,24]$. | |
| Strong crystallographic textures in powder bed fusion-based metal AM result from the directional solidification of metal alloys-in the form of cells or dendrites-which follow the steep thermal gradients promoted during the localized melting of powders [6,19]. To date, the main strategies for crystallographic texture control in powder bed fusion-based metal AM include tuning the processing parameters to vary | |
| \footnotetext{\begin{itemize} | |
| \item Corresponding author. | |
| \end{itemize} | |
| \href{https://doi.org/10.1016/j.addma.2022.103111}{https://doi.org/10.1016/j.addma.2022.103111} | |
| Received 28 February 2022; Received in revised form 19 August 2022; Accepted 22 August 2022 | |
| Available online 27 August 2022 | |
| 2214-8604/© 2022 Elsevier B.V. All rights reserved. | |
| } | |
| the ratio between thermal gradient and solidification velocity at the solid/liquid interface [15], or the melt pool shape and thus, the solidification direction [16-18,25]. | |
| The current challenge in this texture control materials design paradigm, however, is that texture orientation in the build cannot be arbitrary. Strong, bulk $<100>$ crystallographic textures in cubic alloys are typically found parallel to the build direction (BD) [20,26] or along the laser scanning direction (SD) [16-18,27-32]. These $<100>$ textures result from epitaxial growth of crystals along these specific directions following local and global thermal gradients during production, which depend on the melt pool geometry. In cubic alloys, in fact, the easy growth direction of crystals is $\langle 100>$ [16,33-35]. Since thermal gradients are perpendicular to melt pool boundaries [16], it becomes difficult to align them along other arbitrary directions within the build and achieve three-dimensional (3-D) texture control. However, this capability would open a new degree of freedom in the design of structural alloys with controlled functionality of the materials such as mechanical [5,18,36], corrosion [18,37], and magnetic properties [38]. A notable application would be for cellular solids, where aligning crystallographic texture with strut orientation could lead to significant improvements in mechanical performance [39]. | |
| This work aims at advancing texture control capabilities in LPBF by using $\beta$-type titanium-niobium (Ti-Nb) alloy. This class of Ti alloys exhibits low modulus and excellent bio-mechanical properties, making them suitable for biomedical implants owing to their high compatibility with human cortical bone $[20,26,40]$. In this context, 3-D texture control would be extremely valuable to produce structures with tuneable elastic properties, since the modulus of elasticity is a function of crystallographic texture $[20,26,40]$. We demonstrate the ability of promoting $<100>$ textures along all the three reference coordinate axes, namely the BD, the SD, and the direction perpendicular to both SD and BD (i.e., PD). We achieve this result by promoting keyhole melt pools in the alloy. We elucidate the different texture formation mechanisms at play in the three different cases and assess the corresponding mechanical properties of the material. While the elastic modulus along the $<100>$ axis is the same regardless of texture direction, we find that the samples with the $<100>$ texture along PD exhibit the highest strength, work hardening, and ductility. Our results open new opportunities for tuning texture-dependent properties of $\beta-\mathrm{Ti}$ alloys and may be extended to other cubic alloys such as stainless steel 316 L and Inconel 718. | |
| \section*{2. Materials and methods} | |
| \subsection*{2.1. Materials} | |
| Our experiments involve in-situ alloying [41] of gas atomised, pure, and spherical titanium powders (CP Ti, Grade 2 ASTM B348, supplied by Tecnisco Advance Material Pte Ltd, Singapore) and niobium powders ( $99 \%$ purity, supplied by Stanford Advanced Materials, California, USA) during LPBF process. The powder particle size distribution of Ti ranged between $20 \mu \mathrm{m}$ and $63 \mu \mathrm{m}$, with a median diameter, $\mathrm{d}_{50}$ of $42.9 \mu \mathrm{m}$. Since the melting temperature of $\mathrm{Nb}(\sim 2750 \mathrm{~K})$ is significantly higher than that of $\mathrm{Ti}(\sim 1941 \mathrm{~K})$, we chose Nb powders with reduced particle size distribution between $15 \mu \mathrm{m}$ and $45 \mu \mathrm{m}$ to ensure complete melting using our LPBF process parameters (see Section 2.2). Nb is a $\beta$-phase stabiliser in Ti alloys, with a molybdenum equivalency $\left(\mathrm{Mo}_{\mathrm{eq}}\right)$ contribution equivalent to $0.28(\mathrm{wt} \% \mathrm{Nb})$ [42]. Mo $\mathrm{eq}_{\text {eq }}$ is a metric that defines the stability of a $\beta$ phase in a Ti-base alloy at ambient temperatures [42] and is estimated as the sum of the weighted averages of the elements as given in Eq. (1) below: | |
| \begin{align*} | |
| M o_{e q .} & =1.0(\mathrm{wt} . \% \mathrm{Mo})+0.67(\mathrm{wt} . \% \mathrm{~V})+0.44 \quad(\mathrm{wt} . \% \mathrm{~W}) \\ | |
| & +0.28(\mathrm{wt} . \% \mathrm{Nb})+0.22(\mathrm{wt} . \% \mathrm{Ta})+2.9 \quad(\mathrm{wt} . \% \mathrm{Fe}) \\ | |
| & +1.6(\mathrm{wt} . \% \mathrm{Cr})+1.25(\mathrm{wt} . \% \mathrm{Ni})+1.70 \quad(\mathrm{wt} . \% \mathrm{Mn}) \\ | |
| & +1.70(\mathrm{wt} . \% \mathrm{Co})-1.0(\mathrm{wt} . \% \mathrm{Al}) \tag{1} | |
| \end{align*} | |
| It may be noted that since Al is an $\alpha$ stabilizer, therefore, the minus sign in Eq. (1) is used to account for the negative weighted contribution from Al . Ti alloys with $10<\mathrm{Mo}_{\mathrm{eq}}<30$ are known to retain a metastable $\beta$ phase. Therefore, in this work, we chose an alloy composition of Ti$45 \mathrm{wt} \% \mathrm{Nb}$ ( $30 \mathrm{at} \%$ ) which translates to a Mo $\mathrm{Moq}_{\text {eq }}$ value of 12.6 (obtained by substituting $45 \mathrm{wt} \%$ in Eq. (1) as Nb 's contribution and 0 from the other elements since the alloy is binary). | |
| \subsection*{2.2. Material processing} | |
| We mixed the pure elemental Ti and Nb powders using a highcapacity tumbler mixer (Inversina 20 L , Bioengineering AG) in an argon atmosphere at a rotational speed of 30 rpm for 6 h . The resulting uniform powder blend is shown in Fig. 1a. We carried out our LPBF experiments using an EOS M290 system equipped with a 400 W Yb-fiber laser in Ar atmosphere. We maintained a constant layer thickness of 0.03 mm for the $\mathrm{Ti}-45 \mathrm{Nb}$ alloy powders and used a bidirectional scanning strategy with no rotation in-between layers across all experiments. We varied laser power, scan speed, and hatch spacing, and studied how these parameters affect the resulting microstructure and crystallographic texture. For the initial design of experiments, we printed cube samples with a side of 8 mm . We report a summary of all these experiments and the corresponding microstructural analysis in the Appendix and in Fig. A1. Here, we only show and discuss those which led to builds with low porosity and low fraction of un-melted Nb . From this database, we selected three sets of parameters giving rise to samples with strong $<100>$ textures along SD, BD, and PD. These textured samples were then printed again with dimensions of 23 (L) $\times 10$ (B) $\times 10(\mathrm{H}) \mathrm{mm}^{3}$, which we show in Fig. A1e, to carry out detailed characterization and testing. Hereafter, we refer to these textures as $<100>\| S D$, $<100>\| \mathrm{BD}$, and $<100>\| \mathrm{PD}$, respectively, and the corresponding samples as SD-sample, BD-sample, and PD-sample, respectively. | |
| \subsection*{2.3. Microstructural characterization and orientation mapping} | |
| We determined the relative densities and porosities of the printed cube Ti-45 Nb samples through Archimedes' principle using the XS204 Density Kit (Mettler Toledo, Columbus, Ohio, United States). To assess the alloys microstructure, we prepared the samples following standard metallographic techniques, which include grinding, polishing (using $\mathrm{OPS}+20 \% \mathrm{H}_{2} \mathrm{O}_{2}$ ), and etching with Kroll's Reagent ( 2 vol $\%$ Hydrofluoric acid, 6 vol $\%$ Nitric acid, 92 vol $\%$ water). We used an Axioscope 2 (Carl Zeiss AG, Germany) optical microscope to study the melt pool geometry and a JEOL 7800 F Prime field emission scanning electron microscope (FESEM) equipped with a Symmetry S2 detector by Oxford Instruments (UK) to visualize the microstructure of our specimens and carry out electron backscattered diffraction (EBSD) measurements on the YZ plane i.e., PD-BD plane. We run EBSD at an accelerating voltage of 20 kV and a probe current of 20 nA on the polished surfaces. We fixed the minimum number of pixels to be considered a grain to 5 , the grain tolerance angle to $5^{\circ}$, and the step size to $1 \mu \mathrm{m}$ for all the EBSD measurements. We determined the $\%$ of un-melted Nb from each SEM image using ImageJ software. We also identified and analyzed the constituent phases in our samples by means of X-ray diffraction (XRD, PANalytical | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-03(2)} | |
| \end{center} | |
| (a) | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-03} | |
| \end{center} | |
| (b) | |
| Fig. 1. (a) Energy dispersive spectroscopy (EDS) map of a pre-mixed Ti-45 Nb alloy powder showing the distribution of Ti and Nb particles; (b) Schematics of the tensile specimens cut out of builds with different $<100>$ textures. The black rectangle on each tensile specimen in (b) shows the location of EBSD measurements. | |
| Empyrean, Netherlands), using a Cu-K $\alpha$ radiation and a step size of $0.01^{\circ}$. | |
| \subsection*{2.4. Mechanical testing} | |
| We performed uniaxial tensile tests on dog-bone shaped samples with gauge length of 6 mm , width of 2 mm and thickness of 1 mm using a Shimadzu AGX 10 kN equipped with a laser extensometer at a strain rate of $10^{-3} / \mathrm{s}$. We tested all samples along the direction parallel to their respective $<100\rangle$ crystallographic texture, as shown schematically in Fig. 1b. From the data, we extrapolated the alloys modulus of elasticity, yield strength, UTS, and elongation to failure. To understand the deformation behavior of the different samples, we polished the side surfaces of the fractured samples and analyzed the microstructure using both FESEM and EBSD. | |
| \section*{3. Experimental Results} | |
| \subsection*{3.1. Crystallographic texture control} | |
| Owing to a difference of 1082 K in melting temperatures between Ti and Nb , it is difficult to obtain Ti-Nb alloys that exhibit both high density and homogeneous composition (i.e., do not contain un-melted Nb particles) by LPBF in the as-built conditions. Several works discuss the porosity-unmelted particles trade off in $\mathrm{Ti}-\mathrm{Nb}$ alloys and propose strategies to mitigate it, including variations in volumetric energy density\\ | |
| (VED) [26], cross hatching style with an angle of $74^{\circ}$ between the layers [40], and laser intensity profile [20]. Here, we leverage on the work of Fischer et al. [26] and perform a large matrix of experiments with varying VEDs to identify a processing window that yields highly dense $\mathrm{Ti}-45 \mathrm{Nb}$ builds with minimal un-melted Nb content. We provide a detailed description of the optimization process and process parameter windows in the Appendix. We confirm that the porosity and un-melted Nb generally scale inversely with VED and identify two working windows that are suitable for our alloy composition as given in Fig. A1. The first is characterized by VED between 125 and $200 \mathrm{~J} / \mathrm{mm}^{3}$ and relatively high laser power (from 300 W to 350 W ). In the second, VED ranges between 265 and $290 \mathrm{~J} / \mathrm{mm}^{3}$ and requires relatively low laser power ( $\leq$ 100 W ). Fig. 2a shows a SEM micrograph of an area of 2 mm by 1.5 mm from a Ti-45 Nb sample that is representative of the build quality we obtain when using the initially optimized process parameters as shown in the green zones in Fig. A1a and Fig. A1b. The material contains a negligible number of un-melted particles (indicated by the orange arrows) and pores (indicated by the white arrows). The XRD spectrum from the same representative sample (shown in Fig. 2b) confirms that the Ti-45 Nb alloy consists of a $100 \%$ BCC phase. This is because the $\mathrm{Mo}_{\text {eq }}$ of the alloy is 12.6 (see Eq. 1), which is greater than the critical value of $10 \%$ required for retaining the $\beta$ phase at room temperature. Moreover, the fast-cooling rates during the LPBF process further facilitate the $\beta$ phase retention at room temperature. Similar $\beta$ phase stability has been shown in other in-situ alloyed Ti-Nb alloys processed by LPBF techniques previously $[20,43]$. | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-03(1)} | |
| \end{center} | |
| (b) | |
| Fig. 2. (a) Representative SEM image showing the build quality of the samples produced using optimized process parameters to minimize both porosity (indicated by white arrows) and fraction of un-melted Nb particles (indicated by orange arrows); (b) XRD pattern of the same sample as in (a) showing a 100\% $\beta$ phase in Ti45 Nb alloy. | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-04} | |
| \end{center} | |
| Fig. 3. Inverse pole figure grain orientation maps and pole figures of (a-d) $<100>\|$ SD textured sample; (e-h) $<100>\|$ BD textured sample, (i-l) $<100>\|$ PD textured sample. Please note that in this work, we represent the build direction as Z and the scan direction as X. MUD in the texture intensity scale bar stands for Multiples of Uniform Density, and indicates the texture strength of a given material. The cross section for EBSD measurements is shown in Fig. 1b in the small rectangular insets on the tensile specimens. | |
| Table 1 | |
| Process parameters used to obtain the strong $<100>$ crystallographic textures along scanning direction (SD), build direction (BD), perpendicular to scan direction (PD). | |
| \begin{center} | |
| \begin{tabular}{|c|c|c|c|c|c|c|c|} | |
| \hline | |
| S. No. & Samples & Rotation Angle $\left({ }^{\circ}\right)$ & Laser power $(\mathrm{W})$ & Hatch spacing (mm) & Scan speed $(\mathrm{mm} / \mathrm{s})$ & Layer thickness (mm) & Volumetric Energy Density $\left(\mathrm{J} / \mathrm{mm}^{3}\right)$ \\ | |
| \hline | |
| 1 & $<100>\| S D$ & 0 & 100 & 0.12 & 100 & 0.03 & 277.78 \\ | |
| \hline | |
| 2 & $<100>\| \mathrm{BD}$ & 0 & 350 & 0.05 & 1200 & 0.03 & 194.44 \\ | |
| \hline | |
| 3 & $<100>\| \mathrm{PD}$ & 0 & 350 & 0.12 & 600 & 0.03 & 162.04 \\ | |
| \hline | |
| \end{tabular} | |
| \end{center} | |
| Within the initially optimized process parameter windows, we ran an additional design of experiments (DOE) to investigate the crystallographic textures attainable and identify three different sets of process parameters that lead to a strong $<100>$ texture along each of the three principal axes, BD, SD, and PD (as shown in Fig. 3). We detail the specific combination of parameters that we used to produce these three samples in Table 1. To the best of our knowledge, a strong $<100>\|$ PD texture | |
| Table 2 | |
| Grain size and aspect ratio of the $<100>\|\mathrm{SD},<100>\| \mathrm{BD}$, and $<100>\|$ PD textured samples. | |
| \begin{center} | |
| \begin{tabular}{llllll} | |
| \hline | |
| \begin{tabular}{l} | |
| S. \\ | |
| No. \\ | |
| \end{tabular} & Sample & \begin{tabular}{l} | |
| Mean \\ | |
| Grain Size \\ | |
| $(\mu \mathrm{m})$ \\ | |
| \end{tabular} & \begin{tabular}{l} | |
| Min. Grain \\ | |
| Diameter \\ | |
| $(\mu \mathrm{m})$ \\ | |
| \end{tabular} & \begin{tabular}{l} | |
| Max. Grain \\ | |
| Diameter \\ | |
| $(\mu \mathrm{m})$ \\ | |
| \end{tabular} & \begin{tabular}{l} | |
| Grain \\ | |
| Aspect \\ | |
| ratio \\ | |
| \end{tabular} \\ | |
| \hline | |
| 1 & $<100>\|$ & $32 \pm 29$ & 7 & 220 & 3.86 \\ | |
| & SD & & & & $\pm 1.95$ \\ | |
| 2 & $<100>\|$ & $54 \pm 36$ & 15 & 216 & 5.82 \\ | |
| & \begin{tabular}{l} | |
| BD \\ | |
| $<100>\|$ \\ | |
| PD \\ | |
| \end{tabular} & $29 \pm 24$ & 7 & 146 & 0.76 \\ | |
| & & & & $\pm 0.41$ & \\ | |
| \hline | |
| \end{tabular} | |
| \end{center} | |
| has never been reported in the literature. By contrast, strong $<100>$ crystallographic textures along the SD and BD i.e., $<100>\|$ SD and $<100>\| \mathrm{BD}$ have been reported in the past in various BCC and FCC alloys [15,17-19,26]. | |
| From visual inspection of the EBSD maps and the corresponding pole figures in Fig. 3, we observe a stark contrast in grain morphology among the three samples. While SD- and BD-samples exhibit long, columnar grains, the PD-samples consist of grains with lower aspect ratio and smaller average size. We ascertain the complex grain morphology of the three samples by estimating the grain size using four different metrics i. e., mean grain size, minimum grain diameter, maximum grain diameter, and grain aspect ratio, which we present in Table 2. To calculate the mean grain size, we approximate the grain by a circle and compute the area-weighted mean of equivalent diameters. From Table 2, we note the mean grain size and maximum grain diameter in SD- and BD-samples are significantly higher as compared to the PD-samples. However, it may be noted that these measurements are acquired along the build direction from micrographs in Fig. 3 and should not be taken as the "standard" (e. g., 3-D) grain size measurements. Since the PD samples exhibit the | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-05} | |
| \end{center} | |
| Fig. 4. 3-D representation of grain morphology in PD-samples. | |
| smallest grains with aspect ratio closest to 1 , we investigate the 3-D morphology of these grains by sectioning the PD-samples along the $\mathrm{XY}, \mathrm{XZ}$, and YZ planes and build a 3-D representation of the microstructure, which we report in Fig. 4. The representation confirms that the grains in PD-samples have small aspect ratio across all cross sections, which is atypical for LPBF alloys with highly columnar and textured microstructures. Typically, the grains in AM-produced samples with a strong $<100>$ texture are elongated, owing to the epitaxial growth of the cellular structures, resulting in columnar grained microstructures with large aspect ratio. | |
| \subsection*{3.2. Mechanical properties} | |
| To study the effects of the three different microstructures on the mechanical behavior of the alloy, we analyze the elastic modulus, strength, and ductility of our samples by means of tensile testing along the $<100>$ texture direction-i.e., $<100>\|$ PD, $<100>\|$ BD, $<100>\|$ SD-as shown in Fig. 1b. We measure the average elastic modulus along the $<100>$ texture in all the three cases to be in the range of 56-59 GPa (Table 3). This value is significantly lower compared to that of conventional Ti alloys such as Ti64 (110-120 GPa). Because of the low modulus of elasticity, $\beta$-Ti alloys are deemed particularly suitable for biomedical applications, where significant efforts are being made to produce biocompatible metallic implants with elastic moduli as close as possible to that of human cortical bone ( $\sim 30 \mathrm{GPa}$ ) to minimize stress shielding effects $[20,26,40]$. Our results confirm that the elastic modulus in $\beta$-TiNb alloys is insensitive to the mesostructure imparted by LPBF, including the variable and directional grain morphology, the cell structure, and the melt pool shape. Indeed, the elastic modulus is a material property that is a function on the interatomic bond force and the type of crystal structure formed, while it is independent of the microstructure, particularly in microcrystalline materials [44,45]. Previous studies, in fact, reported that the modulus of Ti-Nb alloys is mainly | |
| Table 3 | |
| Results from tensile testing of the three Ti- 45 Nb alloys tested along their respective strongest $<100>$ crystallographic orientation directions. | |
| \begin{center} | |
| \begin{tabular}{|c|c|c|c|c|c|} | |
| \hline | |
| \begin{tabular}{l} | |
| S. \\ | |
| No. \\ | |
| \end{tabular} & \begin{tabular}{l} | |
| Loading \\ | |
| direction \\ | |
| \end{tabular} & \begin{tabular}{l} | |
| Elastic \\ | |
| modulus \\ | |
| $(\mathrm{GPa})$ \\ | |
| \end{tabular} & \begin{tabular}{l} | |
| $0.2 \%$ offset \\ | |
| yield strength \\ | |
| (MPa) \\ | |
| \end{tabular} & \begin{tabular}{l} | |
| Ultimate \\ | |
| tensile \\ | |
| strength \\ | |
| (MPa) \\ | |
| \end{tabular} & \begin{tabular}{l} | |
| Ductility \\ | |
| (\%) \\ | |
| \end{tabular} \\ | |
| \hline | |
| 1 & SD & $59.2 \pm 4.5$ & $687 \pm 5$ & $690 \pm 10$ & \begin{tabular}{l} | |
| 21 \\ | |
| $\pm 3.7$ \\ | |
| \end{tabular} \\ | |
| \hline | |
| 2 & BD & $56.8 \pm 3.7$ & $596 \pm 19$ & $613 \pm 25$ & \begin{tabular}{l} | |
| 17 \\ | |
| $\pm 1.5$ \\ | |
| \end{tabular} \\ | |
| \hline | |
| 3 & PD & $57.2 \pm 3.1$ & $668 \pm 1$ & $684 \pm 3$ & \begin{tabular}{l} | |
| 23 \\ | |
| $\pm 1.5$ \\ | |
| \end{tabular} \\ | |
| \hline | |
| \end{tabular} | |
| \end{center} | |
| influenced by the Nb content, which determines the stability of the BCC phase. The particularly low value of the elastic modulus we measure stems from the orientation-dependent elastic response of BCC Ti alloys. Indeed, the $<100>$ orientation is known to exhibit the lowest elastic modulus. Lee et al. [19], showed that the Young's modulus of a Ti-15Mo-5Zr-3Al alloy is the highest ( $\sim 120 \mathrm{GPa}$ ) along the $<111>$ orientation and the lowest ( $\sim 44.4 \mathrm{GPa}$ ) along the $<100\rangle$. Since the alloy composition of our samples is kept constant and the tensile axis is always parallel to the $<100>$ orientation, we find similar, low elastic moduli values across all three samples. | |
| We present the tensile stress-strain curves of the three samples in Fig. 5a and report the nominal mechanical properties in Table 3. We observe that the PD-samples exhibit the best combination of strength and ductility. By contrast, the BD-samples demonstrate the lowest strength and ductility. The SD-samples also exhibit high strength, a reasonable ductility of $21 \%$, and a dip in the strength post yielding, which is similar to the case of BD-samples. To interpret the differences in mechanical responses and investigate the deformation mechanisms at play in the three samples, we plot strain hardening curves (Fig. 5b) and analyze the microstructure evolution upon deformation (Figs. 6 and 7). From the strain hardening curves, it is evident that the three different samples display classical transformation induced plasticity (TRIP) behavior characterized by a conventional transition from elastic to the plastic region (stage I), followed by a large increase in the strain hardening rate from the elastic limit to a plastic strain, $\varepsilon$, of 0.06 (stage II), and finally a gradual decrease in strain hardening up to failure (stage III). In previous works on metastable $\beta$-Ti alloys [46,47], the "hump" seen in the strain hardening curves (stage II) was ascribed to the formation of stress-induced martensite ( $\alpha^{\prime \prime}$ ) (SIM) and mechanical twinning, which continuously interact with each other throughout the plastic deformation regime. This phenomenon is commonly referred to as transformation induced plasticity/twinning induced plasticity (TRIP/TWIP) [47], and is prominent in metastable $\beta$-Ti alloys. To assess whether $\beta$ to $\alpha^{\prime \prime}$ transformation occurs in our samples, we performed XRD post-deformation. The results, plotted in Fig. 6, provide unambiguous evidence of peaks corresponding to both $\beta$ and $\alpha$ " phases, confirming the SIM transformation/TRIP phenomenon in our Ti-Nb alloys, regardless of their microstructure. | |
| Based on the strain hardening and XRD curves, we speculate that the active deformation mechanism governing the plasticity of the alloy changes from dislocation glide to mechanical twinning alongside $\alpha^{\prime \prime}$ transformation in all the samples. To confirm the occurrence of mechanical twinning, we analyze the samples post-facto failure at the necked regions by means of EBSD. Fig. 7a-c show representative grain orientation maps and Fig. 7d-f show the corresponding kernel average misorientation (KAM) maps computed from the raw EBSD data. The KAM maps are computed by calculating the average misorientation between each pixel and a kernel $(3 \times 3)$ of surrounding pixels. From Fig. 7, we notice a dense network of deformation twins that spans across all the three samples in the necked region. It is reasonable to expect deformation twinning in $\beta$-Ti alloys, due to the low shear strain required to generate $\{332\}<113>$ twins upon deformation, which makes it an energetically favourable deformation mechanism [48,49]. Therefore, both $\alpha^{\prime \prime}$ SIM and deformation twinning dictate the shape of the strain-hardening curves in Fig. 5 b. The $\alpha^{\prime \prime}$ precipitation provides a significant contribution to the observed macroscopic strain-hardening, inducing a "plateau" shortly followed by a strong "hump" in the strain hardening curves (Fig. 5b). This "hump" can be interpreted as the elastic deformation contribution of the newly formed $\alpha^{\prime \prime}$ martensite to the overall stress-strain behavior during the plastic deformation of the BCC matrix, thus, playing the role of an "elastic inclusion". The elastic contribution ends when the martensite itself starts to deform plastically (at $\varepsilon \approx 0.06$ for SD-samples and PD-samples, and $\varepsilon \approx 0.04$ for BD-samples). This interpretation is also in agreement with previous works on other $\beta$-Ti alloys such as Ti-12Mo and Ti-8.5Cr-1.5Sn alloys [50]. | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-06} | |
| \end{center} | |
| Fig. 5. (a) True stress-true strain curves under tension and (b) work hardening curves of the three Ti-45 Nb alloys tested along their respective $<100>$ crystallographic orientation directions. TD refers to the tensile direction. | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-06(1)} | |
| \end{center} | |
| Fig. 6. X-ray diffraction of the deformed Ti-45 Nb alloys. | |
| \section*{4. Discussion} | |
| \subsection*{4.1. Solidification microstructure and texture formation} | |
| We gain insights into the texture formation mechanisms that yield the microstructures shown in Fig. 3 by analyzing the melt pool shapes and the orientation of the cellular structure, which we reveal after chemical etching. Indeed, $<100>$ crystallographic textures in cubic alloys produced by fusion-based AM are typically parallel to the solidification direction, which is aligned with the maximum thermal gradient $[16,18]$. The melt pool shapes visible in the optical and electron micrographs in Fig. 8 indicate that all three samples entail a keyhole mode of melting, with deep melt pools spanning several layers in depth. This result is expected given that we produced all these textured samples using high VED (of $>160 \mathrm{~J} / \mathrm{mm}^{3}$ which facilitates the melting of Nb and homogenisation of the alloy). However, there are some obvious differences in melt pool geometry among the three samples, which stem from the different laser process parameters used (i.e., power, scan speed, and hatch spacing) and lead to the different textures shown in Fig. 3. It may be noted that the scan strategy i.e., bidirectional scanning without rotation between layers, is kept constant across all the samples. | |
| In SD-samples, produced by low laser power and higher VED, we observe a nail-head-like melt pool geometry in the YZ plane (see Fig. 8a). This mode of melt pool formation has been observed previously in alloys produced by LPBF when using the same scan strategy which we employ in this work-i.e., a bidirectional serpentine pattern without rotation between layers [51]. This specific melt pool geometry is attributed to the positive thermocapillary flow (i.e., the Marangoni effect) in the molten alloy. Due to the curvature of the melt pool walls, the direction of the thermal gradients varies across the melt pool [52]. Along the melt pool centerline, the heat flow is vertical and leads to segregation cells (and therefore, grains) that solidify with a $<100>$ orientation parallel to BD and grow epitaxially across multiple layers (see Fig. 3a). At either side of the centerline, however, the cells grow at $\pm 45^{\circ}$ with respect to the BD. Direct epitaxial growth of these cells across adjacent melt pools is ensured and is also assisted by side-branching on some parts of the melt pools [53], as seen in Fig. 8b. This phenomenon results in a $<110>$ texture component along the BD and consequently, a $<100>\|$ SD texture. This particular $\{100\}<110>$ bi-axial texture-also called rotated cube texture (rotated by $45^{\circ}$ )—has been reported in LPBF stainless steel 316 L [17,51] and other cubic alloys [54]. Because of this epitaxial growth of crystals across multiple layers, the resulting grains formed also have high aspect ratio, as seen in Fig. 3a-c and Table 2 . | |
| By contrast, in BD-samples we observe melt pools that overlap within the YZ (PD-BD) plane to a greater extent owing to the smaller hatch spacing used during processing (Fig. 5c). The increased overlap between subsequent melt tracks results in greater lateral remelting, which preserves growth of cells at the melt pool centerline but disrupts the symmetric $\pm 45^{\circ}$ crystal growth [55]. In other words, crystal growth along BD is preferred. This can be observed in Fig. 5d where some cells not growing along BD are disrupted by the cells growing along BD upon remelting (adjacent track). This results in the epitaxial growth of cells across adjacent melt pools [55] and leads to the establishment of a strong $<100>\|$ BD texture $[54,56]$ with a weak near-cube texture. Despite a near-cube texture, we refer to it as $<100>\| B D$ in this manuscript as the strongest $<100>$ texture component is along BD. Because of the copious remelting induced by a greater melt pool overlap,\\ | |
| $<100>\|$ SD | |
| \begin{center} | |
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| \end{center} | |
| (a) | |
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| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-07} | |
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| (d) $<100>\|$ BD | |
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| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-07(4)} | |
| \end{center} | |
| (b) | |
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| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-07(1)} | |
| \end{center} | |
| (e) | |
| $$ | |
| <100>\| \text { PD } | |
| $$ | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-07(3)} | |
| \end{center} | |
| (f) | |
| Fig. 7. EBSD after necking of (a) SD-sample; (b) BD-sample; (c) PD-sample; Corresponding kernel average misorientation (KAM) maps after necking in (d) SDsample; (e) BD-sample; (f) PD-sample. | |
| BD-samples exhibit large, columnar grains with high aspect ratio (Table 2), which we observe directly in Fig. 3e-g. Such grain structures have been commonly reported in additively manufactured parts and laser beam welded joints [57]. Moreover, the absence of side-branching is conducive to the highest texture strength amongst all samples investigated here (Fig. 3 h ). Since these solidification cell growth mechanisms for SD- and BD-samples are in line with what has been reported previously-for instance, in references [17,20], respectively-we do not discuss them further. | |
| Finally, PD-samples display the deepest keyhole melt pools amongst all our samples (as confirmed in Fig. A1d) owing to the highest laser power used to produce these specimens. While the direction of the thermal gradient changes within the melt pool generally, the long, vertical melt pool walls are conducive to thermal gradients that are within the plane of the powder layer, and thus to cells growing along the direction perpendicular to SD and BD, as indicated by the white solid arrows in Fig. 8f. The case of $<100>\|$ PD texture is an important result from this work as it shows a novel texture formation mechanism during LPBF. Fig. 8e and 8 f show that this $<100>\|$ PD growth extends across melt pool boundaries. This evidence suggests that epitaxial growth is maintained both within the layer (horizontally, across adjacent melt tracks) as well as across subsequent layers. | |
| To understand the evolution of this PD texture, we perform a detailed microstructural analysis by corelating the electron micrographs of the etched cell structure with the corresponding EBSD maps (Fig. 9). Based on this analysis, we propose that the PD texture forms as a result of keyhole melt pool "nesting", which leads to the concentric patterns seen in Fig. 9a. This phenomenon is a result of many remelting events across multiple layers. Any cross section of a melt pool reveals the deep "nesting" of multiple melt pools inside one another resembling stackable tall glass tumblers as shown in Fig. 9a. For this reason, we call this a "deep nesting" melting mode. During "deep nesting" mode of melting, a single melt pool penetrates deep inside the bulk, remelting most of the previously solidified-and cold-material directly below. Because of the relatively low temperatures of the surrounding metal, strong thermal gradients develop perpendicular to the vertical melt pool boundaries, promoting epitaxial growth of cells along PD (Fig. 9a). Because of the high density of melt pool boundaries-which stems from melt pool "deep nesting"-this PD growth is also remelted several times. As a result, grain selection occurs in a relatively small volume, leading to a strong $<100>$ texture along PD. Noteworthy is that PD samples also exhibit a weak $<100>$ texture along the BD (see pole figure in Fig. 3 1), which yields a near $<100>$ cube texture. Since the highest texture strength is along the PD direction, we refer to this texture as $<100>\|$ PD as indicated earlier. The weak texture along BD stems, once again, from the melt pool centerlines (Fig. 8f), which are characterized by cells growing along the BD as depicted by the dashed arrows in Fig. 8f. These centerlines interrupt the PD growth. | |
| We study the orientation relationship of centerlines with respect to the PD-textured grains using EBSD (Fig. 9b). Due to the presence of the centerline thermal gradient, a grain selection process in the region surrounding centerlines drives the growth of crystals with $<100>$ axes parallel to both BD and PD (see centerline 1 in Fig. 9b with the ideal $<100>$ orientation along BD and PD ). This phenomenon results in the establishment of a strong bi-axial texture, albeit only in these regions where the two perpendicular thermal gradients (PD and BD) co-exist. Not all centerlines, however, exhibit this biaxial texture (see centerline 2 and 3 in Fig. 9b). In some cases, epitaxial growth of centerline grains is interrupted by slight misalignments of melt pools in consecutive layers. This apparently stochastic misalignment of melt pools may be due to an irregular remelting during the multi-layer printing which results in the deviation from the ideal orientation [17]. In these cases, the centerline grains continue to grow along the dominant thermal gradient i.e., PD (following epitaxial growth), therefore continuing to maintain $\mathrm{a}<100>$ orientation along PD as seen from grains corresponding to centerlines 2 and 3 in Fig. 9b. From these observations, we conclude that the "deep nesting" mode of melting is conducive to the establishment of two prominent crystal growth directions: one along PD on either side of the melt pool and one along BD at the melt pool centerlines. We expect this crystal growth configuration to be specific to the PD-sample. Indeed, it is unlikely that the shallower keyhole melt pools seen in BD- and SD-samples may generate prominent thermal gradients and crystal growth directions parallel to PD. | |
| Another important difference in PD-samples is that grains are bound | |
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| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-08(1)} | |
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| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-08(4)} | |
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| (c)\\ | |
| \includegraphics[max width=\textwidth, center]{2024_07_13_1419f509943821a0a42ag-08(2)} | |
| (SD) | |
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| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-08} | |
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| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-08(3)} | |
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| (d) | |
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| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-08(5)} | |
| \end{center} | |
| (f) | |
| Fig. 8. Optical micrographs, melt pool evolution simulations, and crystal growth orientation of (a, b) SD-samples; (c, d) BD-samples; (e, f) PD-samples | |
| by centerlines (as seen in Fig. 4), which interrupt their growth and thus limit their size (Table 2). Indeed, these centerlines are also present in the SD-samples, where they interrupt grain growth along the Y axis (Fig. 3ac). The centerline formation mechanism is discussed in detail in other works $[17,31,57]$. However, the key difference between the SD- and PDsamples, despite both exhibiting centerline grains, is the growth direction of the solidification cells. In the case of SD-samples, since the growth direction is $\pm 45^{\circ}$, they grow epitaxially between layers, therefore resulting in columnar grain growth along the Z direction. However, in the case of PD-samples, since the growth direction is $90^{\circ}$, grains remain short because restricted between two melt pools centerlines and within a few layers. | |
| Beside the effects of the "deep nesting" mode of melting on epitaxial growth, texture direction, and grain morphology, we also observe marked differences in the density of geometrically necessary dislocations (GNDs), It is commonly understood that LPBF processes result in metal parts with a GND density $\sim 2$ orders of magnitude higher than their annealed counterparts $[36,58,59]$. We assess the density of GNDs, $\rho$, in our samples from KAM maps computed from the EBSD data (Fig. 10) by using [60]: | |
| $\rho=\frac{\alpha \theta}{X b}$ | |
| Here, $\alpha=2$ for high angle grain boundaries, $\theta$ corresponds to the local misorientation angle, X is the step-size used during the EBSD scan, and $b$ corresponds to the Burgers vector's magnitude. We notice that the GND density (Fig. 10d) varies as: $\rho$ (PD) $<\rho$ (SD) $<\rho$ (BD). Since GNDs originate from the thermal stresses caused by the repeated thermal cycles $[59,61]$ and rapid cooling rates, to understand the origin of the | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-09(1)} | |
| \end{center} | |
| (a) | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-09} | |
| \end{center} | |
| Fig. 9. (a) Schematics of the novel growth mechanism in "deep nesting" melt pools similar to the stackable glass tumblers that results in a $<100>$ texture perpendicular to SD and BD, (b) Electron micrograph and EBSD maps of the melt pools of PD-samples depicting the orientation relationship of the centerline grains with the PD textured grains. | |
| differences in GNDs among the three samples, we estimate the cooling rates these samples underwent from the analysis of the solidification microstructure (cell spacing) shown in Fig. 8. Indeed, the higher the cooling rate, $\dot{T}$, the smaller the size of the solidification microstructure-whether it consists of dendrites or cells [62,63]. This relationship is qualitatively described by the empirical power-law [64]: | |
| $\lambda_{c}=K|\dot{T}|^{n}$ | |
| Here, $\lambda_{c}$ is the primary spacing of solidification cells and K and n are material constants. To the best of our knowledge, no previous work derived the K and n values for the Ti- 45 Nb alloy system used here. However, in Ti alloys, there is an inverse correlation between the cell spacing and cooling rate, with n values ranging between -0.31 to -0.39 and K assumes a value of 49 [62,63]. From our SEM images (Fig. $8 \mathrm{~b}, \mathrm{~d}, \mathrm{f}$ ), we measure $\lambda_{\mathrm{c}}$ in the three samples from grains having the same orientation and using the line intercept method. Table 4 lists these values, which follow the order $\lambda_{c}$ (PD) $>\lambda_{c}$ (SD) $>\lambda_{c}$ (BD); with PD-samples having nearly twice as large $\lambda_{c}$ value than that measured in BD-samples. Therefore, we conclude that the three samples undergo significantly different cooling rates, following the order $\dot{T}$ (PD) $<\dot{T}$ (SD) $<\dot{T}$ (BD). Although oversimplified, this analysis is in line with the observed differences in the initial GND density across the three samples. Indeed, higher cooling rates result in higher initial dislocation densities in the additively manufactured materials. | |
| \subsection*{4.2. The effect of microstructure on yielding} | |
| Loading the three samples along their fixed $<100>$ orientation allows us to probe the individual contributions of different microstructural features to the mechanical properties of our complex LPBF Ti-45 Nb alloys. Such features include melt pool geometry, grain structure, solidification structure, and crystallographic textures. | |
| As seen from the Fig. 8 and discussed in Section 3.2, despite the samples nominally having the same crystallographic texture along the tensile direction, they exhibit markedly different yield strength. Specifically, PD-samples have the highest yield strength, followed by SDand BD-samples. While the $<001>$ axis is constant along the tensile loading direction for all the three samples, both the in-plane grain orientation distribution as well as the grain structure differ substantially in each sample and may explain the differences in yield strength. | |
| We first consider the effect of grain orientation. Since the initial deformation mechanisms at play in $\beta-\mathrm{Ti}$ alloys is dislocation slip, we compute the Schmid factors for $\{110\}<111>$ slip systems for the SD, BD , PD samples from the EBSD measurements to identify the samples showing most favourability to slip. The results are reported in Fig. 11. We note that the average Schmid factors are nearly the same for the three samples, with PD samples showing a marginally lower value. Since this difference is not significant, we conclude that the trends in yield strength cannot be ascribed to the type of $<100>$ texture and the change in the in-plane orientation. | |
| Next, we analyze grain size and morphology, since dislocation glide is governed by the interactions between slip bands and grain boundaries [65]. The PD-samples exhibit grains with lower aspect ratio and finer mean grain size compared to the SD- and BD-samples (Fig. 3, Table 2). In fact, the maximum grain size of the PD-samples is about $70-80 \mu \mathrm{m}$ lower than that of the SD- and BD- samples. Therefore, it is reasonable to expect higher yield strength according to the Hall Petch relationship [66]. Interestingly, we find that SD-samples also have a high yield strength, which is comparable to that of PD-samples (Table 3) despite | |
| \begin{center} | |
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| (d) | |
| Fig. 10. Kernel average misorientation (KAM) maps in as-printed (a) SD-sample; (b) BD-sample; (c) PD-sample and (d) estimated average GND density of the three samples computed from the KAM maps. | |
| Table 4 | |
| Measurement of cell spacing by the line intercept method from the scanning electron microscopic (SEM) images in Fig. 8. | |
| \begin{center} | |
| \begin{tabular}{lll} | |
| \hline | |
| S. No. & Material & Cell spacing $\left(\lambda_{c}\right)(\mu \mathrm{m})$ \\ | |
| \hline | |
| 1 & $<100>\| \mathrm{SD}$ & $0.45 \pm 0.06$ \\ | |
| 2 & $<100>\| \mathrm{BD}$ & $0.37 \pm 0.06$ \\ | |
| 3 & $<100>\| \mathrm{PD}$ & $0.78 \pm 0.10$ \\ | |
| \hline | |
| \end{tabular} | |
| \end{center} | |
| \begin{center} | |
| \includegraphics[max width=\textwidth]{2024_07_13_1419f509943821a0a42ag-10(3)} | |
| \end{center} | |
| Fig. 11. A histogram of Schmid factor (SF) distribution with the respective average SFs and corresponding ranges for $\{110\}<111>$ slip system for the SD, BD-, and PD- samples. consisting of coarser grains. By contrast, BD-samples exhibit a relatively inferior yield strength ( $\sim 80-100$ MPa lower than the SD-, PD-samples). To understand the significant differences in strength among the BD-, SDand PD-samples, we probe into the solidification structure, since several previous works have demonstrated how solidification cells in LPBF alloys contribute to yield strength, albeit to a lower extent in comparison to grain boundaries $[67,68]$. Indeed, solidification cell walls are decorated with solute elements-such as Nb in our case-and copious dislocations, which provide additional resistance to dislocation motion and, thus, increased strength [6]. We note that the SD-samples and BD-samples, appear to have finer solidification structures compared to PD-samples, as shown in Table 4. Since both SD- and BD-samples have relatively large grain size and fine cell size, the fine solidification cell size does not explain the difference in the yield strength. We, therefore, ascribe the additional strengthening in the SD- and PD-samples to the presence of numerous fine centerline grains (with a size range of $10-30 \mu \mathrm{m}$ ). These centerline grains, formed as a result of the vertical heat flow at the center of the melt pools (Section 4.1), act as additional barriers for dislocation motion as illustrated in Fig. 12, therefore bringing about additional strength in the SD- and PD-samples. Since the BD samples consist of only columnar grains without any additional centerline grains, the resistance to dislocation motion is lower, therefore exhibiting a relatively inferior yield strength. | |
| From the tensile stress-strain curves in Fig. 5, we also notice that SDand BD-samples undergo a slight dip in the stress levels during yielding by $\sim 10-25 \mathrm{MPa}$, which is not the case in PD-samples. This phenomenon-referred to as yield point phenomenon-was previously observed in other $\beta$-Ti alloy systems, both conventionally produced $[69,70]$ as well as fabricated by LPBF [65]. In BCC alloys, this phenomenon is typically associated with dislocations overcoming interstitials [67]. However, we expect no appreciable difference in interstitials-e.g., oxygen atoms-in our samples, since only two out of three exhibit this phenomenon and all of them were fabricated with the same LPBF machine in Ar environment. | |
| \begin{center} | |
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| \end{center} | |
| (a) | |
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| (b)\\ | |
| S: Source | |
| $\perp$ Dislocation | |
| \section*{/ Grain \\ | |
| Boundary} | |
| \includegraphics{smile-lyjj8pm1sntflvxr4s.png} | |
| (SD) | |
| Fig. 12. Schematic illustration of the grain structure and dislocation motion in the (a) SD- and PD- samples, where the presence of fine centerline grains further restrict dislocation motion; and (b) BD-sample where such centerline grains are not present. All the boundaries in the illustration represent high angle grain boundaries. | |
| It is plausible that other barriers to dislocation motion may exist to a different extent in the three samples. As discussed in the foregoing, the SD- and BD-samples-which exhibit the yield point phenomenon-consist of a solidification microstructure that is finer compared to that found in PD-samples (Table 4). The higher density of cell boundaries in these samples may require higher stress levels to reach the upper yield point, after which dislocations could cut through the cell boundaries, causing a sudden drop in the lower yield point. By contrast, because of the coarser solidification cell size in PD-samples, we speculate the yield point phenomenon not to be as prominent as in the other two microstructures. This difference justifies the plateau we find in the stress-strain curves of BD- and SD-samples (Fig. 5a). Furthermore, both these samples are characterized by a relatively higher GND density compared to PD-samples (as discussed in Section 4.1). This difference may also contribute-although less significantly-to the upper yield point by obstructing the movement of newly generated dislocations upon yielding. These speculations are in line with the observations reported recently in a different $\beta$-Ti alloy produced by LPBF [65]. Further investigations on the yield point phenomenon are beyond the scope of this work and will be explored in a follow-up study. | |
| \subsection*{4.3. The effect of microstructure on work hardening} | |
| Despite the similarities in texture orientation along the tensile axis and the deformation mechanisms at play, PD-samples exhibit a remarkably higher work hardening rate ( $\sim 900 \mathrm{MPa})$ compared to the other two samples ( $\sim 400-500 \mathrm{MPa}$ ), and a peculiar "hump" in the curve (Fig. 5). To elucidate the origin of these differences, we analyze the fraction of $\alpha^{\prime \prime}$ and the local GND density from the XRD measurements (Fig. 6) and the KAM maps (Fig. 7d-f) computed from the high magnification EBSD scans in Fig. 7a-c. The XRD patterns suggest the presence of a much higher volume fraction of $\alpha^{\prime \prime}$ SIM and deformation twinning in PD-samples compared to the others, as observed from the higher XRD peak in Fig. 6. We believe the higher SIM fraction in this sample to be one of the factors leading to the "hump" in the corresponding strain hardening curve seen in the PD-samples. Furthermore, the KAM maps indicate higher local misorientation within twin variants across the matrix, suggesting that high GND densities are stored within the twins and where twins intersect grain boundaries. This heterogeneous strain localisation has been observed before and is known to be due to the increased plastic activity caused as a result of the interaction between twins and grain boundaries [71]. | |
| We also observe unindexed regions in the EBSD images in Fig. 7 at the intersections between the same twin variants. Based on our XRD results (Fig. 6), we confirm that these correspond to the $\alpha^{\prime \prime}$ needles and we attribute the lack of signal to the high local strains and to the presence of a network of martensitic $\alpha^{\prime \prime}$ needles that form within the twin lamella at every twin intersection, and which makes indexing at the junctions very challenging by means of EBSD [71]. The reason for their occurrence at grain boundaries is that martensitic $\alpha^{\prime \prime}$ needles typically form to accommodate the local stress/strain incompatibilities between the highly hardened twinned grains and the soft $\beta$ matrix neighbours. Therefore, TRIP and TWIP modes operate simultaneously in the three different textures, as observed previously [48], albeit to a different extent in each case. | |
| Despite all the samples exhibiting concurrent TRIP and TWIP phenomenon, we still capture the differences between the PD-, BD-, and SDsamples in terms of the twin density. We note that the twin multiplication (twin density) and volume fraction of $\alpha^{\prime \prime}$ SIM are significantly higher in PD-samples, as evidenced from Fig. 7. We believe that this is caused by the smaller grain size, particularly by the low aspect ratio of grains in PD-samples. Indeed, it is known that decreasing the grain size of the parent phase lowers the martensitic start temperature (Ms), as a result of lowering the elastic and friction energy [72,73]. Therefore, we see higher volume fraction of $\alpha^{\prime \prime}$ SIM and twin density in PD-samples which, in turn, result in higher strain hardening compared to what we measure in SD- and BD-samples. As twins multiply in the microstructure across the grains, they lead to the formation of additional boundaries that act as barriers to dislocation motion and they decrease the dislocation mean free path, further improving the strain hardening of the alloy following the dynamic Hall-Petch mechanism [71,74]. While these twin boundaries are also sites of dislocation pile-up and stress concentration (which could potentially lead to strain localization), the presence of $\alpha^{\prime \prime}$ SIM results in a synergistic cooperation between the hardening mechanism (by twins) and strain accommodation mechanism (by $\alpha^{\prime \prime}$ SIM). The result is a stable plastic flow and a strong strain hardening. Similar observations have been made previously in TRIP/TWIP Ti alloys [75]. Therefore, we attribute the high strain hardening and ductility in PD-samples to the presence of higher $\alpha^{\prime \prime}$ SIM and twin fraction. While there is appreciable strain hardening in the SD- and BD-samples, their larger grain size is not conducive to the same extent of $\alpha^{\prime \prime}$ SIM, twin multiplication, and dynamic Hall-Petch effect seen in PD-samples, resulting in lower strain hardening and early failure [76]. We attribute the lowest ductility of BD-samples to the higher density of interfaces across the sample's mesostructure-such as melt pool boundaries-which are aligned along the $<100>\|$ BD. Since these boundaries are perpendicular to the loading axis (which is parallel to the BD in these samples), they act as strain localization sites impeding\\ | |
| uniform elongation and leading to premature failure [77]. Thus, the excellent combination of plasticity and strain-hardening in PD-samples stem from the reduced dislocation mean free path via the synchronous activation of TRIP and TWIP, as well as from the backstresses generated by dislocation pile-up at obstructive interfaces [48]. However, it may be noted that due to the relatively higher $\operatorname{MoE}(\sim 12.6)$ and $\beta$ phase stability of the $\mathrm{Ti}-45 \mathrm{Nb}$ alloy, the extent of stress-induced transformation is limited [78], and the deformation is mediated through both slip as well as TRIP/TWIP. Therefore, we see an overall limited ductility than what is typical of TRIP/TWIP Ti alloys [76]. | |
| We believe that the novel $<100>\|$ PD texture with low aspect ratio (near-equiaxed) grains is a promising microstructure to enable a combination of low modulus, superior strength, strain hardenability, and ductility in the current $\mathrm{Ti}-45 \mathrm{Nb}$ alloy system. As such we envision this microstructure to be of interest for biomedical applications. The novel PD-texture associated with this microstructure may also be extended to other alloy systems to decouple the high aspect ratio grains and strong textures to result in favourable mechanical properties in AM alloys. | |
| \section*{5. Conclusions} | |
| In this work, we demonstrate the feasibility of producing a strong $<100>$ crystallographic texture along three perpendicular directions in an in-situ alloyed cubic Ti alloy by means of laser powder bed fusion (LPBF). We achieve this capability by varying the melt pool shapes in the keyhole melting regime to promote directional, epitaxial growth along the laser scan direction (SD), the build direction (BD), and the direction perpendicular to both SD and BD, which we call PD. The key findings of our work are summarized below: | |
| \begin{enumerate} | |
| \item We find a novel $<100>$ texture along PD in our $\beta \mathrm{Ti}$ alloy, which we explain on the basis of a "deep nesting" mode of melting. | |
| \item By contrast to BD- and SD-samples-which exhibit long columnar grains with high aspect ratio (> 3.8)—we find low aspect ratio grains ( 0.76) in PD-samples. This difference stems from the unique melt pool shapes and texture formation mechanism found in these samples. | |
| \item Owing to this unique microstructure, the $<100>\|$ PD textured samples show the best combination of strength, strain hardening, and ductility amongst all samples. | |
| \end{enumerate} | |
| Our work extends the scope of AM by providing opportunities to design novel components with engineered crystallographic textures that can be spatially and directionally varied in all the three dimensions (3D) to adapt to the local stress fields and enable significantly improved functionality of metallic materials. | |
| \section*{CRediT authorship contribution statement} | |
| Sravya Tekumalla: Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization, Writing - original draft, Writing - review \& editing. Jian Eng Chew: Methodology, Investigation. Sui Wei Tan: Methodology. Manickavasagam Krishnan: Methodology. Matteo Seita: Conceptualization, Writing - review \& editing. | |
| \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*{Data Availability} | |
| Data will be made available on request. | |
| \section*{Acknowledgments} | |
| This work was supported by the NTU Presidential Postdoctoral Fellowship (Grant number: 04INS000761C160). Access to shared experimental facilities used in this work was provided by the School of Mechanical and Aerospace Engineering and the Facility for Analysis Characterization Testing and Simulation (FACTS) at NTU. | |
| \section*{Appendix A. Supporting information} | |
| Supplementary data associated with this article can be found in the online version at doi:10.1016/j.addma.2022.103111. | |
| \section*{References} | |
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