A digital twin of synchronized circular laser array for powder bed fusion additive manufacturing

The formation of undesirable microstructures and defects hinders the widespread use of additive manufacturing, e.g., the formation of columnar grains in Ti–6Al–4 V leads to undesirable anisotropic mechanical properties. Here, we investigate the application of a novel synchronized circular laser array in the powder bed fusion technique to alter the microstructure of printed parts toward the preferable equiaxed grains. This feat is not achievable with the single laser powder bed fusion technique for Ti–6Al–4 V alloy. The temporal temperature distributions for different process parameters (laser power, scanning speed, and internal distance between lasers in the array) were obtained by an anisotropic heat transfer model, and the Hunt criterion was employed to construct the solidification map. The results revealed that a degree of overlap between lasers is recommended to form a coherent melt pool, avoid degeneracy in surface quality, and maintain adequate resolution for all processing windows. However, laser overlap is not required for low scanning speed and high power scenarios. Finally, microstructure prediction shows that 45% of printed track includes equiaxed grains at a high power regime (500 W). However, the volume fraction of the equiaxed microstructure is reduced by decreasing laser power.


Introduction
Additive manufacturing (AM) is executed through a layerby-layer material deposition from a digital model, which enables the production of complex components and devices [1,2] with a diverse set of materials [3]. Among various AM techniques, considerable attention has been paid to the laser sintering technique, i.e., directed energy deposition (DED) [4,5] and laser powder bed fusion (LPBF) [6,7], for rapid prototyping of metals and ceramics. In this technique, the laser melts and fuses the powder material layer by layer to form a three-dimensional object. Although, one of the technological issues in the LPBF is the formation of the columnar β grains [8,9] across the build's height, leading to anisotropic mechanical behavior [10]. Additionally, the appearance of the α′ phase (fine acicular martensite) in the microstructure lowers the printed part's ductility compared to the conventional manufacturing methods. Therefore, tremendous research studies have focused on techniques for forming the preferred equiaxed grain structure and obtaining isotropic mechanical behavior in the LPBF. Recently, the application of multi-laser powder bed fusion (MLPBF) has gained attraction due to its potential to alter the material's microstructure/properties and control residual stress, i.e., residual stress affects the likelihood of crack formation in LPBF. However, most of these studies in MLPBF were focused on residual stress variation due to changes in thermal gradients for various laser configurations [11][12][13][14][15] and studies of the MLPBF on the material's microstructure/properties are scarce and contradictory. The experimental results of the dual scanning strategy (two synchronized lasers) with a slight coaxial offset showed a meaningful improvement in the maximum bending strength [16], although a multi-laser scanning technique showed no effect on the creep response of Inconel [12] and a lack of drastic change in the microhardness and tensile strength [17,18]. The modulated laser radiation (6 × 6 square [19] and 1 × 3 linear beam array [20]) was implemented in to study the melt pool dimension and spatter in a synchronized laser array. However, it still lacks microstructural analysis. Also, the Rosenthal solution was adopted to study the microstructural change for two coordinated laser beams [21]. The results showed no change in printed parts' thermal gradients and microstructure. These findings were confirmed in [20], which reported that the second laser's post-treatment forms a more uniform microstructure but does not alter the columnar microstructure.
In contrast, applying a multi-laser head resulted in the appearance of a basketweave α-β microstructure and attaining fine equiaxed β grains at higher scanning speeds (200 mm/min) [22]. Among all existing experimental and numerical studies, a detailed study on the effect of a coordinated multi-laser array on microstructure (columnar/equiaxed/mixed) is still missing. Here, the finite element analysis (FEA) was used to study the effect of MLPBF processing parameters (laser power, scanning speed, and internal spacing among the lasers in the array) on the microstructure of Ti-6Al-4V as a model material. The printing laser head consists of four synchronized lasers with constant internal spacing distance in a circular configuration. The constructed solidification map shows the appearance of the equiaxed grains, which is not achievable by the single LPBF for Ti-6Al-4V alloy. These results show the promise of the MLPBF technique to control the microstructure toward forming preferable equiaxed grains, i.e., the columnar microstructure causes anisotropy in mechanical properties, which is undesirable. It is worth noting that this is the first comprehensive study on the possibility of using a circular laser array to tailor the microstructure of Ti-6Al-4V alloy.

Computational model
The MOOSE (Multi-physics Object-Oriented Simulation Environment) [23] software was used to solve the anisotropic heat conduction equation. The model provides the temporal and spatial temperature distribution in a Ti-6Al-4V sample as the model material and obtains melt  The anisotropic thermal model has been widely used to model LPBF-AM due to its simplicity, low computational cost, and good agreement with experimental results [24][25][26][27].
The lists of equations, variables, and thermo-physical properties are in the Supplementary material, Tables S1-3. The powder bed dimensions are 5 × 1.5 × 1.5 mm for highpower and low-velocity scenarios (P = 500 W and v = 100 mm/s), 1 × 0.5 × 0.5 mm for the low-power regime, and 3 × 1.5 × 1.5 mm for the rest of the simulations. The eightnode hexahedral elements with dimensions of 3 × 3 × 3 µm were employed to mesh the simulation domain. The laser power and velocity range, Table 1, were selected to avoid the keyholing scenario [28]. All model parameters and laser characteristics are summarized in Table 1. Figure 1f illustrates the circular laser configuration consisting of five lasers with internal distancing r. The heat flux of each laser follows the Gaussian distribution, and the array's laser profile for P = 300 W, beam radius of 75 µm, and various internal laser spacings, r = 50-250 µm is shown in Fig. 1a-e. The high-intensity heat flux occurs at the small spacing, and it reduces with an increase in r. It is worth noting that the overall shape of heat flux at the surface is controlled by r, e.g., a star-shaped heat profile is generated at r = 75 µm, Fig. 1b. The laser power and speeds in the array are identical, and the internal spacing among lasers was kept constant during each simulation.

Results and discussions
Model verification The anisotropic heat transfer model was verified against a single laser's experimental melt pool dimensions due to the lack of experimental studies on the synchronized laser array. Figure 2 shows the model's melt pool width/height against the experimental results [26]. There is a good agreement between predicted and experimental depth. However, the model overestimates the width. The maximum 18.3% deviation in width is acceptable due to model and experimental uncertainties, i.e., the temperature dependence of laser absorption coefficient [30] and thermal conductivity enhancement factors, variation of density and thermal conductivity with powder porosity [25], and different possible mathematical equations for modeling laserbeam heat sources [27].

Melt pool prediction and solidification map
The solidification maps for all processing parameters, e.g., scanning speed, laser power, and internal spacing, are plotted in Fig. 3. The equations for thermal gradient (G) and solidification rate (R) were summarized in the supplementary material, Table S2. A 50-W laser results in columnar microstructure (Fig. 3a), i.e., the typical microstructure of LPBF-AM. However, raising the power to 300-500 W moves the G-R lines toward the right-hand side of the solidification map, accompanied by the appearance of equiaxed grains in the printed track, Fig. 3b, c. Therefore, any further increase in power is expected to increase the equiaxed portion of the track; however, it may result in keyholing. In all modeled scenarios, increasing the scanning speed increases the R × G value, indicating a grain size reduction. Also, more uniform grain size is expected in the high scanning speed regime for P = 300-500 W, i.e., the (G, R) points conform better to constants R × G lines. Figures 4, 5, and 6 illustrate the melt pool shape and dimensions (width and depth) for all processing parameters.
The heat flux of each laser in the array contributes to the overall melting pool shape/dimensions based on their internal spacings, i.e., it is based on the superposition principle and thermal cross-talk among the temperature field of each laser. Generally, the width increases by increasing internal spacing distance due to heat distribution over a larger Fig. 4 Melt pool shape, width, and depth, for various processing parameters (beam velocity and internal laser distancing) at the constant power scenario (P = 50 W). a The melt pool shape for different velocity sets and internal laser distancing. The red contour presents the liquidus temperature (T L ), and the blue line identifies the melting temperature (T M ). b The melt pool width and depth for P = 50 W surface area, although the depth shows an opposite trend, i.e., it shows a decrease in heat penetration into the powder bed. Also, melt pool dimensions (depth and width) are decreased by increasing scanning velocity due to reducing laser-matter interaction time at high scanning speeds, which agrees with experimental and numerical studies of the single laser case [26]. It is worth noting that the dimensions of the discrete melt pool are not shown in Figs. 4, 5, and 6b because forming an incoherent melt pool is not desirable due to potential technical issues such as reducing surface quality and unwanted remelting from adjacent printing track. For example, four separate melt pools are formed for P = 50 W, v = 100 mm/s, and r = 250 µm case, Fig. 4a; in this scenario, the thermal cross-talk among lasers causes a higher temperature in the back laser melt pool than in the others. Therefore, the back laser dominates the melting, and the two sides' lasers only remelt the existing printed track. Also, an irregular melt shape appears for intermediate internal spacing (P = 50 W, v = 100 mm/s, and r = 150 µm), potentially creating issues at the printing edges. A similar trend for high laser powers (P = 300-500 W) was also observed, Figs. 5 and 6. Generally, a degree of overlap among lasers (r ≤ 50 µm) is recommended to obtain a coherent melt pool shape and avoid any degradation in surface quality or dimensional inaccuracy at the edges. However, a high-power laser (500 W) with a slow-scanning speed (100 mm/s) increases the critical internal spacing to 250 µm for obtaining a coherent melt pool, Fig. 6a. Therefore, by pushing the laser power beyond P ≥ 500 W and using a low scanning speed, v ≤ 100 mm/s, the critical internal spacing can go beyond 250 µm. Note that this is accompanied by increases in melt pool width and a reduction in printing resolution. Finally, the melt pool shapes for all processing parameters on the symmetric plane (x-z) and the top surface (x-y) are depicted in Figs. S1-3 in the supplementary document.

Microstructure prediction
The Hunt criterion [31] was employed to identify various microstructural zones (columnar, equiaxed, and mixed) on the liquidus line, i.e., columnar: G 1.91 ∕R > 1.92 × 10 6 K 1.91 ∕cm 2.91 .s and equiaxed: G 1.91 ∕R < 1.04 × 10 6 K 1.91 ∕cm 2.91 .s . The projections of critical G 1.91 ∕R lines for each microstructural zone on the y-z Fig. 5 Melt pool shape, width, and depth for various processing parameters (beam velocity and internal laser distancing) at the constant power scenario (P = 300 W). a The melt pool shape for different scanning velocity sets and internal laser distancing. The red contour presents the liquidus temperature (T L ), the blue line identifies the melting temperature (T M ), and the green line represents the evaporation temperature (T E ). b The melt pool width and depth for P = 300 W Fig. 6 Melt pool shape, width, and depth, for various processing parameters (beam velocity and internal laser distancing) at the constant power scenario (P = 500 W). a The melt pool shape for different velocity sets and internal laser distancing. The red contour presents the liquidus temperature (T L ), the blue line identifies the melting temperature (T M ), and the green represents the evaporation temperature (T E ). b The melt pool width and depth for P = 500 W Fig. 7 The projection of critical G 1.91 ∕R values into the y-z plane that passes through the deepest point of the melt pool for two representative cases, i.e., regular vs. irregular. The red line identifies the liquidus line. The green and blue lines represent the Hunt criterion for mixed and equiaxed regions. a P = 300 W, v = 100 mm/s, and r = 50 µm. b P = 300 W, v = 500 mm/s, and r = 200 µm plane are illustrated in Fig. 7 for some representative cases. The enclosed area by each critical line was used to approximate the volume fraction of each microstructural zone. Figure 8 shows the columnar and equiaxed volume fractions for P = 300-500 W at various scanning speeds and internal spacings. It is worth noting that the volume fraction of irregular/ incoherent melt pool shapes was omitted from Fig. 8. The microstructure of side lasers, Fig. 7b, is predominantly mixed or columnar for irregular/incoherent melt pools. Therefore, the side lasers remelt and alter the microstructure back to the columnar in the second printing track. Figure 8 shows that the equiaxed volume fraction increases by increasing power. Also, the equiaxed volume fraction is more sensitive to scanning velocity variation at intermediate power (P = 300 W), i.e., the volume fraction increases from 20% for v = 100 mm/s to 35.1% for v = 500 mm/s; however, this increase is only 4.62% for P = 500 W. The interplay between velocity and power on absorbed heat can justify the decrease in velocity sensitivity by increasing power. In the low power regime, the scanning velocity becomes dominant, although, in the highpower regime, the power dominates the effect of velocity on R and G values and consequently on microstructure. The same trend is deduced for the internal spacing. The equiaxed volume fraction is reduced by increasing the internal spacing in a low power regime, although the distance between lasers in the array has a minor influence on the volume fractions in the high-power regime. The high power and the low velocity with a degree of overlap among lasers are recommended as the optimum processing window for the synchronized circular laser array. This setting can provide a coherent melt pool, adequate resolution, and a large volume fraction of the equiaxed microstructure.

Conclusion
The final microstructure of Ti-6Al-4 V alloy via a novel synchronized laser array was predicted for various processing parameters, such as scanning speed, laser power, and internal laser spacing. The results recommend using some overlap between lasers for low and intermediate laser powers (50-300 W) to form a continuous melt pool. However, the overlap is not required in the high-power scenario (500 W). Also, the best processing windows to maximize the equiaxed volume fraction are high power and low scanning velocity regimes. The equiaxed volume fraction in the high power regime is less sensitive to scanning speed and internal spacing. Further experimental studies should be conducted to verify these numerical predictions and also investigate the possibility of this approach to reducing residual stress. These predictions can guide future experiments and potentially open up a new direction toward adaptive microstructure control in laser-based metal additive manufacturing, i.e., an adaptive control over the internal laser spacing can locally alter the microstructure.

Acknowledgements
The support of Wright State University is gratefully acknowledged, and the authors extend their special thanks to Dr. Mikhail Vorontsov for the initial discussions. Availability of data and materials The datasets used or analyzed during the current study are partially available from the corresponding author upon reasonable request.

Code availability
The code is partially available from the corresponding author on reasonable request. Fig. 8 The volume fraction of equiaxed and columnar microstructures for P = 300-500 W, v = 100-1000 mm/s, and r = 50-250 µm