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 [27]. 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 [31] and thermal conductivity enhancement factors, variation of density and thermal conductivity with powder porosity [26], and different possible mathematical equations for modeling laser-beam heat sources [28].
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 4–6 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 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 intection time at high scanning speeds, which agrees with experimental and numerical studies of the single laser case [27]. It is worth noting that the dimensions of the discrete melt pool are not shown in Figures 4-6b 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, Figure 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, Figure 5-6. Generally, a degree of overlap among lasers (r150 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, Figure 6a. Therefore, by pushing the laser power beyond P500 W and using a low scanning speed, v100 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 Figures S1-3 in the supplementary document.
Microstructure Prediction - The Hunt criterion [32] was employed to identify various microstructural zones (columnar, equiaxed, and mixed) on the liquidus line, i.e., columnar: \({G}^{1.91}/R>1.92\times {10}^{6} {K}^{1.91}/{cm}^{2.91}.s\) and equiaxed: \({G}^{1.91}/R<1.04\times {10}^{6} {K}^{1.91}/{cm}^{2.91}.s\). The projection of critical \({G}^{1.91}/R\) lines for each microstructural zone on the y-z 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 high-power 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 is 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.