It was previously explained in Part I that the thermal distribution is crucial to accurately capture the stresses and strains generated during LPBF. This requires accurate prediction of nodal temperatures, cooling rates, and the heat transfer between the different material states (i.e., liquid, solid and powder states). The von Mises stress distributions are shown for the ED and HL models simulated with three different τ values in Figure 6. The stress is concentrated in the solidified regions (melted track and substrate). The powder bed has no stress (see the dark blue region in Figure 6) because it has negligible stiffness. Other researchers who have not considered the powder state have over-predicted stresses in the powder regions during LPBF (Irwin and Michaleris 2016). This demonstrates the importance of considering the material state while simulating the LPBF process.

The stress distributions are similar between HL τ = 5 and the ED models. The stress-affected zones on the surface of the cross-sections have similar sizes and magnitudes. Both simulations have similar maximum stress amplitude situated at the center of the track. As τ increases, the stress-affected zone shrinks and the peak intensity decreases due to the heat source being integrated over a longer distance, resulting in reduced peak temperatures. This effect could be reduced by calibrating the HL coefficients for every τ value. The implemented heat transfer coefficients are calibrated in Part I (Tangestani et al., 2021) by minimizing the error for four τ values ( τ = 5, 10, 15, and 20).

The distribution of the residual stress components, along with the von Mises stress for ED and three different τ values in the HL model, are shown in Figure 7, 8 for line 1 (longitudinal) and line 2 (transverse) in Figure 2, respectively. In general, the maximum stresses are observed at the center of the track, where the expansion and contraction of the material are the most constrained by surrounding material. The stresses decrease to nearly zero close to the edges where the solidified material is free from constraints. The peak stresses are observed in the longitudinal direction (S_XX in Figures 7, 8). The stress magnitude is lowest in the build direction (S_ZZ) due to the free surface, consistent with previous LPBF single track simulations (Walker et al., 2019). The primary contribution to the von Mises stress comes from the X-direction stress. Stresses are mostly tensile in the X- and Z-directions, while they remain compressive in the Y-direction. The negative peak stress values observed at the edges for the S_YY and S_XX in Figure 7 are due to edge effects.

The HL model accurately reproduces the results of the ED model along the laser direction in Figure 7. The average variations between the ED and HL models are below 3% for all τ values in the S_XX stresses. As the τ value increases, the stress oscillation is lengthened because the heat input is distributed over a longer region. This reduces the peak temperature as discussed in Part I (Tangestani et al., 2021). Each stress oscillation represents one heat input step, and the larger the heat increment, the larger the variation in stress magnitude compared to the ED model. This is more noticeable in the Y- (mean variation = 12%) and Z- (mean variation 80%) directions when τ = 20. Nevertheless, the Y- and Z-stresses have limited effect on the overall stress as shown by the accuracy in the von Mises stress (mean variation = 5%) distributions. Increasing the τ value has a similar effect on the variation of stress distribution calculated perpendicularly to the laser direction in Figure 8. On the contrary, the width of the stress distribution decreases with increasing τ due to the difference in melt pool size described in Part I (Tangestani et al., 2021).

Figure 9 shows the impact of τ on the computational efficiency of the mechanical model for the track-scale simulations using a consistent mesh. The HL model is over 6 times faster than the ED model when τ = 5 and is over 30 times faster when τ = 20. This shows that the time step increment has a bigger impact on the thermal model (1,500 times faster for τ = 20 in (Tangestani et al., 2021)) compared to the mechanical model (30 times faster for τ = 20), as the ED model requires more calculations for the thermal model. The time step increments thus have a smaller effect on the mechanical model. The total computational efficiency gain is the summation of the gain from the thermal and mechanical models for consistent meshes.

Element size is another important factor when considering the computational efficiency of the model. It is desirable to have a small mesh size in regions where the laser interacts with the powder bed to increase the resolution of the model. However, decreasing the element size decreases the time step. Therefore, it is desirable to use the maximum possible element size for part-scale simulations and motivates the use of dynamic re-meshing.

Dynamic re-meshing is applied to the part-scale simulations as the printed layers are added. The ED model cannot be compared due to infeasible simulation time at the part scale. However, the estimated computational times for the ED model in addition to the HL model, with and without dynamic re-meshing, are compared in Table 3. The estimated times are calculated by comparing the processing times of the ED and HL single track models for the thermal and mechanical simulations. The ratio of computation time is multiplied by the HL part-scale simulation time to estimate the time required for the ED model applied at the part scale. Dynamic re-meshing decreases the thermal and mechanical models computational time by 3.3 times, allowing the thermal and mechanical models to be run in parallel. Since the mechanical model is 3.6 times slower than the thermal model, it controls the total run time.

Currently, there is no consensus on the effect of laser power on residual stress. Some researchers have shown that laser power has little effect on residual stress (C. Chen et al., 2020), while others have demonstrated both positive and negative correlation on residual stress (Xiao et al., 2020). In Part I of this series, it is shown that the laser power has a strong effect on the melt pool size but a limited effect on the cooling rate. Therefore, it is expected that the laser power will have a small impact on the simulated residual stresses.

The simulated residual stresses obtained with laser powers of 180 and 220 W are shown in Figure 11. Only the perpendicular scanning patterns (see Figure 1) are shown here as the other scanning patterns exhibit similar results. The part-scale models are sectioned through the center to show the internal stresses. There is minute difference in the residual stress magnitudes and distributions for the different laser powers observed in Figure 11. It should be noted that the laser powers in these studies are limited to a small range. A larger laser power range could have a larger effect on the residual stresses.

The longitudinal stress component (S_XX) in Figure 11A–B is highest close to the top of the build. However, the S_ZZ and the von Mises stress in Figure 11C–F shows the largest stresses at the center of the part. The S_ZZ stress is near-zero at the top of the parts due to the free surface. The stress at the bottom of the part is reduced due to relaxation of the boundary conditions described in HL Part Scale Model. The S_YY stress is not presented because it does not change with laser scanning pattern and provides smaller contributions to the stress state. This is due to plate theory, which states that only limited load can be supported through the thickness direction in thin wall structures, as shown in (Chakraborty et al., 2021). Note that the inconsistency in the stress distribution around the center line is due to the mesh-to-mesh mapping, as shown in (Hajializadeh and Ince 2019).

The distributions of the cooling rates (not shown here) are similar for the three laser powers considered in this study. The maximum in-process cooling rate is 5.3 × 10⁶ K/s for 220 W laser power and the cooling rate decreases to 4.3 × 10⁶ K/s when the laser power is reduced to 180 W. These cooling rates are consistent with values commonly reported for LPBF processing (Wang et al., 2019). For such an infinitesimal variation in the cooling rate with laser power, the effect on residual stresses is expected to be minimal. This is consistent with Figure 11, which shows minimal effect of laser power on the residual stresses.

Laser printing patterns have been previously investigated by other researchers (Kruth et al., 2012; Setien et al., 2019; Serrano-Munoz et al., 2021). Generally, the scan strategy affects the final microstructure and part distortion more than the laser power (Xiao et al., 2020). Important parameters for investigating the effect of laser scanning strategy are the vector length (laser path length) and the laser path rotation angle between the layers. Kruth et al. (Kruth et al., 2012) found that longer laser passes increase part distortion. Laser path rotation reduces the directionality of the residual stresses and creates a more homogenous quasi-isotropic stress state (Parry et al., 2016; Setien et al., 2019). However, these studies focused mainly on “island” scanning patterns for thick part components (Cheng and Chou 2015; Serrano-Munoz et al., 2021). To the authors knowledge, there have been no studies on the effect of scanning patterns on thin-wall structures.

This study focuses on thin-wall geometries where perpendicular and longitudinal scanning patterns have short and long vector lengths, respectively. Moreover, two rotation angles (90° and 45°) between the layers are investigated. The predicted residual stresses for the four different scanning strategies are shown in Figures 12, 13, 14 for the longitudinal (S_XX), build (S_ZZ) and transverse (S_YY) directions, respectively. For each case, limits are placed on the contour plots to eliminate numerical artifacts from stress concentrations at the edge of the parts or due to mesh-to-mesh mapping (Hajializadeh and Ince 2019).

Maximum stresses are observed in the longitudinal direction (Sxx) for all scan strategies and have the same peak magnitude as the single-track simulations in Figure 7A. In the single-track simulation, it is observed that the stress along the build direction (S_ZZ) is negligible. However, for the part-scale simulation, there is an accumulation of S_ZZ stress at the center of the part height. This indicates the importance of considering both build geometry and height to compare residual stresses in LPBF. The S_YY stress plots in Figure 14 shows layer-laminated structure for the 90° and 45° rotation patterns. This is due to the directional stresses and mismatches between the layers, resulting in a non-homogenous stress distribution as discussed in (Kruth et al., 2012; Parry et al., 2016; Serrano-Munoz et al., 2021). The S_YY component is significantly lower (>2X lower than Sxx) than the other directions due to the thin wall builds, as explained in Effect of Laser Power on Residual Stresses.

There is increased residual stress along the laser travel direction. This is shown in Figure 12B, where the laser runs parallel to the part, and in Figure 14A, where the laser travels perpendicular to the part. The long vector length generates more tensile residual stress (average S_XX = 505 Mpa) along the part length (Figure 12B), and the short vector length causes more residual stress (average S_YY = 89.2 Mpa) in the through-thickness direction (Figure 14A). The resulting residual stress is proportional to the path length, as seen by comparing the peak stresses in the perpendicular and longitudinal laser passes. Therefore, aligning the laser path with the thickness will reduce tensile residual stresses in thin-wall parts, as shown by comparing Figures 12A,B.

The minimization of the tensile residual stress comes at the cost of increasing compressive residual stresses in the build direction, shown in Figure 13. The short vector length in Figure 13A drastically increases the compressive residual stress in the build direction compared to the long vector length in Figure 13B. The difference is approximately 3 times higher for the short vector length. This increase in compressive residual stress will negatively impact the limiting build height in thin-wall components, as observed in (Chakraborty et al., 2021).

The two rotation patterns shown in parts of Figures 12C,D, 13C,D, 14C,D have a layered quasi-isotropic residual stress distribution. This is consistent with previous studies showing more isotropic stress distribution when the laser path is rotated from layer to layer (Parry et al., 2016). It is more apparent in Figures 12, 14 where the longitudinal and transverse stresses are dominant due to the variation from layer to layer in the sectioned plane (Z-X). The stress distribution for the rotation patterns is a combination of both perpendicular and longitudinal patterns, with the 45° rotation pattern exhibiting less variation between neighboring layers.