# Numerical Analysis of Laser Pattern Effects to Residual Stress on Metal 3D Printing
## 3 FEM Analysis Result
### Numerical Simulation Results of Additive Process  
Based on numerical analysis, the heat input process achieved by stacking the pattern and stacking layers sequentially was confirmed. Based on the analysis results shown in Figure 4, it can be confirmed that the heat source was applied to the powder layer, and the temperature increased depending on the heat input. In addition, it was confirmed that the heat source propagated based on the irradiation position of the laser, and traces remained in the longitudinal direction. Furthermore, two and three layers were stacked, and the heat input process was continued.  
To examine the effect of the lower layer due to the heat input of the upper layer, the temperature and residual stress changes were confirmed. As the heat source propagated, the temperature changed in the six points at the center of the first layer shown in Figure 2. The results are illustrated in Figure 5, and the resulting residual stress changes are shown in Figure 6. The direction of the laser heat source in each layer is in the opposite direction, and accordingly, the order of temperature change and residual stress change at six points is also reversed.  
When the laser was irradiated at the first layer and the melting process was simulated, the temperature of the element increased and residual stress formed rapidly; the temperature and residual stress changed owing to the second and third laminations. It was inferred that re-melting can be confirmed based on the temperature change in the first layer, which was affected by the second and third layers, and that fusion between the layers can be performed, as in the actual process. It was confirmed that the residual stress changed, owing to the heat applied to the upper layer. When the laser was irradiated at the second and third layers, residual stress was relaxed by the heat of the upper layer instantaneously and restored to a different value. Based on these results, it was confirmed that the cooling rate was changed depending on the location and the temperature of the element, thereby affecting the residual stress.  
As shown in Figure 7, the final residual stress and temperature distribution above the last layer were simulated. It was confirmed that heat generated by laser irradiation was conducted and dissipated through the base material and powder, whereas residual stress was generated in a specific pattern. This imbalance in the residual stress resulted in distortion and cracking.  
Figure 4: Laser heat input simulation result: (a) 68 ms—early stage of first layer heat input; (b) 1121 ms—second layer heat input; (c) 1904 ms—third layer heat input.  
In particular, in the case of the 180\({}^{\circ}\) pattern, a force was applied to the base material in the same direction as the path, as previously confirmed in the basic analysis, owing to the repetition of the same pattern [10]. The residual stress in the lower region was amplified based on the laser path, which was confirmed through changes in the residual stress on the lower surface.  
Figure 5: Results of temperature changes in the first layer (6 points shown in Figure 2).  
Figure 6: Results of residual stress changes in the first layer (6 points shown in Figure 2).