# Numerical Analysis of Laser Pattern Effects to Residual Stress on Metal 3D Printing
## 4 Conclusions  
In this study, a metal 3D printing process was simulated using FEM, and a specimen was printed under the same conditions to validate the analysis results. Owing to the characteristics of the 3D printing process using laser, various thermal and structural phenomena occurred, and they were difficult to observe directly. Therefore, the 3D printing process was analyzed via FEM, which is a numerical analysis technique. In particular, the phenomenon that occurred during lamination was confirmed via a thermal-structure two-way coupled analysis. The elastic behavior due to thermal deformation and thermal expansion was considered, enabling the residual stress to be calculated more realistically. In addition, to  
Figure 12: Maximum residual stress results of simulations.  
simulate the 3D printing process conditions, a subroutine was configured to propagate based on the path and layer in which the heat input position by the laser was set.  
Based on previous studies, the lamination process of three layers was simulated for an area measuring 5 mm \(\times\) 5 mm. Hatching with a snake pattern was simulated on the inner area after border processing to emulate the actual process. Four cases with different rotation angles of the layer pattern were calculated using FEM to confirm the difference based on the pattern. Subsequently, the specimens were printed under the same conditions, and the results obtained were compared with the analysis results. To confirm the printing state of the specimen, CT was performed to examine the pores and cracks in the specimen. Subsequently, the residual stress was measured and compared to verify the analysis results, and consistency between results was confirmed.  
In the 180\({}^{\circ}\) specimen, a significant error in residual stress was indicated; consequently, residual stress relief occurred owing to cracks in the lower region of the specimen, as confirmed by the CT results. Based on the stacked analysis results, it appeared that internal cracks occurred owing to excessive stress in a specific area. In the specimens with patterns of different angles, the overlap of stress was offset or insufficient stress was applied, resulting in cracks.  
These results confirmed that the 3D printing FEM model conducted in this study can be used to analyze residual stress and cracks in materials that were difficult to analyze in previous studies. The model used in this study applies various variables in combination, from the material to the process conditions of the printing equipment, and it can be used to understand the complex phenomenon of the variables as well as verify changes that cannot be easily measured in processes. The FEM model configured in this study is expected to facilitate investigations into the 3D printing process and the design of more efficient methods. In the future, an analysis will be conducted such that the hatch pattern is placed repeatedly in the adjacent area, and the phenomenon that occurs during coarse shape processing will be investigated. For various applications, additional studies regarding the differences in laser pattern and process variables are required, and these studies are expected to advance the FEM model of this study.  
Conceptualization, C.-h.J., M.G.L. and Y.J.; methodology, C.-h.J., M.G.L. and Y.J.; software, C.-h.J.; validation, C.-h.J. and C.N.; investigation, C.-h.J.; writing--original draft preparation, C.-h.J.; writing--review and editing, C.-h.J. and M.G.L.; supervision, Y.J.; funding acquisition, Y.J. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20206410100080).  
Not applicable.  
The authors declare no conflict of interest.