# Numerical Analysis of Laser Pattern Effects to Residual Stress on Metal 3D Printing
## 1 Introduction  
Three-dimensional (3D) printing technology can process various shapes beyond the limitations of conventional cutting processes; as such, it has been recently extensively investigated. In particular, the development of metal 3D printing technology has resulted in continuous efforts to produce materials more efficiently and to be applicable to mass-produced products [1].  
Among the relevant processes, selective Laser melting (SLM) uses a laser as a heat source to melt and solidify the metal powder. Consequently, rapid temperature differences and complex thermal gradients occur in the powder and products while passing through the adjacent laser path [2].  
In other words, melting and solidification occur instantaneously along the laser path, and residual stress occurs owing to the movement of the metal melting pool and thermal expansion. The residual stress generated causes deformation and cracking in the entire material, and cracks occur owing to the stress and distortion generated by the laser pathwhen printed at a high aspect ratio shape [3]. Therefore, heat and residual stress changes that occur during metal lamination can be verified in advance, such that the post-treatment process after product production can be reduced significantly or the processing accuracy of the product can be increased.  
Various analytical approaches to metal 3D printing have been reported. In the study of [PERSON] et al., the phenomenon occurring as powder particles melt and solidify was analyzed through flow analysis [4]. Considering the shape of the powder particles and the buoyancy and convection that occur in the molten state, the actual melting phenomenon and the process in which pores occur were simulated. However, the analysis area is extremely small, thus, it is difficult to apply it to large parts. In the study of [PERSON] et al., the phenomena occurring during melting and surface changes were analytically implemented through thermo-fluid analysis [5]. Ambient air, solids and powder were analyzed based on the density fraction, and the resulting surface curvature and roughness were specifically analyzed. However, due to the characteristics of the analysis method, it was difficult to analyze the stacking process of multiple layers.  
[PERSON] s analyzed the process of forming a thin-walled structure by repeatedly stacking a single laser path through FEM [6]. Unlike previous studies, thermal and structural analyses were conducted, but heat transfer to the surrounding powder was not considered, and temperature changes due to adjacent paths were not considered.  
[PERSON] analyzed the residual stress of metal 3D printing materials using the inherent strain method and conducted optimization studies to minimize deformation by applying a porous grid structure [7]. However, the deformation of the structure by heat was applied only to the initial inherent strain. Since the strain application per layer and heat transfer to adjacent structures are not considered, a detailed analysis is limited.  
However, studies that verify the heat input process or residual interlayer stress based on the laser path inside one stacked surface are insufficient. Based on previous studies, SLM was simulated via a thermal-structure coupled analysis in this study. As shown in Figure 1, a thermal-structure coupled analysis module was constructed to analyze the structure of the material properties, laser heat sources, and paths applied to the SLM process numerically [8]. The 3D printing process was simulated on each layer based on the laser path, and the deformation, temperature change and residual stress occurring in the process were confirmed. Subsequently, the specimen was printed under the same process conditions to compare and verify the analysis results with the residual stress measurements.  
Figure 1: Schematic illustration of SLM simulation [8]: (green arrow) forces due to thermal expansion; (red arrow) repulsive force due to thermal expansion; (orange arrow) heat transfer into the material interior.