## 3 Results and Discussion
### Residual Stress Distribution Characteristics of the Spot Weld Joint According to the Nugget Size  
An analysis system was developed to examine the residual stress distribution characteristics of the spot welding nugget. Using this system, the residual stress distribution characteristics were analyzed in relation to variations in nugget size. The geometry of the nugget in the FEM analysis was compared to the macro section obtained through experimental procedures, and good agreement was confirmed. Four nugget sizes--\(3\sqrt{t}\), \(3.5\sqrt{t}\), \(4\sqrt{t}\)  
Figure 8: Welding residual stress distribution in nugget obtained using X-ray diffraction analysis and the hole-drilling method. Figure 9: Comparison of welding residual stress distribution in spot welds based on experimental and numerical results: (**a**) x-direction; (**b**) y-direction. and 4.5\(\sqrt{t}\)--were selected for the analysis, which was conducted using identical material properties across all sizes. As increasing the nugget size requires a corresponding increase in heat input, the nugget size was varied by adjusting current conditions, consistent with the approach used in actual experiments. Residual stress was examined in the x-, y-, and z-directions, extending from the nugget center to the nugget edge. The numerical simulation results are illustrated in Figure 10, which displays the residual stress distribution along the nugget. For nugget sizes up to 4\(\sqrt{t}\), the residual stress in all directions exhibited similar maximum values and followed the same trends. However, for the largest nugget size (4.5\(\sqrt{t}\)), the residual stress at the nugget center was slightly reduced. The analysis model included spacers on both sides, which introduced tensile forces (spring-back effects) due to the spacer. It is inferred that the tensile forces overlapped with the residual stresses induced by welding at the spot weld joint. As the nugget size decreased, the tensile stress increased, whereas the influence of pure residual stress became more dominant with larger nugget sizes. This trend was attributed to the increased stiffness of the nugget, which reduced the impact of tensile forces caused by the spacer. This phenomenon was particularly evident in the z-direction residual stress, where the tensile force was relatively pronounced. Regarding the influence of the spacer on spring-back effects, it is concluded that the level of residual stress decreases as the nugget size increases, as greater stiffness enhances resistance to spring back. An increase in nugget size correlates with a reduction in z-direction residual stress, which influences spring-back behavior. In 3\(\sqrt{t}\), where spring-back effects are most pronounced, significant tensile forces are observed at the nugget periphery. As the nugget size enlarges, these tensile forces diminish, and compressive stresses become more prevalent. This trend suggests that larger nugget sizes mitigate the risk of failure by alleviating stress concentrations at the nugget boundary. This observation aligns with existing research indicating that larger weld nuggets enhance joint strength and alter stress distributions favorably [6]. For instance, studies have shown that increasing nugget diameter reduces the likelihood of interfacial failure. Additionally, larger nuggets distribute stresses more evenly, reducing peak stresses that can lead to crack initiation and propagation. Therefore, optimizing nugget size is crucial in resistance spot welding to improve joint performance and durability. Figure 10: Welding residual stress distribution obtained using different nugget sizes in the (**a**) x-, (**b**) y-, and (**c**) z-directions using FE-analysis. Figure 11 illustrates the z-direction stress distribution, highlighting the notch effect introduced by the spacer on nugget stress. For the \(3\sqrt{t}\) nugget, the stress at the nugget edge exceeded that at the nugget center.