## 4 Conclusions  
In this study, quantitative examinations were conducted using both experimental and numerical methods to investigate the welding residual stress characteristics of recently developed high-strength steel for spot welding, which has been widely applied in automotive body construction. Additionally, the residual stress distribution characteristics of  
Figure 13: Residual stress distribution in each direction with spacer (nugget size: \(3\sqrt{t}\)).  
the nugget, as influenced by sheet thickness and nugget size, as well as the effects of the presence or absence of the spacer, were examined. The following conclusions were drawn.  
When the residual stress of the spot weld joint was measured at both the nugget center and the affected area, based on nugget size, using the XRD and HDR methods, it was found that tensile residual stress, lower than the yield stress, was distributed at the nugget center. Furthermore, a numerical analysis system was developed to examine the residual stress distribution at the spot weld joint, yielding results in good agreement with the experimental findings.  
When examining the effect of nugget size in the presence of the spacer, it was observed that the tensile residual stress at the nugget center decreased as the nugget size increased, indicating an improvement in the fracture stability of the weld joint. Regarding the distribution of residual stress in the z-direction, significant tensile residual stress was found at the nugget edge for a nugget size of \(3\sqrt{t}\), thereby reducing fracture stability and increasing the likelihood of fracture. However, for nugget sizes of \(3.5\sqrt{t}\) or larger, fracture resistance was judged to increase due to the reduction in tensile stress at the nugget edge.  
Through the examination of stress changes in the nugget, based on sheet thickness and nugget diameter, it was found that tensile stress was consistently distributed at the nugget edge for a nugget size of \(3\sqrt{t}\), regardless of sheet thickness. Consequently, the part is expected to be vulnerable to fracture under tensile loading. However, as the nugget size increases, higher sheet thicknesses are more favorable for ensuring fracture safety.  
Regarding the residual stress distribution in the nugget based on the presence or absence of the spacer, the spring back induced by the spacer generated tensile stress, leading to a larger distribution of tensile stress at the nugget edge. In the absence of the spacer, compressive stress was observed at the nugget edge. The stress level at the nugget was influenced by the spring back caused by the spacer, with its magnitude varying according to the nugget size. Specifically, the stress distribution at the nugget edge shifted from tensile residual stress to compressive residual stress as the nugget size increased.  
[PERSON] and [PERSON] jointly conceived and designed the experiment, performed the experiment, and conducted data analysis. [PERSON] and [PERSON] analyzed the data, plotted the figures, and wrote this paper. [PERSON] provided scientific guidance. All authors have read and agreed to the published version of the manuscript. This research was supported by the \"Regional Innovation Strategy (RIS)\" through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE) (2021 RIS-002). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: No new data were created or analyzed in this study. Data sharing is not applicable to this article. This is supported by POSCO project No. 20230094, Korea. Also, this work was partly performed under the Joint Usage/Research Center at the Joining and Welding Research Institute, the University of Osaka, Japan. Conflicts of Interest: Author [PERSON] was employed by the company POSCO. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.