## 2 Materials and Methods
### Method for Examining Residual Stress Distribution Characteristics of Spot Weld Joints  
#### 2.2.1 Residual Stress Measurement by Experimental Method  
This study analyzed the residual stress distribution on the surface of spot weld joints to identify the residual stress characteristics in the nugget. Residual stress was measured using the XRD and hole-drilling HDR methods, both commonly employed for evaluating welding residual stress on specimen surfaces [21; 22]. For XRD measurements, residual stress was recorded at 2 mm intervals along the length (y-direction) and width (x-direction) up to 10 mm from the center of the nugget, as shown in Figure 4a. The XRD measurements were conducted in accordance with ASTM E915-16 and ISO EN 15305 (2008) standards [23; 24]. Residual stress refers to internal stresses that remain within a material in the absence of external forces. Accurate measurement of these stresses is crucial for assessing material performance and preventing potential failures. X-ray diffraction (XRD) is a widely used non-destructive technique for evaluating residual stresses, particularly in crystalline materials. \begin{table}
\begin{tabular}{c c} \hline \hline
**Electrode Type** & **DR-Type, Tip Face Diameter: 6 mm, Cu-Cr** \\ \hline Electrode force & 3730 N \\ \hline Welding current & 3400 A \\ \hline Squeeze time & 5 cycle/50 Hz \\ \hline Holding time & 10 cycle/50 Hz \\ \hline Welding time & 14 cycle/50 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Welding conditions used in the study. Figure 3: Vickers hardness distribution in SPOT welding area. This method leverages the interaction between X-rays and the crystal lattice to determine stress-induced changes in lattice spacing. When X-rays are directed at a crystalline material, they are diffracted by the crystal planes according to Bragg's Law using Equation (1). \[n\lambda=2d\sin\theta \tag{1}\]  
\(n\): order of diffraction;  
\(\lambda\): wavelength of the X-rays;  
\(d\): interplanar spacing;  
\(\theta\): Bragg angle (the angle of diffraction). Residual stresses cause distortions in the crystal lattice, leading to changes in the interplanar spacing \(d\). These changes result in shifts in the diffraction angle \(\theta\). By precisely measuring these shifts, the strain within the material can be determined, which is then used to calculate the residual stress. Surface preparation is crucial in X-ray diffraction (XRD) measurements to ensure accurate residual stress analysis. In this study, scratches on the sample surface were addressed using an electrolyte solution, as such imperfections can introduce residual stresses that may skew results. The sample, a spot weld, exhibited a concave central region, resulting in a non-flat surface. To accommodate this geometry, the reflection angle was adjusted by repositioning the XRD contactor during measurement. Residual stress measurements were conducted using the Xstress 3000+G2R system from stress tech Oy (Helsinki, Finland). After removing the superficial stress at the measurement location using electropolishing equipment, the metal components were analyzed with XRF equipment (X-MET8000, HITACHI, Hitachi, Japan), and the data were correctly aligned. To ensure data reliability, the collimator size was increased to 2 mm, and sufficient exposure time was applied. Given the larger measurement size and extended exposure time, the results are considered reliable. Additionally, for the measurement of the nugget area in SPOT welding, a tilting detector was utilized to determine the interplanar spacing for crystals with varying orientations. This was achieved by segmenting the measurements into specific angles and repeatedly measuring the same point, allowing for precise analysis. An X-ray diffractometer equipped with appropriate optics and detectors is used to direct X-rays onto the sample and measure the resulting diffraction patterns. The diffraction angle \(\theta\) is measured at various tilt angles to capture the strain in different orientations.