Application of the three-dimensional residual stress estimation method using X-ray diffraction and eigenstrain theory to a resistance spot-welded plate

Resistance spot-welding is widely used in automotive body production, but the residual stresses generated by welding negatively impact fatigue strength. Therefore, non-destructive evaluation of the three-dimensional residual stress distribution in resistance spot-welded materials can ensure product reliability. Currently, various methods for evaluating residual stresses are available. X-ray diffraction is a non-destructive technique that measures residual stress only at the surface. Neutron diffraction enables three-dimensional non-destructive measurements; however, it requires specialized equipment and cannot be used on-site. Consequently, a three-dimensional residual stress estimation method based on X-ray diffraction and the eigenstrain theory has been proposed. This method involves the use of surface elastic strains measured by X-ray diffraction to estimate three-dimensional eigenstrains via inverse analysis. The estimated eigenstrain is input into an FE model to calculate the three-dimensional residual stress distribution. The purpose of this study is to apply this method to an actual resistance spot-welded material, and to demonstrate the reasonable accuracy on surface. To reduce the number of unknowns in the eigenstrain generated by resistance spot welding, the distribution shape of the eigenstrain was approximated using functions. As a result, reasonable agreement was achieved on the surface outside the vicinity of the welded area. A method for approximating the distribution of eigenstrain in the thickness direction, and thus improving the estimation accuracy, was developed. Ultimately, residual stresses could be estimated with reasonable accuracy even on the surface near the welded area. The robustness of this method against measurement errors has been demonstrated by error sensitivity analysis.