Finite Element Correction for Residual Stress Distribution Measured by X-ray Surface Removal Method

Abstract

The X-ray diffraction technique is widely used for measuring the residual stress on metal surfaces. Since the penetration depth of X-rays is shallow, the surface removal method has been adapted to measure the in-depth distribution of the residual stress. The measured stress distribution needs to be corrected to take into account of the redistribution due to surface removal. In this study, the correction of measured stress was performed using finite element analysis (FEA). For FEA, we prepared multi-layer solids with differential thermal coefficients of expansion. Uniform temperature change caused continuous residual stress distribution in the solids. Step-by-step surface layer removal of a flat plate and a cylinder was carried out in simulation, and then the matrices for stress correction were obtained. FEA correction for entire surface layer removal was confirmed to be identical to the theoretical solution. In the case of local surface removal, it was clarified that the correction matrix obtained for a particular residual stress distribution is applicable to arbitrary stress distribution. Using this method, the difference in the stress correction for entire surface layer removal and local surface removal was determined and it was applied to residual stress distribution correction for a carburized steel bar. Moreover, we have discussed in depth how the stress correction for the entire surface layer removal can be applied for the local surface removal.