An area-average approach to peening residual stress under multi-impacts using a three-dimensional symmetry-cell finite element model with plastic shots

We estimate realistic peening residual stress based on area-averaged solution using a 3D multi-impact symmetry-cell finite element (FE) model. The analytical model includes elaborate factors reflecting actual peening phenomena and plastic shot effect. Area-averaged solution is much closer to X-ray diffraction (XRD) experimental solution than four-node-averaged solution in plastic shot FE model. The area-averaged solution, moreover, converges to the perfect equi-biaxial stress state. From this, based on the area-averaged solution, we obtained the FE Almen curve, and then derived related equations among FE arc height, FE coverage and shot velocity. The FE Almen curve corresponds well with experimentally obtained by Kim et al. [Kim T, Lee JH, Lee H. An Effective 2D FE model with plastic shot for evaluation of peening residual stress. J Mater Process Technol, submitted for publication; Kim T, Lee H, Lee JH. A 3D phenomenological FE model for unique solution of peening stress due to multi-impacts. Int J Numer Methods Eng, submitted for publication]. Using the FE Almen curve, we examine the FE area-averaged solution in major peening materials. The FE solutions of surface, maximum compressive residual stress and deformation depth quite reach experimental solutions. The FE Almen curve is thus confirmed to be useful for estimation of residual stress solution. Consequently, we validated that the concept of area-averaged solution is the systematical analytical method for evaluation of real peening residual stress.