An iterative approach combined with multi-dimensional fitting of limited measured stress points to reconstruct residual stress field generated by laser shock peening

In this paper, an iterative approach combined with least squares fitting of limited measured points is introduced to reconstruct residual stress distribution after laser shock peening (LSP) treatment. The iterative approach is started by introducing prescribed stress components in the data measurement region (the mapped zone) in the finite element (FE) model, then a static equilibrium analysis is conducted, which will cause the stress distribution in the mapped zone and unmapped zone both redistribute if they don't converge to the target stresses. By repeatedly introducing the input stress in the mapped zone to converge to the prescribed stress components, the complete residual stress distribution in the whole region can be obtained. Firstly, to validate the viability of this method, based on the full stress components information of ‘measured’ sample points extracted from FE models, residual stress reconstructions of single-pass welding of a thick plate and a single shot of LSP have been carried out, respectively. After that, to examine the robustness of the method, the iterative approach combined with multi-dimensional least squares fitting is tested using a limited set of ‘measured’ sample points extracted from the FE model of single shot LSP treatment. It is found that besides the commonly studied depth direction, the in-plane stress components are also varied with its in-plane locations, which are due to “edge effects”. The residual stress fields for the whole region reconstructed by the proposed approach agree well with the actual stress fields even if some of the non-critical stress information are missing. Finally, the results are compared with those reconstructed by the eigenstrain method. It is shown that the proposed iteration approach can reconstruct the residual stress distribution in the whole region at a satisfactory level by solving a direct linear elastic static equilibrium problem, while the eigenstrain method needs to solve an inverse problem to obtain the appropriate eigenstrain distribution.