Eigenstrain modelling of residual stress generated by arrays of laser shock peening shots and determination of the complete stress field using limited strain measurements

This paper presents a hybrid explicit finite element (FE)/eigenstrain model for predicting the residual stress generated by arrays of adjacent/overlapping laser shock peening (LSP) shots where the use of a completely explicit FE analysis may be impractical. It shows that for a given material, the underlying eigenstrain distribution (in contrast to the resulting stress field) representing a laser shock peen is primarily dependent on the parameters of the laser pulse and the number of overlays rather than the precise component geometry. Consequently the residual stress introduced by complex laser peening treatments can be built up by using static FE models and superposition of individual eigenstrain distributions without recourse to further computationally demanding explicit FE analyses. It is found that beneath a small LSP array the magnitude of the compressive residual stress is higher than for a wider array of LSP shots and that with increasing numbers of layers the compressive stress increases as does the depth of the compressive zone. The model predictions for the eigenstrain distributions are compared well with experimental measurements of plastic strain (full-width-at-half-maximum) obtained by neutron diffraction. The eigenstrain method is also extended to construct the full residual stress field using measured residual elastic strains at a finite number of measurement locations in a component.