Investigation on the bending deformation of laser peen forming with a simplified eigenstrain-based finite element model

Laser peen forming (LPF) is promising to form large-scale metal sheets in various applications. Understanding the bending deformation of the LPF process is of particular importance for accurate shape prediction and process planning elaboration. This study established a simplified eigenstrain-based finite element (FEM) model by incorporating loading sequence and geometric non-linearity to explore the bending deformation and shape prediction of the LPF process. The simplified eigenstrain was inversely determined based on the arc heights of plates subjected to full-covered LPF. The above model incorporating loading sequence and geometric non-linearity was verified by the comparison of experimental results, and it improved shape prediction accuracy considerably compared to the common beam bending analytical model. Moreover, the bending deformation processes and mechanisms of LPF plates were elucidated. It was found that biaxially curved surfaces were formed for thick plates with 5 mm or larger thickness, in which the geometric non-linearity and flattening effects played significant roles on their formation. On the other side, monoaxially curved surfaces were obtained for thin plates with 4 mm or smaller thickness after the LPF process. Three stages, i.e., forward bending, reverse flattening, and buckling, occurred and contributed to the formation of the monoaxially curved surface. With the increase in the eigenstrain amplitude and side length, and the decrease in plate thickness, the LPF plates transit from a biaxially curved shape to a monoaxially curved one.