An Analytical Model for Estimating the Bending Curvatures of Metal Sheets in Laser Peen Forming

Laser peen forming (LPF) is suitable for shaping sheet metals without the requirement for die/mold and without causing high temperatures. An analytical model for estimating the bending curvatures of LPF is convenient and necessary for better understanding of the physical processes involved. In this paper, we describe a new analytical model based on internal force balance and the energy transformation in LPF. Experiments on 2024 aluminum alloy sheets of 1-3 mm thickness were performed to validate the analytical model. The results showed that for 1 mm and 3 mm thick-thin plates, the curvature obtained by the analytical model changes from -14 × 10^-4 mm^-1 and -1 × 10^-4 mm^-1 to 55 × 10^-4 mm^-1 and -21 × 10^-4 mm^-1, respectively, with the increase of laser energy, which is consistent with the experimental trend. So, when either the stress gradient mechanism (SGM) or the shock bending mechanism (SBM) overwhelmingly dominated the forming process, the analytical model could give relatively accurate predicted curvatures compared with the experimental data. Under those conditions where SGM and SBM were comparable, the accuracy of the model was low, because of the complex stress distributions within the material, and the complex energy coupling process under these conditions.