Analytical Approach to Investigate the Effects of Through-Thickness Stress on Springback in Bending of Isotropic Sheet Metal

Abstract Within contemporary sheet metal forming processes like electromagnetic forming, the sheet experiences pronounced out-of-plane compression stress. This study focuses on the predicting the springback in the bending of an isotropic sheet metal in the presence of through-thickness compressive normal stress. In the analytical method, the longitudinal stress distribution across sheet thickness was calculated via equilibrium equations and the associated flow rule in incremental plasticity based on the power law hardening model, obtaining the reverse bending moment. During the unloading phase, the external load was lifted, and the springback angle was estimated by assuming linear elastic behavior and neglecting the Bauschinger effect, employing the superposition method. A case study was conducted on an aluminum alloy sheet for different compressive stresses and bend curvatures. Subsequently, the reverse bending moments and springback angles obtained for each case were compared to the numerical outcomes from finite element (FE) modeling. Analytical results indicate that elevating the compressive normal stress on the sheet surface to 75% and 100% of the yield stress will lead to a reduction in springback by 17.4% and 32%, respectively. At the compressive normal stress of 75% of the yield stress, the numerical model exhibited a 4.4% difference from the analytical model. For the validation of the analytical model, a four-point bending test was conducted with varying initial bend curvatures and angles. This involved comparing the experimental springback angle and curvature with both numerical and analytical predictions. In comparison, both the numerical and analytical models demonstrated strong agreement with the experimental results.