Analytical prediction of springback based on residual differential strain during sheet metal bending

Abstract

As the springback of sheet metal during unloading may cause deviation from a desired shape, accurately predicting springback is essential for the design of sheet stamping operations. Finite-element models have not been successful in predicting springback; hence there is a need for analytical models to make such predictions. In this study, a model based on differential strains after relief from the maximum bending stress is derived for six different deformation patterns in order to predict springback analytically. The springback for each deformation pattern is estimated by the residual differential strains between outer and inner surfaces after elastic recovery. Each of the six deformation patterns has a valid region of applicability, based on elastic modulus, yield strength, applied tension, and bending geometry. Analytical equations for the springback of the sheet deformed under these six deformation patterns are derived. Traditional analytical models for springback prediction have been based on elastic unloading from a bending moment. Traditional models also require the knowledge of the stress distribution through the thickness of the sheet, whereas the residual differential strain model only requires the stress state on the outer and inner surfaces of the sheet. In order to compare the residual differential strain model with the traditional bending moment model, a bending moment model is derived for the same exact deformation patterns. Results from the two models are compared for various materials.