Investigation of the variable elastic unloading modulus coupled with nonlinear kinematic hardening in springback measuring of advanced high-strength steel in U-shaped process

Abstract

Advanced high strength steels are widely used in the automotive industry due to their appropriate strength to weight ratio. This alloy has unique hardening behavior and variable unloading elastic modulus. In this paper, an analytical model is introduced to predict springback in U-shaped bending process of normal and pre-strained DP780 dual phase steel stripes. It is based on the Hill48 yield criterion and plane strain condition. In this model, the effect of forming history, sheet thinning and the motion of the neutral surface on the springback is taken into account. The anisotropic nonlinear kinematic hardening model (ANK) is used to consider the impact of complex deformation including stretching, bending and reverse bending. This model is able to investigate the Bauschinger effect, transient behavior and permanent softening. Also, a nonlinear function of plastic strain is implemented to capture the variable unloading elastic modulus. This model is used for the Numisheet2011 benchmark U-shaped bending problem. The effect of the sheet holder force, the coefficient of friction, thickness, material anisotropy, hardening parameters, pre-strain and variable elastic modulus on the sheet springback is studied. It can be seen that analytical model with constant young's modulus has better accuracy in predicting springback angles than FEM solutions. Also in the case of variable young's modulus, FEM solution has better agreement with experiments in comparison with the analytical model.