On Springback Prediction With Special Reference To Constitutive Modeling

The springback phenomenon that occur in thin metal sheets after forming is mainly a stress driven problem, and the magnitude is roughly proportional to the ratio between the magnitude of the residual stresses after forming and Young’s modulus. An accurate prediction of residual stresses puts, however, high demands on the material modeling. A phenomenological plasticity model is made up of several ingredients, such as a yield criterion, a plastic hardening curve, a hardening law, and a model for the degradation of elastic stiffness due to plastic straining. The authors have recently, Ref. [1], showed the importance of a correct modeling of a cyclic stress-strain behavior via a phenomenological hardening law, in order to obtain an accurate stress prediction. The main purposes of the present study are to study the influence of two other constitutive ingredients: The yield criterion and the material behavior during unloading. The material behavior during unloading is evaluated by loading/unloading/reloading tension tests, where the material is unloaded/reloaded at specific plastic strain levels. The slope of the unloading curve is measured and a relation between the “unloading modulus” and the plastic strains is established. In the current study, results for four different materials are accounted for. The springback of a simple U-bend is calculated for all the materials in the rolling-, transverseand diagonal directions. From the results of these simulations, some conclusions regarding constitutive modeling for springback simulations are drawn.