On the modelling of the bending–unbending behaviour for accurate springback predictions

The prediction of springback is probably the area in sheet forming simulation where the least success has been achieved in terms of solution accuracy. The springback is caused by the release of residual stresses in the workpiece after the forming stage. An accurate prediction of residual stresses puts, in turn, high demands on material modeling during the forming simulation. Among the various ingredients that make up the material model, the hardening law is one of the most important ones for an accurate springback prediction. The hardening law should be able to consider some, or all, of the phenomena that occurs during bending and unbending of metal sheets, such as the Bauschinger effect, the transient behaviour, and permanent softening. The complexities of existing hardening laws do of course vary within quite wide ranges. One of the purposes of the present study was to try to identify a model of reasonable complexity that at the same time can fulfill the requirements concerning accuracy. Five different hardening models have been evaluated in the present investigation. The simplest model, the isotropic hardening one, involves only one history variable, while the most advanced model involves ten history variables and four additional material parameters. In the current report, results for four different materials will be accounted for. The kinematic hardening parameters have been determined by inverse modeling of a three-point bending test. A response surface method has been used as an optimization tool, together with a finite-element model of the bending test set-up. The springback of a simple U-bend has been calculated for one of the materials, and from the results of these simulations some conclusions regarding the choice of hardening law are drawn.