Dynamic forming limits and numerical optimization of combined quasi-static and impulse metal forming

Subject of this work is the incorporation of forming limits in the numerical optimization of technological forming processes for sheet metal. Forming processes with non-linear load paths and strongly varying strain-rate, such as, e.g., combinations of deep drawing and electromagnetic forming are of particular interest. While in the latter impulse forming process inertial forces play a significant role, the first one is of quasi-static nature such that inertial forces may be neglected. Although classical forming limit diagrams provide an easily accessible method for the prediction of forming limits, they cannot be applied in situations involving pulsed loading along non-linear strain paths. Hence, they are extended to forming limit surfaces here. The target function to be minimized is computed via finite-element simulation. To avoid a large number of simulations, an interior point method is employed as optimization method. In this algorithm, forming limits appear via a logarithmic barrier function, which has to be computed sufficiently fast. The optimization algorithm is exemplarily applied to an identification problem for a two-stage forming process.