Finite element simulation of deep drawing with initial and induced anisotropy

Abstract

Deep drawing is a forming process widely used to obtain parts of suited shape from sheets initially flat. These sheets are obtained generally by rolling and thus present an initial orthotropic anisotropy. Several behaviour models have been proposed to predict their induced anisotropy evolution at large strains. The models frequently used in finite element simulation are the phenomenological ones. This work concerns the prediction of the macroscopic behaviour of thin sheets and of the final part properties in deep drawing. A dislocation-based micro-structural hardening model taking into account the strain-path induced anisotropy is considered, together with anisotropic yield surfaces. The numerical integration of the constitutive equations in order to implement the model in finite element codes is discussed. Consequently, several explicit schemes for the integration of the model (forward Euler, 2nd and 4th order Runge-Kutta) are implemented. In order to asses the relative accuracy of these schemes, we compare experimental and simulated rheological tests for different grades of steel sheet. Finally, finite element computations are performed to predict the spring-back and its dependence on deep drawing process parameters.