Micromechanically motivated phenomenological modeling of induced flow anisotropy and its application to sheet forming processes with complex strain path changes

Abstract

Sheet metal forming involves large strains and severe strain path changes. Large plastic strains lead in many metals to the development of persistent dislocation structures resulting in strong flow anisotropy. This induced anisotropic behavior manifests itself in the case of a strain path change by very different stress-strain responses depending on the mode of the strain path change. While many metals exhibit a drop of the yield stress (Bauschinger effect) after a load reversal, some metals show an increase of the yield stress after an orthogonal strain path change (i.e., so-called cross hardening). To model the Bauschinger effect, kinematic hardening has been successfully used for years. However, the usage of the kinematic hardening leads automatically to a drop of the yield stress after an orthogonal strain path change contradicting tests exhibiting the cross hardening effect. So already this example demonstrates that the concept of the combined isotropic-kinematic hardening used in the conventional plasticity has to be extended in order to better simulate processes with complex strain path changes. However, an extension on the phenomenological basis only is a formidable task since one has to make theoretical assumptions with regard to the rather abstract concept of the yield surface. On the other hand, since the deformation mechanisms on the grain level are understood fairly well, polycrystalline simulations yield in a natural way more accurate prediction of the hardening behavior. Admittedly, due to very high numerical costs they cannot be applied to complex industrial simulations. But polycrystalline modeling can be used to better understand the effective macroscopic behavior and can help to develop more realistic phenomenological models. In this work we present such a phenomenological material model whose structure is motivated by polycrystalline modeling that takes into account the evolution of polarized dislocation structures on the grain level - the main cause of the induced flow anisotropy on the macroscopic level. The model considers besides the movement of the yield surface and its proportional expansion as it is the case in conventional plasticity also the changes of the yield surface shape (distortional hardening) and is able to better describe the induced anisotropic behavior with regard to complicated loading histories. The capability of the model is demonstrated on sheet forming processes with complex strain path changes.