Modeling of sheet metal forming processes taking into account distortional hardening

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. 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 (so-called cross hardening). In this work we present 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 accounts for the pressure dependence of the flow stress. All these additional attributes turn out to be essential to model the stress-strain response of dual phase high strength steels subjected to non-proportional loading.