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Accurate hardening modeling as basis for the realistic simulation of sheet forming processes with complex strain-path changes

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 type 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 (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 experimental results for materials exhibiting the cross hardening effect. Another effect, not accounted for in the classical elasto-plasticity, is the difference between the tensile and compressive strength, exhibited e.g. by some steel materials. 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 high-strength steels subjected to non-proportional loading. The model is implemented into LS-DYNA via the user material interface. After a LS-OPT based parameter identification for a dual phase high strength steel with the help of one- and two-stage loading tests, we demonstrate the capability of the model to predict the spring-back in processes with complex strain path changes.

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