Anisotropic Plasticity During Non-proportional Loading

Abstract

AbstractModeling of the elasto-plastic behavior of isotropic and anisotropic metals for applications to forming process simulations is discussed. In particular, the macroscopic flow theory of plasticity combined with the concept of isotropic hardening, in which a single monotonic stress-strain curve serves as a reference, is briefly reviewed. Selected non-proportional loading test procedures are described and the main deviations of the material behavior compared to an isotropic hardening response are discussed on the basis of underlying mechanisms of deformation at lower scale. The failure of isotropic hardening to accurately capture the behavior of a material subjected to non-linear strain paths demonstrates the need for more advanced hardening theories. Thus, theories based on kinematic hardening, possibly combined with distortional plasticity concepts, are succinctly reviewed. A pressure-dependent, distortional-only, plasticity approach recently proposed is discussed in more details and its relevance is illustrated with the prediction of stress-strain curves of advanced high strength steel sheets deformed along non-linear strain paths. A finite element (FE) implementation of this distortional plasticity model is outlined, with special attention to the formulation of the stress integration algorithm and the elasto-plastic tangent tensor. Application examples on several steel sheet samples subjected to various strain path changes are given for validation purpose. Simulations are conducted with a stand-alone (SA) code containing the constitutive equations only and a FE code with only one element. Comparisons between these predictions and experimental results demonstrate the accuracy of the model and the excellent performance of the FE implementation. Applications on advanced high strength steel (AHSS) sheet demonstrate why the pressure-dependency in the model is an important feature.