A micro-mechanically based quadratic yield condition for textured polycrystals

Abstract In the present paper a two‐scale approach for the description of anisotropies in sheet metals is introduced, which combines the advantages of a macroscopic and a microscopic modeling. While the elastic law, the flow rule, and the hardening rule are formulated on the macroscale, the anisotropy is taken into account in terms of a micro‐mechanically defined 4th‐order texture coefficient. The texture coefficient specifies the anisotropic part of the elasticity tensor and the quadratic yield condition. The evolution of the texture coefficients is described by a rigid‐viscoplastic Taylor type model. The advantage of the suggested model compared to the classical v. Mises‐Hill model is first, that macroscopic anisotropy parameters can be identified based on a texture measurement, and second, that the anisotropy of the elastic and the plastic behavior is generally path‐dependent and that this path‐dependence is related to a micro‐mechanical deformation mechanism. An explicit modeling of the plastic spin is circumvented by the aforementioned micro‐mechanical approach. The model is implemented into the FE code ABAQUS and applied to the simulation of the deep drawing process of aluminum.