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 coefficient 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 pathdependent, 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.

Numerical investigation and experimental validation of a plasticity model for sheet steel forming

“…With this indicator, continuous strain-path changes are still detected, independently of the strain-increment size. The SPCI ξ is defined as 18) and the evolution of the second-order tensor G is defined as…”

“…Full micromechanical models may be used to calculate only a small part of the yield locus, in the vicinity of the current loading point [14,15]. Alternatively, the entire yield surface can be approximated by plastic potentials whose parameters are fitted with respect to a Taylor-model approximation of the initial anisotropy [16][17][18]. The parameters of such potentials can be further updated to account for the evolution of the anisotropy.…”