Delineation of first-order closures for plastic properties requiring explicit consideration of strain hardening and crystallographic texture evolution

Microstructure Sensitive Design (MSD) is a novel mathematical framework that facilitates development of invertible linkages between statistical description of the material’s microstructure and its effective properties. Property closures are an important outcome of the MSD methodology, and delineate the complete set of theoretically feasible effective (homogenized) anisotropic property combinations in a given material system for a selected homogenization theory. In recent publications, we have reported first-order closures for the elastic and yield properties of both cubic and hexagonal polycrystalline materials. In this paper, we present major extensions to the previously reported framework to enable rigorous consideration of strain hardening and the concomitant evolution of the crystallographic texture with imposed plastic strain. These new extensions facilitate delineation of first-order closures for properties associated with finite plastic strains (e.g. ultimate tensile strength, uniform ductility). The proposed approach has been successfully applied to an aluminum alloy and a copper alloy, and the results are presented and discussed in this paper.