Planar Double‐Slip Micromechamcal Model for Polycrystal Plasticity

Abstract

The kinematics and kinetics of a planar double‐slip system are used to model the response of a single crystal in plane large plastic deformations. Based on the kinematics of the double‐slip element, the orientation distribution function (ODF) of an infinite number of such elements, modeling a polycrystalline material, is obtained analytically for plane deformations by solving its differential equation of evolution. The ODF models the texture development of the polycrystalline aggregate. Based on the corresponding kinetics of the double‐slip element, the ODF is used to obtain by integration in closed‐form analytical expressions for the deviatoric stress components and associated yield surface of the polycrystal during general plane large plastic deformations, accounting for the ongoing texture development. The general theoretical development is illustrated by examples for simple shear and plane strain rolling deformation processes, and in the former case is compared successfully with experiments.