Finite element analysis of polycrystalline deformation with the rate-dependent crystal plasticity

Abstract

Constitutive models for the crystal plasticity have the common objective which relates the behavior of microscopic single crystals in the crystallographic texture to the macroscopic continuum response. This paper presents the texture analysis of polycrystalline materials using the rate-dependent single crystal plasticity to develop a multi-scale description of the mechanism at the grain and aggregate levels. The texture analysis requires a numerical algorithm for integrating the constitutive equations. The implicit deformation gradient approach is employed to update the stresses and texture orientations as an integration algorithm. It considers elastic or plastic deformation gradient as the primary unknown variables and constructs the residual of the elastic and plastic velocity gradients as the governing equations. This algorithm is shown to be an efficient and robust algorithm in rather large time steps. The texture analysis of the asymmetric rolling process is also presented to show investigation of the effect of texture evolution based on the finite element analysis as a numerical example. The analysis result for texture evolution is investigated by comparing the pole figure before and after the asymmetric rolling process.