An efficient parallel-operational explicit algorithm for Taylor-type model of rate dependent crystal plasticity

Abstract

Low computational efficiency and instability remain the greatest obstacle for crystal plasticity model applied to industrial practice. Herein, an explicit algorithm was deduced by introducing Taylor series expansion to recast the high-order nonlinear equation (for shear strain rate of slip systems) of rate dependent crystal plasticity into a set of linear equations. By virtue of a new approach to perform constitutive update in the crystallographic system, the linear model was so built with unknowns of the increments of stress and deformation resistance of slip systems. It was then solved directly by the complete pivot Gaussian elimination method within a two-level solving procedure. Full-strain-constraints (FC) Taylor model and crystal plasticity finite element method (CPFEM) model were utilized to verify the reliability, efficiency and stability of the presented algorithm. Then, texture evolution in two typical forming processes, in-plane shear and ideal plane-strain compression, was analyzed through pole figures and orientation distribution functions (ODF). The results achieved indicated that the presented algorithm was of high efficiency, especially in parallel operation with multiple CPUs, together with acceptable accuracy in the prediction of stress–strain response and texture evolution.