A robust integration algorithm for implementing rate dependent crystal plasticity into explicit finite element method

Severe numerical instability in the integration of rate dependent crystal plasticity (RDCP) model is one of the main problems for implementing RDCP into finite element method (FEM), especially for simulating dynamic/transient forming process containing complicated contact conditions under large step length, large strain and high strain rate. In order to overcome the problem, an implicit model is deduced with the primary unknowns of shear strain increments of slip systems under the corotational coordinate system in the paper. The homotopy auto-changing continuation method combined with the Newton–Raphson (N–R) iteration is adopted. The subroutine VUMAT is developed for implementing RDCP model in ABAQUS/Explicit. Simulation results show that the algorithm is stable and accurate in 3D FE simulations on both dynamic simple loading and complicated loading process containing nonlinear contacts under the conditions of the maximal step length of 3.5 × 10⁻⁶ s, the maximal strain of 1.05, the maximal loading speed of 120 mm s⁻¹, and the minimal material rate sensitivity coefficient of 0.01. The predictions of the model on crystal behaviors of anisotropy, rate sensitivity and elasticity, as well as ear profiles in deep cup drawing are in agreement with experiments.