Wavelet-enriched adaptive hierarchical FE model for coupled crystal plasticity-phase field modeling of crack propagation in polycrystalline microstructures

Abstract

This paper develops a novel, wavelet-enriched adaptive finite element model for solving coupled crystal plasticity-phase field models to simulate crack propagation in polycrystalline microstructures. No a-priori assumption of the crack path is needed. Crack propagation under conditions of finite deformation is driven by stored elastic energy that accounts for material anisotropy and tension–compression asymmetry, and defect energy resulting from slip system dislocation glide and hardening. The resulting finite element model is capable of simulating both brittle and ductile crack propagation in material microstructures. A major contribution of this work is the creation of the adaptive, multi-resolution wavelet-based hierarchical enrichment of the FE model. The adapted enrichment follows the path of crack growth and is able to successfully overcome the challenges of high resolution required for the regularized crack in the coupled model. The multi-resolution wavelet basis functions adaptively construct optimal enrichment basis for the high gradients in the phase field order parameter near the crack path. The wavelet-enriched adaptive finite element model is found to be robust with excellent convergence characteristics in multiple validation tests conducted with the polycrystalline Ti–6V–4Al alloy.