Fatigue crack initiation and propagation in highly heterogeneous titanium alloys at polycrystal microstructural scale is essential for aerospace applications. However, simulations of cracking in polycrystalline-microstructures require modeling complex crack topologies, e.g. crack deflection at grain boundaries, branching, and interactions with slip bands. In this work, a coupled crystal-plasticity-phase field approach is developed to overcome the difficulties. The phase field method introduces a continuous auxiliary global field to approximate the sharp crack discontinuity. It does not require any artificial criteria, and the crack propagation rate and path are the natural outcomes from thermodynamics analysis and the gamma-convergent approximation of Helmholtz free energy. Promising results are obtained in crack propagation and stress-strain response in benchmark mode I & II fracture and three-point bending tests.
The difficulties of this method appear in numerical feasibility. Solving phase field using classical FEM has the heavy restriction that the mesh must be ultra-fine to capture the high gradient of the phase field variable that represents sharp cracks, which implies a prohibitive computational cost to simulate large grain number polycrystals. To overcome this problem, a novel wavelet-based adaptive hierarchical FEM method is developed, which uses 2nd generation wavelet functions to locally enhance the phase field resolution according to the evolution of problem. The preliminary results showed a significant reduction in the computational cost without sacrificing the accuracy.