  A novel FFT-based phase-field fracture framework for modelling fatigue crack
initiation and propagation at the microscale is presented. A damage driving
force is defined based on the stored energy and dislocation density, relating
phase-field fracture with microstructural fatigue damage. The formulation is
numerically implemented using FFT methods to enable modelling of sufficiently
large, representative 3D microstructural regions. The early stages of fatigue
cracking are simulated, predicting crack paths, growth rates and sensitivity to
relevant microstructural features. Crack propagation through crystallographic
planes is shown in single crystals, while the analysis of polycrystalline
solids reveals transgranular crack initiation and crystallographic crack
growth.
