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.

翻译：提出了一种基于快速傅里叶变换(FFT)的新型相场断裂框架，用于模拟微观尺度下疲劳裂纹的萌生与扩展。定义了一种基于存储能量和位错密度的损伤驱动力，将相场断裂与微观结构疲劳损伤相关联。该公式采用FFT方法进行数值实现，能够对足够大的代表性三维微观结构区域进行建模。模拟了疲劳裂纹的早期阶段，预测了裂纹路径、扩展速率及其对相关微观结构特征的敏感性。在单晶中展示了裂纹沿晶面的扩展过程，而对多晶固体的分析则揭示了穿晶裂纹萌生与晶体学裂纹扩展。