This study presents prediction of crack propagation in polycrystalline materials under cyclic loads using Peridynamic (PD) theory. The PD fatigue model utilizes the strain-load cycle (ε-N) data and introduces the “remaining life” of each bond calculated from its cyclic strain, which changes over time. The model also captures the traditional Paris law, which is widely used for computing the fatigue crack growth. Moreover, a new crack tip detection algorithm is introduced to adaptively detect the crack tip which is necessary for the PD fatigue model. Finally, several numerical cases are considered to investigate the effect of the strength of grain boundaries and the size of grains on the fatigue behaviour of polycrystalline materials.

这项研究提出了使用周期性动力学（PD）理论预测在循环载荷下多晶材料中裂纹扩展的方法。PD疲劳模型利用应变-载荷循环（ε-N）数据，并引入了根据其循环应变计算出的每个键的“剩余寿命”，其随时间变化。该模型还捕获了传统的巴黎定律，该定律被广泛用于计算疲劳裂纹扩展。此外，引入了新的裂纹尖端检测算法来自适应地检测PD疲劳模型所需的裂纹尖端。最后，考虑了几个数值案例来研究晶界强度和晶粒尺寸对多晶材料疲劳行为的影响。