Stress intensity factors and fatigue growth life of crescent-shaped cracks initiated from a spherical cavity

For various metal materials in service, fatigue cracks tend to be initiated at tiny defects such as holes and cavities, or inclusions, especially in additive manufactured or welded structures, and alloys subjected to very-high-cycle fatigue. Here we established a fracture mechanics model for crescent-shaped cracks initiated from a spherical cavity inside linear elastic solids. The stress intensity factors of the crescent crack (with shape factor a/c ranging from 0.5 to 2 and size factor a/r ranging from 0.05 to 1) and of the annular crack (with factor a/r ranging from 0.02 to 5), were comprehensively calculated using finite element method and empirically formulated for fatigue durability analyses of structures with micro-crescent-cracks initiated from spherical or similar shaped defects. Validation against experimental data of ultra-high cycle fatigue life obtained in literatures using steel specimens, where crack initiated from internal defects, shows the crescent crack model and the obtained stress intensity factor formula can make effectively prediction.