Modeling and Simulation of Fatigue Crack Initiation Process Based on Field Theory of Multiscale Plasticity (FTMP) Part II: Modeling Vacancy Formation and Coupling with Diffusion Analysis

Cyclic straining simulations using incompatibility-incorporated crystal plasticity-FEM, which exhibit PSB ladder structure evolutions as detailed in Part I, are coupled with diffusion analyses of produced vacancies. We introduce a new vacancy source model based on the Field Theory of Multiscale Plasticity (FTMP), interpreting the relationship between the incompatibility rate and the flux of dislocation density as edge dipole annihilation processes. Both direct and indirect coupling diffusion analyses, with and without cyclic straining, demonstrate that varying incompatibility rates tend to further promote vacancy diffusion, leading to surface grooving, enhanced extension rates, and eventual transition to cracks. The findings reveal that: (i) the evolved PSB ladder structure serves as a site for vacancy formation, (ii) it provides a diffusion path toward the specimen surface, and (iii) it significantly enhances groove extension rates. These factors effectively facilitate the transition from a "groove" to a "crack," evidenced by the abrupt acceleration of the extension rate, mirroring systematic experimental observations by Nakai et al. These achievements validate the FTMP's capability to simulate complex phenomena and significantly deepen our understanding of slip band-fatigue crack transition mechanisms.