Unified SIF at different stress ratios and the physical insight on the exponent of the Paris law

The Paris law has been broadly employed to describe fatigue crack growth (FCG) at steady state. It establishes the relationship between FCG rate and stress intensity factor (SIF) range. However, its physical insight remains an issue of controversy. The study aims to employ dislocation dynamics to explore two aspects associated with the Paris law: how does the stress-ratio affect the application of the Paris law? What is the microcosmic mechanism behind the Paris exponent in Paris law? We limit our exploration on the scenarios that dislocation nucleation and dislocation glide dominate FCG in an ideally isotropic single crystallite. Our exploration revealed that (1) a unified SIF range without empirical parameters could be adopted to account for the stress ratio effect, and this observation is in line with existing experiments, and (2) SIF affects FCG by influencing the nucleation of dislocation sources and activity of dislocations before crack tips. The stress-dependent dislocation nucleation time is correlated with the exponent of the Paris law.