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.

中文翻译：

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不同应力比下的统一SIF以及对巴黎定律指数的物理洞察

巴黎定律已广泛用于描述稳态下的疲劳裂纹扩展 (FCG)。它建立了 FCG 率和应力强度因子 (SIF) 范围之间的关系。然而，它的物理洞察力仍然是一个有争议的问题。该研究旨在利用位错动力学来探讨与巴黎法相关的两个方面：应力比如何影响巴黎法的适用？巴黎法中巴黎指数背后的微观机制是什么？我们将我们的探索限制在理想各向同性单晶中位错成核和位错滑移主导 FCG 的情况。我们的探索表明：（1）可以采用没有经验参数的统一SIF范围来解释应力比效应，并且这一观察结果与现有实验一致；（2）SIF通过影响位错源的成核来影响FCG，裂纹尖端前的位错活动。应力依赖性位错成核时间与巴黎定律的指数相关。