The present contribution investigates the crack‐size effects on Paris' law in accordance with dimensional analysis and intermediate asymptotics theory, which makes it possible to obtain a generalised equation able to provide an interpretation to the various empirical power‐laws available in the Literature. Subsequently, within the framework of fractal geometry, scaling laws are determined for the coordinates of the limit‐points of Paris' curve so that a theoretical explanation is provided to the so‐called short cracks problem. Eventually, the proposed models are compared with experimental data available in the literature which seem to confirm the advantage of applying a fractal model to the fatigue problem.

中文翻译：

---

亚临界疲劳裂纹扩展中的尺度和分形：裂纹尺寸对巴黎定律和疲劳阈值的影响

本论文根据尺寸分析和中间渐近理论研究了裂纹尺寸对巴黎定律的影响，这使得有可能获得一个广义方程，该方程能够为文献中的各种经验幂定律提供解释。随后，在分形几何学的框架内，确定了巴黎曲线极限点坐标的定标定律，从而为所谓的短裂纹问题提供了理论解释。最终，将提出的模型与文献中的实验数据进行了比较，这些数据似乎证实了将分形模型应用于疲劳问题的优势。