The present contribution investigates size effects on Wöhler's curve in accordance with dimensional analysis and intermediate asymptotics theory. These approaches provide a generalised equation able to interpret the specimen‐size effects on Wöhler's curve. Subsequently, using a different approach based on lacunar fractality concepts, analogous scaling laws are found for the coordinates of the limit‐points of Wöhler's curve, so that a theoretical explanation is provided to the decrement in fatigue resistance by increasing the specimen size. Eventually, the proposed models are compared with experimental data available in the Literature, which seem to confirm the advantage of applying fractal geometry to the problem.

中文翻译：

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疲劳强度的比例和分形：样品大小对沃勒曲线和疲劳极限的影响

本论文根据尺寸分析和中间渐近理论研究了尺寸对沃勒曲线的影响。这些方法提供了一个广义方程，能够解释样本大小对沃勒曲线的影响。随后，使用基于腔隙分形性概念的另一种方法，发现了类似的比例定律，用于确定沃勒曲线极限点的坐标，因此，通过增加试样尺寸可以为疲劳强度的降低提供理论解释。最终，将提出的模型与文献中提供的实验数据进行了比较，这似乎证实了将分形几何应用于该问题的优势。