Size effect in S–N curves: A fractal approach to finite-life fatigue strength

It has experimentally been observed that the finite-life fatigue strength of metallic materials in the high-cycle regime decreases with increasing the specimen size. In the present paper, such a decrease is explained by considering the fractal nature of the reacting cross-sections of structures. Accordingly, the so-called fractal (or renormalized) fatigue strength is represented by a force amplitude acting on a surface with a fractal dimension lower than 2, where such a dimensional decrement depends on the presence of heterogeneity, cracks, defects, voids, etc. in the material ligament. Moreover, it is shown that this decrement tends to progressively diminish with increasing the structure size. Two scaling laws (monofractal and multifractal, respectively) for the finite-life fatigue strength of metals are proposed, and some experimental results are examined to show how to apply such a theoretical fractal approach.