Self-similarity and fractals in the Paris range of fatigue crack growth

There is some experimental evidence that crack propagation in certain materials submitted to fatigue loading might not conform, also in the so-called medium amplitude range, to the Paris law owing to crack-size effects on the growth rate. In the present paper, both similarity methods and fractal concepts are used to derive a crack-size dependent Paris law. Such a law is based upon the assumption of an incomplete self-similarity in the fatigue crack growth phenomenon or, on the other hand, the modelling of crack surfaces as self-similar invasive fractals.