A multifractal analysis of size effect on fatigue crack growth

Strength of materials is influenced by both the specimen (or structure) size and the material microstructure. In particular, several experimental tests have shown a decrease of the material strength under static or fatigue loading by increasing the structure size with respect to the size of the material microstructure. As far as fatigue crack growth is concerned, limited information on size effect is available in the literature. In the present paper, by exploiting some concepts of fractal geometry, a definition of stress intensity factor based on physical dimensions different from the classical ones is discussed. Then, a multifractal size-dependent fatigue crack growth law (expressing crack growth rate against stress intensity factor range) is proposed. Finally, such a law is used to interpret relevant experimental data related to concrete.