A fractal analysis of size effect on fatigue crack growth

As is well-known, strength of materials is influenced by the specimen or structure size. In particular, several experimental campaigns have shown a decrease of the material strength under static or fatigue loading with increasing structural size, and some theoretical arguments have been proposed to interpret such a phenomenon. 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, new definitions of fracture energy and stress intensity factor based on physical dimensions different from the classical ones are discussed. Then, a size-dependent crack growth law (expressing crack growth rate against stress intensity factor range) is proposed. Finally, such a law is herein used to interpret relevant experimental data related to concrete.