A multifractal analysis of fatigue crack growth and its application to concrete

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 structure 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, particularly for so-called quasi-brittle materials like concrete. In the present paper, by exploiting concepts of fractal geometry, some definitions of fracture energy and stress intensity factor based on physical dimensions different from the classical ones are discussed. A multifractal size-dependent fatigue crack growth law (expressing crack growth rate against stress intensity factor range) is proposed and used to interpret relevant experimental data related to concrete.