Scale effects on strength and toughness of grained materials: An extreme value theory approach

Abstract

The present paper provides a statistical model to the size effect on grained materials tensile strength and fracture energy. It has been already demonstrated by using extreme value theory that the scaling law obtained for the tensile strength introducing a doubly truncated distribution of flaws, under the hypothesis of Weibull's weakest link, resembles the Multi-Fractal Scaling Law (MFSL), already proposed by the first Author through fractal concepts. Since the weakest link in grained materials is usually represented by the interface between the matrix and the grains, in the present paper we assume that the flaw distribution can be represented by the grain size distribution, rather than by an arbitrary flaw distribution. Furthermore, introducing a micromechanical model for the critical displacement w_c, we draw a link between the fracture energy and the largest aggregate grain on crack surfaces. In this way we are able to compute the tensile strength and the fracture energy as a function of the specimen size. The obtained scaling laws are substantially in agreement with the MFSL for the fracture energy proposed by the first Author. A further result provided by the proposed approach is the description of the scatter increase of both tensile strength and fracture energy values when testing small specimens. This trend is confirmed by experimental data available in the literature. Eventually, the influence of the aggregate grading upon the size effect for strength and toughness is analyzed.