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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 (Carpinteri et al. [1]) 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. A recent improvement of the model has been proposed (Carpinteri et al. [2]) observing that the weakest link in grained materials is usually represented by the interface between the matrix and the grains. Thus, the flaw distribution can be represented by the grain size distribution, expressed as a probability density function (PDF) of the grain diameters, rather than by an arbitrary flaw distribution. In this work, introducing the size-independent fractal cohesive model and considering micromechanical models for the critical displacement wc, we draw a link also between the fracture energy and the largest aggregate grain inside the specimen and compute the fracture energy as a function of the specimen size. The obtained scaling law is again in substantial 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.