Size effect upon grained materials tensile strength: The increase of the statistical dispersion at the smaller scales

The present paper provides a statistical model to the size effect on grained materials tensile strength; it is based on an Extreme Value Theory approach. Since the weakest link in grained materials is usually represented by the interface between the matrix and the aggregates, it is assumed that the flaw distribution can be represented by the aggregate distribution, expressed as a probability density function (pdf) of the grain diameters. Under the hypothesis that the strength of the material depends on the largest flaw, the tensile strength is computed as a function of the specimen size. In this way, two remarkable results are obtained: (i) a size effect for the average tensile strength that substantially agrees with the multifractal scaling law (MFSL) proposed by the first author and (ii) an increase of scatter of the tensile strength values when testing small specimens. Both these trends are confirmed by experimental data available in the literature.