Statistical strength of brittle materials with strongly interacted collinear microcracks

The coalescing process from microcracks to a fatal macroscopic crack is dominated by the strong interaction among neighbouring microcracks. The distribution of microcracks modifies the strength and toughness of a brittle material. The present paper focuses on the case of strongly interacting collinear microcracks, and quantifies the influence by the statistical distributions of crack lengths and ligament sizes. The strength of a brittle solid decreases as the standard deviation of those distributions increases. Furthermore, we predict the scale dependency of brittle materials: a specimen of large size would have lower strength than a small specimen with the same microcrack density. The analysis indicates that the statistical strength of a brittle material with strongly interacting collinear microcracks can be correlated by a three-parameter Weibull distribution.