A generalized weakest-link model for size effect on strength of quasi-brittle materials

The work contributes to the statistical approach to unitedly characterize the random variation and size effect of brittle fracture strength of materials. Current practices rely on the conventional Weibull statistics and more recently on the weakest-link statistical model conforming to the uniform spatial distribution of microcracks. Based on the understanding that the weakest-link postulate is built on the mutual independence of microcracks and is not necessarily bounded to the uniform spatial distribution of microcracks, this work develops a generic weakest-link statistical formulation pertaining to a power-law spatial distribution of mutually non-interactive microcracks to synchronize the random variation and size effect of brittle fracture strength. The formulation encompasses both Weibull statistics and the uniform spatial distribution law-based weakest-link model as its subordinate members. A resultant master curve behavior between a compound parameter and the nominal fracture strength is identified for size scaling of strength and is validated by the strength data of a wide spectrum of quasi-brittle materials including wood, concrete, coal, gamma titanium aluminum alloy, nuclear-grade graphite and aluminum foam on geometrically self-similar specimens under same loading conditions.