Theoretical aspects of the statistical variation of strength

Abstract

A modified version of Weibull's statistical theory of the strength of brittle materials is proposed, in which the expression for failure probability contains an additional term. While this term is negligible when failure originates from a flaw of relatively large size, it becomes increasingly significant as the flaw size is reduced. The resulting revised expressions for failure probability under uniform, uniaxial tension and under Hertzian indentation loading are given, and the effect of a bimodal flaw size distribution is considered in both cases. The implications with regard to the assumed invariance of Weibull statistical parameters under different experimental conditions are discussed.