Abstract
A Statistical theory of material strength is proposed. Materials are considered to be imperfect heterogeneous continua composed of discrete volume elements whose characteristics are related to material structure and imperfections. The strength of the elements is assumed to be a statistic a quantity, and as the material is loaded elements fracture randomly throughout the body causing localized stress concentrations. The accumulation of these breaks results in overall failure. By relating strength to material structure this theory attempts to bridge the gap between the microscopic and continuum approaches to fracture mechanics. The theory is applied to composite materials reinforced with whiskers and continuous fibers. Comparisons with experimental data show good agreement. Results for whisker-reinforced composites appear to provide a good prediction of strength and an explanation of the disparity between the strength of individual whiskers and the strength of the composites made from them.
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