A Statistical Theory of Fracture in a Two-Phase Brittle Material

A statistical theory of a two-phase material consisting of a brittle matrix with a dispersion of tougher second-phase particles is developed. In this material, failure does not occur immediately a microfracture is initiated at a flaw in the matrix. Stable cracks spanning the second-phase particles are possible and many will form before final failure occurs, especially in large specimens. The expected number of such cracks that are formed at any stress level is calculated. The statistical strength distribution for specimens under both tension and bending is obtained. It is shown that in a two-phase material the ratio of bending to tensile strength of a beam decreases with size, whatever flaw-size distribution is assumed.