A statistical strength criterion for low temperature brittle fracture of metals

A statistical approach is presented to strength analysis of metals under conditions of low-temperature embrittlement. The approach involves two categories of defects leading to fracture: primary defects, present in the original structure in the form of microvoids, microcracks, inclusions etc., and secondary defects, formed under load through the action of the dislocational mechanisms involved in initiation of crack nuclei.An arbitrary pattern of primary and secondary defects is considered, on the assumption of approximate stochastic independence. This permits determination of the probability of brittle fracture under any mode of stressing. Development of a major crack is treated as a multistage process, whereby fracture may be considered either as a sequence of violated limit equilibria, or as a discontinuous Markov process. The role of thermal fluctuations in the latter case is demonstrated. As an example, limiting fracture-stress curves are determined for a plane model based on Stroh's mechanism. Results show that the temperature dependence of the fracture stress is governed by the mode of stressing and by the structure of the material.