A STATISTICAL THEORY OF BRITTLE FRACTURE
脆性断裂统计理论

A statistical approach is proposed in order to establish a connection between microscopic process and macroscopic process of brittle fracture, and an attempt is made to base the theory of brittle fracture on the statistical foundation of micro-crack kinetics.The brittle fracture is described as a non-equilibrium process in which micro-cracks nucleate and grow, and the single main crack propagates under very small plastic deformation.A differential-integral equation describing this non-equilibrium process is derived. The micro-crack kinetics is studied from the dislocation mechanism. The statistical distribution function of micro-cracks and the fracture probability of metal sample are obtained, and thus the elongation, brittle strength, ductile work, fracture toughness, critical crack length, ductile-brittle transition temperature and their statistical deviation are all deduced theoretically.