A statistical dislocation theory of brittle fracture of crystals is suggested. The process of brittle fracture is described as a stochastic process by which microcracks form, grow and propagate under very small plastic deformation. A differential equation describing this stochastic process is derived, and a statistical distribution function of microcrack size is obtained.A quantitative description of the important part played by the plastic deformation and work hardening and the number of active slip sources in the process of brittle fracture is given. In the past, the effect of plastic deformation was only ambiguously included in the conception of effective surface energy, and the effect of work hardening and the number of active slip sources had been neglected.The statistical distribution function of fracture strength is derived from statistical distribution function of microcrack size and the condition of microcrack propagation, and from which the criteria of brittle fracture, brittle strength and brittle-ductile transition temperature have been deduced.
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