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本文试图从位错理论出发来探索晶体脆性断裂的统计理论。脆性断裂过程,实质上是微裂缝在极小的范性形变过程中形成长大和传播的随机过程。本文导出了描述这种随机过程的微分方程,利用微裂缝形成长大的位错机理,解出了微裂缝大小的统计分布函数。文中给出了范性形变、加工硬化和活动位错源数目与微裂缝数目和大小之间的函数关系。过去研究脆性断裂时,范性变形只是含糊地包括在有效表面能之内,而加工硬化和活动位错源数目则一向被略去。从微裂缝大小的统计分布函数和微裂缝的传播条件,导出了强度的统计分布函数,从而求得了脆性断裂判别式、脆性断裂强度及脆性-范性转变温度。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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