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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。
This article attempts to explore the statistical theory of brittle fracture of crystal from the dislocation theory. The brittle fracture process is essentially a stochastic process in which microcracks form and propagate during the extremely small normal deformation. In this paper, the differential equation describing the stochastic process is deduced, and the statistical distribution function of the size of microcracks is solved by using the dislocation mechanism of microcrack growth. In this paper, the relationship between the number of normal deformation, work hardening and the number of active dislocations and the number and size of micro-cracks is given. In the past when studying brittle fracture, the normal deformation was only vaguely included in the effective surface energy, while the number of work hardening and dislocation sources was always omitted. According to the statistical distribution function of microcrack size and the propagation condition of microcracks, the statistical distribution function of strength is derived, and the brittle fracture criterion, the brittle fracture strength and the brittleness - transition temperature are obtained.