Abstract

Mechanics of defects in solids across a wide span of length scales is commonly formulated using the dislocations theory. This paper revisits the classical problem of interaction between an elastic edge dislocation and a circular cavity. A heuristic, yet, mechanistic approach is taken to obtain the stress solution to this problem. The approach uses complex variable theory of elasticity, along with method of images. For this purpose, a definition and formulation of elastic dipole singularities similar to dipole charges in electrostatics is developed. It is shown that an image dislocation with Burger’s vector of the same strength as the real dislocation but in opposite direction, as well as a set of four singularities including a dislocation dipole, a moment-dilatation dipole, and two centers of dilatation would establish a circular, traction-free boundary in an infinite elastic medium. Adding a Volterra dislocation to the finite-length edge dislocation from this study would recover the related problem of interaction between an infinite-length edge dislocation and circular cavity. The interesting analogy between the considered elastic problem and the electrostatic problem of interaction between a line electric charge and a cylindrical conductor is discussed.

中文翻译：

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晶体固体中边缘错位和圆形腔的图像求解方法

摘要

通常使用位错理论来公式化在各种长度范围内的固体中的缺陷力学。本文回顾了弹性边缘位错与圆形腔之间相互作用的经典问题。采取了一种启发式但机械的方法来获得该问题的应力解决方案。该方法使用弹性的复杂变量理论以及图像方法。为此，开发了类似于静电中的偶极电荷的弹性偶极奇异性的定义和公式。结果表明，具有与真实位错强度相同但方向相反的Burger向量的图像位错，以及包括位错偶极子，矩扩张偶极子和两个扩张中心的四个奇异点的集合，将建立一个圆，无限弹性介质中的无牵引力边界。从这项研究中将Volterra位错添加到有限长边缘位错中，将恢复无限长边缘位错与圆形腔之间相互作用的相关问题。讨论了所考虑的弹性问题和线电荷与圆柱导体之间相互作用的静电问题之间的有趣比喻。