Shima Hiroyuki, Umeno Yoshitaka, Sumigawa Takashi
Department of Environmental Sciences, University of Yamanashi, 4-4-37, Takeda, Kofu, Yamanashi 400-8510, Japan.
Institute of Industrial Science, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8505, Japan.
R Soc Open Sci. 2022 Jun 8;9(6):220151. doi: 10.1098/rsos.220151. eCollection 2022 Jun.
Explicit and tractable formulation of the internal stress field around edge dislocations is indispensable for considering the mechanics of fine crystalline solids, because the motion of edge dislocations in a slanted direction with respect to the free surface often plays a vital role in the plastic deformation of the solids under loading. In this study, we formulated an analytical solution for the stress distribution that occurs around edge dislocations embedded in a semi-infinite elastic medium. This formulation is based on the image force method and the Airy stress function method; it describes the variation in the stress distribution with changes in the slanted angle between the traction-free flat surface of the medium and the Burgers vector of the edge dislocation. Furthermore, our analytical solution shows that the attractive force acting on the edge dislocation due to the presence of the free surface is always perpendicular to the surface, regardless of the relative angle of the Burgers vector with the surface.
对于考虑细晶固体的力学特性而言，明确且易于处理的刃型位错周围内应力场公式不可或缺，因为相对于自由表面沿倾斜方向的刃型位错运动在加载下固体的塑性变形中往往起着至关重要的作用。在本研究中，我们针对嵌入半无限弹性介质中的刃型位错周围出现的应力分布制定了一种解析解。该公式基于镜像力法和艾里应力函数法；它描述了应力分布随介质无牵引平面与刃型位错的柏氏矢量之间倾斜角度变化的情况。此外，我们的解析解表明，由于自由表面的存在而作用在刃型位错上的吸引力始终垂直于表面，而与柏氏矢量相对于表面的相对角度无关。
