纵向剪切下含共焦椭圆孔椭圆夹杂中压电螺位错的干涉效应  

The interference effect between a screw dislocation and an elliptical inhomogeneity containing a confocal elliptic hole under longitudinal shear

作　　者：余敏[1,2] 刘又文[2] 宋豪鹏[2] 

机构地区：[1]中南林业科技大学流变力学与材料工程研究所,湖南长沙410004 [2]湖南大学机械与运载工程学院,湖南长沙410082

出　　处：《中南林业科技大学学报》2011年第2期115-121,共7页Journal of Central South University of Forestry & Technology

基　　金：湖南省教育厅一般项目((09C1016);中南林业科技大学青年科学研究基金项目(2009043B)

摘　　要：研究了无穷远纵向剪切和面内电势共同作用下压电螺型位错与含共焦椭圆孔椭圆夹杂的电弹干涉问题。运用复变函数的分区全纯理论、柯西型积分、应力函数奇性主部分析方法与Rieman边值理论,获得了位错位于基体区域时应力场的级数形式精确解,讨论了夹杂内部孔洞和裂纹对基体内位错干涉的扰动规律,并由此导出了位错像力以及应力强度因子(SIF)和电位移强度因子(EDIF)的解析表达式。定量分析结果表明:夹杂内部的椭圆孔对位错与夹杂的干涉起了扰动作用,明显增强了软夹杂对位错的吸引作用,降低了硬夹杂对位错的排斥作用。椭圆夹杂的形状对位错与夹杂的干涉也有着不可忽视的影响,随着椭圆夹杂曲率的增大,对位错的吸引或排斥力增大。基体中的位错对软夹杂中的钝裂纹具有反屏蔽效应,而对硬夹杂中的钝裂纹具有屏蔽效应。The interference between a screw dislocation inside the matrix and an elastic elliptical inhomogeneity which contains a confocal elliptic hole under longitudinal shear was investigated. By using the technical of conformal mapping and the method of analytic continuation, the stress fields of matrix was obtained explicitly in the series form, and the image force acting on the screw dislocation was obtained when the screw dislocation was located in the matrix. The intervention law of the interaction between holes in inhomogeneity and dislocation in matrix was discussed; therefore the analytical expressions of image force, stress intensity factor （SIF） and electric displacement intensity factor （EDIF） are calculated. As a result, quantitative analyses show that the influence of the elliptic hole on the interaction effect between a screw dislocation and an elliptical inhomogeneity was significant. The elliptic hole had strong influence on the interference between screw dislocation and inhomogeneity. It evidently strengthen the repulsion to the dislocation when the inhomogeneity was soft and weaken the attraction to the dislocation when the inhomogeneity was hard. The shape of elliptical inhomogeneity had strong influence on the interaction between screw dislocation and inhomogeneity, that as the accretion of inhomogeneity＇s curvature the repulsion or attraction force was increasing. In addition, dislocation in matrix had retardation effects on blunt crack in hard inhomogeneity and anti retardation effects in soft inhomogeneity.

关 键 词：压电螺位错 椭圆夹杂 共焦椭圆孔 复变函数方法 位错力 应力强度因子 

分 类 号：O33[理学—一般力学与力学基础]