压电复合材料圆形夹杂中螺型位错和界面裂纹的干涉分析  

Analysis of a Screw Dislocation Inside a Circular Inclusion With Interfacial Cracks in Piezoelectric Composites

作　　者：郑健龙[1] 方棋洪[2] 刘又文[2] 

机构地区：[1]长沙理工大学公路工程学院,长沙410076 [2]湖南大学工程力学系,长沙410082

出　　处：《应用数学和力学》2005年第8期957-964,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10472030)

摘　　要：研究了无穷远纵向剪切和面内电场共同作用下,压电复合材料圆形夹杂中螺型位错与界面裂纹的电弹耦合干涉作用.运用Riemann_Schwarz对称原理,并结合复变函数奇性主部分析方法,获得了该问题的一般解答.作为典型算例,求出了界面含一条裂纹时基体和夹杂区域复势函数和电弹性场的封闭形式解.应用广义Peach_Koehler公式,导出了位错力的解析表达式.分析了裂纹几何参数和材料的电弹性常数对位错力的影响规律.结果表明,界面裂纹对位错力和位错平衡位置有很强的扰动效应,当界面裂纹长度达到临界值时,可以改变位错力的方向.该结果可以作为格林函数研究圆形夹杂内裂纹和界面裂纹的干涉效应.其公式的退化结果与已有文献完全一致.The electroelastic interaction of a screw dislocation inside a circular inclusion with interfacial cracks in piezoelectric composite materials under anti_plane shear and in_plane electric loads at infinity is investigated. The general solution to this problem was obtained by means of Riemann_Schwarz's symmetry principle integrated with analysis of singularities of corresponding complex potentials. As a typical example, closed form expressions of the complex potentials and electroelastic field components in the matrix and inhomogeneity regions were derived explicitly when the interface contains a single crack. The image force acting on the screw dislocation was calculated by using the generalized Peach_Koehler formula. The influence of interfacial crack geometry and piezoelectric material property combinations upon the image force was discussed in detail. The results show that interfacial crack has significant perturbation effect on the image force and the equilibrium position of the screw dislocation. The presence of the interfacial crack can change the direction of the image force when the length of the crack goes up to a critical value. The obtained explicit solutions can be used as Green's functions to study the problem on the interaction between interfacial cracks and arbitrary shape crack inside the inclusion. The present solutions can lead to previously known results as the special case.

关 键 词：螺型位错 界面裂纹 复变函数方法 位错力 

分 类 号：O343.7[理学—固体力学]