三维压电介质中不同电边界条件的裂纹分析  

CRACK ANALYSIS OF DIFFERENT ELECTRIC BOUNDARY CONDITIONS IN THREE-DIMENSIONAL TRANSVERSELY ISOTROPIC PIEZOELECTRIC MEDIA

作　　者：赵明皞[1] 韩海涛 

机构地区：[1]郑州机械研究所,郑州450052 [2]郑州纺织机械厂,郑州450053

出　　处：《机械强度》2003年第4期445-449,共5页Journal of Mechanical Strength

基　　金：河南省杰出青年科学基金资助项目~~

摘　　要：在不可导通、可导通和半可导通等三种电边界条件下 ,系统研究并给出三维无限横观各向同性压电介质中平行于各向同性面的、任意形状的平片裂纹在任意载荷作用下的不连续位移和不连续电势边界积分方程方法。无论平片裂纹的形状如何 ,结果都表明 :对不可导通裂纹 ,应力强度因子只与机械载荷有关 ,电位移强度因子只与电载荷有关 ;而可导通裂纹的应力强度因子和电位移强度因子只与机械载荷有关 ,电位移强度因子由机械载荷通过压电效应产生。半可导通裂纹所对应的边界积分方程组为非线性方程组 ,文中给出一种迭代解法。在均布的机械载荷和电载荷作用下 ,裂纹腔内的电位移为一常数 ,只与外加载荷有关 。The displacement discontinuity and electric potential discontinuity boundary integral equation method is presented for a planar crack of arbitrary shape in a three-dimensional transversely isotropic piezoelectric medium. The planar crack is parallel to the plane of the isotropy of the medium. Three types of electric boundary conditions, i.e., electrically impermeable, permeable and semi-permeable cracks, are considered on the crack faces. The results show that the stress intensity factor depends only on the mechanical loading, while the electric displacement intensity factor depends only on the electric loading for impermeable cracks. For permeable cracks,however, both the stress and the electric displacement intensity factors are all related to the mechanical loading and independent of the electric loading, and the electric displacement intensity factor is induced by piezoelectric effect. Under the electrically semi-permeable condition, the boundary value problem is non-linear, and an iterative method is presented to solve the non-linear boundary integral equations. For the case of uniformly distributed applied mechanical and electrical loadings on the crack faces, the results demonstrate that the electric displacement in the cavity of the crack is a constant depending on the applied loadings, but independent of the crack shape.

关 键 词：压电介质 平片裂纹 边界积分方程 强度因子 超奇异积分 

分 类 号：TB381[一般工业技术—材料科学与工程] O346[理学—固体力学]