压电多层材料中的电极-陶瓷界面裂纹和椭圆夹杂  

ELECTRODE-CERAMIC INTERFACIAL CRACKS AND ELLIPTICAL INCLUSION IN PIEZOELECTRIC MULTILAYER MATERIALS

作　　者：王旭[1] 沈亚鹏[1] 

机构地区：[1]西安交通大学工程力学系,西安710049

出　　处：《力学学报》2002年第6期881-894,共14页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10132010)资助项目。

摘　　要：首先解析研究了压电多层材料中的电极-陶瓷界面裂纹,它是对Ru最近研究工作（见ASMB J·APPI.Mech.,2000年,67卷）的补充和完善.工作表明与 Ru的结论不同,对于一般的两相压电介质,仍可获得对于这种电极-陶瓷界面裂纹的精确解答.分析显示在界面处的电弹性场仍可显现出两类奇异性:振荡型奇异性一1/2土iε。和实指数型奇异性一1/2士 k,其中ε和k 由上下两相压电材料的本构常数加以确定.获得了界面电弹性场以及裂尖处能量释放率的显式和实形式解答.也讨论了在坐标变换下界面上物理量的一些不变性质.其次探讨了压电多层材料中的椭圆夹杂问题,并获得了当压电复合系统受到远场均布机电载荷时的通解.分析表明当压电基体受到远场均布机电载荷作用时。As supplement and perfection to Ru's most recent research effort, the interface cracks between embedded compliant electrode layer and anisotropic piezoelectric ceramic matrix is strictly analyzed in this paper. It is demonstrated that contrary to Ru's statement, an exact elementary solution to this interface crack problem can still be obtained when the bimaterials are general anisotropic piezoelectric ceramics. The analyses show that the electroelastic fields on the interface exhibit two kinds of singularities: oscillatory singularity -l/2眎e and real power form singularity ?1/2 ?k, here e and k are two small and real quantities determined by the constitutive constants of the bimaterials. Explicit and real form solutions to the interfacial electroelastic fields and energy release rate at the crack tip are also obtained. In addition, some invariant properties of the solutions under coordinate transformation are discussed. The problem of piezoelectric elliptical inclusion in multilayer piezoelectric materials is also solved. General solutions for the case in which the piezoelectric matrix is subject to remote uniform loading are derived respectively. The present work shows that electroelastic fields within the elliptical inclusion are still uniformly distributed and that the elliptical inclusion is an equi-potential body when the piezoelectric matrix is subject to remote uniform electro-mechanical loading.

关 键 词：压电多层材料 电极-陶瓷界面裂纹 椭圆夹杂 混合边值问题 Stroh公式 

分 类 号：TM22[一般工业技术—材料科学与工程]