含非完整界面的功能梯度压电材料Ⅲ型裂纹问题  

Mode-Ⅲ Crack Problems for Two Bonded Functionally Graded Piezoelectric Materials with Imperfect Interface

作　　者：李冉 万永平[1] LI Ran;WAN Yongping(School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学航空航天与力学学院

出　　处：《力学季刊》2019年第4期740-752,共13页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11832014)

摘　　要：本文研究了含非完整界面的功能梯度压电复合材料的Ⅲ型裂纹问题.此裂纹垂直于非完整界面,采用弹簧型力电耦合界面模型模拟非完整界面.界面两侧材料的性质,如弹性模量、压电常数和介电常数均假定呈指数函数形式且沿着裂纹方向变化.运用积分变换法将裂纹面条件转换为奇异积分方程,并使用Gauss-Chebyshev方法对其进行数值求解.根据算例结果讨论了一些退化问题并分析了裂纹尖端强度因子与材料的非均匀系数和非完整界面参数的关系.A mode-Ⅲ crack inside one part of the two infinite different functionally graded piezoelectric material with imperfect interface is investigated.The crack is assumed to be perpendicular to the imperfect interface which is characterized by a coupled imperfect interfacial model.The properties of two materials,such as elastic modulus,piezoelectric constant and dielectric constant,are assumed to vary in exponential forms along the crack direction.The Fourier Integral transform method are used to transform the crack surface conditions to the singular integral equations,which can be solved by using the Gauss-Chebyshev integration technique.The influences of the material non-homogeneity parameters as well as the imperfect interface parameters on the stress intensity factors are discussed.The solutions for some degenerated problems are also obtained and discussed.

关 键 词：压电功能梯度复合材料 非完整界面 积分变换 奇异积分方程 应力强度因子 

分 类 号：O346.1[理学—固体力学]