【作者】 李冬；

【导师】 宋天舒；

【作者基本信息】 哈尔滨工程大学 ， 结构工程， 2008， 硕士

【摘要】 由于存在力和电的耦合作用,特别是在动力学问题中,压电材料的电致疲劳和电致裂纹情况时有发生,因而对压电材料中断裂行为的研究越来越受到重视。本文采用Green函数方法研究了含界面裂纹的双相压电材料受SH波和面内电位移联合作用时的动力反平面问题。首要工作是构造一个适合于本文问题的位移Green函数和电位势Green函数,它们应当是各向同性压电材料的弹性半空间在其水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移场的解答和在任意一点放置一沿z轴的正电荷线源时电位势函数的基本解。有了Green函数这一工具,就可以求解一类界面缺陷及复杂缺陷对SH波的动态响应问题。一般在求解过程中,将问题的模型视为“契合”问题:即将其剖分为两个压电介质的弹性半空间,分别在其剖分面上加置未知的出平面荷载,并在欲出现裂纹位置加置出平面反力使之产生可导通裂纹,利用Green函数写出界面位移的连续性条件,建立决定未知外力系的第一类Fredholm积分方程组。对于界面裂纹问题,裂纹尖端点的附加外力系可以代换成应力强度因子,这样采用直接离散的办法将定解积分方程组转化为线性代数方程组后,就可以直接求解出动应力强度因子的值。就典型问题给出了具体的算例结果,讨论了不同波数条件、不同外加电位移强度、不同材料常数组合对界面裂纹动应力强度因子的影响,部分计算结果与其他文献进行了比较。更多还原

【Abstract】 As a result of the behaviors of electromechanical coupling, especially in the dynamic problems, fracture or failure often occurs prematurely in newly developed piezoelectric materials. More attention is paid to the investigation of the failure behaviors on piezoelectric materials.This paper provides a comprehensive treatment of the dynamic character caused by an interface crack in piezoelectric bi-materials under steady-state inplane electrical and antiplane mechanical loads based on Green’s function method. The first important step is to develop a couple of suitable Green’s functions, which are fundamental solutions of elastic displacement field and electric potential field for a semi-infinite piezoelectric medium impacted by a pair of time-harmonic line force and line charge at the surface, respectively. Once the special Green’s functions are obtained, various dynamic response problems of SH-waves by a kind of interface blemish or complex flaw can be solved. The model of the problem is composed of two semi-infinite piezoelectric media. Then additional anti-plane forces are applied at the interface in order to satisfy boundary continuity conditions. While the crack can be made in this method, which meets traction free condition at the crack’s surface. A series of Fredholm integral equations of first kind for determining the unknown forces can be established by solving boundary value problem. The added force at the interface crack tip can be replaced by expression including dynamic stress intensity factor. The integral equations for determining the unknown forces can be transformed into algebraic equations. Some cases are calculated and the results are graphically presented. The calculation results show the influence of wave number, applied inplane electrical loads and combination of different materials and geometric parameters upon dynamic stress intensity factors. Some of them are compared with other published documents.更多还原