正交异性压电双材料反平面界面裂纹应力分析

Stress Analysis of Antiplane Interface Crack in Orthotropic Piezoelectric Bimaterial

分析了正交异性压电双材料在反平面无穷远处机械载荷和面内电载荷作用下的反平面界面中心裂纹,通过运用复合函数法和待定系数法,使双层板反平面界面中心裂纹尖端断裂转换为求解偏微分方程组的边值问题,求解边值偏微分方程组,在裂纹尖端邻近,对相应电位移强度因子和应力强度因子进行定义,从而得到应力场、电位移场、应力强度因子、电位移强度因子表达式。结果表明应力总是促进裂纹扩展,应力强度因子、电位移强度因子和能量释放率与力电载荷、裂纹长度有关。数值研究了机械能应变释放率与材料参数的差异、外加载荷、裂纹长度之间的关系。

In this paper,the anti-plane interface central crack problem of orthotropic piezoelectric bimaterials subjected to mechanical and in-plane electric loads at infinity of the antiplane is studied. The fracture problem of the anti-plane interface crack tip of the piezoelectric bimaterials is transformed into a boundary value problem for solving partial differential equations using the composite function method and the undetermined coefficient method.The expressions of stress intensity factor,electric displacement intensity factor,stress field and electric displacement field are obtained by solving partial differential equation and defining stress intensity factor and electric displacement intensity factor near crack tip. The results show that the stress always promotes the crack propagation,and the stress intensity factor and energy release rate are related to the electromechanical load and crack length. The effects of material parameters,crack length and external loading on strain release rate of mechanical energy are numerically analyzed.