中文摘要：

利用Stroh公式，在精确边界条件下求解二维无限大压电介质中椭圆型孔口在无穷远力-电联合载荷作用下的精确解，在此基础上利用自洽法得到裂纹的真实张开位移。基于应变能密度因子理论，研究Ⅰ型裂纹的断裂失效行为。结果表明，应变能密度因子随着电场的增加而增大，正电场加速裂纹扩展，而负电场阻止裂纹扩展。真实裂纹的应变能密度因子总是介于可导通和不可导通裂纹之间。可导通裂纹的应变能密度因子与外加电场无关，在正电场的情形下，不可导通裂纹的应变能密度因子大于可导通裂纹的应变能密度因子，而在负电场下则相反。

英文摘要：

The analytical solution of an elliptical cavity in an infinite piezoelectric medium under remotely applied combined mechanical-electrical loading is obtained under the exact boundary conditions. Based on the solution and the self-consistent method, the solution for a crack is deduced and the real crack opening is derived. The real profile of the crack opening is an elliptical curve, and the self-consistent method requires that the minor axis equals the maximum crack opening. By using the strain energy density theory, the mode Ⅰ crack is studied. The results show that the minimum strain energy density factor considering the real crack opening increases with the applied electric field, and the positive electric filed assists the occurring of fracture, while the negative electric field retards the fracture. It is demonstrated again that the impermeable crack and the permeable crack are two extremes, and the value of the minimum strain energy density factor of the real crack opening model is between those of the impermeable and permeable crack models. The minimum strain energy density factor based on the permeable crack model is independent of the applied electric field. The strain energy density factor of impermeable crack is larger than that of permeable crack for positive applied electric field, but the strain energy density factor of impermeable crack is less than that of permeable crack for negative applied electric field.