双压电材料内含椭圆孔孔边界面裂纹的反平面问题

利用复变函数方法，研究了横观各向同性压电双材料中椭圆孔孔边界面裂纹的反平面问题．首先，利用保角变换函数将椭圆孔保角变换到一直线裂纹；其次，基于孔边及裂纹表面均电不可穿透并且自由的假设，利用Stroh公式分别得到了本问题的复势函数、裂尖场集中系数的解析表达式；最后，在面内电载荷及面外机械载荷的作用下，分析了椭圆孔尺寸、裂纹长度和外载对裂尖场集中系数的影响，并得到了一个有意义的结论：椭圆孔一边裂纹长度的改变对另一边裂纹裂尖场的影响有限，然而一旦椭圆孔退化为竖直裂纹，该影响将变得非常显著．

The Anti-Plane Problem for a Cracked Elliptical Hole at the Interface of Bi-Materials

By using the complex variable method, the problem of an elliptical hole with edge cracks at the interface of the transversely isotropic piezolelctric bi-materials was studied. Firstly, the mapping function which maps the ellipse to a line crack was obtained. Secondly, based on the assumption that the surface of the cracks and hole is electrically impermeable and traction-free, the expressions for the complex potential, and the fields intensity factors were presented by using the Stroh formulation, respectively. Finaly, under the electric and the mechanical loadding, the influences of the hole size, the crack length and the mechanical/electric loading on the field intensity factors were analysed. An interesting result was obtained: the effect of changing of one side crack length on the other crack tip’s fields was limited for the elliptical hole. However, once the elliptical hole degenerates into a vertical crack, this effect becomes very significant.