有限高狭长压电体中共线双半无限裂纹问题的解析解

Exact Solutions of Two Semi-Infinite Collinear Cracks in a Piezoelectric Strip

通过引入合适的保角变换,利用复变函数法,分析了部分裂纹面上受反平面剪应力和面内电载荷共同作用下有限高狭长压电体中含共线双半无限裂纹问题,导出了电不可通边界条件下两个裂纹尖端场强度因子和机械应变能释放率的解析解.当不考虑电场作用时,所得解可退化到经典弹性材料的情况.而当两裂纹尖端的距离趋于无穷大时,也可退化为狭长压电体中半无限裂纹问题的解.最后,通过数值算例,讨论了受载长度、狭长体高度、机电载荷对机械应变能释放率的影响规律以及两个裂纹之间的相互作用.结果表明,两裂纹尖端的距离越短,材料越容易破坏;且机电载荷对左尖端裂纹的扩展影响更为显著.

Using the complex variable function method and the technique of the conformal mapping, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip was studied under the anti-plane shear stress and in-plane electric load on the partial crack surface. The analytic solutions of the field intensity factors and the mechanical strain energy release rate were derived under the assumption that the surface of crack was electrically impermeable. The present results can be reduced to the well-known solutions for a purely elastic material in the absence of electric load. Moreover, when the distance between the two crack tips tends to infinity, the analytic solutions of a semi-infinite crack in a piezoelectric strip were obtained. Finally, numeriCal examples were given to show the influences of the loaded crack length, the height of strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It shows that the material is easier to fail when the distance between the two crack tips becomes shorter. Moreover, the mechanical/electric loading has greater influence on the propagation of the left crack than that of the right one.