有限宽狭长压电基体中单边裂纹问题分析

Analysis of a finite width piezoelectric strip with a single edge crack

为了研究有限宽狭长压电复合材料基体中单边裂纹面上受反平面剪应力和面内电载荷共同作用,采用保角变换和复变函数方法,给出电不可通边界条件下裂纹尖端场应力强度因子和机械能释放率的解析解.当狭长体的宽度增大到一定程度时,可得到无限大压电体中边裂纹的解析解.通过数值算例,分析裂纹长度、狭长体宽度以及机电载荷对机械应变能释放率的影响规律.

Using the complex variable method and the technique of the conformal mapping,the fracture problem of a finite crack in one side of a piezoelectric strip was studied under the anti-plane shear stress and the in-plane electric load.The analytic solutions of the field intensity factors and the mechanical strain energy release rate were presented under the assumption that the surface of the crack was electrically impermeable.When the width of the strip tends to infinity,the analytic solutions of an infinitely large piezoelectric solid with a finite crack in one side were obtained.Moreover,numerical examples were given to show the influence of the width of the strip and the applied mechanical electric loads on the mechanical strain energy release rate.