压电材料裂纹顶端条状电饱和区模型的力学分析

ANALYSIS OF STRIP ELECTRIC SATURATION MODEL OF CRACK PROBLEM IN PIEZOELECTRIC MATERIALS 1)

在线性压电本构方程框架下，对裂纹顶端条状电饱和区模型进行了严格的数学分析．完整地考虑了各向异性力电耦合效应．建立了电饱和区尺寸与外加电场的依赖关系．证实了当裂纹垂直极化轴时，压电材料的断裂应力随着外加正电场的增加而减小，随着外加负电场的增加而增加．当裂纹平行于极化轴时。

This paper presents a fully anisotropic analysis of strip electric saturation model proposed by Gao, Zhang and Tong for piezoelectric materials. A complete exact solution is obtained for a single crack in an infinite pizoelectric media. The relationship between the size of the strip saturation zone ahead of a crack tip and the applied electric field is established. It is found that the size of the strip saturation zone ahead of a crack tip is independent of the applied stress. The explicit formula for the stress intensity factors is obtained. The stress intensity factors are not only dependent on the applied stresses but also on the applied electric field. The critical condition for crack propagation is discussed in detail. It is revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric field and increases linearly with the increase of the negative applied electric field. For a crack parallel to the poling axis, the failure stress is not effected by the parallel applied electric field.