压电介质中裂纹与邻近微孔洞的交互作用

基于线性压电理论，文中对裂纹和微孔洞的交互作用进行有限元计算分析。结果表明，(1)电场对裂纹启裂起促进还是抑止作用，与外加电场方向和裂纹面电学边界条件密切相关。(2)电-力载荷比、电学边界条件和微孔洞裂纹之间的韧带长度对裂纹前缘应力场均有一定影响，但无论对于何种裂纹电学边界条件(可导或绝缘)，裂纹前端的微孔洞只有在韧带长度小于2倍微孔洞直径时，才对裂纹前缘应力场有明显的影响。(3)在一定的电-力加载比和一定的韧带长度范围内，微孔洞对裂纹的启裂有屏蔽作用，且微孔洞对导通裂纹的屏蔽作用比绝缘裂纹要明显得多。此外，文中还给出韧带上张开应力的分布。

Interaction between a crack and near microvoid in piezoelectric materials

Based on the linear piezoelectricity theory and finite element method (FEM), interaction between a crack and near microvoid in a double edge notch (DEN) plate of piezoelectric ceramics PZT-4 is investigated. The results indicate: (1) Whether electrical filed promotes or impedes initiation and propagation of the crack not only depends on the direction of the electrical filed but also the crack electric boundary conditions. (2) The stress field in the vicinity of the crack tip is influenced by electrical to mechanical load ratios, crack electric boundary conditions and the length of the ligament between the crack-tip and microvoid. But whatever the crack electric boundary conditions (permeable or impermeable) would be, the microvoid has visible effects on the stress field in the vicinity of the crack tip only when the ligament length is shorter than twice diameter of the microvoid. (3) Under certain electrical to mechanical load ratios the microvoid in certain range of the ligament length has shielding effects to impede the crack initiation and propagation. And the microvoid has stronger shielding effect to the permeable crack than the impermeable crack. In addition, the opening stress on the ligament is shown. The conclusions obtained in the current study have significant guidelines for investigating the interactions between the crack and microvoid in piezoelectric materials.