三相压电复合本构模型中的弧形界面裂纹

深入研究了三相同心圆柱压电复合本构模型中的弧形绝缘界面裂纹问题。采用复势方法获得了该问题的级数形式的解答，并给出了应力、应变、电位移和电场强度等物理量在全场及界面上的分布，同时推导了裂尖处广义强度因子及裂面张开位移和裂面上电势差的表达式。具体计算表明该级数解答收敛迅速，同时显示出第三相混杂区的影响是不能忽略的。由于裂尖处应力奇异性为－1／2，则这种解答不会出现平面应变状态下界面裂纹裂尖处的振荡奇异性，从而不会产生违反物理实际的裂面相互嵌入现象，则该弹性解答也是建立了坚实的物理基础之上。

ARC INTERFACE CRACK IN A THREE-PHASE PIEZOELECTRIC COMPOSITE CONSTITUTIVE MODEL

the problem of an arc shaped interface insulating crack in a three phase concentric circular cylindrical piezoelectric composite constitutive model is investigated in detail. An exact solution in series form is derived by employing the complex variable method. In addition, distributions of those physical quantities such as stresses, strians, electric displacements and electric fields in the whole field and along the interface are also presented. Explicit expressions for crack opening displacement, jump in electric potential on the crack surface and the electro elastic field intensity factors at the crack tips are obtained. The concrete calculations demonstrate that the convergence of the series form solution is satisfactory and that the outer phase (composite phase) will exert a significant effect on the electro mechanical coupling response of the composite system. Due to the fact that stresses and electric displacements still possess the traditional inverse square root singularities, then those oscillating singularities near the crack tip under plane strain condition will be absent, and as a result the unphysical interpenetration phenomenon of the two crack surfaces will not occur. In conclusion, the elastic solution obtained is also based on solid physical foundations.