复合材料中压电螺型位错与含刚性核夹杂的电弹干涉

Electro-elastic interactions between a piezoelectric screw dislocation and an inhomogeneity containing a rigid core in the composite material

为了研究压电复合材料中位于基体的压电螺型位错与含共焦椭圆导电刚性核椭圆夹杂的电弹相互作用,基于复变函数方法,获得了基体和夹杂区域的精确级数形式解析解。运用广义Peach-Koehler公式,导出了作用在位错上像力的解析表达式。在此基础上讨论了椭圆刚性核和材料电弹特性对位错像力以及位错平衡位置的影响规律,同时讨论了压电夹杂和弹性基体的复合情况。结果表明:椭圆刚性核对位错有着明显的排斥作用,可以增强硬夹杂对位错的排斥,减弱软夹杂对位错的吸引;对于软夹杂,在界面附近位错存在一个不稳定的平衡位置;在基体和夹杂的界面上,像力迅速增大;当夹杂的剪切模量远小于基体时,界面附近不会出现位错的平衡位置。

The electro-elastic coupling interactions between a piezoelectric screw dislocation, which located in the matrix, and an elliptical inhomogeneity containing an electrically conductive confocal elliptical rigid core in piezoelectric composite material was studied. Based on the complex variable method, the analytical solutions of the complex potentials in the matrix and the inclusion regions were obtained explicitly in the series form. The image force acting on the piezoelectric screw dislocation was calculated using the generalized Peach Koehler formula. The effects of the elliptical rigid core and the electro-elastic properties of the piezoelectric materials on the image force and the equilibrium position of the dislocation were discussed. In addition, piezoelectric inclusion and elastic matrix composites was studied in this paper. The main results show that, the elliptical rigid core has a significant repelling action, which enhances the repulsive force acting on the dislocation produced by the stiff inhomogeneity and weakens the attractive force produced by the soft inhomogeneity. For the soft inhomogeneity, there is an unstable equilibrium position near the interface. The image force increases rapidly near the interface of the matrix and the inhomogeneity. There is no equilibrium position of the dislocation near the interface when the shear modulus of the inhomogeneity is much smaller than that of the matrix.