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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。
In order to study the electro-elastic interaction between the piezoelectric screw dislocation located in the matrix and the elliptical inclusions with confocal elliptical conductive nuclei in the piezoelectric composite, the accurate series of the matrix and the inclusion regions were obtained based on the complex variable function method solution. The generalized Peach-Koehler formula is used to derive the analytical expression of the image force acting on the dislocation. On this basis, the influences of elliptical rigid nuclei and the electro-elastic properties of materials on the position of the dislocation image and the position of dislocation are discussed, and the compounding of piezoelectric inclusion and elastic matrix is discussed. The results show that the elliptical rigid alignment dislocation has obvious repulsive effect, which can enhance the exclusion of hard inclusions and reduce the soft inclusions’ dislocation attraction. For soft inclusions, there is an unstable equilibrium position near the interface. The image force increases rapidly at the interface between the substrate and the inclusions. When the shear modulus of the inclusions is much smaller than that of the substrate, there will be no equilibrium position of the dislocations near the interface.