压电材料中两个非对称平行裂纹的基本解

Basic Solution of Two Parallel Non-Symmetric Permeable Cracks in Piezoelectric Materials

采用Schmidt方法分析压电材料中非对称平行的双可导通裂纹的断裂性能.利用Fourier变换使问题的求解转换为求解两对以裂纹面位移之差为未知变量的对偶积分方程.为了求解对偶积分方程,直接把裂纹面位移差函数展开成Jacobi多项式形式.最终得到了裂纹的应力强度因子与电位移强度因子之间的关系.数值结果表明,应力强度因子和电位移强度因子与裂纹间的距离、裂纹的几何尺寸有关;与不可导通裂纹有关结果相比,可导通裂纹的电位移强度因子远小于相应问题不可导通裂纹的电位移强度因子.同时可以发现裂纹间的“屏蔽”效应也在压电材料中出现.

The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading is studied by the Schmidt method for the perrmeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations in which the unknown variables are the jumps of displacements across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials.