夹层压电材料中垂直于界面的共线双裂纹动力学问题分析

Dynamic Behavior of Two Collinear Permeable Cracks in a Piezoelectric Layer Bonded to Two Half Spaces

采用Schmidt方法分析了在简谐反平面剪切波作用下,两个半空间夹层压电材料中的共线裂纹的动力学行为.压电材料层内裂纹垂直于界面,电边界条件假设为可导通.通过Fourier变换,使问题的求解转换为两对三重积分对偶方程.通过数值计算,给出了裂纹的几何尺寸、压电材料常数、入射波频率等对于应力强度因子的影响.结果表明,在不同的入射波频率范围,动力场将阻碍或促使压电材料内裂纹的扩展.与不可导通电边界条件相比,导通裂纹表面的电位移强度因子比不可导通裂纹的电位移强度因子要小许多.

The dynamic behavior of two collinear cracks in a piezoelectric layer bonded to two haft spaces under harmonic anti-plane shear waves was investigated by means of Schmidt method. The cracks are vertically to the interfaces of the piezoelectric layer. The boundary conditions of the electrical field were assumed to be the permeable crack surface. By using the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations. Numerical examples were presented to show the effect of the geometry of the interacting cracks, the piezoelectric constants of the materials and the frequency of the incident waves upon the stress intensity factors. The results show that the dynamic field will impede or enhance the propagation of the crack in a piezoelectric material at different stages of the frequency of the incident waves. It is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than the results for the impermeable crack surface conditions.