层状磁电复合材料界面共线裂纹平面问题分析

本文研究了面内电磁势载荷作用下双层压电压磁复合材料中共线界面裂纹问题．考虑了压电材料的导磁性质和压磁材料的介电性质，引入了界面电位移和磁感强度的连续性条件．利用Fourier 变换得到一组第二类Cauchy 型奇异积分方程．进一步导出了相应问题的应力强度因子、电位移强度因子和磁感强度强度因子的表达式，给出了应力强度因子的数值结果．结果表明电磁载荷会导致界面裂纹尖端I、II 混合型应力奇异性，同时还伴随着电位移和磁感强度的奇异性．比较了双裂纹左右端的应力强度因子，发现在面内极化方向上施加面内磁势载荷时共线裂纹内侧尖端区域的两个法向应力场发生互相干涉增强．

Analysis for the Plane Problem of Layered Magnetoelectric Composites with Collinear Interfacial Cracks

A plane fracture problem of collinear interfacial cracks in layered magnetoelectric composites is studied under in-plane magnetic or electric loading. The magnetic permittivity of the piezoelectric material and the dielectric constant of the piezomagnetic material are considered. A system of singular integral equation of the second kind with Cauchy kernel is obtained by means of Fourier transform and further solved by using Jacobi polynomials. The primary interfacial fracture parameters, such as the stress intensity factors, the electric displacement intensity factors, the magnetic induction intensity factors are then obtained. It is found that a magnetic or electric loading normal to the crack surfaces can lead to a mixture of mode I and mode II type stress singularities at crack tips. The stress intensity factors at the right and left ends of the two cracks are compared. It is found that when the in-plane magnetization load is applied in the in-plane polarization direction, the two normal stress fields in the inner tip region of the collinear cracks interfere with each other.