各向异性介质中SH波引起的裂纹扩展

THE EXTENSION OF A CRACK BY SH-WAVE IN ANISOTROPIC MEDIA

本文利用Green函数法,求解各向异性介质中半无限长裂纹在SH波作用下,以任意速度扩展的问题。首先,利用Laplace变换和Cagniard-de Hoop反演法求解各向异性介质中反平面问题的Green函数,并利用它建立了求解裂纹扩展问题的积分方程。因为方程为Abel型的,所以可得到在SH波作用下,半无限长裂纹扩展问题的解析解。还可求得裂纹端点附近的应力和裂纹表面上位移的表达式。并对裂纹端点附近的奇异性进行讨论。最后讨论了裂纹尖端附近任一点的能量关系。并应用Griffith的能量准则,对裂纹扩展规律进行了讨论。

Green's function method is used to solve the problems of extension of semi-infinite crack with arbitrary velocity by SH-wave in anisotropic media. At first, the Green's function of out-plane problem is solved in anisotropic media using the Laplace transform and Cagniard-de Hoop inverse method, then the integral equation for solving the problem of extension crack is given. The equation is Abel integral equation. The analytical solution for the problem is given in this paper. The expressions of stress ahead the crack tip and displacement of the surface behind the crack tip are obtained and the singularity of stress and ve locity near the tip of the crack are analysed.At last, the relation of energy near the tip of the crack and the Griffith's energy criterion of extension of crack are discussed.