在冲击载荷作用下不同正交异性材料结合面上的裂纹问题

SHOCK PROBLEM OF PROPAGATION CRACK IN INTERFACES BETWEEN DIFFERENT ORTHOTROPIC MEDIA

本文给出了正交异性材料反平面间题波动方程的函数不变解。根据这个解,对正交异性体具有任意自相似指数的反平面弹性动力学问题给出了完全解。对受冲击载荷作用,在不同正交异性材料结合面上扩展的裂纹动力学问题,利用结合面的条件及本文给出的完全解,可以化为解析函数论中的Keldysh-Sedov混合问题。文中求解了这一问题,并得到了解的解析表达式。利用这个解,我们分析了不同材料常数及裂纹扩展速度对应力场分布及动应力强度因子的影响,得到具有实际意义的结论。

In this paper the functionally invariant solution of the wave equation of anti-plane problems in the orthotropic material is obtained. On the basic of this solution, a complete solution for anti-plane elasticity dynamic problems with an arbitrary index of self-similarity in the orthotropic body is given. Using conditions of interface and the complete solution, the shock problem of propagating crack in interface between different orthotropic media can be changed into the Keldysh-Sedov mixed problem of theory of analytic functions. In the paper, the closed solution of this problem is given. Using this solution, we have analysed effect to the dynamic stress intensity factor by the constant of media and the velocity of crack propagation.