正交异性复合材料界面上反平面动态自相似扩展裂纹问题的解

Solution of Anti-plane Dynamic Self-similar Propagation Crack Problem along Interfaces of Orthotropic Composite Materials

采用复变函数论的方法,对复合材料界面上的裂纹扩展问题进行研究,并根据任意的自相似指数的断裂动力学问题,进行自相似求解,导出解析解的一般表示。应用该法可以迅速地将所论问题转化为Riemann—Hil-bert问题,并可以相当简单地得到问题的闭合解。文中分别对裂纹中心受阶跃载荷、裂纹面受到瞬时脉冲载荷作用下的界面裂纹扩展问题进行求解,得到了裂纹的位移、尖端的应力和动态应力强度因子的解析解,应用该解并通过叠加原理,就可以很容易的求得任意复杂问题的解。

By the theory of complex functions, the general representations of the analytical solutions were reduced for crack problems of arbitrary index of self-similarity propagating along the interfaces of ortho-tropic composite materials. The Riemann-Hilbert problems could be formulated correctly and their closed solutions were obtained simply by the ways of this method. The problems for the cracked body subjected to a Heavyside load concentrated at the origin of coordinates, an instantaneous impulse load at the edges of the cut, could be solved respectively. The analytical solutions on the displacements of the crack, the stresses of crack tip and dynamic stress intensity factors could be attained. By the application of superposition theorem and these solutions, it is very easily to find the solutions of arbitrarily complex problems.