与界面相交的裂纹尖端的应力奇异性分析

ON THE STRESS SINGULARITY OF A CRACK TERMINATING AT THE INTERFACE

为了确定与结合材料的界面相交的裂纹尖端附近的应力奇异性次数 ,提出了一种基于最小势能原理的一维特殊有限元法 .以奇异点为原点半径为r0 的扇形奇异区域 ,可以简化为一维线性领域 ,即一条以代表结合材料的两个自由表面为端点的线段 .对该一维线性领域作网格划分 ,采用三节点一维等参数二次单元 .数值计算结果与已有理论解的比较表明 ,该方法具有很高的精度和效率 .最后 ,利用文中给出的方法 ,得到了各向异性结合材料中与界面以任意角相交的裂纹尖端的奇异性次数随裂纹角的变化规律 .

In order to determine the stress singularity of a crack terminating at the interface of the bonded dissimilar materials, a special one-dimensional finite element method which is based on the principle of minimum potential energy is proposed. The sectorial singular field whose origin locates at the tip of the crack and radius is r 0 can be degenerated into one-dimensional linear region, which is one segment bounded by two points representing the two free crack faces. Three nodes one-dimensional isoparametric quadrilateral elements are adopted while we descretize the region. The numerical results show that the method is efficient and has very high accuracy while comparing with the existent solutions. The relation between the stress singularity and the ply angle of the crack terminating at the interface of bonded dissimilar anisotropic materials can be easily obtained by this method.