插值矩阵法分析与复合材料界面相交的平面裂纹奇异应力场

Analysis of the stress singularity of the plane cracks terminating at the interface in bonded dissimilar composite materials by the interpolating matrix method

提出了用插值矩阵法分析与各向异性材料界面相交的平面裂纹应力奇异性。基于V形切口尖端附近区域位移场渐近展开,将位移场的渐近展开式的典型项代入线弹性力学基本方程,得到关于平面内与复合材料界面相交的裂纹应力奇异性指数的一组非线性常微分方程的特征值问题,运用插值矩阵法求解,获得了平面内各向异性结合材料中与界面以任意角相交的裂纹尖端的应力奇异性指数随裂纹角的变化规律,数值计算结果与已有结果比较表明,本文方法具有很高的精度和效率。

In this paper,a method for calculating the singularity orders of the crack terminating at the interface in the anisotropic planes by the interpolating matrix method is proposed.Based on the asymptotic expansion of the generalized displacement fields at the notch tip,and by introducing the generalized displacement functions in the asymptotic expansion into the linear elasticity equilibrium equation,the governing equations of a crack terminating at the interface of the bonded dissimilar materials are transformed into a set of nonlinear characteristic ordinary differential equations（ODEs）with the singularity orders.Then the interpolating matrix method is introduced to solve the derivative ODEs.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.The numerical results show that the method is efficient and has very high accuracy while comparing with the existent solutions.