非均匀复合材料的动态热弹性断裂力学分析

DYNAMIC FRACTURE MECHANICS ANALYSIS FOR NON-HOMOGENEOUS COMPOSITE MAYERIAL WITH MULTIPLE CRACKS

对非均匀复合材料的动态热弹性断裂力学问题进行了研究，假设材料参数沿厚度方向为变化的，沿该方向将复合材料划分为许多单层，取每一单层材料参数为常数，应用Fourier变换法，在Laplace域内推导出了控制问题的奇异积分方程组，给出了热应力强度因子的表达式，然后利用Laplace数值反演，得出了裂纹尖端的动态应力强度因子．本文的方法具有以下特点：（1）多个垂直于厚度方向的裂纹，（2）材料可以为正交各向异性：（3）考虑了惯性效应．作为算例，研究了带有两个裂纹的功能梯度结构，分析了材料参数的变化对应力强度因子的影响．

The problem considered here is the response of a nonhomogeneous composite materialcontaining some cracks subjected to dynamic thermal loading. It is assumed that all the materialproperties only depend on the coordinates y (along the thickness direction). In the analysis, theelastic region is divided into a number of strips of infinite length. The material properties are takento be constants for each strip. By utilizing the Laplace transform and Fourier transform technique,the singular integral equations are derived and solved by weighted residuals method. Attention isfocused on the time-dependent full field solutions of stresses, stress intensity factor. The specialfeatures of the present analysis are: (1) multiple cracks perpendicular to the thickness direction,(2) material may be orthotropic and (3) take into account. of the inertia effect. As a numericalillustration, the dynamic stress intensity factor of a functionally graded material with two cracksunder sudden applied thermal flux on the upper boundary and the lower boundary of the materialare presented for various material non-homogeneity parameters.