A MATHEMATICAL APPROACH OF THE INTERFACE CRACK BETWEEN DISSIMILAR ANISOTROPIC COMPOSITE MATERIALS

1)分析了无限大均布载荷作用下各向异性复合材料界面裂纹端部的应力和位移。在前文[1]的基础上，利用傅里叶变换给出了弹性解的傅里叶级数形式。裂纹张开位移呈光滑闭合形状，裂纹尖端附近应力集中有限。数值结果表明：2)土木工程结构中经常使用纤维混凝土、岩石等复合材料。有时必须考虑这些材料的强烈各向异性特性。尽管各向同性材料界面裂纹的弹性解很多，但关于各向异性复合材料界面裂纹问题的文献很少。3)在文献[1]和[3]中，作者给出了一个三角级数…利用傅立叶变换得到了不同各向同性弹性材料界面裂纹的S解。本文在前人工作的基础上，求出了裂纹尖端应力集中有限且裂纹张开位移平稳的两个不同的各向异性半平面间界面裂纹的傅里叶级数弹性解。4)将文献[1]和[2]中描述的数学模型推广到求解各向异性材料界面裂纹的弹性问题。类似于各向同性材料界面裂纹的情况，在裂纹尖端附近形成了一个过程区，在该过程区内出现了伴随着裂纹张开位移的有限应力集中。裂纹尖端张开位移(CTOD)和总势能下降率(J积分)[3]也可以很容易地从解中得到。从数值结果看，该模型在土木工程材料断裂分析中具有一定的实用价值。较少

1) In this research the stresses and displacements near the end of a interface crack between dissimilar anisotropic composite materials under uniform loading at infinity is analyzed. Following the Authors previous paper [1] , a elastic solution in the form of a Fourier series is given by the Fourier transforms. The crack opening displacement is with a smoothly closed shape, and the stress concentration is finite near the crack tip. Some numerical results are shown.2) Composite materials, such as fiber reinforced concrete, rock and so on are often used in the civil engineering structures. Sometime the strongly anisotropic characteristics of these materials must be taken into account. Although many elastic solutions have been given in the interface cracks between dissimilar isotropic materials , the references on the problems of interface cracks between dissimilar, anisotropic composite materials are looked little.3) In the Refs [1] and [3], the Authors have given a trigonometrical serie … More s solution for the interface crack between dissimilar isotropic elastic matters by the Fourier transform. The present work is based on the these previous papers, to get the Fourier series elastic solutions for the interface crack between two dissimilar, anisotropic half-planes, in which the stress concentration is finite at the crack tip with a smoothly crack opening displacement. The model may be more practical to analysis the civil engineering materials fracture [3].4) A mathematical model which was described in the Refs [1] and [2] is extended to solve the elastic problem of the interface crack between dissimilar, anisotropic materials. Similar to the case of interface crack between dissimilar isotropic materials, a process region near the crack tip is formed, in which the finite stress concentration appears accompanied by the crack opening displacement. The crack tip opening displacement (CTOD) and the rate of decrease of total potential energy (J-integral) [3] can also be obtained easily from the solution. From the numerical results, it may be said the proposed model is of practical use in the civil engineering material fracture analysis. Less