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

不同种各向异性复合材料界面裂纹的数学方法

基本信息

批准号：
62550331
负责人：
NAKAGAWA Kenji
金额：
$ 1.28万
依托单位：
Gifu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1987
资助国家：
日本
起止时间：
1987 至 1989
项目状态：
已结题

项目摘要

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

1)本文分析了在无限远处均布载荷作用下，不同各向异性复合材料界面裂纹尖端的应力和位移。在文献[1]的基础上，通过傅里叶变换，给出了一个傅里叶级数形式的弹性解。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。2）纤维混凝土、岩石等复合材料是土木工程结构中常用的材料。有时必须考虑这些材料的强各向异性特性。虽然在各向同性材料界面裂纹问题中已有许多弹性解，但在各向异性复合材料界面裂纹问题中，文献中的研究却很少 ...更多信息用傅里叶变换法给出了不同各向同性弹性材料界面裂纹的解。本文在前人工作的基础上，求出了两个各向异性半平面间界面裂纹的Fourier级数弹性解，其中裂纹尖端的应力集中是有限的，裂纹的张开位移是光滑的。将文献[1]和[2]中的数学模型推广到求解不同各向异性材料界面裂纹的弹性问题。类似于各向同性材料之间的界面裂纹，在裂纹尖端附近形成一个过程区，在该过程区中出现有限的应力集中，并伴随着裂纹张开位移。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获得。从数值结果来看，该模型在土木工程材料断裂分析中具有一定的实用价值。少