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

1)分析了各向异性复合材料在无限远均布载荷作用下界面裂纹末端附近的应力和位移。根据作者之前的论文[1]，用傅里叶变换给出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。给出了一些数值结果。2)复合材料，如纤维增强混凝土、岩石等，在土木工程结构中经常使用。有时必须考虑到这些材料的强各向异性特性。不同各向同性材料间界面裂纹的弹性解已经得到了很多，但关于不同各向异性复合材料间界面裂纹问题的文献却很少。3)在参考文献[1]和[3]中，作者用傅里叶变换给出了不同各向同性弹性物质之间界面裂纹的三角级数解。本文在前人的基础上，得到了裂纹尖端应力集中有限且裂纹张开位移平滑的两个不同的各向异性半平面之间的界面裂纹的傅立叶级数弹性解。该模型对土木工程材料断裂分析具有较强的实用价值。(4)将参考文献[1]和[2]中描述的数学模型推广到求解不同各向异性材料之间界面裂纹的弹性问题。与异种各向同性材料之间的界面裂纹类似，在裂纹尖端附近形成一个过程区域，在该过程区域内出现有限应力集中并伴有裂纹张开位移。由该解可以很容易地求得裂纹尖端张开位移（CTOD）和总势能（j积分）下降速率[3]。数值结果表明，该模型在土木工程材料断裂分析中具有实际应用价值。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