表面荷载下横观各向同性介质中水平裂纹分析

首先采用基于横观各向同性双材料基本解的一种数值方法计算半无限介质的弹性场,然后根据线弹性断裂力学叠加原理获得裂纹处的内应力,再利用另一种数值方法获得裂纹面的张开或滑移位移,最后应用应力强度因子(SIF)与裂纹面位移之间的关系,获得裂尖SIF值。基于建议的方法,讨论了表面矩形荷载作用下横观各向同性半无限介质中的单条裂纹问题以及两条裂纹间的相互影响问题。分析结果表明:加载面中心点下单条裂纹应力强度因子开始随距离自由面深度的增加而增大,达到一定深度后减小;相邻裂纹的存在对加载面中心点下裂纹的影响除相隔最近的相邻裂尖外均为抑制效应;而加载面中心点下裂纹的存在对相邻裂纹的影响主要体现在相隔最近的相邻裂尖上。

Analysis on Horizontal Crack Problems in a Transversely Isotropic Medium Subject to Surface Loading

Based on the fundamental solutions for two joined transversely isotropic solids, a novel numerical method used to analyze the problem of the crack in a transversely isotropic half-space was developed. The stress fields of a transversely isotropic half-space without cracks were firstly calculated by one numerical method based on the same fundamental solutions. And the traction acting on the crack surfaces was obtained according to the superposition principle in fracture mechanics. The discontinuous displacements of crack surfaces were then gained by another numerical method also based the same fundamental solutions. The stress intensity factor (SIF) was finally achieved by the relation between the SIF and the discontinuous displacements. A single crack and its interaction with the other crack were respectively investigated using the proposed method. Results show that the SIF value of a single crack under the center point of the loading area increases with the depth of the crack from free surface at the beginning and decreases after reaching a certain depth. The crack under the center point of loading area presents suppression effects except for the nearest neighboring crack tip due to the existence of adjacent crack. But the influence of the crack under the center point of the loading area on another adjacent crack mainly appears on the nearest neighboring crack tip from the crack under the center point.