Abstract

The problems of periodic mode I 3 D cracks for an elastic layer are reduced to an integro-differential equation (IDE). The principal part of the IDE is the same as in the classical Griffith problem for one crack in an elastic full space. The periodic system of elliptic cracks, featuring equal spaces between neighboring cracks, lies in the middle plane of the layer. Each crack is parallel to the layer’s faces. Four types of boundary conditions are considered on the layer’s faces (sliding or rigid support, stress-free state, sliding support in between elastic layers). The regular asymptotic method has been applied to solving the problems as it proves effective for some fairly big spaces between cracks as well as for relatively thick layers. The stress intensity factor (SIF) has been calculated for a variety of geometric and mechanical parameters. It was compared to that for the well-known case of a single crack in a layer. It has been shown that the SIF for the crack system can be smaller or greater than that for a single crack depending on the boundary conditions on the layer’s faces.

摘要

周期模式的问题I弹性层的 3D 裂纹简化为积分微分方程 (IDE)。IDE 的主要部分与经典的 Griffith 问题中的弹性满空间中的一个裂缝相同。椭圆裂纹的周期系统，具有相邻裂纹之间相等的空间，位于层的中间平面。每个裂缝都平行于层的面。在层的表面上考虑了四种类型的边界条件（滑动或刚性支撑、无应力状态、弹性层之间的滑动支撑）。规则渐近法已被应用于解决这些问题，因为它证明了对于裂缝之间的一些相当大的空间以及相对较厚的层是有效的。已经针对各种几何和机械参数计算了应力强度因子 (SIF)。将其与层中单个裂缝的众所周知的情况进行了比较。已经表明，裂纹系统的 SIF 可以小于或大于单个裂纹的 SIF，具体取决于层面上的边界条件。