正交异性材料I + II + III混合型裂纹尖端应力分析
Crack-Tip Stress Analysis for Orthotropic Materials under Mixed-Mode I + II + III Loading

大多数工程材料显示出脆性特征(例如，复合材料)，而脆性材料中的裂纹已公认为是工程结构破坏的主要原因，裂纹尖端应力场必然是建立断裂判据的基础。因此，本文重点讨论I + II + III混合型加载下的裂纹尖端应力，采用线弹性力学方法解决正交异性材料典型应力边值问题。首先确定三维空间问题的弹性力学基本方程，基于复变函数理论求解控制方程。接着利用应力函数和坐标变换求解基本方程。最终获得了混合型加载下正交异性材料裂纹尖端附近的应力分量通解。
Most engineering materials exhibit brittle behavior, such as composites. The main cause for failures of engineering structures has been generally recognized to be the cracks in brittle materials. The crack-tip stress field must be the basis for establishing fracture criteria. So this paper will focus the discussion on crack-tip stresses under mixed mode I + II + III loading. Typical stress boundary problem for the orthotropic materials is considered to be solved by the method of linear elastic mechanics. First, the basic equations of elastic mechanics are determined for three-dimensional space problems, and the governing equations are solved based on the theory of complex variable function. Second, the basic equations are solved by using the stress functions and the coordinate transformation. And finally, the general solutions of stress components near the crack-tip are derived for the orthotropic materials under mixed mode loading.