正交异性材料平面裂纹尖端应力场

Stress field in plane crack-tip of orthotropic materials

根据正交各向异性材料力学性能确定出了用应力函数表示的弹性力学基本方程,利用坐标变换和复变函数方法求解了正交异性材料平面裂纹体的应力边值问题。借鉴一般断裂力学解法构造了I型和II型裂纹问题的应力函数,推导出了正交各向异性板裂纹尖端区的奇异应力场。通过数值计算说明了裂纹尖端应力表达式的正确性,验证了裂尖前沿应力变化规律,即σx与材料特征参数h2成正比,而σy和τxy不随材料特性变化。

The basic equation of elastic mechanics is derived by the stress function on the basis of the mechanical characteristic of orthotropic materials.The stress boundary problem about the orthotropic plate with a crack is solved by using coordinate translation and complex variable method.In terms of general fracture mechanical method,the stress functions for mode I and mode II crack problems are made up.And the singular stress fields near the crack-tip are derived for the orthotropic plate.The validity of stress fields is confirmed by the numerical results.The varying regularity of the stresses in front of the crack tip is verified,namely,σx is direct ratio with the feature parameter h2 of the materials.However,σy andτxy are not varying with the material character.