正交异性复合材料板Ⅰ型三裂纹尖端场分析

Crack-Tip Stress Analysis on Three Cracks of Orthotropic Composite Materials for Mode Ⅰ

研究了正交异性复合材料板三裂纹的平面问题。通过复合材料断裂中的力学模型,将此问题归结为一类偏微分方程的边值问题,构造保角映射,将均匀分布三裂纹映射为复平面上的平行周期裂纹,通过引入适当的westergaard应力函数,采用复变函数方法和待定系数法对复合材料Ⅰ型平行周期裂纹尖端的应力场进行了力学分析。最后再利用该保角映射的逆变换,将平行周期裂纹尖端的应力场变换到原均匀分布三裂纹的应力场,得到了远场受均匀分布载荷作用下的应力场和位移场的解析解。研究结果为结构和材料的强度设计提供了有意义的参考。

This paper studies the plane problems about three cracks of orthotropic composite materials. Plane frac-ture problems of composite materials can be converted into a class of boundary value problems of partial differential equation by fracture mechanics model of composite materials. It can be mapped to cracks parallel to the cycle on the complex plane by introducing the appropriate conformal mapping. The right westergaard stress function,together with the complex function method and the method of undetermined coefficients,is properly chosen to deduce the crack-tip stress on cycle of parallel cracks of orthotropic composite materials for mode Ⅰ. The parallel cycle uni-form distribution of crack-tip stress field can be transformed into the original three of stress field of crack by using the inverse transformation of conformal mapping,far field of analytical solutions of stress field and displacement field was obtained under the uniformly distributed load. The results provides a meaningful reference to the strength design of structure and material.