正交异性双材料Ⅱ型界面裂纹问题研究  

Researches on Interface Crack Problems for Mode Ⅱ of Double Dissimilar Orthotropic Composite Materials

作　　者：杨维阳[1] 张少琴[1] 李俊林[1] 马玉兰[1,2] 

机构地区：[1]太原科技大学应用科学学院,太原030024 [2]北京工商大学数理系,北京100037

出　　处：《应用数学和力学》2009年第5期547-555,共9页Applied Mathematics and Mechanics

基　　金：山西省自然科学基金资助项目(2007011008)

摘　　要：探讨正交异性双材料Ⅱ型界面裂纹问题,给出了它的力学模型.将控制方程化为广义重调和方程,借助复变函数方法推出了含两个应力奇异指数的应力函数.基于边界条件得到了两个八元非齐次线性方程组.求解该方程组,在双材料工程参数满足适当的条件下确定了两个实应力奇异指数.根据极限的唯一性定理推出了应力强度因子的公式和裂纹尖端应力场的理论解.作为特例,当两种正交异性材料相同时,可以推出正交异性单材料Ⅱ型断裂的已有结果.The fracture problems near interface crack tip for mode Ⅱ of double dissimilar orthotropic composite materials are studied. The mechanical models of interface crack for mode Ⅱ were given. By translating the governing equations into generalized bi-harmonic equations, the stress functions containing two stress singularity exponents were derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations was found. Two real stress singularity exponents were determined under appropriate conditions of bi-material engineering parameters through solving this system. According to the theorem of limit uniqueness, both the formulae of stress intensity factors and theoretical solutions of stress field near interface crack tip were deduced. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode Ⅱ crack of orthotropic single material were obtained.

关 键 词：Ⅱ型界面裂纹 应力强度因子 双材料 正交异性 

分 类 号：O346.1[理学—固体力学] O174.5[理学—力学]