具有非均匀界面相的颗粒和纤维增强复合材料弹性静力学问题的解析解  

Analytical Solutions for Elastostatic Problems of Particle- and Fiber-Reinforced Composites With Inhomogeneous Interphases

作　　者：段慧玲[1] 王建祥[1] 黄筑平[1] 黄红波[1] 

机构地区：[1]北京大学湍流与复杂系统国家重点实验室力学与工程科学系,北京100871

出　　处：《应用数学和力学》2005年第3期309-315,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10032010;10072002;10372004)

摘　　要：　通过将以位移表示的平衡方程转化为黎卡提方程,得到了具有非均匀界面相的颗粒和纤维增强复合材料非均匀界面相内弹性场的解析解·　所得的解析解是弹性模量呈幂次方变化的非均匀界面相解的通用形式·　任意给定1个幂指数,可以得到具有非均匀界面相的颗粒和纤维增强复合材料体积模量的解析表达式·　通过改变幂指数及幂次方项的系数,此解析解可适用于具有多种不同性质的非均匀界面相·　结果表明:界面相模量和厚度对复合材料模量有很大的影响,当界面相存在时。By transforming the governing equations for displacement components into Riccati equations, analytical solutions for displacements, strains and stresses for RVEs of particle- and fiber-reinforced composites containing inhomogeneous interphases were obtained. The analytical solutions derived here are new and general for power-law variations of the elastic moduli of the inhomogeneous interphases. Given a power exponent, analytical expressions for the bulk moduli of the composites with inhomogeneous interphases can be obtained. By changing the power exponent and the coefficients of the power terms, the solutions derived here can be applied to inhomogeneous interphases with many different property profiles. The results show that the modulus variation and the thickness of the inhomogeneous interphase have great effect on the bulk moduli of the composites. The particle will exhibit a sort of 'size effect', if there is an interphase.

关 键 词：非均匀界面相 颗粒增强复合材料 纤维增强复合材料 解析解 体积模量 

分 类 号：TB330.1[一般工业技术—材料科学与工程]