增强相周期分布的多涂层纤维复合材料反平面问题的解析方法

AN ANALYTICAL METHOD FOR MULTIPLY COATED FIBER COMPOSITES WITH PERIODIC REINFORCEMENT PHASE UNDER ANTIPLANE SHEAR

采用增强纤维周期分布模型,通过引入非均匀的本征应变并结合双准周期Riemann边值问题理论,将非均匀介质问题转化为均匀介质的周期本征应变问题,获得了反平面载荷作用下多涂层纤维复合材料纤维、各涂层和基体中弹性场的解析解答。与有限元、广义自洽和渐进均匀化等方法的比较显示了该文方法的精度。讨论了涂层厚度和刚度等材料微结构参数对界面应力集中系数和有效反平面剪切模量的影响。该文为研究多涂层复合材料界面效应提供了一个有效的分析工具。

A composite model with periodic distributed reinforcement is adopted to study the elastic behaviour of multiply coated fiber composites under antiplane shear forces. Referring to the concept of eigenstrain and using the theory for doubly quasi-periodic Riemann boundary value problems, the problem of periodic distributed inclusions is transformed into that of homogeneous materials with periodic distributed eigenstrains. The elastic fields in the fibers, coatings and matrix are obtained in series form. Several comparisons with the finite element method, generalized self-consistent method and asymptotic homogenization method are made to demonstrate the accuracy of the present method. The influences of the thickness and stiffness of coatings on interfacial stress concentration and effective longitudinal shear modulus are discussed. The present method provides an efficient tool for interfacial effect analysis of multiply coated fiber composites.