功能梯度界面相对周期分布纤维增强复合材料反平面剪切的影响  

Influence of a Functionally Graded Layer on the Anti-plane Shear Behavior of a Periodic Fibrous Composite

作　　者：杨绘峰[1,2] 高存法[1] Huifeng Yang;Cunfa Gao(Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics&Astronautics,Nanjing,210016;School of Naval Architecture&Ocean Engineering,Jiangsu University of Science and Technology,Zhenjiung,212003)

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016 [2]江苏科技大学船舶与海洋工程学院,镇江212003

出　　处：《固体力学学报》2021年第1期53-62,共10页Chinese Journal of Solid Mechanics

基　　金：国家自然基金面上项目(11872203);江苏高校优势学科建设工程项目资助。

摘　　要：基于复变函数理论和边界配点法,探索了功能梯度界面相在周期均匀分布纤维增强复合材料反平面剪切问题中所起的作用.由于纤维在复合材料基体中的周期分布是均匀的,将其简化成含一功能梯度界面相夹杂的方形单胞.采用分层均匀化方法,将功能梯度界面相离散成K层界面层.当K足够大时,每个界面层可视为匀质材料,同时计算得到的复合材料宏观性能趋于定值.根据单胞内的基体、界面相和夹杂的几何外形特点,分别给出复势函数的级数形式,这些复势函数在各组分的相邻界面应满足连续性条件,在单胞的外边界应满足周期性边界条件和远场加载条件,从而确定复势函数中的待定系数,进而根据平均场理论确定复合材料有效模量.主要探讨了夹杂体积分数、各组分模量、功能梯度界面相的模量渐变形式等因素对纤维增强复合材料性能的影响.结果表明:不管基体模量相对于夹杂模量是大还是小,都有对应的界面相模量渐变形式可使夹杂周围的等效应力集中系数减小;另外还发现仅当夹杂模量较大时,功能梯度界面相模量的变化方式对复合材料有效模量产生不可忽视的影响.Based on the complex variable techniques combined with the boundary collocation method,a semi-analytical procedure is proposed to explore the influence of a functionally graded layer on the anti-plane shear behavior of a periodic fibrous composite.The distribution of the inclusions in the matrix is assumed to be periodically uniform so that the composite is represented by a square unit cell with a single inclusion coated with a functionally graded layer.The elastic properties of the functionally graded layer are assumed to vary continuously in the normal direction of the interface so that we may use a group of homogeneous perfectly-bonded sublayers(each having individual elastic constants)to describe approximately the mechanical response of the functionally graded layer to the interaction between it and the surrounding bulk(inclusion and matrix).Specific series with unknown coefficients are introduced to describe the complex potential functions of the representative unit cell of the composite.The unknown coefficients are determined from the continuity conditions on the interface and the periodic boundary conditions imposed on the edge of the unit cell.Once the complex potential functions are determined,the effective moduli of the composite are obtained according to the average-field theory.The effects of the fiber volume fractions,modulus of each component and material gradient parameter of the functionally graded layer on the properties of the composite are discussed via several numerical examples.The results show that whether the modulus of the matrix is larger or smaller than that of the inclusion,one may always design an appropriate material gradient parameter of the functionally graded layer to reduce the equivalent stress concentration around the inclusion.In addition,it is found that the material gradient parameter of the functionally graded layer may have a non-negligible influence on the effective moduli of the composite only when the inclusion is stiffer than the matrix.

关 键 词：复合材料 复变函数 功能梯度界面相 周期分布 

分 类 号：TB33[一般工业技术—材料科学与工程]