纤维排列方式对复合材料总体粘弹性常数的影响

对于金属基或高分子聚合物基复合材料，在特定情况下会表现出明显的粘弹性特性。本文采用Riemann—Liouville形式的分数阶导数模型描述基体的粘性特性，通过渐进均匀化方法给出了预测纤维加强复合材料整体本构关系的解析表达式，给出应用于基体具有Makris粘弹性关系的具体形式。最后，考察了圆截面纤维正方形排列和对角排列时的总体粘弹性弹性常数随纤维比的变化曲线。结果表明，这类复合材料仍具有粘弹性特性，其整体粘弹性本构关系的弹性部分综合了纤维弹性和基体弹性的贡献，粘性部分来自基体粘性的贡献，复合材料具有和基体相同的粘性系数和分数阶。为分析微结构特征对整体特性的贡献，须求解两类局部问题。在相同纤维体积比情况下，正方形排列的总体弹性系数大于正方形对角排列，而粘性常数相反。

The Viscoelastic Response of Fiber-Reinforced Composite Material

Under some circumstances, metal-based or polymer-based composite may behave viscoelasticaly. In the present paper, the fractional derivative model in Riemann-Liouville form is adopted to describe the viscous property of the matrix. Then the global constitutive relationship of fiber reinforced composite is formaluted, based on the asymptotic homogenization method. An application of the method is given when the matrix is of Makris's viscoelastic relation. The case of rectangular arrangement and staggered arrangement of fibers with circular cross-section are cited, the curves of global elastic constants and global viscous constants vs volume ratio of fibers are calculated. It can be concluded that, such composite is also viscoelastic, with the global elastic part is made up of the elasticity of both fibers and matrix, while global viscous part solely comes from matrix. The compoiste has the same viscous coefficient and fractional derivative as the matrix. In order to determine the microstructural parameters in global constitutive relations, two types of local problems have to be solved. At the same volume ratio of fibers, the global elastic constants of rectangular arrangement are greater than that of staggered arrangement, while the viscous constants behave counter to them.