摘要
在某些纤维增强复合材料(FRC)中使用金属或高分子聚合物作为基体材料。在高温等情况下,这类材料具有明显的粘弹性特性。本文采用Riemann-Liouville形式的分数阶导数模型描述基体的粘弹性特性。通过渐近均匀化方法给出了预测FRC整体三维本构关系的解析表达式。给出了应用于基体具有Makris粘弹性关系的具体形式。以圆截面纤维正方形排列的情形为例,给出了等效模量随纤维体积比的变化曲线。结果说明,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。可以看出,在整体的等效模量中包含了局部变形的贡献,局部变形增加了复合材料的耦合刚度。
Polymer is frequently used to be as the matrix of fiber reinforced composite (FRC). It behaves viscoelasticaly under high temperature. In the present paper a new concept of 'fractional derivative' was adopted to describe the viscoelastic property of the matrix. Based on the asymptotic homogenization method a global three-dimensional constitutive relation for viscoelastic FRC was formulated. An application of the method was given when the matrix is of Makris's viscoelastic relation. The case of rectangular arrangement of fibers with circular cross-section was cited as an example. The curves of global elastic constants and global viscous constants vs volume ratio of fibers were obtained. It can be concluded that the viscoelastic constitutive relations of FRC can still be expressed in the same form of Kelvin-Voigt's as the matrix. The golbal elastic part is made up of elasticity of both fibers and matrix, while golbal viscous part solely comes from matrix, which can be expressed by means of fractional derivative. The viscoelastic FRC has the same viscous coefficient and fractional derivative as the matrix. In order to determine the micro-structural parameters in global constitutive relations two types of local problems were solved. Equivalent moduli include the contribution of local deformation. Local deformation is thought to increase the coupling stiffness of FRC.
出处
《力学季刊》
CSCD
北大核心
2003年第2期191-197,共7页
Chinese Quarterly of Mechanics
关键词
复合材料
粘弹性
渐近均匀化方法
分数阶导数
composite material
viscoelastic
asymptotic homogenization
fractional derivative model
