纤维增强塑料的粘弹性参数

对于弹性纤维增强的复合材料,当其基体的粘弹性行为用分数阶导数型本构关系描述时,给出了预测整体三维本构关系的解析表达式。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共同贡献。粘性部分同样可以表示成分数阶导数的形式,这一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。建模采用渐近均匀化方法。为分析微结构特点对整体特性的贡献,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。给出了应用于基体具有Makris粘弹性关系的具体形式。以圆截面纤维错排的情形为例,给出了整体等效模量随纤维比的变化曲线。

Viscoelastic Parameters of Fiber Reinforced Plastics

Polymer is frequently used to be as the matrix of the fiber reinforced plastic(FRP).It behaves viscoelastic when undergoes deformation.In the present paper a new concept of "fractional derivative" is adopted to describe the viscoelastic property of the plastic matrix.Then a global three-dimensional constitutive relation for viscoelastic FRP is formulated.The viscoelastic constitutive relations of FRP can still be expressed in the same form as Kelvin-Voigt's as the matrix is.The global elastic part is made up of elasticity of both fibers and matrix,while global viscous part solely comes from matrix,which can be expressed by means of fractional derivative.The viscoelastic FRP has the same viscous coefficient as the matrix.Modeling is based on the asymptotic homogenization method.In order to determine the microstructural parameters in global constitutive relations,two types of local problems have to be solved.Equivalent moduli include the contribution of local deformation.Local deformation is thought to increase the coupling stiffness of FRP.An application of the method is given when matrix is of Makris's viscoelastic relation.The case of staggered arrangement of fibers with circular cross-section is cited as an example.The curves of global elastic constants and global viscous constants vs volume ratio of fibers are gained.