高分子熔体和浓溶液的流变性能研究──（Ⅱ）高分子流体的本构方程和其物料函数

Study on Rheological Behavior for Polymer Melts and Concentrated Solutions (Ⅱ) The Integral Constitutive Equation and Material Function for Polymer Melts and Concentrated Solutions

从前一报所提出的具有多重缠结限制作用的高分子非线性粘弹性理论出发，推导出了高分子流体的回忆函数、一般化的积分型本构方程和多种流场分布下的多种物料函数：１）稳态简单剪切流；２）稳态单轴拉伸流；３）小振幅的振动剪切流；４）稳态剪切流前和后的应力增长和应力松弛；５）稳态拉伸流动停止后的应力松弛．提出了一种从流动曲线来测定物料函数中的粘弹性参数ηｏ，Ｇ，ｎ＇和α的新方法．从多重缠结和多重蠕动机理推导出了ηｏ和τｔ同Ｍ的定量关系式，并得到了实验证实．最后以大量高分子流体的流变性能实验数据（η（γ），ψｌ（ω）和η（ω））对所得的静、动态剪切物料函数进行了验证，证实了所提出的非线性粘弹性分子理论与实验有较好的符合．

An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of ηo and τt on M3.4 were derived from the theory or non-linear viscoelashcity with constraints of entanglements for polymer melts. Some material functions of the constitutive equation related to certain test now are examined as follows: (1) simple steady shear flow; (2) steady elongation flow;(3)small-amplitude oscillatory shear flow;(4) stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and complinace). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.