A Study on Constitutive Equations of Polymer Solutions: Application of Double-Step Stress Relaxation

Abstract

Stress relaxation after application of double-step shear strains was measured on two concentrated solutions of polystyrene in diethyl phthalate with a cone-plate type relaxometer. The first strain s1 was applied to the sample at time t=-t1, the second strain s2 was added at t=0 either in the same direction as the first or in the opposite direction, and then the shear stress was measured as a function of time t. A simple case of this type of deformation in which s1=-s and s2=s>0 was found to be useful to examine the applicability of various models of single-integral type constitutive equations such as proposed by Carreau, Yamamoto, and Takahashi et al. No constitutive equation of this type was able to explain the experimental results quantitatively, except in the case of very small strains. The discrepancy between theoretical and experimental values of stress became more marked as the value of time interval t1 was smaller. A new type of strain-dependent constitutive equation presented here, however, was able to represent quantitatively the stresses obtained for the type of deformation history investigated here, unless the value of t1 was very small. This equation is of the same form as Yamamoto's, but contains the invariant of strain-tensor defined on the reference time different from that of Yamamoto's equation.