Studies on Constitutive Equations for Polymer Liquids

Abstract

Studies on integral and differential constitutive equations by the present authors are summarized and some new results are presented. Applicability of various constitutive equations to some typical deformation modes is investigated. In integral equations, superiority of the BKZ model is established. But it is also known that the model fails in a prediction of stress relaxation for double‐step shear strains in which the second step strain is applied in the opposite direction to the first. A stress dependent constitutive model of integral type proposed by the present authors can describe this double‐step stress relaxation very well as well as ordinary single‐step stress relaxation and shear rate dependence of viscosity. Compared to integral equations, applicability of differential equations is limited. The Leonov model is very useful to predict viscoelastic functions in steady shear flow, but it fails in describing both stress relaxations for a step strain and after cessation of steady shear flow. The Giesekus model gives slightly better predictions for steady shear flow and for these stress relaxations, but fundamentally the Giesekus and Leonov models cannot be accepted as exact models for stress relaxation. On the other hand, the Larson model can describe both stress relaxations well, but it gives too strong shear rate dependences for viscosity and coefficient of first normal stress difference. It is concluded that further studies on stress dependent model of either integral or differential type will yield fruitful development of constitutive equations.