Applicability of Integral Type Constitutive Equations, Including a New Model

Abstract

Present-day constitutive equations, including the rate-dependent model of Carreau and the deformation-dependent model of Yamamoto, can be classified according to the dependences of Lkn and τkn-1 on certain tensor invariants. Here Lkn, and τkn-1 are the rate of creation of network strands and the probability of the disappearance of junctions, respectively, as defined by Lodge. A new constitutive equation is presented here, in which Lkn depends on the invariant of relative strain and τkn-1, on that of rate of strain.The applicability of integral type constitutive equations, including the new one presented here, is examined by comparing their predictions with the experimental results on the non-linear and unsteady response of concentrated polymer solutions. The non-linear viscoelastic phenomena examined are steady-shear flow, stress-overshoot, interrupted flow, stress relaxation under large strain, two-step stress relaxation, stress relaxation after cessation of steady flow, and stress relaxation after stress development.By using constitutive equations having memory functions whose relaxation time depends on the rate of strain, the experimental results can be explained fairly well, except for the two-step stress relaxation. On the other hand, the model with strain-dependent relaxation time does explain the two-step relaxation qualitatively, although it does not satisfactorily explain the results of interrupted flow, stress relaxation under large strain, and stress relaxation after cessation of steady flow.It was found that no constitutive equation of the integral type can consistently describe stress relaxation under large strain and two-step stress relaxation.