Linear Viscoelastic Relation Concerning Shear Stresses at the Start and Cessation of Steady Shear Flow

Abstract

This paper deals with the linear viscoelastic relations for transient shear stresses at the start and cessation of steady shear flow. Viscosity growth function η(t) and viscosity decay function η(t) were defined as the limiting values at vanishing rate of shear, of the ratios of shear stresses to the rate of shear at the start and cessation, respectively, of steady shear flow. A short review was given for exact interrelations among η(t), η(t), and other linear viscoelastic functions. Approximation equations for evaluating various functions from the relaxation modulus could be easily transformed into equations for evaluating various functions from η(t). Proposed approximation formulae for complex viscosity and relaxation spectrum proved usable when examined numerically in the cases of wedge- and box-type relaxation spectra. The approximation formulae for the relaxation spectrum may be employed for determining the rate-dependent relaxation spectrum of nonlinear viscoelasticity.