Creep Behavior of the Factorable BKZ Constitutive Model

Abstract

The factorable BKZ constitutive models including that of the Doi-Edwards tube model theory is not capable of describing steady shear flow behavior at constant stress. The existence of the steady shear involving large strains at very small stresses requires that the damping function must always remain unity for very slow deformation. If a steady shear flow is attained in the creep at high stresses, the damping function may not decrease indefinitely with increasing strain but must tend to approach a finite value η(γ)/η₀ where η(γ) is the steady shear viscosity and η₀ is the zero-shear viscosity. These features can be introduced to the model if an effective strain, that does not increase indefinitely in the case of gradually increasing strain, is used in the place of the strain in the damping function. The effective strain may be defined by counting only the strain applied to the material not earlier than t-2τ_A where t is the current time and τ_A is an average relaxation time defined as the product of viscosity and the steady shear compliance. With this modification of the model the values of steady shear viscosity evaluated for the creep and for the flow of fixed rate of shear are consistent with each other up to a moderate rate of shear.