A Network Theory of Nonlinear Viscoelasticity

Abstract

Two kinds of relaxation processes are introduced for the theory of nonlinear viscoelasticity of temporarily crosslinked network structure. One is the chain-slip and the other is the change in number of chains as a function of time. Three assumptions are made for this theory: (1) The relaxation process for the chain-slip is a linear process characterized by a single relaxation time; (2) The chain breakage coefficient is proportional to the absolute value of the average force acting on a chain; (3) The rate of chain creation is constant. The following results are obtained for typical deformations. (1) The viscosity in the steady flow with a constant shear rate is non-Newtonian and at high shear rates its molecular weight dependence deviates from the 3, 4-th power law of viscosity. (2) The stress growth at the onset of the shear flow with a constant shear rate shows a stress overshoot which is prominent at a high shear rate. (3) The stress relaxation at a constant deformation shows a non-linear strain dependence corresponding to relatively short periods of time and a linear relaxation tendency for relatively long periods of time. (4) The stress relaxation at a sudden termination of the shear flow shows a strain rate dependence initially and a linear tendency for long periods of time. A new type of constitutive equation in which the memory function is one of the invariants of the internal strain determined by the slip equation was found by investing the relation between the present theory and the phenomenological constitutive equation.