THE DECAYING SPRINGS MODEL FOR IRREVERSIBILITY IN POLYMER MELTS

In this work, entanglements in a polymer melt are modeled as a system of parallel springs which form and decay spontaneously. The springs ar e assumed to be nonlinear, and a certain fraction of them is torn apar t by a certain strain. Based on these assumptions, a model of behavior in simple shear is developed. This model is shown to predict a behavi or comprising that of a Wagner fluid, and is generalized to a tensoria l model of single integral type. The integrand depends on a product of a material function, modeling reversible behavior, and a material fun ctional which takes irreversible processes into account. Irreversibili ty of network disentanglement, which may occur when deformation change s or reverses direction, can be modeled in this way. It is shown that the two well-known Wagner constitutive equations with and without irre versibility assumptions are special cases of the model developed. In c ase of a deformation which does not change directions, the new materia l function and the material functional are multiplied to yield Wagner' s damping function. When the rate of spring formation is a function of temperature, the developed model is shown to predict thermorheologica lly simple behavior. A constitutive equation for non-isothermal flow o f polymers is developed with this assumption.