A Nonlinear Viscoelastic Model for Representing Nonfactorizable Time‐Dependent Behavior in Cured Rubber

Abstract

A nonlinear constitutive equation is advanced for cured rubber where the elastic and relaxation contributions to the overall response have separate generalized deformational dependences. Predictions of viscoelastic behavior based on this theory are then compared to transient and dynamic data acquired in two strain fields on a natural rubber gum vulcanizate. It is shown that the model successfully predicts the nonfactorizability of time and strain effects observed for the large strain and the incremental strain, stress relaxation functions, and for the incremental storage modulus. However, in the case of the incremental loss modulus, these effects are observed to be factorizable, a behavior also predicted by the model. Further, the observed deformational dependence of the incremental loss tangent is well characterized by the theory. The relaxation spectrum as defined by the linear theory of viscoelasticity is shown for this elastomer to be independent of the state of deformation in the two strain fields for strains up to 130%. This is observed despite the nonfactorizable behaviors shown by the stress relaxation and the incremental storage and relaxation modulus data. Finally, factorizability of time and strain effects in incremental loss modulus results is shown to be a necessary and sufficient condition for the relaxation spectrum to be independent of the state of strain.