Nonseparable Behavior in Rubber Viscoelasticity

Abstract

Abstract New large-strain rubber viscoelasticity results for a filled and an unfilled IIR vulcanizate and previously published results for two NR gum vulcanizates have been discussed. The data show that the “mixed” response functions of large-strain stress relaxation, and the incremental storage and relaxation moduli do not demonstrate factorizability of time and strain effects. This is a consequence of the elastic and relaxation contributions in each of the mixed functions being different. The incremental dynamic data also show that the loss modulus for the filled IIR and unfilled NR vulcanizates (unavailable for the unfilled IIR) are separable functions of time and strain. This directly shows that the relaxation spectra for the filled IIR and unfilled NR vulcanizates are independent of strain for the deformations studied. In fact, it is argued that a necessary and sufficient condition for the relaxation spectrum to be independent of strain is that the loss modulus is a factorizable function of time and strain effects. The quantitative success of the Generalized Solid-Liquid (GSL) model in representing the viscoelastic behavior of the gum NR vulcanizate has been reviewed. Although the GSL model applies only to unfilled vulcanizates, it has also been successfully used to qualitatively interpret the results for the filled IIR compounds. Both successes are attributed to the physical assumptions intrinsic to the GSL model; more specifically, 1) the relaxation spectrum is independent of the state of strain, and 2) the deformational dependences of elastic and relaxation contributions to the overall response of the system need not be the same. Physical arguments justifying these assumptions have been covered. It has also been shown with the aid of the GSL model, that a material might exist which demonstrates factorizability in stress relaxation and incremental loss modulus behaviors but nonfactorizability in the incremental storage and relaxation moduli.