Analysis of the tensile stress‐strain behavior of elastomers at constant strain rates. I. Criteria for separability of the time and strain effects

Abstract

AbstractConsidering the case where the relaxation time spectrum is preserved at finite deformations, a theoretical analysis of the tensile stress‐strain relation of elastomers at constant strain rates has been carried out. The finite strain effect is taken into account by replacing the Cauchy strain by a general strain function, ƒ(ϵ), in the Boltzmann superposition integral. The analysis shows that there are two cases where the time and strain effects are separable when: (1) the segment of the stress relaxation modulus which coincides with the experimental time of stretching can be represented by a single power law; and (2) the general strain function, ƒ(ϵ), is linearly proportional to the Cauchy strain. Separability of the time and strain effects, therefore, can be achieved by adjusting the stretching time (or strain) and temperature, if the relaxation time spectrum remains unchanged by the deformation. The tensile stress‐strain relations derived from the theoretical analysis were applied to analyze data on a crosslinked styrene butadiene rubber obtained in the temperature range −40 to 60°C. Γ(ϵ), which describes the strain dependence of tensile stress, Bϵ, the ratio of isochronal stresses at different strains, and ai, slope of a segment of the relaxation modulus Ei(t) on log t plot, were obtained directly from the experiment. Values of Γ(ϵ), Bϵ and ai obtained at −40°C are quite different from those obtained at −30°C or higher. Results obtained from our analysis are generally in agreement with those obtained by an empirical method for analyzing the experimental data.