Stress as a Reduced Variable: Stress Relaxation of SBR Rubber at Large Strains

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Abstract
Stress relaxation measurements on SBR were carried out at temperatures from −5 to +60°C and at initial strains of up to 550%. The effects of strain and time were found to be factorable, so that the isochronal stress-strain curve may be written as a modified Hooke's law with a time dependent modulus: S = E(t)ef(α), where f(α) is an appropriate function of the strain. By defining a strain-reduced stress S* = S / f(α), i.e., a strain-reduced modulus E*(t) = E(t)f(α), it can be shown that Ferry's method of reduced variables may be extended to large deformations. An appropriate strain function was obtained from the empirical Martin-Roth-Stiehler equation [Trans. Inst. Rubber Ind. 32, 189 (1956)] as f(α) = α−2 expA (α−α−1) with A =0.40. Although it cannot yet be certain that A is truly a constant and the same for all elastomers, this equation has the advantage of being valid right out to the breaking strain.