Temperature and filler effects on the relaxed response of filled rubbers: Experimental observations on a carbon-filled SBR and constitutive modeling

The self-heating temperature of filled rubbers under cyclic loading at environmental conditions is well-known. This increase in temperature seriously affects the constitutive stress-strain behavior by producing a thermal softening of the rubber compound. Although this feature is well-recognized and considered as important to its function, few constitutive thermo-mechanical models attempt to quantify the stress-temperature relationship. In this work, a physically-based model is developed to describe the large strain relaxed response of filled rubbers over a wide range of temperatures. The non-linear mechanical behavior is described via a Langevin formalism in which the temperature and filler effects are, respectively, included by a network thermal kinetics and an amplification of the first strain invariant. Experimental observations on the relaxed state of styrene-butadiene rubber hourglass-shaped specimens with a given carbon-black content are reported at different temperatures. A hybrid experimental-numerical method is proposed to determine simultaneously the local thermo-mechanical response and the model parameters. In addition, the predictive capability of the proposed constitutive thermo-mechanical model is verified by comparisons with results issued from micromechanical simulations containing different arrangements of the microstructure. The results show that the model offers a satisfactory way to predict the relaxed response of filled rubbers at different temperatures.