A thermo-visco-hyperelastic model for the heat build-up during low-cycle fatigue of filled rubbers: Formulation, implementation and experimental verification

In a previous contribution (Ovalle Rodas et al., 2014), a finite strain thermo-visco-elastic constitutive model, in accordance with the second thermodynamics principle, has been developed to predict the heat build-up field in rubbers during low-cycle fatigue. Using a viscous dilatation tensor, related to the time-dependent response of the rubber material, as an internal variable of the specific free energy potential, both the mechanical behavior and the heat build-up have been predicted for different strain rates and stretches. In the present contribution, the finite strain thermo-mechanical constitutive model is extended by using a stretch amplification factor to account for the effect of carbon-black filler on the heat build-up. Experimental observations on the mechanical response and the heat build-up during fatigue tests of carbon-black filled styrene-butadiene rubber (SBR) containing different filler contents are reported at room temperature. The increasing effect of the filler content on the heat build-up is evidenced. The proposed constitutive model is implemented into a finite element code and the same thermo-mechanical boundary conditions regarding the experimental tests are simulated. The model parameters are identified using experimental data issued from SBR filled with a given carbon-black content under a given strain rate and different stretches. Predicted evolutions given by the proposed constitutive model for other strain rates and amounts of carbon-black are found in good agreement with the experimental data.