||Nowadays, filled-rubbers are frequently used in several technical components in industrial sectors related with the transport mainly due to their damping properties. As a matter of fact, rubber components are submitted to cyclic loading under common operating conditions. Due to the thermo-mechanical coupling, in connection with the viscous-related rubber behavior, the material heats up. Experimental results have shown that the order of magnitude of the self-heating is related with the strain rate, the maximum strain, the geometry of the specimen and the filler volume fraction.
A detailed thermo-visco-hyperelastic constitutive model , compatible with the dissipation principle in the form of the Clausius-Duhem inequality, is formulated to describe the self-heating evolution in filled-rubbers under cyclic loading. The proposed model is based on a Zener rheological representation in which the mechanical response is decomposed into two components: a relaxed component that takes into consideration the material state after long-time stress relaxation and a second component that takes into consideration the non-linear time-dependent deviation from the relaxed response. The thermo-mechanical coupling is defined by postulating the existence of a dissipation pseudo-potential, function of the viscous dilatation tensor. The non-linear mechanical behavior is described via a Langevin formalism in which the filler effects are included by an amplification of the first strain invariant. Experimental observations on the self-heating of styrene-butadiene rubber (SBR) dogbone specimens with different carbon-black contents are reported. The proposed model is fully three-dimensional and has been implemented into a finite element code where the same conditions regarding the experimental tests have been simulated.
The model parameters are identified using the SBR experimental data obtained at a given strain rate and predicted evolutions provided by the proposed thermo-visco-hyperelastic model are compared for other strain rates. As an example Fig. 1 presents the self-heating evolution on a SBR dogbone sample for three strain rates and two stretch values (λ11 = 1.2 and λ11 = 1.4) at a given filler volume fraction vf = 0.19. The capability of the thermo-visco-hyperelastic model to take into account the filler effects on the SBR self-heating behavior is discussed.