This research study was devoted to the modeling of the mechanical behavior of three carbon black/silica natural rubber/butadiene rubber (NR/BR) compounds under a tensile load. These compounds were prepared on a two‐roll mill, and the tensile testes were carried out on a dumbbell‐shaped specimen and three rubber‐strip specimens with different widths. Heat buildup tests were also performed, and the temperature rise was determined. The time‐independent behavior of the rubber was described by traditional hyperelastic models, including those of Marlow and Yeoh. The viscoelastic behavior was studied with two linear (Prony series) and nonlinear [Bergstrom–Boyce (BB)] models. A previously developed methodology by the authors, which was based on the finite element modeling of the tension of the rubber strips, was used to determine the parameters of the mentioned equations. It was shown that neglecting the viscoelasticity would have given rise to large errors in predicting the mechanical deformation in the rubbers. However, the linear viscoelastic model failed to predict the correct behavior at a large strain, particularly for wider samples. On the other hand, not only could the combination of the Yeoh hyperelastic model with the BB equation describe the mechanical behavior at low to medium strains, but also the large strains were taken into consideration. Both the linear and nonlinear hyperviscoelastic models accurately described the hysteresis in rubbers, and this could be used for the evaluation of the rolling resistance in tires. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

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The present study discusses that filler–filler mechanical engagement resulting from the grafted long-chain silanes on the silica surface is indeed a reinforcing mechanism in rubber composites, as already speculated by nonlinear viscoelastic properties in our previous study. The existence and severity of such a phenomenon are assessed purely by isolating the energetic contribution of reinforcement from interfering with filler mechanical engagement in the silica network formation and breakdown processes. In a novel approach, the driving force of fillers to flocculate energetically at elevated temperatures was defined using surface energy theories, and it was adjusted to be similar in two composites having silica treated by short- and long-chain silanes. Filler–filler mechanical engagement was monitored by tracking network formation (filler flocculation) in a matrix of styrene–butadiene rubber and also by conducting various dynamic viscoelastic experiments on liquid paraffin suspensions having short- and long-chain silica of similar surface energy. Results consistently confirmed the existence of mechanical engagement between silica particles having the long-chain silane in both rubber compounds and paraffin suspensions. The results may find applications in the rolling resistance of tires, for example, where stabilization of the filler network by displacing the peak energy dissipation of the network breakdown from applied service strains to larger values would be of technical importance.

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We evaluated the significance of mechanical engagement and energetic interaction between a polymer and a filler as two reinforcing mechanisms in SBR composites containing silica modified by short- and long-chain silanes. To exclude mechanical contributions of reinforcement from that of energetic contributions, surface energy of silica particles was systematically adjusted to prepare fillers of identical and diverse surface energies. Having analyzed interactions using a temperature sweep in a small-strain oscillatory test and a uniaxial tension test, results indicated that the chain length of the silane has remarkable influence on energetic filler–filler and filler–polymer interactions, but no detectable difference associated with filler–polymer mechanical engagement was observed from these experiments. However, dynamic strain sweep experiments showed that the rate of breakage of the filler network (Payne effect) is less for the composite having long-chain silane compared to that having short-chain silane. It was hypothesized that this behavior could be correlated to mechanical engagements of long-chain silanes existing on the filler structure.