The nonlinear stress relaxation behavior after a step shear of star-shaped styrene-butadiene rubber filled with precipitated silica: Experiment and simulation

The nonlinear stress relaxation behavior after a step shear strain of star-shaped SSBR/silica compounds containing 21 vol% filler of various surface areas was measured and simulated using constitutive equations. A styrene-butadiene rubber (SBR) gum and SBR filled with silica having BET surface areas of 55, 135, 160, and 195 m(2)/g were used. Relaxation modulus behavior of the filled compounds was found to be dependent on surface area. Specifically, stress relaxation tests indicated that an increase in surface area led to increase in values of relaxation moduli in both the linear and nonlinear regimes. The time-dependent relaxation modulus exhibited a plateau at long times of relaxation in compounds containing silica of high surface area. Additionally, good time-strain superpositions were achieved for all samples at intermediate times of relaxation, and the strain-dependent damping function decreased with filler surface area. The constitutive equations proposed by Leonov and Simhambhatla and Leonov, modified to include multimodal relaxation of the particle network, were used to predict the time evolution of the relaxation modulus in the nonlinear regime for all samples. The simulations provided good results for the SBR gum for all tested strain levels. Also, in the compounds filled with silica, both models satisfactorily described the experimental observation in the nonlinear regime at low strain levels. However, at higher strain levels, due to a possible slip effect, the simulations overpredicted measured values of the relaxation moduli, thus leading to only qualitative predictions of the observed behavior. It is also possible that neither model accurately captured the floc rupture kinetics of these complex rubber compounds.

Automated summary

The study investigated the nonlinear stress relaxation behavior of star-shaped SSBR/silica compounds with different filler surface areas, concluding that the relaxation modulus behavior of filled compounds is influenced by surface area. Higher surface area fillers resulted in increased relaxation moduli, particularly in compounds with high surface area silica. While both models were effective in describing experimental observations at low strain levels, at high strain levels there was a tendency for the simulations to overpredict the measured values, possibly due to slip effects.