On the Visco-Hyperelasticity Relationship in Modeling Styrene Butadiene Rubber Under Uniaxial Cyclic Loadings: Experiments and Parameter Identification

The mechanical response of Styrene Butadiene Rubber (SBRs) reinforced by carbon black particles is investigated under cyclic tension. An experimental characterization carried out in Diabolo specimens submitted to cyclic loading at constant strain rate 10−3 s−1 for different stretch level. Some of the key observations from the experiments is the strong influence of hard particles on the deviation from the nonlinear viscoelastic virgin network mechanical behavior in cyclic loadings. Indeed, semi-logarithmic plots of normalized stress vs loading cycles elucidated the appearance of two stress softening fatigue behaviors as function of the loading conditions: a linear pattern for low stretch ratio and CB amount, and the second behavior (a deviation from the linear pattern) is seen at higher value of stretch amplitude, loading cycles and CB particles amount. In order to describe the stress softening of the SBRs materials, a modified visco-hyper-elastic model is developed to incorporate the irreversible changes of the microstructure. Using a nonlinear optimization methods, an identification process from the experimental data was employed to determine the parameters of the constitutive function. The predictive capability of the developed model showed a good accordance between the experimental and the predicted results. ANOVA tests were carried out to analyze the main effect of both carbon black filler and imposed maximum displacement factors the model constants. It is found that the CB filler play an important role on the viscoelastic behavior and stress softening phenomena almost 60% of increase in the constitutive function parameters.