Parameter determination and experimental verification of Bergström–Boyce hysteresis model for rubber compounds reinforced by carbon black blends

• We have prepared 10 rubber compounds using different carbon black types and amounts.
• Hyper-viscoelastic behaviors of these samples were modeled using Bergström–Boyce equation.
• Relationship between particle size and structure of carbon black and model parameters were discussed.

This research work is devoted to the modeling of the hyper-viscoelastic behavior of rubber compounds using Bergström–Boyce hysteresis model. Two series of rubber compounds reinforced by different carbon black types and amounts were prepared. In the first series single type filler was used while in the second series the blend of two carbon black types was employed. The mechanical behaviors of these samples were studied using a hyper-viscoelastic model which was based on the combination of Yeoh hyperelastic model and Bergström–Boyce hysteresis model implemented in the Abaqus software. A hybrid numerical/experimental technique developed in our previous works was employed to determine the parameters of the Bergström–Boyce model for the mentioned samples. In this technique uniaxial tests were carried out on three rubber strips specimens and the data of force vs. extension were recorded. These data were used in three finite element models to calibrate the material parameters for the aforementioned model and the relationship between particle size and structural measure of the carbon black with parameters of the Bergström–Boyce model were completely discussed.