A Constitutive Model in Finite Viscoelasticity of Particle-reinforced Rubbers

Two series of tensile relaxation tests are performed on natural rubber filled with high abrasion furnace black. To fit observations, constitutive equations are derived for the nonlinear viscoelastic behavior of a particle-reinforced elastomer. A filled rubber is modeled as a composite medium, where inclusions with low concentrations of junctions are randomly distributed in the host matrix. The inclusions are treated as equivalent networks of macromolecules, where strands can separate from temporary junctions as they are thermally agitated. The bulk medium is thought of as a permanent network of chains. Unlike conventional concepts of transient networks, the concentration of strands in inclusions is assumed to be affected by mechanical factors: under active loading, inter-chain interactions weaken and some strands that were prevented from detachment from their junctions in a stress-free compound become free to separate from the junctions in a deformed medium. Unloading strengthens interactions between macromolecules, which results in an increase in the number of permanent strands. By using the laws of thermodynamics, stress–strain relations for a particle-reinforced rubber are developed. Adjustable parameters in the constitutive equations are found by fitting the experimental data. It is demonstrated that mechanical pre-loading and annealing of specimens at an elevated temperature noticeably affect concentrations of inclusions with various activation energies for rearrangement of strands.