Finite Viscoelasticity of Particle-Reinforced Elastomers: the Effect of Filler Content

Abstract

Constitutive equations are derived for the time-dependent behavior of particle-reinforced rubbers at isothermal loading with finite strains. An elastomer is thought of as a network of macromolecules bridged by junctions that slip with respect to the bulk material under straining. A filled rubber is treated as an ensemble of meso-regions where sliding of junctions occurs at different rates. Two types of domains are distinguished: passive, where slippage of junctions is prevented by intermolecular links, and active, where the sliding process is not affected by interchain forces. Activation of passive meso-regions under loading is modelled as mechanically-induced breakage of van der Waals links between strands. Stress–strain relations are developed using the laws of thermodynamics. For tensile relaxation tests, these equations are determined by four adjustable parameters that are found by fitting experimental data on gum rubber, unfilled rubber, and carbon black-filled natural rubber at longitudinal strains in the range from 100 to 250%. It is revealed that the rate of sliding and the concentration of active meso-regions are noticeably affected by stretching, whereas the distribution of potential energies for sliding of junctions is independent of strains, but is severely influenced by the filler content.