Modelling reinforcement of rubber with carbon black filler

Mechanical reinforcement of rubber (soft phase) by random distribution of reinforcing units (hard phase), representing carbon black (CB) filler, has been modelled by finite element (FE) analysis. Using a hybrid numerical experimental method, approximate modulus and effective volume fraction of CB reinforcing units, as well as local stress/strain in two phases of the model, were calculated. Non-linear elastic properties of rubber phase and its corrected cross-link density were employed in the model. Strain amplification factor in the rubber phase, as a measure of rubber reinforcement by CB, was estimated and compared with springs in series model of Mullin and Tobin. It was concluded that mechanical behaviour of particulate filled rubber composites agrees with the springs in series model and follows the state of uniform stress rather than the state of uniform strain.