Filler reinforcement in rubber carbon-black systems

Reinforcement of elastomers by fine particulate fillers has long been a subject of interest. Einstein (1906 , 1911 ), introduced a well known viscosity law for rigid spherical particles embedded in a continuous liquid. His theory of viscosity gave rise to similar theories for suspended colloidal particles in any medium, be it liquid or solid. This led to the formulation of the stiffness prediction at small strains for spherical and rod shaped filler particles in an elastomer matrix by Guth & Gold (1938) . The nature of the increased stiffness experienced by vulcanised rubber due to the inclusion of fine particulate fillers is further investigated here using micro-structural finite element analysis models. The approach adopted consists of modelling rigid spherical and rod particle unit cells using appropriate strain energy functions at various filler volume fractions. These models are then evaluated in tension to predict the increase in the Young’s Modulus. Comparisons are then made between the experimental work of Mullins & Tobin (1966) as well as Guth–Gold’s (1938) and Guth’s (1945 ) theoretical relationships. From this investigation an insight into the nature of the reinforcing behaviour of filled elastomers is deduced.