Modelling Filler Reinforcement in Elastomers
Reinforcement of elastomers by fine particulate fillers has long been a subject of interest. Einstein (1906, 1911), developed a viscosity law for rigid spherical particles embedded in a continuous liquid. His hydrodynamic theory of viscosity gave rise to similar relationships for the increase in stiffness at small strains due to the incorporation of spherical and rod shaped filler particles in an elastomer matrix by Guth & Gold (1938). These theories are limited in scope to regular shaped well dispersed fillers incorporated at low volume fractions working at small strains. A large number of empirical relationships have been derived to predict the reinforcement of real filled elastomer materials. However, these relationships tend to only work for specific applications and rarely take into consideration the actual microstructural changes under strain. This thesis aims to evaluate the use of microstructural Finite Element Analysis (FEA) models to predict the stiffness of filled elastomers over a range of strains. Unit cells containing rigid spherical and rod shaped filler particles have been modelled using appropriate strain energy functions to describe the elastomer behaviour for a range of filler volume fractions. These models have been strained to evaluate the change in the Young’s Modulus with strain. Comparisons are then made between the experimental work of Mullins & Tobin (1965) as well as Guth-Gold’s (1938) and Guth’s (1945) theoretical relationships. This research shows that two-dimensional FEA modelling only gives an indication of filled rubber behaviour. At small strains three-dimensional FEA models were able to predict the first loading behaviour without recourse to nano structural interactions. Further experimental work was also conducted using Isoprene rubber filled with model steel wires to represent rod shaped fillers at various filler volume fractions and orientations. Also the effects of the slippage of the rubber over the filler surface has been investigated using FEA techniques and compared with well established theories for the origin of the viscoelastic behaviour of filled elastomers. At large strains the effect of slippage at the filler-rubber interface dominates and there is good correlation for FEA models with regular shaped fillers. The critical shear stress friction model predicts the loading cycle well but not the unloading where filler breakdown is more prominent. From these investigations an insight into the nature of the reinforcing behaviour of filled elastomers is deduced.