Deformation behaviour of silica filled rubber under monotonic and cyclic straining

A new constitutive equation of rubber is derived by employing a non-affine molecular chain network model for an elastic deformation behaviour and the reptation theory for a viscoelastic deformation behaviour. The deformation behaviours of two-dimensional rubber unit cells containing silica fillers under monotonic and cyclic straining are investigated by computational simulation with the proposed constitutive equation and the homogenisation method. The effect of a silica coupling agent, whose condensation reaction creates a cross-linking agent that increases the number of entangled points, on the deformation behaviour is introduced through the non-affine constitutive equation of rubber. The precise TEM observation suggests the generation of complex interfillers connecting phases where the characteristics of rubber intricately changed depending on the volume fraction of the silica coupling agent and the location of rubber phase. The obtained results clarified the essential physical enhancement mechanisms of deformation resistance and hysteresis loss, i.e. the Mullins effect, for rubber filled with silica. The volume fraction of the silica coupling agent essentially affects the deformation behaviour of silica filled rubber, suggesting the high controllability of the material characteristics of silica filled rubber compared with carbon black filled rubber.