Payne effect

The Payne effect is a particular feature of the stress–strain behaviour of rubber,[1] especially rubber compounds containing fillers such as carbon black.[2] It is named after the British rubber scientist A. R. Payne, who made extensive studies of the effect (e.g., Payne 1962). The effect is sometimes also known as the Fletcher-Gent effect, after the authors of the first study of the phenomenon (Fletcher & Gent 1953).[3]

Strain amplitude dependence of storage and loss moduli in filled rubber.

The effect is observed under cyclic loading conditions with small strain amplitudes, and is manifest as a dependence of the viscoelastic storage modulus on the amplitude of the applied strain. Above approximately 0.1% strain amplitude, the storage modulus decreases rapidly with increasing amplitude. At sufficiently large strain amplitudes (roughly 20%), the storage modulus approaches a lower bound. In that region where the storage modulus decreases the loss modulus shows a maximum. The Payne effect depends on the filler content of the material and vanishes for unfilled elastomers.

Physically, the Payne effect can be attributed to deformation-induced changes in the material's microstructure, i.e., to breakage and recovery of weak physical bonds linking adjacent filler clusters.[4] Since the Payne effect is essential for the frequency and amplitude-dependent dynamic stiffness and damping behaviour of rubber bushings, automotive tires and other products, constitutive models to represent it have been developed in the past (e.g., Lion et al. 2003).[5] Similar to the Payne effect under small deformations is the Mullins effect that is observed under large deformations.