Payne effect

File:Payne Effect in filled rubber.png

The Payne effect is a particular feature of the stress–strain behaviour of rubber,{{cite journal |last1=Payne |first1=A. R. |title=The Dynamic Properties of Carbon Black-Loaded Natural Rubber Vulcanizates. Part I |journal=J. Appl. Polym. Sci. |date=1962 |volume=6 |issue=19 |pages=57–63 |doi=10.1002/app.1962.070061906}} especially rubber compounds containing fillers such as carbon black.{{cite journal |last1=Medalia |first1=A. I. |title=Effect of Carbon Black on Dynamic Properties of Rubber Vulcanizates |journal=Rubber Chemistry and Technology |date=1 July 1978 |volume=51 |issue=3 |pages=437–523 |doi=10.5254/1.3535748 |url=https://doi.org/10.5254/1.3535748 |access-date=7 September 2022}} 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).{{cite journal |last1=Fletcher |first1=W. P. |last2=Gent |first2=A. N. |title=Non-Linearity in the Dynamic Properties of Vulcanised Rubber Compounds |journal=Trans. Inst. Rubber Ind. |date=1953 |volume=29 |pages=266–280 |doi=10.5254/1.3543472 |url=https://doi.org/10.5254/1.3543472 |access-date=7 September 2022}}

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,{{cite journal |last1=Kraus |first1=Gerard |title=Mechanical losses in carbon-black-filled rubbers |journal=Journal of Applied Polymer Science, Applied Polymer Symposia |date=1984 |volume=39 |pages=75–92 }} i.e., to breakage and recovery of weak physical bonds linking adjacent filler clusters.{{cite journal |last1=Wang |first1=M. J. |title=The role of filler networking in dynamic properties of filled rubber. |journal=Rubber Chemistry and Technology |date=1999 |volume=72 |issue=2 |pages=430–448 |doi=10.5254/1.3538812 |url=https://doi.org/10.5254/1.3538812 |access-date=7 September 2022}} 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).{{cite journal |last1=Lion |first1=A. |last2=Kardelky |first2=C. |last3=Haupt |first3=P. |title=On the Frequency and Amplitude Dependence of the Payne Effect: Theory and Experiments |journal=Rubber Chemistry and Technology |date=2003 |volume=76 |issue=2 |pages=533–547 |doi=10.5254/1.3547759 |url=https://doi.org/10.5254/1.3547759 |access-date=7 September 2022}} Similar to the Payne effect under small deformations is the Mullins effect that is observed under large deformations.