Saturday, June 29, 2019

Flocculation and the Payne effect

With the quality of racing in contemporary Formula One reaching something of a nadir, some parties have sought a quick-fix by proposing that Pirelli revert to their thicker-gauge 2018 tread design. With tyres back on the agenda, then, perhaps it's a good moment to look a little bit deeper at the composition of a racing tyre tread. 

A modern pneumatic tyre-tread contains rubber. Rubber itself consists of long chains of polymer molecules. The chains are mutually entangled, and in its raw form it is a highly-viscous liquid. It is not, however, elastic. It only becomes a viscoelastic solid when it undergoes 'vulcanization', whereby sulphur crosslinks are created between the molecular chains. This transforms the already entangled collection of polymer chains into a 3-dimensional network. 

So far, so familiar. However, a modern tyre-tread is a rubber composite. In addition to the network of vulcanized rubber, it contains a network of 'filler' particles. These filler particles are not just dispersed as isolated particles in the rubber matrix; rather, they agglomerate into their own 3-dimensional network. (The term for this agglomeration is 'flocculation').

The rubber network and filler network interpenetrate each other. Hence, the elasticity, viscosity, and ultimately the frictional grip of a tyre-tread is attributable to three sources: (i) the cross-links and friction between rubber polymer molecules; (ii) the bonds between filler particles; and (iii) the bonds between filler particles and the rubber molecules.

'High-performance' racing tyres, of course, are something of a world of their own, and tend to use carbon-black as a filler in high concentrations because it increases hysteresis (i.e., viscous dissipation) and grip. One can find statements in the academic literature such as the following:

"For a typical rubber compound, roughly half of the energy dissipation during cyclic deformation can be ascribed to the agglomerated filler, the rest coming from [rubber polymer] chain ends and internal friction [of polymer network chains]," (Ulmer, Hergenrother and Lawson, 1988, 'Hysteresis Contributions in Carbon Black-filled rubbers containing conventional and tin end-modified polymers').

Given the higher concentration of filler in a racing tyre, one might expect more than half of the energy dissipation, and therefore the frictional grip, to come from the agglomerated filler.

And now comes the interesting bit. Filled rubber compounds suffer from the 'Payne effect'. This is typically defined by the variation in both the storage modulus, and the loss modulus (or tan-delta) of the tyre when it is subjected to a strain-sweep under cyclic loading conditions. (The storage modulus is related to the elasticity or stiffness of the material, and the loss modulus is related to the viscous dissipation).

Typical graphs, such as that above, show that the storage modulus decreases as the amplitude of the strain is increased, whilst the loss-modulus or tan-delta reaches a peak at strains of 5-10%.

The Payne effect is typically attributed to the breaking of bonds between filler particles, as Pirelli World Superbike engineer Fabio Meni attests:

'Riders constantly talk about how their tires "take a step down" after a few laps, so I asked Meni what physical process in the rubber is responsible for this perceived drop in properties. "This has a name", he began. "It is called the Payne effect."

"In the compound," Meni continued, "the carbon-black particles are not present as separate entities but exist as aggregates - clusters of particles. As the tire is put into service, the high strains to which it is subjected have the effect of breaking up these aggregates over time, and this alters the rubber's properties."

Meni went on to say that it is not so much that the tire loses grip as it feels different to the rider. This is 'the step' that the rider feels after a few laps, after which the tire's properties may change little through the rest of the race.

In fact, I would quibble with this slightly: in the world of Formula One tyres, the way in which a tyre is treated at the beginning of a stint will often determine the subsequent degradation slope. If you abuse a tyre, it remembers it, and punishes you. Damage to the filler network appears to reduce grip, not merely soften a tyre.

One intriguing twist to the Payne effect is that there may be circumstances in which it is possible for a tyre to recover from damage to the filler network: "Much of the softening remains when the amplitude [of the strain in a cyclic strain-sweep] is reduced back to small values and the original modulus is recovered only after a period of heating at temperatures of the order of 100 degrees C or higher," (A.N.Gent, 'Engineering with Rubber', 2012, p115).

So heat is capable of annealing a damaged filler network, restoring the bonds between filler particles. The anneal temperature quoted here by Gent is not dissimilar to the maximum tyre-blanket temperatures currently permitted by Pirelli in Formula One...

As a final flourish on this subject, for those who like a bit of scanning electron microscopy, images of filler-reinforced rubber which has been in a state of slip across a rough surface, reveal that there is a modified 'dead' surface layer, about a micron-thick, in which the carbon-black filler particles are absent, (image below from work conducted by Marc Masen of Imperial College).

To paraphrase Homer Simpson, "Here's to tyres: the cause of, and solution to, all of Formula One's problems."

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