A "crazy" theory to explain the Rubinstein, Cohen & Fineberg’s Detachment fronts of friction
Recent experiments in sliding friction are a major embarassment for all present understanding of friction using Coulomb or Rice-Ruina-Dieterich-Prakash rate-state dependent theories, which are the subject of large research programs. In particular, Rubinstein et al; (Detachment fronts and the onset of dynamic friction. Nature 430, 1005—1009. 2004) suggest that the contact area is not significantly altered by the fast fronts which perhaps are only precursors to the most important "slow fronts" travelling at speeds about 1/10 of the Rayleigh speed.
Here, with a little "crazy" theory, we suggest that are the fronts of contact renewal of asperities, for which the average number of microcontacts is conserved, but any contact death is, on average, associated with the birth of a new fresh microcontact at an uncorrelated position. Considering a fraction of the energy is dissipated by as adhesive or viscoelastic processes, we use an analogy with the recent mechanism suggested by Chaudhurya-Kim (Shear-induced adhesive failure of a rigid slab in contact with a thin conned film, Eur. Phys. J. E 23, 175—183, 2007) for the velocity of propagation of bubbles in the sliding of thin conned films of rubber on a rigid plate, which is due to an elastic instability in the rubber layer.
The analogy suggests that the macroscopic friction laws do not correctly take into account of the processes occurring at the asperity level, despite they recognize the crucial role played by asperities in deriving the constitutive law. Process of formation birth and death of asperity contacts is the key to understand the friction detachment, as rate-state dependent friction already partly recognize. Using the same equations of the Chaudhurya-Kim bubbles, and correcting only for the different elastic modulus in the PMMA with respect to the rubber, shows surprisingly the asperity "slow fronts" are predicted to move at speed about one order of magnitude lower than the Rayleigh speed, as experimentally noticed in Rubinstein et al (2004). While we don’t beleive there are "bubbles" strictly speaking, this striking result cannot be pure coincidence, and calls for more investigation. It may well be that rate-state dependent friction is just an improvement over Coulomb friction, but not a major one!
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maybe the theory is not crazy after all .... if only:
If only we consider that the basic mechanism for bubble formation is compression of thin layers, which clearly in rubber and with no asperity makes the slow Schallamach "waves" (or better, fronts) that we have been able to see already with technology of the 1960's. But there is no reason not to admit bubbles can also be generated within asperities of micron scale, at nanometer scale, so that we cannot see them.... Yet! But together, we see their movement. I wish de Gennes were alive, I was supposed to meet him last year in Trieste at a workshop, I cannot tell you how disappointed I was not to have had the chance to meet with him. Now, I could have stepped into his office in Paris and he would have confirmed or disprooved my theory in less than a second.
So this seems to be one case where, as Michel de Montaigne says, "I only took other people's flowers, and all I did was to find the chord to bind them"! So here the idea may not be that crazy, just the natural step forward on the shoulders of giants like Bowden, Tabor, Johnson and ... especially de Gennes!
mciava@lms.polytechnique.fr