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Article Dans Une Revue Physical Review Letters Année : 2016

Self-Amplification of Solid Friction in Interleaved Assemblies

Résumé

It is nearly impossible to separate two interleaved phone books when held by their spines. A full understanding of this astonishing demonstration of solid friction in complex assemblies remains elusive. In this Letter, we report on experiments with controlled booklets and show that the force required increases sharply with the number of sheets. A model captures the effect of the number of sheets, their thickness, and the overlapping distance. Furthermore, the data collapse onto a self-similar master curve with one dimensionless amplification parameter. In addition to solving a long-standing familiar enigma, this model system provides a framework with which one can accurately measure friction forces and coefficients at low loads, and that has relevance to complex assemblies from the macro-to the nanoscale. Many of us are familiar with a classical demonstration of the strength of friction: take two phone books, interleave their sheets, and try to separate them by pulling on their spines. This demonstration has been carried out spectacularly by attempting to pull the books apart with people, or by lifting a car [1] or even with two military tanks [2], only to fail and suggest that the inner friction between these sheets prevails. The simple explanation often given is that gravity provides the normal force that generates the tangential friction, but this hypothesis is easily proven to be wrong as there is no discernible difference between such an experiment carried out in the vertical or horizontal direction. In this Letter, we study the force needed to separate two books as a function of the number of sheets, the thickness of the sheets, and the interleaving distance. In particular, we show that the force required to separate the books increases abruptly with the number of sheets. The strength of the system is due to the operator: the person, car, truck, or tank, amplifies any small friction arising from the normal force acting on the boundaries of the stack. We present a simple model that captures all the data into a self-similar master curve. The model depends on one single dimensionless amplification parameter, and thus gives insight into the mechanisms at play in this deceivingly complex system. In addition to solving a long-standing familiar enigma related to the classical problem of friction, this model system provides a framework within which one can accurately measure friction forces and coefficients at low loads, and opens the way to the technologically relevant engineering of friction in complex assemblies from the macro-to the nanoscale. The first-known systematic studies of friction were carried out five centuries ago by da Vinci [3,4] who discovered basic rules that were later confirmed by Amontons [3]. In particular, these laws establish that the friction force is independent of the contact area and proportional to the applied load during sliding, the proportionality constant being the coefficient of kinetic friction. Coulomb rediscovered these laws and further determined that, during sliding, friction is independent of the relative speed between the surfaces [3]. This simple set of rules, collectively known as the Amontons-Coulomb (AC) laws, has been well studied in macroscopic experiments over the centuries. During the last decades, efforts on the micro-and nanoscale, and towards biology [5] have resulted in a resurgence of activity in tribology. For example, tools like the surface force apparatus and the atomic force microscope have fuelled experimental efforts [6–8], as well as advanced theoretical treatments that go well beyond phenomenology [9–11]. Interest in the development of microelectromechanical systems and mechanical devices that operate on small length scales has driven much of this research. At the extreme limit, down to the nano-scale, it was found that the energy dissipation in friction depends on both electronic and phononic contributions, and that differences in the electron-phonon coupling between single and bilayer sheets of graphene result in variations in friction [12]. Furthermore, friction was probed in experiments on multiwalled carbon nanotubes and boron nitride nanotubes [13–15]. In such investigations, the inner tubes could be slid out of the outer tube, revealing vanishingly small molecular friction for carbon, and a much stronger, area-dependent, molecular friction for boron nitride [15]. Clearly, such works reveal drastic departures from the simple AC laws, as one approaches the nanoscale. Moreover,
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Dates et versions

hal-01481242 , version 1 (09-12-2023)

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Héctor Alarcón, Thomas Salez, Christophe Poulard, Jean-Francis Bloch, Élie Raphaël, et al.. Self-Amplification of Solid Friction in Interleaved Assemblies. Physical Review Letters, 2016, 116, ⟨10.1103/PhysRevLett.116.015502⟩. ⟨hal-01481242⟩
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