On the origin of Amonton’s friction law

Bo N J Persson, Ion Marius Sivebæk, Vladimir N Samoilov, K. e. Zhao, Alexander I Volokitin, Zhenyu Zhang

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Amonton's law states that the sliding friction force increases linearly with the load. We show that this result is expected for stiff enough solids, even when the adhesional interaction between the solids is included in the analysis. As a function of the magnitude of the elastic modulus E, one can distinguish between three regions: (a) for E > E-2, the area of real contact (and the friction force) depends linearly on the load, (b) for E-1 <E <E-2, the area of real contact depends nonlinearly on the load but vanishes for zero load, and (c) for E <E-1 the area of real contact depends nonlinearly on the load and is non-vanishing at zero load. In this last case a finite pull-off force is necessary in order to separate the solids. Based on molecular dynamics calculations, we also discuss the pressure dependence of the frictional shear stress for polymers. We show that the frictional shear stress is independent of the normal pressure p(0) as long as p(0) is much smaller than the adhesional pressure p(ad), which depends on the atomic corrugation of the solid surfaces in the sliding interface. Finally, we discuss the origin of why the contact area between a soft elastic solid (e. g. rubber) and a flat substrate decreases from the JKR (adhesive contact) limit at zero or small sliding velocities, to the Hertz (non-adhesive) limit at high sliding velocities.
Original languageEnglish
JournalJournal of Physics: Condensed Matter
Volume20
Issue number39
Pages (from-to)395006-395017
ISSN0953-8984
DOIs
Publication statusPublished - 2008

Keywords

  • STATIC FRICTION
  • ELASTIC SOLIDS
  • ADHESION
  • SURFACE
  • STICK-SLIP
  • SHEAR
  • RUBBER-FRICTION
  • CONTACT
  • KINETIC FRICTION
  • TEMPERATURE

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