On the origin of Amonton’s friction law

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.

Contact between rough surfaces and a criterion for macroscopic adhesion

“…The results indicate a general trend with increasing adhesion (29). At first, adhesion leads to an increase in the ratio of contact area to load.…”

“…Persson's theory starts at large length scales and gradually introduces finer and finer structure (26)(27)(28)(29)(30). The value of Δr is not explicitly included, but a scale-dependent work of adhesion is introduced that may capture some of the effects of the interaction range.…”

“…In recent work, Persson has extended his theory to include adhesion and presented numerical solutions of his equations for several cases (26)(27)(28)(29)(30). The results indicate a general trend with increasing adhesion (29).…”

Shearing Nanometer-Thick Confined Hydrocarbon Films: Friction and Adhesion

“…For soft elastic solids when an adhesive interaction occur between the solids as in the case studied in this paper, the area of real contact will also increase in which case (3) with κ ≈ 2 is no longer accurate. In this case one must distinguish between two cases [24][25][26]: (a) If the adhesive interaction is not too strong, (3) is still approximately valid, but κ is larger than 2. In this case, if adhesion hysteresis is negligible, no adhesion will be observed in a pull-off experiment.…”

Numerical tribology of a dry contact

“…This generalisation was to be the basis of many other models proposed to describe contact surfaces by more or less complex functions developed by the combination of trigonometric functions [21], by the use of fractal model [22] or by numerical models involving finite element (FE) approaches [23,24,25,26,27,28]. …”