Size-scale effects on the friction coefficient: from weak faults at the planetary scale to superlubricity at the nanoscale

In the present paper, two size-effect laws for the friction coefficient of rough surfaces are proposed and compared. The former is based on purely dimensional analysis arguments and is related to the fractality of the contact domains. This scaling law applies from the macro to the planetary scales, where contact is almost elastic. The latter, holding at the micro and nanoscales, is based on the adhesion theory of friction and assumes that the friction resistance is governed by the strong adhesive bonds at the asperities, caused by elasto-plastic deformations. Whereas the fractal scaling law suggests a friction coefficient decreasing with the size of the nominal contact area, the opposite trend is predicted by the adhesion theory. The application of these two scaling laws to Zircalloy (Zr-4), Stainless Steel (SS304) and Nickel (Ni200) permits to determine the scale range of validity of each scaling law and to show that they may coexist. Finally, it is found that the length scale which marks the transition between the two regimes is a function of the plasticity index proposed by Mikic.