The most commonly observed friction behavior for sliding systems is that described by Amontons laws of friction. In this case, sliding friction is independent of the gross or apparent area of contact between the materials and a linear function of the applied normal load, where the constant of proportionality is called the friction coefficient. However, for dry sliding solids in contact via a single-asperity junction, Amontons (linear) friction–load behavior is not strictly relevant. In experiments measuring sliding friction between a silicon tip and a quartz surface using an atomic force microscope (AFM), a transition from linear to non-linear friction–load behavior has been observed. This is proposed to result from a nanoscale ‘conditioning’ of a multiple-contact tip–surface interface to form a single-asperity contact.
Reitsma, M. G., Cain, R. G., Biggs, S., & Smith, D. (2006). Observed transition from linear to non-linear friction-load behavior using a lateral force microscope. Applied Surface Science, 252(14), 4964-4968. https://doi.org/10.1016/j.apsusc.2005.08.003