Friction between Clean Surfaces and the Effects of Surface Randomness

Abstract

It is well known that the Coulomb-Amonton’s law of friction holds in a usual situation; (i) The frictional force does not depend on an apparent area of contact surfaces. (ii) The frictional force is proportional to the normal load. (iii) The kinetic frictional force does not depend on the relative velocity of contact surfaces and is less than the maximum static frictional force. The law as regards the static friction has been accounted for based on the existence of the surface roughness and plastic deformation and adhesion at actual contact points[1]. Actually it is known that surface roughness plays an important role in the friction in a usuall situation where the Coulomb-Amonton’s law holds. From this point of view that the surface roughness is crucial for the Coulomb-Amonton’s law to hold, quite a different behavior of friction is expected between clean surfaces without roughness. In fact in a simple model of friction of clean surfaces described below we can show the existence of the frictional transition, which is the phase transition between states with and without finite maximum static frictional force, as a function of the strength of interatomic force between two bodies. The simplest case of 1-dimension(D) where the atoms of the one body are fixed, the model of clean surface reduces to the Frenkel-Kontrova model[2]. In that model such a phase transition is known to exist when the ratio of mean atomic distances of two bodies is irrational, i.e., in the incommensurate case. This transition is called Aubry’s breaking of analyticity transition[3]. Hirano and Shinjo have claimed the existence of such a frictional transition even in a 3D model, and that the static frictional force can vanish between pure metals with incommensurate clean surfaces, e.g., (111) and (110) surfaces of α-iron[4]. All of these studies are, however, based on the model where atoms of the one body are held fixed. Nothing is known about the frictional transition in a more realistic model where both atoms can relax and the effects of randomness are included.