Elastic deformation and the laws of friction

Abstract

This paper examines whether the hypothesis of elastic deformation of surface protuberances is consistent with Amontons's law, that the friction is proportional to the applied load. For a single elastic contact, the area of contact A is known to be proportional to the $\frac{2}{3}$ power of the load W. Since the frictional force is generally assumed to be proportional to A, it has been thought that in elastic deformation Amontons's law would not be obeyed. However, conforming surfaces usually touch at many points, and it is shown that in these circumstances A and W become nearly proportional. Experiments are described which show that the general law is that the friction is proportional to the true area of contact; whether or not Amontons's law is obeyed depends upon the surface topography. For highly elastic materials such as Perspex, Amontons's law is obeyed when contact is made at many points, and other relations between A and W are observed when the contacts are few. Experiments with lubricated brass specimens show that the same conclusions apply to carefully prepared or well run-in metal surfaces running in conditions where the damage is small.