A Theory for the Effects of Film Thickness and Normal Load in the Friction of Thin Films

The effect of film thickness in solid friction is reviewed. Two regimes are distinguished: (a) increasing coefficient of friction with decreasing film thickness which occurs for ultrathin films and (b) decreasing coefficient of friction with decreasing film thickness which occurs for thin films. The former regime has previously been treated by the author; consequently, attention is focused on the latter regime. A review of the thin film phenomenon establishes that it is very much dependent on the type of deformation occurring at the contact and concludes that no single expression can uniquely describe it for all materials situations. A special theory is put forth for the contact situation corresponding to a model of an elastic layer of much less rigidity than its substrate and indenter. This situation corresponds to practically all naturally occurring and bonded nonmetallic solid lubricant films of industrial and scientific interest. It is shown that coefficient of friction f obeys the relation f ∝ $1/P$ for variable load P and constant thickness h, f ∝ $h$ for constant load and variable film thickness, and f ∝ $h/P$ for the general case. These expressions are verified by use of data from pin-on-disk tests, Falex tests, 4-ball tests, modified MacMillan tests, and other types of tests. The experimental data are for naturally formed graphite on diamond, SiO₂ bonded PbO on stainless steel, and phenolic bonded 9MoS₂-1 graphite films on steel and aluminum.