Material compressibility effects for the squeeze of very thin films

Abstract

The purpose of the present work is the study and clarification of the essential role played by the material compressibility of very thin solid layers such as for instance appear in surface force experiments. For the sake of simplicity, attention will be focused on an elastic film squeezed between rigid surfaces. The starting point is the classical lubrication theory reformulated within the framework of linear elasticity (Incompressible Reynolds Model). This model is then extended to include compressibility effects. This extension is based on a phenomenological analysis of the stress and strain fields obtained in some simple model cases and which are shown to correspond to an oedometric squeeze inside the contact with boundary corrections. This results in the oedometric Reynolds model which is then applied to two special cases: a uniform film of constant thickness under plane strain condition and the interfacial film occurring in the sphere/plane contact. These two problems confirm the fact that compressibility cannot be neglected for very thin films and show that the governing adimensional parameters combine compressibility and thinness.