Adhesive Contact of a Compliant Sphere to an Elastic Coated Substrate: The Thin Film Limit

Experimental results for adhesive contacts on substrates coated with elastomeric thin films have recently been obtained by Tardivat and Léger [1 Tardivat , C. and Léger L. , J. Adhesion Sci. Technol. 15 , 1055 – 1078 ( 2001 ).[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] by the so-called Johnson-Kendall-Roberts (JKR) test, which provides both adhesion energy and elastic modulus. These data show that on substrates coated with thin films the adhesion and effective elastic modulus of the sphere depend upon the film thickness. In keeping with the experimental conditions, we try to interpret these data using a simple model [4 Barthel , E. and Perriot , A. , J. Phys. D: Appl. Phys. 40, 1059–1067 (2007).[Crossref] , [Google Scholar]] in the thin film limit, i.e., when the film thickness is small compared with the contact radius. Although the film does impact the local crack tip stress field, we show that no effect on the macroscopic contact variables is expected for the adhesion to coated substrates in such confined geometries. The deviations from the experimental results are ascribed to the idealized contact boundary conditions assumed in the model.