Adhesive contact of a compliant sphere to an elastic coated substrate: the thin film limit

TL;DR

This paper investigates the adhesive contact mechanics of a compliant sphere on an elastic coated substrate in the thin film limit, showing that the film's presence minimally affects macroscopic contact variables despite local stress field influences.

Contribution

The study provides a theoretical analysis of adhesive contact in the thin film limit, explaining why macroscopic contact variables are unaffected by the coating despite local stress variations.

Findings

No effect on macroscopic contact variables in the thin film limit

Local stress fields are influenced by the thin film

Deviations from experiments are due to idealized boundary conditions

Abstract

Experimental results for adhesive contacts on substrates coated with elastomeric thin films have recently been obtained by C. Tardivat and L. L\'{e}ger (J. Adhesion Sci. Technol. 15 1055-1078 (2001)) by the so-called 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 (E. Barthel and A. Perriot, J. Phys. D 40, 1059-1067 (2007)) in the thin film limit, ie when the film thickness is small compared to 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.