Adhesive contact between a rigid axisymmetric indenter and an incompressible elastic thin film

Advances in surface force spectroscopy (SFS) have stimulated the research on the adhesion of two solid surfaces on the microscale. The Johnson-Kendall-Roberts (JKR) adhesion theory is extensively used in investigating the adhesion behaviour of thin films by using the SFS. However, the JKR theory is based on the contact between two spheres or a sphere and an elastic half space. Its application in thin films remains an open question. This work presents a rigorous analysis of the adhesive contact between an incompressible elastic thin film and a rigid axisymmetric indenter under the condition of the contact radius much larger than the film thickness. It turns out that, for the adhesive interaction between a rigid spherical indenter and the thin film the pull-off force is proportional to the indenter diameter and independent of the film thickness with the perfectly bonded condition between the thin film and the substrate requesting the highest pull-off force to separate the indenter from the substrate. For a conical indenter, the pull-off force depends on the film thickness. For the frictionless condition, the pull-off force is proportional to the square root of the film thickness, while it is proportional to 3/4 power of the film thickness for the bonded condition.