Adhesion between a power-law indenter and a thin layer coated on a rigid substrate

In the present paper we investigate indentation of a power-law axisymmetric rigid probe in adhesive contact with a "thin layer" laying on a rigid foundation for both frictionless unbounded and bounded compressible cases. The investigation relies on the "thin layer" assumption proposed by Johnson, i.e. the layer thickness being much smaller than the radius of the contact area, and it makes use of the previous solutions proposed by Jaffar and Barber for the adhesiveless case. We give analytical predictions of the loading curves and provide indentation, load and contact radius at the pull-off. It is shown that the adhesive behavior is strongly affected by the indenter shape; nevertheless below a critical thickness of the layer (typically below 1 µm) the theoretical strength of the material is reached. This is in contrast with the Hertzian case, which has been shown to be insensitive to the layer thickness. Two cases are investigated, namely, the case of a free layer and the case of a compressible confined layer, the latter being more "efficient", as, due to Poisson effects, the same detachment force is reached with a smaller contact area. It is suggested that high sensitive micro-/nanoindentation tests may be performed using probes with different power law profiles for characterization of adhesive and elastic properties of micro-/nanolayers.