Asymptotic solution to axisymmetric indentation of a compressible elastic thin film

Abstract Using the perturbation theory, the axisymmetric indentation of a compressible elastic thin film bonded to a rigid substrate is analyzed for the contact radius much larger than the thickness of the thin film. Explicit expression of the nominal contact stiffness is obtained, which is proportional to the contact area and inversely proportional to the thickness of the thin film, independent of indenter. The effect of surface interaction on the indentation of compressible elastic films is also discussed by following the Johnson–Kendall–Roberts approach. Closed-form solutions are obtained for the indentation load–indentation depth relation under the action of the surface interaction. It turns out that, for spherical indenters, the pull-off force to detach the indenter from the surface of the thin film is independent of elastic properties of the thin film. This analysis provides us a new approach to evaluate mechanical properties of ultra-thin films by using the nanoindentation technique.