In this paper an analytical solution of an elastic isotropic thin-film on an elastic
substrate under an axisymmetric loading on the plane surface is presented. The
analysis is intended to model the micronanoindentation tests to evaluate some of the
relevant properties of thin films and provide information about the influence of
interface conditions between the film and the substrate.
The theoretical solution of the equations of three-dimensional elasticity is
obtained by using Dini and Fourier–Bessel expansions for the displacement field. To
describe the elastic mechanical interaction between the indenter and the film for
low load, we make use of the pressure distribution for contact between two
homogeneous bodies, and the corresponding displacement field is solved in
explicit form. The contact law is obtained with two different ideal interface
conditions between the film and the substrate: perfectly bonded and frictionless
contact.
This form of the elastic solution may be utilized for different axisymmetric
pressure distributions performed to model the interaction between the indenter and
the film, thus obtaining an analytical framework for comparing experimental and
numerical results.
