Abstract

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.

Keywords

elasticity, contact mechanics, thin film, nanoindentation

Authors