Analysis of Spherical Indentation of an Elastic Bilayer Using a Modified Perturbation Approach

Accurate mechanical property measurement of films on substrates by instrumented indentation requires a solution describing the effective modulus of the film/substrate system. Here, a first-order elastic perturbation solution for spherical indentation on a film/substrate is presented. Finite element method (FEM) simulations were conducted for comparison with the analytical solution. FEM results indicate that the new solution is valid for a practical range of modulus mismatch, especially for a stiff film on a compliant substrate. It also shows that effective modulus curves for the spherical punch deviates from those of the flat punch when the thickness is comparable to contact size. The work is applicable in tribological films and other engineering systems requiring hard, protective coatings.