Analysis of spherical indentation of porous ceramic films

Spherical indentation of a porous brittle La0.6Sr0.4Co0.2Fe0.8O3 ceramic film (porosity = 39.7%) on a stiffer elastic Ce0.9Gd0.1O1.95 substrate is simulated by finite element modelling incorporating the Gurson model to account for densification. The simulated load-displacement curves, apparent elastic modulus E, indentation hardness H and densification profile are all in good agreement with experimental data for the film. The simulations show that E and H are not sensitive to film residual stress. However E is very sensitive to the indent depth-film thickness ratio f, although H is less so for f < 0.3. The simulated dependence of E and H on f are highly consistent with experimental data, supporting the extrapolation of E and H measured for 0.1 < f < 0.3, to zero depth for good estimates of the film-alone properties. The inclusion of densification in the simulation makes only a small difference to E, but has a large influence on H as a function of indentation depth.