Nanoindentation shape effect: experiments, simulations and modelling

AFM nanoindentation is nowadays commonly used for the study of mechanicalproperties of materials at the nanoscale. The investigation of surface hardness ofa material using AFM means that the probe has to be able to indent the surface,but also to image it. Usually standard indenters are not sharp enough to obtainhigh-resolution images, but on the other hand measuring the hardness behaviourof a material with a non-standard sharp indenter gives only comparative resultsaffected by a significant deviation from the commonly used hardness scales.In this paper we try to understand how the shape of the indenter affectsthe hardness measurement, in order to find a relationship between the measuredhardness of a material and the corner angle of a pyramidal indenter. To achievethis we performed a full experimental campaign, indenting the same materialwith three focused ion beam (FIB) nanofabricated probes with a highly alteredcorner angle. We then compared the results obtained experimentally with thoseobtained by numerical simulations, using the finite element method (FEM), andby theoretical models, using a general scaling law for nanoindentation availablefor indenters with a variable size and shape.The comparison between these three approaches (experimental, numericaland theoretical approaches) reveals a good agreement and allowed us to find atheoretical relationship which links the measured hardness value with the shapeof the indenter.The same theoretical approach has also been used to fit the hardnessexperimental results considering the indentation size effect. In this case wecompare the measured data, changing the applied load.