Nanoindentation shape effect: experiments, simulations and modelling

AFM nanoindentation is nowadays commonly used for the study of mechanical properties of materials at the nanoscale. The investigation of surface hardness of a 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 obtain high- resolution images, but on the other hand measuring the hardness behaviour of a material with a non- standard sharp indenter gives only comparative results affected by a significant deviation from the commonly used hardness scales. In this paper we try to understand how the shape of the indenter affects the hardness measurement, in order to find a relationship between the measured hardness of a material and the corner angle of a pyramidal indenter. To achieve this we performed a full experimental campaign, indenting the same material with three focused ion beam ( FIB) nanofabricated probes with a highly altered corner angle. We then compared the results obtained experimentally with those obtained by numerical simulations, using the finite element method ( FEM), and by theoretical models, using a general scaling law for nanoindentation available for indenters with a variable size and shape. The comparison between these three approaches ( experimental, numerical and theoretical approaches) reveals a good agreement and allowed us to find a theoretical relationship which links the measured hardness value with the shape of the indenter. The same theoretical approach has also been used to fit the hardness experimental results considering the indentation size effect. In this case we compare the measured data, changing the applied load.