Calibrating a nanoindenter for very shallow depth indentation using equivalent contact radius

Nanoindenter tips are usually modelled as axisymmetric cones, with calibration involving finding a fitting function that relates contact area to contact depth. For accurate calibration of shallow depth indentation, this is not ideal because it means that deeper indents tend to dominate the fitting function. For an axisymmetric object, it is always possible to define an equivalent contact radius (which, in the case, of nanoindentation is linearly related to the reduced modulus) and to obtain a fitting function that relates this equivalent contact radius to indentation depth. The equivalent contact radius approach is used here to provide shallow depth calibration of a nanoindenter tip at three separate times. The advantage of the equivalent contact radius methodology is that it provides a clearer physical interpretation of the changes in tip shape than a conventional area-based fit. We also show that the minimum depth for a reliable hardness measurement is obtainable and increases as the tip blunts with age but that consistent measurements of very near surface elastic moduli can be made if the blunting of the tip over time is fully accounted for in the tip area function calibration.