Uncertainty-based comparison of the effect of the area shape function on material characterisation in nanoindentation testing

Instrumented Indentation Test (IIT) is largely exploited in industry and academia to achieve multi-scale mechanical characterisation, i.e. ranging from nano- and micro-structure to bulk, of several properties, e.g. Young's modulus, stress-strain curve, creep, and relaxation. IIT is particularly suited to cope with the challenges of the current industrial framework to achieve multi-objective characterisation and requirements of zero-defect manufacturing and zero waste. In fact, IIT requires limited sample preparation and is a non-destructive technique with high throughput. IIT consists of applying a loading-unloading force cycle on the specimen. The capability of continuously measuring the indenter displacement in the material, i.e. being a depth-sensing technique, is the essential feature of IIT. This allows the mechanical characterisation by knowing the shape of the indenter and hence the relationship between the indentation depth and the projected area of the surface in contact between the indenter and the specimen. The relationship is described by the area shape function, whose parameters require calibration according to ISO 14577-2:2015. For a given indenter geometry, several alternative models are available in the literature. These describe both the geometry and the possible presence of errors, e.g. blunt tip and wear effect. However, a comparison of the choice of the different alternatives, when they are equally nominally applicable, is lacking in the literature, although it prescribes some applicability ranges. This work exploits a simulative approach based on bootstrap sampling to estimate the uncertainty of the calibration of area shape function parameters in the nano-range, where the effect is critical. The uncertainty is then propagated to compare performances of different area shape function models on the mechanical characterisation, i.e. indentation hardness and Young's modulus estimate, within a rigorous metrological framework. Results are shown for standard reference materials, i.e. SiO2 and W, to ensure proper composition homogeneity and neglect edge effects, i.e. pile-up and sink-in.