On the determination of spherical nanoindentation stress–strain curves

Instrumented nanoindentation experiments, especially with sharp tips, are a well-established technique to measure the hardness and moduli values of a wide range of materials. However, and despite the fact that they can accurately delineate the onset of the elasto-plastic transition of solids, spherical nanoindentation experiments are less common. In this article we propose a technique in which we combine (i) the results of continuous stiffness measurements with spherical indenters – with radii of 1 μm and/or 13.5 μm, (ii) Hertzian theory, and (iii) Berkovich nanoindentations, to convert load/depth of indentation curves to their corresponding indentation stress–strain curves. We applied the technique to fused silica, aluminum, iron and single crystals of sapphire and ZnO. In all cases, the resulting indentation stress–strain curves obtained clearly showed the details of the elastic-to-plastic transition (i.e., the onset of yield, and, as important, the steady state hardness values that were comparable with the Vickers microhardness values obtained on the same surfaces). Furthermore, when both the 1 μm and 13.5 μm indenters were used on the same material, for the most part, the indentation stress–strain curves traced one trajectory. The method is versatile and can be used over a large range of moduli and hardness values.