Indentation size effect in spherical and pyramidal indentations

The indentation size effect (ISE) is studied for spherical and pyramidal indentations on a Ni poly-crystal. The indentation experiments were conducted using a Berkovich geometry as well as different spherical indenters with radii of 0.38, 3.8 and 51.0 µm. A strong ISE is observed for the material yielding a higher hardness at smaller depths or smaller sphere radii. The transition from elastic to plastic behaviour is associated with a pop-in in the load–displacement curve, in contrast to the conventional elastic–plastic transition as discussed by Tabor. The indentation response is modelled using Tabor's approach in conjunction with the uniaxial macroscopic stress–strain behaviour for calculating the statistically stored dislocation density for a given indenter geometry. The geometrically necessary dislocation (GND) density is calculated using a modified Nix/Gao approach, whereas the storage volume for GNDs is used as a parameter for the measured depth dependence of hardness. It will be shown that the ISE for both pyramidal and spherical indentations is related and can be understood within the same given framework. The indentation response of metallic materials can thus be modelled from pop-in to macroscopic hardness.