Correlation between the flow stress and the nominal indentation hardness of soft metals

For the sharp indentation of soft metals, we first reveal a simple relation between the nominal hardness, Hn, and the flow stress, σr, i.e. Hn = 4.4σr. Further, using the relation proposed herein instead of the well-known Tabor’s relation and the analysis performed by Nix/Gao on the geometrically necessary dislocations, a simple indentation nominal hardness–depth relation at the microscale is obtained. The model agrees well with the experiment data in the literature and the simulation based on a strain gradient theory.