The role of rough surface in the size-dependent behavior upon nano-indentation

The hardness measured by nano-indentation on metallic material with rough surface shows a significant deviation from the Nix-Gao relation, which established an important relation between the hardness and indentation depth at small scale (Nix and Gao, 1998). Such effect has been investigated by nano-indentation experiments, and accounted for in a few proposed nano-indentation models in terms of surface roughness. However, the predicted roughness effects based on these models are quite different and even contradictory in some aspects. It is believed that the surface profile and the indentation position nano-indentation tests on copper specimens with fabricated nanoscale rough surfaces were carefully performed. Therefore, current work investigated this effect of nanoscale rough surface by both nano-indentation tests and finite element simulations. The conventional theory of mechanism-based strain gradient plasticity was implemented into ABAQUS for modeling the size-dependent indentations on both nano-grooved and sine-waved surfaces. The effect of the rough surface was analyzed in terms of varying the amplitude, the wavelength and the aspect ratio between them. An updated Nix-Gao relation that accounts for the surface roughness was proposed. The new relation captured well the available nano-indention behavior of Sb–Pd alloy and Nickel.