Influence of roughness and tilt on nanoindentation measurements: A quantitative model

A model, which takes into account the indentation size effect, was proposed to relate hardness and its standard deviation to the quality of the sample surface, i.e., the roughness and the tilt. Stainless steel samples were mechanically polished so as to obtain various roughness and tilt. Then the quality of the surface and the hardness were measured respectively by scanning probe microscopy and by nanoindentation. The model was fitted according to those experimental data. It was shown that the standard deviation only depends on the ratio of the arithmetic roughness over the contact depth of the indent while the average hardness also depends on the contact depth and on the tilt. It was deduced that hardness measurements are performed with an uncertainty lower than 10% if: (i) the ratio of the arithmetic roughness over the contact depth of the indent is lower than 0.05, (ii) the tilt of the sample is lower than 2° and (iii) the difference of roughness between samples is lower than 50%.