Atomistic simulation of the influence of pre-existing stress on the interpretation of nanoindentation data

By using molecular dynamics simulations, we have accurately determined the true contact area during plastic indentation of materials under an applied in-plane stress. We found that the mean pressure calculated from the true contact area varied slightly with applied pre-stress with higher values in compression than in tension and that the modulus calculated from the true contact area is essentially independent of the press-stress level in the substrate. These findings are largely consistent with the findings of Tsui, Pharr, and Oliver. On the other hand, if the contact area is estimated from approximate formulae, the contact area is underestimated and shows a strong dependence on the pre-stress level. When it is used to determine mean pressure and modulus, the empirically determined area leads to large errors. Our simulations demonstrate that this phenomenon, first reported for macroscale hardness measurements dating back to 1932, also exists at the nanometer-scale contact areas, apparently scaling over 10 orders of magnitude in contact area, from ∼mm² to ∼100 nm².