A model to evaluate the nano-indentation hardness of ion-irradiated materials

Nanoindentation is essential to study on mechanical properties of ion-irradiated materials at nanoscale. The measured nanoindentation hardness needs to be converted to the bulk-equivalent hardness by using some computation models. We proposed a modified model based on the popular Nix–Gao model and Korsunsky film/substrate model for the evaluation of the composite hardness of the ion-irradiated materials as well as other material constants that characterize the performance of material during the indentation test. It is developed from two important considerations: (1) Ion-irradiated materials are simply treated as a film/substrate systems consisting of irradiated-hardening layer and the substrate. (2) The substrate starts to contribute to the composite hardness at the relative indentation depth (t) which is less than the films thickness (t0). The fitting results reveal that the modified model describes very well the hardness data obtained from different ion-irradiation systems such as helium and hydrogen ion irradiation. The proposed model not only shows the hardness of irradiated-hardening layer and substrate, but also allows quantitative understanding on the indentation size effect.