Modification of composite hardness models to incorporate indentation size effects in thin films

Abstract

The indentation hardness of copper films of thickness 25 to 1400 nm on oxidized silicon substrates is determined by nanoindentation. The load-displacement curves are analysed using the Oliver and Pharr method. An indentation size effect is observed at low relative indentation depths for the copper films. Composite hardness models are applied to the data without an indentation size effect and the Korsunksy and Puchi–Cabrera models are found to give very good fits to this data. The Nix and Gao mechanism based strain gradient plasticity (MSG) model is used to account for the indentation size effect. An attempt is made to modify the existing composite hardness models using the MSG model to incorporate indentation size effect. By modification of both the Korsunsky and Puchi-Cabrera models a good fit to the entire range of data is obtained.