On the analysis of the stress–strain behaviour of thin metal films on substrates using nanoindentation

Abstract

Based on load–depth data, as measured by nanoindentation with a Berkovich tip, stress–strain curves of metal films (Al, Cu and Ti) with thickness of 1 to 4 µm were determined. This so-called inverse analysis was carried out using a neural network approach. The method uses hardness and stiffness data from indentation into the film/substrate composite with a depth range of 10 to 200% of the film thickness, and yields the material parameters describing a nonlinear elastic–plastic stress–strain curve of the Armstrong–Frederick type. It is shown that the method can only be applied if a sufficient difference in film and substrate hardness is present. For all films investigated, a significant dependence of the film strength on its microstructure, as characterized by focused ion beam microscopy, has been found.

Acknowledgments

We wish to thank the German Research Foundation (DFG) for funding within the Research Grant Hu 844/1-2. We are also very grateful to Dr. C.A. Volkert and W. Schwan for the valuable FIB microscopy and discussion.