Determination of the strain energy release rate for C/a-Si composite film produced in nanoindentation tests

A general mechanical model that describes the contact behavior and deformations arising at all layers (including the substrate) is developed in the present study for multilayer specimens to evaluate the theoretical contact parameters. The governing differential equations for the depth solutions of the indenter tip formed at all layers of the specimen under their contact force and depth are developed individually. These two contact parameters allow the evaluation of the internal stress and strain using the membrane theory. The strain energy release rate can thus be determined if the internal stress is available. The mean value of these pop-in depths is almost constant when operating at various loading rates. The present model is precisely if it has good agreement with experiments. The pop-in internal stress was found to be strongly dependent on the C-film thickness (thus the material properties) but independent of the applied indentation system (thus indentation conditions). The pop-in internal stress and strain energy release rate can be significantly lowered by increasing the C-film thickness. Furthermore, pop-in always formed at a depth near the interface of the C/a-Si composite film and Si substrate.