Indentation Hardness of Film/Substrate System: Discovery of the Unconventional Overshoot and Undershoot Behaviors

When a thin film/substrate system is indented, the measured indentation hardness is always regarded as a weighted average of the hardness of film and that of the substrate material. That is, one usually takes it for granted that the measured hardness should be bounded between that of the film and substrate, and with the increase of indentation depth, the measured hardness should vary monotonically from the intrinsic film hardness to the intrinsic substrate hardness. Using finite element simulations of sharp indentation on film/substrate systems, here we show an “abnormal” behavior that if the film and substrate have close hardness but different plastic behaviors, within a certain range of indentation depth, in some cases the measured hardness may “overshoot” and be higher than both the film and substrate hardness; when the film and substrate materials are reversed, then the measured hardness may “undershoot” and be lower than both the film and substrate hardness. In both cases, the indentation hardness varies non-monotonically with indentation depth. This unconventional behavior may provide some physical insights on correctly interpreting the indentation measurements on thin film/substrate systems.