Indentation behavior of a hard film resting on a soft substrate

The hard film/soft substrate systems are widely found in production and life. In order to better understand the indentation response of those systems, a closed-form indentation model is established based on the theory of plates and the assumption of Hertz contact stress distribution. Inspired by the model, a new method of measuring the mechanical properties of nanofilms by indentation on hard film/soft substrate system is proposed. Then, with the help of finite element method (FEM), the effectiveness of the model and the method is systematically verified. The results show that compared with the Xu-Pharr model which established by the perturbation method, our model can better describe the compliance of the hard film/soft substrate system in a lager range of modulus ratio of the film to the substrate. In order to obtain the modulus of the nanofilms more accurately by our method, the optimum indentation depth for testing is 0.5 times the film thickness to 1 times the film thickness, and it is best to use a softer substrate to make the modulus ratio of the film to the substrate greater than 103. In addition, the radius of the AFM tip is preferably more than 1 times the film thickness and less than 4 times the film thickness, and a smooth surface of the sample is most preferred. Compared with free standing indentation test or bulge test, our research provides a more convenient and cheaper method for measuring the nanofilms’ modulus in laboratory.