| The nanoindentation test has been established as an important and powerful tool for characterizing the near-surface mechanical properties of solid materials. There has been extensive literature concerning the application of nanoindentation tests, and almost all the studies have centered on the determination of hardness, H, and elastic modulus, E, for the test materials.The continuous stiffness measurement (CSM) is a widely adopted nanoindentation test, in which a small harmonic force is added on the indenter, and the harmonic response of the indenter is measured at the excitation frequency. The main advantages of CSM is that it offers the direct measurement of dynamic contact stiffness, S, at any point along the loading curve. With the CSM, the hardness and the Young's modulus of a film–substrate system can be determined continuously as functions of indenter penetration depth. Many authors have tried to discuss the effect of substrate on the mechanical properties of the film–substrate system by directly analyzing the observed penetration-depth-dependence of the hardness and the Young's modulus, and then extracting the mechanical properties of the films.We reported a simple and convenient method to determine the film thickness by nanoindentation tests. This method starts from the analysis of the unloading portion of the measured nanoindentation load-displacement curves according to a quadratic polynomial, P=a(h-hf)2-P0, where P is the indentation load, P0 is the virtual load used to consider the effect of the residual contact stress, h is the indenter displacement (penetration depth), hf is the final displacement after complete unloading which should be determined by curve fitting, and a is a constant. Then the best-fit value of the parameter P0/Pmax is plotted as a function of the maximum penetration depth, hmax. Such a P0 versus hmax curve may pass through a minimum, and hmax corresponding to this minimum would be equal to the film thickness value. An empirical function was proposed to describe the continuous stiffness curves, i.e., Er2/H versus h (where h is the indenter penetration depth), measured with nanoindentation tests for titanium films on glass substrate. By analyzing the variations of the parameters included in this empirical equation with film thickness, the physical meanings of this empirical equation were discussed. It was shown that the mechanical properties of the substrate and the film may be extracted from such analyses. |
