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Determination of the thickness of titanium films on glass substrate by nanoindentation tests

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 = α( h − h f ) 2 − P 0 , where P is the indentation load, P 0 is the virtual load used to consider the effect of the residual contact stress, h is the indenter displacement (penetration depth), h f is the final displacement after complete unloading which should be determined by curve fitting, and α is a constant. Then the best-fit value of the parameter P 0 is plotted as a function of the maximum penetration depth, h max . Such a P 0 versus h max curve may pass through a minimum, and h max corresponding to this minimum would be equal to the film thickness value.