A new method developed to evaluate both the hardness and elastic modulus of a coating–substrate system

The indentation depth, which is generally expressed as a function of the indentation load, can theoretically be converted into the indentation load expressed as a function of the indentation depth. This principle is used in the present study to express the load applied to either the coating or the substrate to generate an indentation depth in the power form. In such a case, the indentation load applied to the composite material is expressed as the sum of the load fractions arising at the coating and the substrate. These two load fractions in exponential form are established as the product values of their load parameters and weight functions. The indentation load expressions for both the loading and unloading processes are determined by the regressions of the experimental data and allow us to separate the mechanical properties of the coating from the response of the composite system. The present method provides the advantage of allowing the mechanical properties of the coating varying in a wide range of indentation depths to be simply be obtained through one composite response with a high indentation load.