Evaluating initial unloading stiffness from elastic work-of-indentation measured in a nanoindentation experiment

Differentiation of the energy-based power function used to represent the nanoindentation unloading response at the peak indentation load generally overestimates the contact stiffness. This is mainly because of the larger curvature associated with this function and the proximity between the contact and maximum penetration depths. Using the nanoindentation data from ceramics and metals, we have shown that these two errors can be eliminated if the derivative is multiplied by the geometric and stiffness correction factors, respectively. The stiffness correction factor is found to be a function of the elastic energy constant and is independent of the peak indentation load. The contact stiffness evaluated by the proposed method is in excellent agreement with that obtained from the power law derivative for a wide range of elastoplastic materials and peak indentation loads. The relationship between the elastic recovery ratio and elastic energy constant developed in this study further simplifies the proposed procedure.