Correcting power-law viscoelastic effects in elastic modulus measurement using depth-sensing indentation

The standard Oliver-Pharr method for measuring the elastic modulus by depth-sensing indentation makes use of the unloading response of the material as it is assumed that the unloading behaviour is purely elastic. However, under certain conditions, the unloading behaviour can be viscoelastic, and if the viscosity effects are not corrected, the calculated modulus can be seriously erroneous. Feng and Ngan have proposed a correction formula which can eliminate the creep effects. However, this formula has been proven to be correct for the case of linear viscoelasticity only; the general case of power-law viscoelasticity has not been proven. In this paper, this formula is proved for the general power-law viscoelastic situation using a Maxwell material model. Finite-element calculations are also performed to illustrate the result. The correction formula is applied to experimental data on amorphous selenium at ambient and elevated temperatures and is found to be effective in correcting for creep effects which are very prominent in this material.