On the measurements of viscoelastic functions of a sphere by nanoindentation

Nanoindentation using such instruments as instrumented nanoindenter and scanning probe microscope is effective for measurements of viscoelastic functions of a sphere in micron or sub-micron scale. In this paper, we provide methods for nanoindentation measurements of linearly viscoelastic functions in both time- and frequency-domains for a viscoelastic sphere under small deformations. In the time-domain, both relaxation and creep functions are determined from three types of loading histories, namely constant-rate loading, ramp loading, and step loading. In the frequency-domain, methods are given for the calculation of complex modulus, or complex compliance under a small amplitude of sinusoidal load superimposed on a carrier load. The effects of the radius of the viscoelastic sphere relative to the indenter tip radius, as well as the deformation of the sphere induced by contact with the flat substrate supporting the sphere are discussed.