Determining the instantaneous modulus of viscoelastic solids using instrumented indentation measurements

Instrumented indentation is often used in the study of small-scale mechanical behavior of "soft" matters that exhibit viscoelastic behavior. A number of techniques have recently been proposed to obtain the viscoelastic properties from indentation load-displacement curves. In this study, we examine the relationships between initial unloading slope, contact depth, and the instantaneous elastic modulus for instrumented indentation in linear viscoelastic solids using either conical or spherical indenters. In particular, we study the effects of "hold-at-the-peak-load" and "hold-at-the-maximum-displacement" on initial unloading slopes and contact depths. We then discuss the applicability of the Oliver-Pharr method (Refs. 29, 30) for determining contact depth that was originally proposed for indentation in elastic and elastic-plastic solids and recently modified by Ngan et al. (Refs. 20-23) for viscoelastic solids. The results of this study should help facilitate the analysis of instrumented indentation measurements in linear viscoelastic solids.