Dynamic Nanoindentation Analysis using Generalized Maxwell Model for Viscoelastic Materials Characterization

P.A. Yuya, N.G. Patel
Clarkson University, US

Keywords: viscoelasticity, dynamic nanoindentation, polymers, characterization


Nanoindentation has become a very useful tool for materials properties characterization at nanoscale. The Kelvin-Voigt (two-parameter) solid has been used as the conventional model for the tip-sample forces for viscoelastic contact where the sample stiffness is represented with a spring of stiffness “k” and the damping represented with a dash-pot with damping “c”. However, the two-parameter model oversimplifies the response of most viscoelastic materials. Because it only incorporates a single relaxation time, it is limited to modeling material response at a single frequency. Furthermore, it cannot account for instantaneous elasticity and therefore underestimates contact forces. In this work, the indenter tip-sample contact forces are modeled using a generalized Maxwell model, which is the most general form for a linear viscoelastic material. Further, this model is used to derive empirical formulas to fit the experimental dynamic nanoindentation data to determine the material parameters. Using this model, the storage and loss indentation moduli can be calculated by applying the fit parameters in the formulas. Important features of the experimental method are discussed and results on natural rubber latex are presented. We compare the results based on Voigt model analysis with results analyzed with Maxwell-standard linear solid (M-SLS).