Analytical model for nanoscale viscoelastic properties characterization using dynamic nanoindentation

Abstract

In the last few decades, nanoindentation has gained widespread acceptance as a technique for materials properties characterization at micron and submicron length scales. Accurate and precise characterization of material properties with a nanoindenter is critically dependent on the ability to correctly model the response of the test equipment in contact with the material. In dynamic nanoindention analysis, a simple Kelvin–Voigt model is commonly used to capture the viscoelastic response. However, this model oversimplifies the response of real viscoelastic materials such as polymers. A model is developed that captures the dynamic nanoindentation response of a viscoelastic material. Indenter tip-sample contact forces are modelled using a generalized Maxwell model. The results on a silicon elastomer were analysed using conventional two element Kelvin–Voigt model and contrasted to analysis done using the Maxwell model. The results show that conventional Kelvin–Voigt model overestimates the storage modulus of the silicone elastomer by ~30%. Maxwell model represents a significant improvement in capturing the viscoelastic material behaviour over the Voigt model.

Keywords:

• generalized Maxwell model
• viscoelasticity
• dynamic nanoindentation

Acknowledgements

The authors are grateful for helpful discussion from Sara Campbell, of National Institute of Standards and Technology, Boulder, Colorado, and Laurel Kuxhaus, of Mechanical and Aeronautical Engineering Department, Clarkson University, Potsdam NY.