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Load-Displacement Relations for Nanoindentation of Viscoelastic Materials



Chien-Kuo Liu, S H. Lee, Li Piin Sung, Tinh Nguyen


A model based on the Burgers viscoelastic concept has been developed to describe the nanoindentation behaviors of polymeric materials. An analytical solution of displacement at the indenter tip has been derived based on the analog of the governing equation of elasticity in the time coordinate system to the governing equation of the viscoelastic model in Laplace transform coordinate system. The solution consists of the elastic, viscous, and plastic displacements during loading and unloading. Nanoindentation experiments have been conducted for poly(methyl methacrylate), polycarbonate, hydroxyethyl methacrylate copolymer, amorphous syndiotactic polystyrene, and fast?cure acrylic polymers to provide data for validating the model. The results show excellent agreement between experimental load?displacement data and model prediction for both the loading and unloading before the contact area decreases for all five polymers. The viscosity decreases, but the hardness increases, with increasing loading rate. The Young s moduli of the interior material obtained by the present study are close to those reported in the literature. Additional analysis showed that the prediction by either the Kelvin or the Maxwell viscoelastic model does not agree with the experimental data generated in this study.
Journal of Applied Physics


Adhesion, ATR, building technology, interface, internal reflection spectroscopy, polymer/glass fiber composites, polymer/substrate, water


Liu, C. , Lee, S. , Sung, L. and Nguyen, T. (2006), Load-Displacement Relations for Nanoindentation of Viscoelastic Materials, Journal of Applied Physics (Accessed July 14, 2024)


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Created August 1, 2006, Updated October 12, 2021