Experimental Mechanics

, Volume 47, Issue 1, pp 87–98

Measurements of Two Independent Viscoelastic Functions by Nanoindentation


DOI: 10.1007/s11340-006-8277-4

Cite this article as:
Huang, G. & Lu, H. Exp Mech (2007) 47: 87. doi:10.1007/s11340-006-8277-4


Current nanoindentation measurement techniques normally assume that one material function (such as the Poisson's function) is a constant, and measures just one material function, such as the creep compliance in shear. For materials with significant viscoelastic effects and unknown viscoelastic functions, assuming a constant for one material function is not satisfactory. Accurate measurements require simultaneously determining two independent material functions. This paper provides a method to use nanoindentation to measure both bulk and shear relaxation functions. Two different nanoindenter tips, namely Berkovich and spherical indenters, are used for nanoindentation on polymers. Any two independent viscoelastic functions, such as bulk relaxation modulus and shear relaxation modulus, have different representations in the load–displacement curves obtained with these two indenters so that the two independent viscoelastic functions can be separated and determined. Two polymers, poly(vinyl acetate) (PVAc) and poly(methyl methacrylate) (PMMA) were used in nanoindentation. Nanoindentation measurements were conducted on PVAc above glass transition temperature (Tg) and on PMMA below Tg. Both shear and bulk relaxation functions determined from nanoindentation were found in a reasonably good agreement with data obtained from conventional tests, providing validation of the method presented. The new method can be applied in measurements of two independent viscoelastic functions at sub-micron scale of very small amounts of materials such as polymeric films on a substrate, heterogeneous materials such as bones, tissues, and nanocomposites.


Viscoelasticity Nanoindentation Polymer Bulk relaxation modulus Relaxation modulus in shear 

Copyright information

© Society for Experimental Mechanics 2007

Authors and Affiliations

  1. 1.Mechanical and Aerospace EngineeringOklahoma State UniversityStillwaterUSA

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