Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-18T11:22:42.982Z Has data issue: false hasContentIssue false
  • English
  • Français

Measuring the constitutive behavior of viscoelastic solids in the time and frequency domain using flat punch nanoindentation

Published online by Cambridge University Press:  31 January 2011

E.G. Herbert ,
W.C. Oliver ,
A. Lumsdaine  and
G.M. Pharr
E.G. Herbert*
Affiliation:
Agilent Technologies, Nanotechnology Measurements Division, Research and Development, Oak Ridge, Tennessee 37830
W.C. Oliver
Affiliation:
Agilent Technologies, Nanotechnology Measurements Division, Research and Development, Oak Ridge, Tennessee 37830
A. Lumsdaine
Affiliation:
Agilent Technologies, Nanotechnology Measurements Division, Research and Development, Oak Ridge, Tennessee 37830
G.M. Pharr*
Affiliation:
University of Tennessee, College of Engineering, Department of Materials Science and Engineering, Knoxville, Tennessee 37996-2200; and Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6132
*
a) Address all correspondence to this author. e-mail: erik.herbert@agilent.com
a) Address all correspondence to this author. e-mail: erik.herbert@agilent.com
Get access

Abstract

The purpose of this work is to further develop experimental methodologies using flat punch nanoindentation to measure the constitutive behavior of viscoelastic solids in the frequency and time domain. The reference material used in this investigation is highly plasticized polyvinylchloride (PVC) with a glass transition temperature of −17 °C. The nanoindentation experiments were conducted using a 983-μm-diameter flat punch. For comparative purposes, the storage and loss modulus obtained by nanoindentation with a 103-μm-diameter flat punch and dynamic mechanical analysis are also presented. Over the frequency range of 0.01–50 Hz, the storage and loss modulus measured using nanoindentation and uniaxial compression is shown to be in excellent agreement. The creep compliance function measured using a constant stress test performed in uniaxial compression and flat punch nanoindentation is also shown to correlate well over nearly 4 decades in time. In addition, the creep compliance function predicted from nanoindentation data acquired in the frequency domain is shown to correlate strongly with the creep compliance function measured in the time domain. Time–temperature superposition of nanoindentation data taken at 5, 10, 15, and 22 °C shows the sample is not thermorheologically simple, and thus the technique cannot be used to expand the mechanical characterization of this material. Collectively, these results clearly demonstrate the ability of flat punch nanoindentation to accurately and precisely determine the constitutive behavior of viscoelastic solids in the time and frequency domain.

Keywords

NanoindentationPolymer
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 626 - 637
Copyright
Copyright © Materials Research Society 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Herbert, E.G., Oliver, W.C., and Pharr, G.M.: Nanoindentation and the dynamic characterization of viscoelastic solids. J. Phys. D: Appl. Phys. 41, 074021 (2008).CrossRefGoogle Scholar
2.Dub, S.N. and Trunov, M.L.: Determination of viscoelastic material parameters by step-loading nanoindentation. J. Phys. D: Appl. Phys. 41, 074024 (2008).CrossRefGoogle Scholar
3.Schiffmann, K.I.: Nanoindentation creep and stress relaxation tests of polycarbonate: Analysis of viscoelastic properties by different rheological models. Int. J. Mater. Res. 97, 1199 (2006).Google Scholar
4.Yang, S., Zhang, Y-W., and Zeng, K.: Analysis of nanoindentation creep for polymeric materials. J. Appl. Phys. 95, 3655 (2004).CrossRefGoogle Scholar
5.Lu, H., Wang, B., Ma, J., Huang, G., and Viswanathan, H.: Measurement of creep compliance of solid polymers by nanoindentation. Mech. Time-Depend. Mater. 7, 189 (2003).CrossRefGoogle Scholar
6.Tweedie, C.A. and Van Vliet, K.J.: Contact creep compliance of viscoelastic materials via nanoindentation. J. Mater. Res. 21, 1576 (2006).CrossRefGoogle Scholar
7.Oyen, M.L. and Cook, R.F.: Load-displacement behavior during sharp indentation of viscous-elastic–plastic materials. J. Mater. Res. 18, 139 (2003).CrossRefGoogle Scholar
8.VanLandingham, M.R., Drzal, P.L., and White, C.C.: Indentation creep and relaxation measurements of polymers, in Fundamentals of Nanoindentation and Nanotribology III, edited by Wahl, K.J., Huber, N., Mann, A.B., Bahr, D.F., and Cheng, Y-T. (Mater. Res. Soc. Symp. Proc. 841, Warrendale, PA, 2005), R5.5.1.Google Scholar
9.Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
10.Johnson, K.: Contact Mechanics (Cambridge University Press, Cambridge, UK, 1989).Google Scholar
11.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 (1987).CrossRefGoogle Scholar
12.Tschoegl, N.W., Knauss, W.G., and Emri, I.: Poisson's ratio in linear viscoelasticity—A critical review. Mech. Time-Depend. Mater. 6, 3 (2002).CrossRefGoogle Scholar
13.Sakai, M.: Time-dependent viscoelastic relation between load and penetration for an axisymmetric indenter. Philos. Mag. A 82, 1841 (2002).CrossRefGoogle Scholar
14.Lakes, R.S.: Viscoelastic Solids (CRC Press, Boca Raton, FL, 1999), pp. 147–148.Google Scholar
15.Ferry, J.D.: Viscoelastic Properties of Polymers, 3rd ed. (John Wiley and Sons, New York, 1980), pp. 13, 58.Google Scholar
16.Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).Google Scholar
17.Flory, A. and McKenna, G.B.: Finite step rate corrections in stress relaxation experiments: A comparison of two methods. Mech. Time-Depend. Mater. 8, 17 (2004).CrossRefGoogle Scholar
18.Cheng, L., Xia, X., Yu, W., Scriven, L.E., and Gerberich, W.W.: Flat-punch indentation of viscoelastic material. J. Polym. Sci., Part B: Pohm. Phys. 38, 10 (2000).3.0.CO;2-6>CrossRefGoogle Scholar