Experimental Mechanics

, Volume 47, Issue 1, pp 87–98

Measurements of Two Independent Viscoelastic Functions by Nanoindentation

Article

Abstract

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.

Keywords

Viscoelasticity Nanoindentation Polymer Bulk relaxation modulus Relaxation modulus in shear 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lu H, Huang G, Wang B, Mamedov A, Gupta S (2006) Characterization of the linear viscoelastic behavior of single-wall carbon nanotube/polyelectrolyte multilayer nanocomposite film using nanoindentation. Thin Solid Films 500:197–202.CrossRefGoogle Scholar
  2. 2.
    Li X, Bhushana B, Takashimab K, Baekc C, Kimc Y (2003) Mechanical characterization of micro/nanoscale structures for MEMS/NEMS applications using nanoindentation techniques. Ultramicroscopy 97:481–494.CrossRefGoogle Scholar
  3. 3.
    Pethica JB, Oliver WC (1987) Tip surface interactions in STM and AFM. Phys Scr T19:61–66.CrossRefGoogle Scholar
  4. 4.
    Syed SA, Wahl KJ, Colton RJ (1999) Nanoindentation and contact stiffness measurement using force modulation with a capacitive load–displacement transducer. Rev Sci Instrum 70(5):2408–2413.CrossRefGoogle Scholar
  5. 5.
    Lu H, Roy S, Sampathkumar P, Ma J (2002) Characterization of the fracture behavior of epoxy nanocomposites. In: Proceedings of American Composite Conference, Purdue University, OctoberGoogle Scholar
  6. 6.
    Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583.Google Scholar
  7. 7.
    Cheng L, Xia X, Yu W, Scriven LE, Gerberich WW (2000) Flat-punch indentation of viscoelastic material. J Polym Sci, B, Polym Phys 38:10–22.CrossRefGoogle Scholar
  8. 8.
    Lu H, Wang B, Ma J, Huang G, Viswanathan H (2003) Measurement of creep compliance of solid polymers by nanoindentation. Mech Time-Depend Mater 7:189–207.CrossRefGoogle Scholar
  9. 9.
    Huang G, Wang B, Lu H (2004) Measurements of viscoelastic functions in frequency-domain by nanoindentation. Mech Time-Depend Mater 8:345–364.CrossRefGoogle Scholar
  10. 10.
    Hutcheson SA, McKenna GB (2005) Nanosphere embedding into polymer surfaces: a viscoelastic contact mechanics analysis. Phys Rev Lett 94:076103-1-076103-4.Google Scholar
  11. 11.
    Odegard GM, Gates TS, Herring HM (2005) Characterization of viscoelastic properties of polymeric materials through nanoindentation. Exp Mech 45(2):130–136.CrossRefGoogle Scholar
  12. 12.
    VanLandingham MR, Chang N-K, Drzal PL, White CC, Chang S-H (2005) Viscoelastic characterization of polymers using instrumented indentation-1 quasi-static testing. J Polym Sci, B, Polym Phys 43(14):1794–1811.CrossRefGoogle Scholar
  13. 13.
    Cheng Y-T, Cheng CM (2005) General relationship between contact stiffness, contact depth, and mechanical properties for indentation in linear viscoelastic solids using axisymmetric indenter of arbitrary profiles. Appl Phys Lett 87:111914.CrossRefGoogle Scholar
  14. 14.
    Lucas BN. Hay JC, Oliver WC (2004) Using multidimensional contact mechanics experiments to measure Poisson's ratio. J Mater Res 19:58–65.Google Scholar
  15. 15.
    Vlassak JJ, Nix WD (1992) A new bulge test technique for the determination of Young's modulus and Poisson's ratio of thin films. J Mater Res 7:3242–3249.Google Scholar
  16. 16.
    Ma Z, Ravi-Chandar K (2000) Confined compression: a stable homogeneous deformation for constitutive characterization. Exp Mech 40:38–45.CrossRefGoogle Scholar
  17. 17.
    Lee EH, Radok JRM (1960) The contact problem for viscoelastic bodies. J Appl Mech 27:438–444.MATHMathSciNetGoogle Scholar
  18. 18.
    Sneddon IN (1965) The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary punch. Int J Eng Sci 3:47–56.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Hibbitt, Karlsson & Sorensen, Inc., ABAQUS/Standard 6.4 User's Manual, 2004.Google Scholar
  20. 20.
    Hertz H (1881) Über die beruhrung fester elastischer körper. J Reine Angew Math 92:156–171.Google Scholar
  21. 21.
    Knauss WG, Kenner VH (1980) On the hygrothermomechanical characterization of polyvinyl acetate. J Appl Phys 51(10):5131–5136.CrossRefGoogle Scholar
  22. 22.
    Deng TH, Knauss WG (1997) The temperature and frequency dependence of the bulk compliance of poly(vinyl acetate). Mech Time-Depend Mater 1:33–49.CrossRefGoogle Scholar
  23. 23.
    Lu H. Zhang X, Knauss WG (1997) Uniaxial, shear and Poisson relaxation and their conversion to bulk relaxation: studies on poly(methyl methacrylate). Polym Eng Sci 37: 1053–1064.CrossRefGoogle Scholar
  24. 24.
    Sane SB, Knauss WG (2001) The time-dependent bulk response of poly(mehyl methacrylate). Mech Time-Depend Mater 5:293–324.CrossRefGoogle Scholar
  25. 25.
    Emri I, von Bernstorff BS, Cvelbar R, Nikonov A (2005) Re-examination of the approximate methods for interconversion between frequency- and time-dependent material functions. J Non-Newton Fluid Mech 129(2):75–84.CrossRefGoogle Scholar
  26. 26.
    Giannakopoulos AE (2000) Strength analysis of spherical indentation of piezoelectric materials. J Appl Mech 67:409–416.CrossRefGoogle Scholar
  27. 27.
    Tschoegl NW, Knauss WG, Emri I (2002) Poisson's ratio in linear viscoelasticity—a critical review. Mech Time-Depend Mater 6:3–51.CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2007

Authors and Affiliations

  1. 1.Mechanical and Aerospace EngineeringOklahoma State UniversityStillwaterUSA

Personalised recommendations