Advertisement

Experimental Mechanics

, Volume 53, Issue 5, pp 731–742 | Cite as

Nonlinearly Viscoelastic Nanoindentation of PMMA Under a Spherical Tip

  • Y. KucukEmail author
  • C. Mollamahmutoglu
  • Y. Wang
  • H. Lu
Article

Abstract

The Oliver-Pharr method has been well established to measure Young’s modulus and hardness of materials without time-dependent behavior in nanoindentation. The method, however, is not appropriate for measuring the viscoelastic properties of materials with pronounced viscoelastic effects. One well-known phenomenon is the formation of unloading “nose” or negative stiffness during unloading that often occurs during slow loading-unloading in nanoindentation on a viscoelastic material. Most methods in literature have only considered the loading curve for analysis of viscoelastic nanoindentation data while the unloading portion is not analyzed adequately to determine the nonlinearly viscoelastic properties. In this paper, nonlinearly viscoelastic effects are considered and modeled using the nonlinear Burgers model. Nanoindentation was conducted on poly-methylmethacrylate (PMMA) using a spherical indenter tip. An inverse problem solving approach is used to allow the finite element simulation results to agree with the nanoindentation load–displacement curve during the entire loading and unloading stage. This approach has allowed the determination of the nonlinearly viscoelastic behavior of PMMA at submicron scale. In addition, the nanoindentation unloading “nose” has been captured by simulation, indicating that the negative stiffness in the viscoelastic material is the result of memory effect in time-dependent materials.

Keywords

Nanoindentation Nonlinear viscoelastic Nonlinear Burgers model Polymer PMMA Finite element method 

Notes

Acknowledgment

We acknowledge the support of NSF under grant CMMI-1132174 with Dr. Clark Cooper as the program director.

References

  1. 1.
    Li X, Bhushan B (2002) A review of nanoindentation continuous stiffness measurement technique and its applications. Mater Charact 48:11–36CrossRefGoogle Scholar
  2. 2.
    Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583CrossRefGoogle Scholar
  3. 3.
    Doerner MF, Nix WD (1986) A method for interpreting the data from depth-sensing indentation instruments. J Mater Res 1:601–609CrossRefGoogle Scholar
  4. 4.
    Cheng L, Xia X, Yu W, Scriven LE, Gerberich WW (2000) Flat-punch indentation of viscoelastic material. J Polym Sci B Polym Phys 38:10–22CrossRefGoogle Scholar
  5. 5.
    Lu H, Wang B, Ma J, Huang G, Viswanathan H (2003) Measurement of creep compliance of solid polymers by nanoindentation. Mech Time Depend Mater 7:189–207CrossRefGoogle Scholar
  6. 6.
    Huang G, Wang B, Lu H (2004) Measurements of viscoelastic functions in frequency-domain by nanoindentation. Mech Time Depend Mater 8:345–364CrossRefGoogle Scholar
  7. 7.
    Zhou Z, Lu H (2010) On the measurements of viscoelastic functions of a sphere by nanoindentation. Mech Time Depend Mater 14:1–24CrossRefGoogle Scholar
  8. 8.
    Odegard GM, Gates TS, Herring HM (2005) Characterization of viscoelastic properties of polymeric materials through nanoindentation. Exp Mech 45:130–136CrossRefGoogle Scholar
  9. 9.
    VanLandingham MR, Chang NK, Drzal PL, White CC, Chang SH (2005) Viscoelastic characterization of polymers using instrumented indentation-1. quasi-static testing. J Polym Sci B Polym Phys 43:1794–1811CrossRefGoogle Scholar
  10. 10.
    Cheng YT, Cheng CM (2005) General relationship between contact stiffness, contact depth, and mechanical properties for indentation in linear viscoelastic solids using axisymmetric indenters of arbitrary profiles. Appl Phys Lett 87 Art No 111914Google Scholar
  11. 11.
    Cheng YT, Ni WY, Cheng CM (2006) Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids. Phys Rev Lett 97 Art No 075506Google Scholar
  12. 12.
    Wei PJ, Shen WX, Lin JF (2008) Analysis and modeling for time-dependent behavior of polymers exhibited in nanoindentation tests. J Non-Cryst Solids 354(33):3911–3918CrossRefGoogle Scholar
  13. 13.
    Oyen ML, Cook RF (2003) Load–displacement behavior during sharp indentation of viscous–elastic–plastic materials. J Mater Res 18(1):139–150CrossRefGoogle Scholar
  14. 14.
    Liu CK, Lee S, Sung LP, Nguyen T (2006) Load–displacement relations for nanoindentation of viscoelastic materials. J Appl Phys 100:033503CrossRefGoogle Scholar
  15. 15.
    Mencik J, He LH, Nemecek J (2011) Characterization of viscoelastic-plastic properties of solid polymers by instrumented indentation. Polym Test 30:101–109CrossRefGoogle Scholar
  16. 16.
    Chen KS, Chen TC, Ou KS (2008) Development of semi-empirical formulation for extracting materials properties from nanoindentation measurements: residual stresses, substrate effect, and creep. Thin Solid Films 516:1931–1940CrossRefGoogle Scholar
  17. 17.
    Jo C, Fu J, Naguib HE (2005) Constitutive modeling for mechanical behavior of PMMA microcellular foams. Polymer 46:11896–11903CrossRefGoogle Scholar
  18. 18.
    Schiessel H, Metzler R, Blumen A, Nonnenmacher TF (1995) Generalized viscoelastic models: their fractional equations with solutions. J Phys A Math Gen 28:6567–6584zbMATHCrossRefGoogle Scholar
  19. 19.
    Hernandez-Jimenez A, Hernandez-Santiago J, Macias-Garcia A, Sanchez-Gonzalez J (2002) Relaxation modulus in PMMA and PTFE fitting by fractional Maxwell model. Polym Test 21(3):325–331CrossRefGoogle Scholar
  20. 20.
    Schmidt A, Gaul L (2002) Finite element formulation of viscoelastic constitutive equations using fractional time derivatives. Nonlinear Dyn 29:37–55zbMATHCrossRefGoogle Scholar
  21. 21.
    Klompen ETJ, Govaert LE (1999) Nonlinear viscoelastic behaviour of thermorheologically complex materials: a modeling approach. Mech Time Depend Mater 3:49–69CrossRefGoogle Scholar
  22. 22.
    Arzoumanidis GA, Liechti KM (2003) Linear viscoelastic property measurement and its significance for some nonlinear viscoelasticity models. Mech Time Depend Mater 7:209–250CrossRefGoogle Scholar
  23. 23.
    Ovaert TC, Kim BR, Wang JJ (2003) Multi-parameter models of the viscoelastic/plastic mechanical properties of coatings via combined nanoindentation and non-linear finite element modeling. Prog Org Coat 47(3–4):312–323CrossRefGoogle Scholar
  24. 24.
    Findley WN, Lai JS, Onaran K (1989) Creep and relaxation of nonlinear viscoelastic materials with an introduction to linear viscoelasticity. Dover Pub, New York, pp 57–64Google Scholar
  25. 25.
    Marin J, Pao YH (1953) An analytical theory of the creep deformation of materials. J Appl Mech 20Google Scholar
  26. 26.
    Richter H, Misawa EA, Lucca DA, Lu H (2001) Modeling nonlinear behavior in a piezoelectric actuator. Precis Eng 25(2):128–137CrossRefGoogle Scholar
  27. 27.
    Shames IH, Cozzarelli FA (1997) Elastic and inelastic stress analysis. Taylor & Francis, Washington, pp 239–242Google Scholar
  28. 28.
    Oyen ML (2005) Ultrastructural characterization of time-dependent, inhomogeneous materials and tissues. PhD Thesis, 84–85, University of MinnesotaGoogle Scholar
  29. 29.
    Liu Y, Varghese S, Ma J, Yoshino M, Lu H, Komanduri R (2008) Orientation effects in nanoindentation of single crystal copper. Int J Plast 24:1990–2015zbMATHCrossRefGoogle Scholar
  30. 30.
    Liu Y, Wang B, Yoshino M, Roy S, Lu H, Komanduri R (2005) Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale. J Mech Phys Solids 53:2718–2741zbMATHCrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2012

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringBartin UniversityBartinTurkey
  2. 2.Department of Mechanical EngineeringThe University of Texas at DallasRichardsonUSA
  3. 3.Intel CorporationChandlerUSA

Personalised recommendations