Skip to main content
SpringerLink
Log in

Theoretical and experimental analysis of indentation relaxation test

  • Article
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

Indentation relaxation test is investigated from theoretical and experimental points of view. Analytical expressions are derived based on the conical indentation of a homogeneous linear viscoelastic half space. Two loading kinetics prior to the hold displacement segment are studied—i.e., constant displacement rate and constant strain rate. Effects of loading procedure on measured relaxation behavior are considered. It is pointed out that a constant strain rate loading is required to perform depth-independent relaxation measurements and the strain rate affects the relaxation spectrum up to a critical time constant. Few experiments on poly(methyl methacrylate) are then performed to check the consistency of the analytical results. Some experimental limitations are also discussed. Good agreement is found between analytical calculations and experimental measurement trends, especially for the constant strain rate loading effect on the measured relaxation behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

FIG. 1
FIG. 2
FIG. 3
FIG. 4
FIG. 5
FIG. 6
FIG. 7
FIG. 8

Similar content being viewed by others

References

  1. J.M. Wheeler, D.E.J. Armstrong, W. Heinz, and R. Schwaiger: High temperature nanoindentation: The state of the art and future challenges. Curr. Opin. Solid State Mater. Sci. 19, 354 (2015).

    Article  Google Scholar 

  2. P.S. Phani and W.C. Oliver: A direct comparison of high temperature nanoindentation creep and uniaxial creep measurements for commercial purity aluminum. Acta Mater. 111, 31 (2016).

    Article  CAS  Google Scholar 

  3. Y. Li, X. Fang, S. Lu, Q. Yu, G. Hou, and X. Feng: Effects of creep and oxidation on reduced modulus in high-temperature nanoindentation. Mater. Sci. Eng., A 678, 65 (2016).

    Article  CAS  Google Scholar 

  4. N.M. Everitt, M.I. Davies, and J.F. Smith: High temperature nanoindentation—The importance of isothermal contact. Philos. Mag. 91, 1221 (2011).

    Article  CAS  Google Scholar 

  5. M. Sakai and S. Shimizu: Indentation rheometry for glass-forming materials. J. Non-Cryst. Solids 282, 236 (2001).

    Article  CAS  Google Scholar 

  6. S. Yang, Y.W. Zhang, and K. Zeng: Analysis of nanoindentation creep for polymeric materials. J. Appl. Phys. 95, 3655 (2004).

    Article  CAS  Google Scholar 

  7. M.L. Oyen: Spherical indentation creep following ramp loading. J. Mater. Res. 20, 2094 (2005).

    Article  CAS  Google Scholar 

  8. M.L. Oyen: Analytical techniques for indentation of viscoelastic materials. Philos. Mag. 86, 5625 (2006).

    Article  CAS  Google Scholar 

  9. C.A. Tweedie and K.J. Van Vliet: Contact creep compliance of viscoelastic materials via nanoindentation. J. Mater. Res. 21, 1576 (2006).

    Article  CAS  Google Scholar 

  10. E.G. Herbert, W.C. Oliver, A. Lumsdaine, and G.M. Pharr: Measuring the constitutive behavior of viscoelastic solids in the time and frequency domain using flat punch nanoindentation. J. Mater. Res. 24, 626 (2009).

    Article  CAS  Google Scholar 

  11. P.E. Mazeran, M. Beyaoui, M. Bigerelle, and M. Guigon: Determination of mechanical properties by nanoindentation in the case of viscous materials. Int. J. Mater. Res. 103, 715 (2012).

    Article  CAS  Google Scholar 

  12. V. Maier, B. Merle, M. Göken, and K. Durst: An improved long-term nanoindentation creep testing approach for studying the local deformation processes in nanocrystalline metals at room and elevated temperatures. J. Mater. Res. 28, 1177 (2013).

    Article  CAS  Google Scholar 

  13. J. Dean, J. Campbell, G. Aldrich-Smith, and T.W. Clyne: A critical assessment of the “stable indenter velocity” method for obtaining the creep stress exponent from indentation data. Acta Mater. 80, 56 (2014).

    Article  CAS  Google Scholar 

  14. M. Sakai, M. Sasaki, and A. Matsuda: Indentation stress relaxation of sol–gel-derived organic/inorganic hybrid coating. Acta Mater. 53, 4455 (2005).

    Article  CAS  Google Scholar 

  15. J. Mattice, A. Lau, M. Oyen, and R. Went: Spherical indentation load-relaxation of soft biological tissues. J. Mater. Res. 21, 2003 (2006).

    Article  CAS  Google Scholar 

  16. C.Y. Zhang, Y.W. Zhang, K.Y. Zeng, L. Shen, and Y.Y. Wang: Extracting the elastic and viscoelastic properties of a polymeric film using a sharp indentation relaxation test. J. Mater. Res. 21, 2991 (2006).

    Article  CAS  Google Scholar 

  17. J.W. Andrews, J. Bowen, and D. Cheneler: Optimised determination of viscoelastic properties using compliant measurement systems. Soft Matter 9, 5581 (2013).

    Article  CAS  Google Scholar 

  18. G. Peng, Y. Ma, Y. Feng, Y. Huan, C. Qin, and T. Zhang: Nanoindentation creep of nonlinear viscoelastic polypropylene. Polym. Test. 43, 38 (2015).

    Article  CAS  Google Scholar 

  19. N.G. Patel, A. Sreeram, R.I. Venkatanarayanan, S. Krishnan, and P.A. Yuya: Elevated temperature nanoindentation characterization of poly(para-phenylene vinylene) conjugated polymer films. Polym. Test. 41, 17 (2015).

    Article  CAS  Google Scholar 

  20. R. Goodall and T.W. Clyne: A critical appraisal of the extraction of creep parameters from nanoindentation data obtained at room temperature. Acta Mater. 54, 5489 (2006).

    Article  CAS  Google Scholar 

  21. M.R. Vanlandingham, N.K. Chang, P.L. Drzal, C.C. White, and S.H. Chang: Viscoelastic characterization of polymers using instrumented indentation. I. Quasi-static testing. J. Polym. Sci., Part B: Polym. Phys. 43, 1794 (2005).

    Article  CAS  Google Scholar 

  22. K.I. Schiffmann: Nanoindentation creep and stress relaxation tests of polycarbonate: Analysis of viscoelastic properties by different rheological models. Int. J. Mater. Res. 97, 1199 (2006).

    Article  CAS  Google Scholar 

  23. J.L. Bucaille, E. Felder, and G. Hochstetter: Identification of the viscoplastic behavior of a polycarbonate based on experiments and numerical modeling of the nano-indentation test. J. Mater. Sci. 37, 3999 (2002).

    Article  CAS  Google Scholar 

  24. G. Kermouche, J.L. Loubet, and J.M. Bergheau: Extraction of stress–strain curves of elastic-viscoplastic solids using conical/pyramidal indentation testing with application to polymers. Mech. Mater. 40, 271 (2008).

    Article  Google Scholar 

  25. W. Findley: Creep and Relaxation of Nonlinear Viscoelastic Materials (Dover Publication, Inc., New York 1978).

    Google Scholar 

  26. N.W. Tschoegl, W.G. Knauss, and I. Emri: Poisson’s ratio in linear viscoelasticity—A critical review. Mech. Time-Depend. Mater. 6, 3 (2002).

    Article  Google Scholar 

  27. T.C.T. Ting: The contact stresses between a rigid indenter and a viscoelastic half-space. J. Appl. Mech. 33, 845 (1966).

    Article  Google Scholar 

  28. G.A.C. Graham: The contact problem in the linear theory of viscoelasticity. Int. J. Eng. Sci. 3, 27 (1965).

    Article  Google Scholar 

  29. A.E.H. Love: Boussinesq’s problem for a rigid cone. Q. J. Math. os-10, 161 (1939).

    Google Scholar 

  30. I.N. Sneddon: Boussinesq’s problem for a rigid cone. Math. Proc. Cambridge Philos. Soc. 44, 492 (1948).

    Article  Google Scholar 

  31. Y.T. Cheng and C.M. Cheng: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004).

    Article  Google Scholar 

  32. M. Vandamme and F.J. Ulm: Viscoelastic solutions for conical indentation. Int. J. Solids Struct. 43, 3142 (2006).

    Article  Google Scholar 

  33. G. Kermouche, J.L. Loubet, and J.M. Bergheau: Cone indentation of time-dependent materials: The effects of the indentation strain rate. Mech. Mater. 39, 24 (2007).

    Article  Google Scholar 

  34. N.W. Tschoegl: The Phenomenological Theory of Linear Viscoelastic Behavior 3rd ed. (Springer Berlin Heidelberg, Berlin, Heidelberg, 1989). p. 1–34.

    Book  Google Scholar 

  35. J.D. Ferry: Viscoelastic Properties of Polymers (John Wiley and Sons, New York, 1980).

    Google Scholar 

  36. F. Schwarzl and A.J. Staverman: Higher approximations of relaxation spectra. Physica 18, 791 (1952).

    Article  CAS  Google Scholar 

  37. J.D. Ferry and M.L. Williams: Second approximation methods for determining the relaxation time spectrum of a viscoelastic material. J. Colloid Sci. 7, 347 (1952).

    Article  CAS  Google Scholar 

  38. B.N. Lucas, W.C. Oliver, G.M. Pharr, and J-L. Loubet: Time dependent deformation during indentation testing. MRS Proc. 436, 233 (1997).

    Article  CAS  Google Scholar 

  39. G. Guillonneau, G. Kermouche, S. Bec, and J.L. Loubet: Extraction of mechanical properties with second harmonic detection for dynamic nanoindentation testing. Exp. Mech. 52, 933 (2012).

    Article  Google Scholar 

  40. J.L. Loubet, M. Bauer, A. Tonck, S. Bec, and B. Gauthier-Manuel: Nanoindentation with a surface force apparatus. In Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures, Vol. 233 (1993); p. 429.

    Article  CAS  Google Scholar 

  41. W.C. Oliver and G.M. Pharr: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).

    Article  CAS  Google Scholar 

  42. G. Guillonneau, G. Kermouche, J-M. Bergheau, and J-L. Loubet: A new method to determine the true projected contact area using nanoindentation testing. C. R. Mec. 343, 410 (2015).

    Article  Google Scholar 

  43. E.G. Herbert, P. Sudharshan Phani, and K.E. Johanns: Nanoindentation of viscoelastic solids: A critical assessment of experimental methods. Curr. Opin. Solid State Mater. Sci. 19, 334 (2015).

    Article  Google Scholar 

  44. A.F. Yee and M.T. Takemori: Dynamic bulk and shear relaxation in glassy polymers. I. Experimental techniques and results on PMMA. J. Polym. Sci. Polym. Phys. Ed. 20, 205 (1982).

    Article  CAS  Google Scholar 

  45. D. Tabor: The hardness of solids. Rev. Phys. Technol. 1, 145 (1970).

    Article  Google Scholar 

  46. P. Fernández, D. Rodríguez, M.J. Lamela, and A. Fernández-Canteli: Study of the interconversion between viscoelastic behaviour functions of PMMA. Mech. Time-Depend. Mater. 15, 169 (2011).

    Article  CAS  Google Scholar 

  47. H. Lu, X. Zhang, and W.G. Knauss: Uniaxial, shear, and poisson relaxation and their conversion to bulk relaxation: Studies on poly(methyl methacrylate). Polym. Eng. Sci. 37, 1053 (1997).

    Article  CAS  Google Scholar 

  48. J.J.C. Cruz Pinto and J.R.S. André: Toward the accurate modeling of amorphous nonlinear materials—Polymer stress relaxation (I). Polym. Eng. Sci. 56, 348 (2016).

    Article  CAS  Google Scholar 

Download references

ACKNOWLEDGMENTS

This work was supported by the LABEX MANUTECH-SISE (ANR-10-LABX-0075) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). The authors would also like to acknowledge financial support from Institut Carnot Ingénierie@Lyon. The authors finally acknowledge Dr. M. Laurent-Brocq and G. Bracq from ICMPE for fruitful discussions.

Author information

Authors and Affiliations

  1. Ecole Centrale de Lyon, LTDS UMR CNRS 5513, Université de Lyon, Ecully, France

    Paul Baral, Gaylord Guillonneau & Jean-Luc Loubet

  2. Ecole des Mines de Saint Etienne, Centre SMS, Laboratoire LGF UMR 5307, Saint Etienne, France

    Guillaume Kermouche

  3. Ecole Nationale d’Ingénieurs de Saint Etienne, LTDS UMR CNRS 5513, Université de Lyon, Saint Etienne, France

    Jean-Michel Bergheau

Authors
  1. Paul Baral
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gaylord Guillonneau
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guillaume Kermouche
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jean-Michel Bergheau
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jean-Luc Loubet
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul Baral.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Baral, P., Guillonneau, G., Kermouche, G. et al. Theoretical and experimental analysis of indentation relaxation test. Journal of Materials Research 32, 2286–2296 (2017). https://doi.org/10.1557/jmr.2017.203

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2017.203

Search

Navigation