Skip to main content
Log in

Analysis of indentation creep

  • Outstanding Symposium Paper
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

Finite element analysis is used to simulate cone indentation creep in materials across a wide range of hardness, strain rate sensitivity, and work-hardening exponent. Modeling reveals that the commonly held assumption of the hardness strain rate sensitivity (mH) equaling the flow stress strain rate sensitivity (ms) is violated except in low hardness/modulus materials. Another commonly held assumption is that for self-similar indenters the indent area increases in proportion to the (depth)2 during creep. This assumption is also violated. Both violations are readily explained by noting that the proportionality “constants” relating (i) hardness to flow stress and (ii) area to (depth)2 are, in reality, functions of hardness/modulus ratio, which changes during creep. Experiments on silicon, fused silica, bulk metallic glass, and poly methyl methacrylate verify the breakdown of the area-(depth)2 relation, consistent with the theory. A method is provided for estimating area from depth during creep.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A.G. Atkins, A. Silverio, D. Tabor Indentation hardness and creep of solids. J. Inst. Met. 94, (Part 11) 369 (1966)

    CAS  Google Scholar 

  2. S.N.G. Chu, J.C.M. Li Impression creep: A new creep test. J. Mater. Sci. 12, (11) 2200 (1977)

    Article  CAS  Google Scholar 

  3. T.O. Mulhearn, D. Tabor Creep and hardness of metals: A physical study. J. Inst. Met. 89, 7 (1960)

    CAS  Google Scholar 

  4. Y-T Cheng, C-M Cheng Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, (4–5) 91 (2004)

    Article  Google Scholar 

  5. A.F. Bower, N.A. Fleck, A. Needleman, N. Ogbonna Indentation of a power law creeping solid. Proc. R. Soc. London, Ser. A 1993, (441) 97 (1911)

    Google Scholar 

  6. R. Hill Similarity analysis of creep indentation tests. Proc. R. Soc. London, Ser. A 1992, (436) 617 (1898)

    Google Scholar 

  7. U.F. Kocks, A.S. Argon, M.F. Ashby Thermodynamics and kinetics of slip Progress in Materials Science Vol. 19 (Pergamon Press, New York 1975)

  8. D. Jang, M. Atzmon Grain-size dependence of plastic deformation in nanocrystalline Fe. J. Appl. Phys. 93, (11) 9282 (2003)

    Article  CAS  Google Scholar 

  9. F. Wang, P. Huang, K.W. Xu Time dependent plasticity at real nanoscale deformation. Appl. Phys. Lett. 90, (16) 161921 (2007)

    Article  Google Scholar 

  10. S.P. Hannula, D. Stone, C.Y. Li Determination of time-dependent plastic properties of metals by indentation load relaxation techniques Electronic Packaging Materials Science edited by E.A. Giess, K-N. Tu, and D.R. Uhlmann (Mater. Res. Soc. Symp. Proc 40, Pittsburgh, PA 1985) 217–224

    Google Scholar 

  11. D.S. Stone, K.B. Yoder Division of the hardness of molybdenum into rate-dependent and rate-independent components. J. Mater. Res. 9, (10) 2524 (1994)

    Article  CAS  Google Scholar 

  12. B.N. Lucas, W.C. Oliver Time dependent indentation testing at non-ambient temperatures utilizing the high temperature mechanical properties microprobe Thin Films: Stresses and Mechanical Properties V edited by S.P. Baker, C.A. Ross, P.H. Townsend, C.A. Volkert, and P. Børgesen (Mater. Res. Soc. Symp. Proc 356, Pittsburgh, PA 1995) 645

    Google Scholar 

  13. M.F. Tambwe, D.S. Stone, A.J. Griffin, H. Kung, Y.C. Lu, M. Nastasi Haasen plot analysis of the Hall-Petch effect in Cu–Nb nanolayer composites. J. Mater. Res. 14, (2) 407 (1999)

    Article  CAS  Google Scholar 

  14. A.A. Elmustafa, S. Kose, D.S. Stone The strain-rate sensitivity of the hardness in indentation creep. J. Mater. Res. 22, (4) 926 (2007)

    Article  CAS  Google Scholar 

  15. W.C. Oliver, G.M. Pharr Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, (1) 3 (2004)

    Article  CAS  Google Scholar 

  16. M.F. Doerner, W.D. Nix A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, (4) 601 (1986)

    Article  Google Scholar 

  17. W.C. Oliver, G.M. Pharr Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, (6) 1564 (1992)

    Article  CAS  Google Scholar 

  18. A.A. Elmustafa, D.S. Stone Strain rate sensitivity in nanoindentation creep of hard materials. J. Mater. Res. 22, (10) 2912 (2007)

    Article  CAS  Google Scholar 

  19. D.L. Goldsby, A. Rar, G.M. Pharr, T.E. Tullis Nanoindentation creep of quartz, with implications for rate- and state-variable friction laws relevant to earthquake mechanics. J. Mater. Res. 19, (1) 357 (2004)

    Article  CAS  Google Scholar 

  20. A. Rar, S. Sohn, W.C. Oliver, D.L. Goldsby, T.E. Tullis, G.M. Pharr On the measurement of creep by nanoindentation with continuous stiffness techniques Fundamentals of Nanoindentation and Nanotribology III edited by K.J. Wahl, N. Huber, A.B. Mann, D.F. Bahr, and Y-T. Cheng (Mater. Res. Soc. Symp. Proc 841, Warrendale, PA 2005) R4.2

    Google Scholar 

  21. K.L. Johnson Contact Mechanics (Cambridge University Press, Cambridge, UK 1985) 452

    Book  Google Scholar 

  22. G. Kermouche, J.L. Loubet, J.M. Bergheau Cone indentation of time-dependent materials: The effects of the indentation strain rate. Mech. Mater. 39, (1) 24 (2007)

    Article  Google Scholar 

  23. G. Kermouche, J.L. Loubet, J.M. Bergheau A new index to estimate the strain rate sensitivity of glassy polymers using conical/pyramidal indentation. Philos. Mag. 86, (33–35) 5667 (2006)

    Article  CAS  Google Scholar 

  24. M. Sakai, T. Akatsu, S. Numata, K. Matsuda Linear strain hardening in elastoplastic indentation contact. J. Mater. Res. 18, (9) 2087 (2003)

    Article  CAS  Google Scholar 

  25. D. Tabor The Hardness of Metals (Clarendon Press, Oxford, UK 1951)

    Google Scholar 

  26. A. Bolshakov, G.M. Pharr Influences of pileup on the measurement of mechanical properties by load and depth-sensing indentation techniques. J. Mater. Res. 13, (4) 1049 (1998)

    Article  CAS  Google Scholar 

  27. R. Quinson, J. Perez, M. Rink, A. Pavan Yield criteria for amorphous glassy polymers. J. Mater. Sci. 32, (5) 1371 (1997)

    Article  CAS  Google Scholar 

  28. C.A. Schuh, T.G. Nieh A survey of instrumented indentation studies on metallic glasses. J. Mater. Res. 19, (1) 46 (2004)

    Article  CAS  Google Scholar 

  29. J.B. Puthoff, J.E. Jakes, H. Cao, D.S. Stone Investigation of thermally activated deformation in amorphous PMMA and Zr–Cu–Al bulk metallic glasses with broadband nanoindentation creep. J. Mater. Res. 24, (3) 1279 (2009)

    Article  CAS  Google Scholar 

  30. S.A.S. Asif, K.J. Wahl, R.J. Colton, O.L. Warren Quantitative imaging of nanoscale mechanical properties using hybrid nanoindentation and force modulation. J. Appl. Phys. 90, (3) 1192 (2001)

    Article  Google Scholar 

  31. J.E. Jakes, C.R. Frihart, J.F. Beecher, R.J. Moon, P.J. Resto, Z.H. Melgarejo, O.M. Suarez, H. Baumgart, A.A. Elmustafa, D.S. Stone Nanoindentation near the edge. J. Mater. Res. 24, (3) 1016 (2009)

    Article  CAS  Google Scholar 

  32. J.E. Jakes, C.R. Frihart, J.F. Beecher, R.J. Moon, D.S. Stone Experimental method to account for structural compliance in nanoindentation measurements. J. Mater. Res. 23, (4) 1113 (2008)

    Article  CAS  Google Scholar 

  33. M. Sakai, Y. Nakano Elastoplastic load–depth hysteresis in pyramidal indentation. J. Mater. Res. 17, (8) 2161 (2002)

    Article  CAS  Google Scholar 

  34. J.H. Strader, S. Shim, H. Bei, W.C. Oliver, G.M. Pharr An experimental evaluation of the constant relating the contact stiffness to the contact area in nanoindentation. Philos. Mag. 86, (33–35) 5285 (2006)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Don S. Stone.

Additional information

Articles in this section are based on presentations that were selected by MRS Meeting Symposium Organizers as outstanding papers. Upon selection, authors are invited to submit their research results to Journal of Materials Research. These papers are subject to the same peer review and editorial standards as all other JMR papers. This is another way by which the Materials Research Society recognizes high quality papers presented at its meetings.

This paper was selected as an Outstanding Symposium Paper for the 2007 MRS Fall Meeting, Symposium AA Proceedings, Vol. 1049.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stone, D.S., Joseph, J.E., Puthoff, J. et al. Analysis of indentation creep. Journal of Materials Research 25, 611–621 (2010). https://doi.org/10.1557/JMR.2010.0092

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/JMR.2010.0092

Navigation