Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-14T09:27:19.821Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of indentation creep

Published online by Cambridge University Press:  31 January 2011

Don S. Stone ,
Joseph E. Jakes ,
Jonathan Puthoff  and
Abdelmageed A. Elmustafa
Don S. Stone*
Affiliation:
Department of Materials Science and Engineering, and Materials Science Program, University of Wisconsin−Madison, Madison, Wisconsin 53706
Joseph E. Jakes
Affiliation:
Materials Science Program, University of Wisconsin−Madison, Madison, Wisconsin 53706; and Performance Enhanced Biopolymers, United States Forest Service, Forest Products Laboratory, Madison, Wisconsin 53726
Jonathan Puthoff
Affiliation:
Materials Science Program, University of Wisconsin−Madison, Madison, Wisconsin 53706
Abdelmageed A. Elmustafa
Affiliation:
Department of Mechanical Engineering and The Applied Research Center–Jefferson Laboratory, Old Dominion University, Norfolk, Virginia 23529
*
a)Address all correspondence to this author. e-mail: dsstone@wisc.edu
Get access

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 (mσ) 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.

Keywords

NanoindentationHardnessStress/strain relationship
Type
Outstanding Symposium Papers
Information
Journal of Materials Research , Volume 25 , Issue 4 , April 2010 , pp. 611 - 621
Copyright
Copyright © Materials Research Society 2010

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.Atkins, A.G., Silverio, A., Tabor, D.Indentation hardness and creep of solids. J. Inst. Met. 94, (Part 11)369 (1966)Google Scholar
2.Chu, S.N.G., Li, J.C.M.Impression creep: A new creep test. J. Mater. Sci. 12, (11)2200 (1977)CrossRefGoogle Scholar
3.Mulhearn, T.O., Tabor, D.Creep and hardness of metals: A physical study. J. Inst. Met. 89, 7 (1960)Google Scholar
4.Cheng, Y-T., Cheng, C-M.Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, (4–5)91 (2004)CrossRefGoogle Scholar
5.Bower, A.F., Fleck, N.A., Needleman, A., Ogbonna, N.Indentation of a power law creeping solid. Proc. R. Soc. London, Ser. A 1993, (441)97 (1911)Google Scholar
6.Hill, R.Similarity analysis of creep indentation tests. Proc. R. Soc. London, Ser. A 1992, (436)617 (1898)Google Scholar
7.Kocks, U.F., Argon, A.S., Ashby, M.F.Thermodynamics and kinetics of slipProgress in Materials Science Vol. 19 (Pergamon Press, New York 1975)Google Scholar
8.Jang, D., Atzmon, M.Grain-size dependence of plastic deformation in nanocrystalline Fe. J. Appl. Phys. 93, (11)9282 (2003)CrossRefGoogle Scholar
9.Wang, F., Huang, P., Xu, K.W.Time dependent plasticity at real nanoscale deformation. Appl. Phys. Lett. 90, (16)161921 (2007)CrossRefGoogle Scholar
10.Hannula, S.P., Stone, D., Li, C.Y.Determination of time-dependent plastic properties of metals by indentation load relaxation techniquesElectronic Packaging Materials Science edited by E.A. Giess, K-N. Tu, and D.R. Uhlmann (Mater. Res. Soc. Symp. Proc 40, Pittsburgh, PA 1985)217224Google Scholar
11.Stone, D.S., Yoder, K.B.Division of the hardness of molybdenum into rate-dependent and rate-independent components. J. Mater. Res. 9, (10)2524 (1994)CrossRefGoogle Scholar
12.Lucas, B.N., Oliver, W.C.Time dependent indentation testing at non-ambient temperatures utilizing the high temperature mechanical properties microprobeThin 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)645Google Scholar
13.Tambwe, M.F., Stone, D.S., Griffin, A.J., Kung, H., Lu, Y.C., Nastasi, M.Haasen plot analysis of the Hall-Petch effect in Cu–Nb nanolayer composites. J. Mater. Res. 14, (2)407 (1999)CrossRefGoogle Scholar
14.Elmustafa, A.A., Kose, S., Stone, D.S.The strain-rate sensitivity of the hardness in indentation creep. J. Mater. Res. 22, (4)926 (2007)CrossRefGoogle Scholar
15.Oliver, W.C., Pharr, G.M.Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, (1)3 (2004)CrossRefGoogle Scholar
16.Doerner, M.F., Nix, W.D.A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, (4)601 (1986)CrossRefGoogle Scholar
17.Oliver, W.C., Pharr, G.M.Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, (6)1564 (1992)CrossRefGoogle Scholar
18.Elmustafa, A.A., Stone, D.S.Strain rate sensitivity in nanoindentation creep of hard materials. J. Mater. Res. 22, (10)2912 (2007)CrossRefGoogle Scholar
19.Goldsby, D.L., Rar, A., Pharr, G.M., Tullis, T.E.Nanoindentation creep of quartz, with implications for rate- and state-variable friction laws relevant to earthquake mechanics. J. Mater. Res. 19, (1)357 (2004)CrossRefGoogle Scholar
20.Rar, A., Sohn, S., Oliver, W.C., Goldsby, D.L., Tullis, T.E., Pharr, G.M.On the measurement of creep by nanoindentation with continuous stiffness techniquesFundamentals 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)R4.2Google Scholar
21.Johnson, K.L.Contact Mechanics (Cambridge University Press, Cambridge, UK 1985)452CrossRefGoogle Scholar
22.Kermouche, G., Loubet, J.L., Bergheau, J.M.Cone indentation of time-dependent materials: The effects of the indentation strain rate. Mech. Mater. 39, (1)24 (2007)CrossRefGoogle Scholar
23.Kermouche, G., Loubet, J.L., Bergheau, J.M.A new index to estimate the strain rate sensitivity of glassy polymers using conical/pyramidal indentation. Philos. Mag. 86, (33–35)5667 (2006)CrossRefGoogle Scholar
24.Sakai, M., Akatsu, T., Numata, S., Matsuda, K.Linear strain hardening in elastoplastic indentation contact. J. Mater. Res. 18, (9)2087 (2003)CrossRefGoogle Scholar
25.Tabor, D.The Hardness of Metals (Clarendon Press, Oxford, UK 1951)Google Scholar
26.Bolshakov, A., Pharr, G.M.Influences of pileup on the measurement of mechanical properties by load and depth-sensing indentation techniques. J. Mater. Res. 13, (4)1049 (1998)CrossRefGoogle Scholar
27.Quinson, R., Perez, J., Rink, M., Pavan, A.Yield criteria for amorphous glassy polymers. J. Mater. Sci. 32, (5)1371 (1997)CrossRefGoogle Scholar
28.Schuh, C.A., Nieh, T.G.A survey of instrumented indentation studies on metallic glasses. J. Mater. Res. 19, (1)46 (2004)CrossRefGoogle Scholar
29.Puthoff, J.B., Jakes, J.E., Cao, H., Stone, D.S.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)CrossRefGoogle Scholar
30.Asif, S.A.S., Wahl, K.J., Colton, R.J., Warren, O.L.Quantitative imaging of nanoscale mechanical properties using hybrid nanoindentation and force modulation. J. Appl. Phys. 90, (3)1192 (2001)CrossRefGoogle Scholar
31.Jakes, J.E., Frihart, C.R., Beecher, J.F., Moon, R.J., Resto, P.J., Melgarejo, Z.H., Suarez, O.M., Baumgart, H., Elmustafa, A.A., Stone, D.S.Nanoindentation near the edge. J. Mater. Res. 24, (3)1016 (2009)CrossRefGoogle Scholar
32.Jakes, J.E., Frihart, C.R., Beecher, J.F., Moon, R.J., Stone, D.S.Experimental method to account for structural compliance in nanoindentation measurements. J. Mater. Res. 23, (4)1113 (2008)CrossRefGoogle Scholar
33.Sakai, M., Nakano, Y.Elastoplastic load–depth hysteresis in pyramidal indentation. J. Mater. Res. 17, (8)2161 (2002)CrossRefGoogle Scholar
34.Strader, J.H., Shim, S., Bei, H., Oliver, W.C., Pharr, G.M.An experimental evaluation of the constant relating the contact stiffness to the contact area in nanoindentation. Philos. Mag. 86, (33–35)5285 (2006)CrossRefGoogle Scholar