Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T14:37:42.552Z Has data issue: false hasContentIssue false
  • English
  • Français

The strain-rate sensitivity of the hardness in indentation creep

Published online by Cambridge University Press:  03 March 2011

A.A. Elmustafa ,
S. Kose  and
D.S. Stone
A.A. Elmustafa*
Affiliation:
Department of Mechanical Engineering, Old Dominion University, Norfolk, Virginia 23529; and Applied Research Center, Old Dominion University, Jefferson Laboratory, Newport News, Virginia 23606
S. Kose
Affiliation:
Department of Civil and Environmental Engineering, University of Wisconsin—Madison, Madison, Wisconsin 53706
D.S. Stone
Affiliation:
Department of Materials Science and Engineering, University of Wisconsin—Madison, Madison, Wisconsin 53706
*
a) Address all correspondence to this author. e-mail: aelmusta@odu.edu
Get access

Abstract

Finite element analysis is used to simulate indentation creep experiments with a cone-shaped indenter. The purpose of the work is to help identify the relationship between the strain-rate sensitivity of the hardness, νH, and that of the flow stress, νσ in materials for which elastic deformations are significant. In general, νH differs from νσ, but the ratio νH/νσ is found to be a unique function of H/E* where H is the hardness and E* is the modulus relevant to Hertzian contact. νH/νσ approaches 1 for small H/E*, 0 for large H/E*, and is insensitive to work hardening. The trend in νH/νσ as a function of H/E* can be explained based on a generalized analysis of Tabor’s relation in which hardness is proportional to the flow stress H = k × σeff and in which the proportionality factor k is a function of σeff/E*.

Keywords

HardnessNanoscale
Type
Articles
Information
Journal of Materials Research , Volume 22 , Issue 4 , April 2007 , pp. 926 - 936
Copyright
Copyright © Materials Research Society 2007

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

1Cottrell, A.H.: Thermally activated plastic glide. Philos. Mag. Lett. 82, 65 (2002).Google Scholar
2Conrad, H.: Cryogenic properties of metals, in High-Strength Materials, edited by Zackay, V.F. (Wiley, NY, Berkeley, CA, 1964), pp. 436–509.Google Scholar
3Kocks, U.F., Argon, A.S., and Ashby, M.F.: Thermodynamics and kinetics of slip, in Progress in Materials Science, Vol. 19 (Pergamon Press: Oxford; New York, 1975), p. xviii.Google Scholar
4Mulford, R.A.: Analysis of strengthening mechanisms in alloys by means of thermal-activation theory. Acta Metall. 27, 1115 (1979).Google Scholar
5Asaro, R.J. and Suresh, S.: Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nano-scale twins. Acta Mater. 53, 3369 (2005).Google Scholar
6Betz, U. and Hahn, H.: Ductility of nanocrystalline zirconia based ceramics at low temperatures. Nanostruct. Mater. 12, 911 (1999).Google Scholar
7Bonetti, E., Pasquini, L., and Savini, L.: Mechanical spectroscopy of nanocrystalline metals, in Structure and Mechanical Properties of Nanophase Materials—Theory and Computer Simulations vs. Experiment, edited by Farkas, D., Kung, H., Mayo, M., Van Swygenhoven, H. and Weertman, J. (Mater. Res. Soc. Symp. Proc. 634, Warrendale, PA, 2000), B1.5.Google Scholar
8Hayes, R., Tellkamp, V., and Laverina, E.: A preliminary creep study of a bulk nanocrystalline Al-Mg alloy. Scripta Mater. 41, 743 (1999).Google Scholar
9Mayo, M.J., Siegel, R.W., Liao, Y.X., and Nix, W.D.: Nanoindentation of nanocrystalline ZnO. J. Mater. Res. 7, 973 (1992).Google Scholar
10Mukai, T., Ishikawa, K., and Higashi, K.: Influence of strain rate on the mechanical properties in fine-grained aluminum alloys. Mater. Sci. Eng., A (Struct. Mater.: Properties, Microstructure and Processing) A204, 12 (1995).CrossRefGoogle Scholar
11Noskova, N.I., Andrievski, R.A., and Ivanov, V.V.: The deformation and peculiarities of the destruction of nanophase materials. Mater. Sci. Forum 307, 211 (1999).Google Scholar
12Semiatin, S.L., Jata, K.V., Uchic, M.D., Berbon, P.B., Matejczyk, D.E., and Bampton, C.C.: Plastic flow and fracture behavior of an Al-Ti-Cu nanocomposite. Scripta Mater. 44, 395 (2001).Google Scholar
13Yoder, K.B., Elmustafa, A.A., Lin, J.C., Hoffman, R.A., and Stone, D.S.: Activation analysis of deformation in evaporated molybdenum thin films. J. Phys. D: Appl. Phys. 36, 884 (2003).Google Scholar
14Tambwe, M.F., Stone, D.S., Griffin, A.J., Kung, H., Lu, Y.C., and Nastasi, M.: Haasen plot analysis of the Hall-Petch effect in Cu-Nb nanolayer composites. J. Mater. Res. 14, 407 (1999).Google Scholar
15Zhang, K., Weertman, J.R., and Eastman, J.A.: The influence of time, temperature, and grain size on indentation creep in high-purity nanocrystalline and ultrafine grain copper. Appl. Phys. Lett. 85, 5197 (2004).Google Scholar
16Hannula, S-P., Stone, D., and Li, C-Y.: Determination of time-dependent plastic properties by indentation load relaxation techniques, in Electronic Packaging Materials Science, edited by Giess, E.A., Tu, K-N. and Uhlmann, D.R. (Mater. Res. Soc. Symp. Proc. 40, Pittsburgh, PA, 1985), p. 218.Google Scholar
17Lucas, B.N. and Oliver, W.C.: Time dependent indentation testing at non-ambient temperatures utilizing the high temperature mechanical properties microprobe, in Thin Films: Stresses and Mechanical Properties V, edited by Baker, S.P., Rose, C.A., Townsend, P.H., Volkert, C.A. and Borgensen, P. (Mater. Res. Soc. Symp. Proc. 356, Pittsburgh, PA, 1995), p. 645.Google Scholar
18Lucas, B.N. and Oliver, W.C.: Indentation power-law creep of high-purity indium. Metall. Mater. Trans. A (Phys. Metall. Mater. Sci.) 30A, 601 (1999).Google Scholar
19Sargent, P.M. and Ashby, M.F.: Indentation creep. Mater. Sci. Technol. 8, 594 (1992).Google Scholar
20Stone, D.S. and Yoder, K.B.: Division of the hardness of molybdenum into rate-dependent and rate-independent components. J. Mater. Res. 9, 2524 (1994).CrossRefGoogle Scholar
21Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
22Goldsby, D.L., Rar, A., Pharr, G.M., and Tullis, T.E.: Nanoindentation creep of quartz, with implications for rate- and state-variable friction laws relevant to earthquake mechanics. J. Mater. Res. 19, 357 (2004).Google Scholar
23Rar, A., Sohn, S., Oliver, W.C., Goldsby, D.L., Tullis, T.E., and Pharr, G.M.: On the measurement of creep by nanoindentation with continuous stiffness techniques, in Fundamentals of Nanoindentation and Nanotribology III, edited by Wahl, K.J., Huber, N., Mann, A.B., Bahr, D.F. and Cheng, Y.-T. (Mater. Res. Soc. Symp. Proc. 841, Warrendale, PA, 2005), pp. 119–124.Google Scholar
24Elmustafa, A.A. and Stone, D.S.: Nanoindentation and the indentation size effect: Kinetics of deformation and strain gradient plasticity. J. Mech. Phys. Solids 51, 357 (2003).Google Scholar
25Atkins, A.G., Silverio, A., and Tabor, D.: Indentation hardness and creep of solids. J. Inst. Met. 94(Part 11), 369 (1966).Google Scholar
26Bower, A.F., Fleck, N.A., Needleman, A., and Ogbonna, N.: Indentation of a power law creeping solid. Proc. R. Soc. London, A (Math. Phys. Sci.) 441, 97 (1993).Google Scholar
27Cheng, Y-T. and Cheng, C-M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. Rep. R44, 91 (2004).Google Scholar
28Chu, S.N.G. and Li, J.C.M.: Impression creep: A new creep test. J. Mater. Sci. 12, 2200 (1977).Google Scholar
29Chu, S.N.G. and Li, J.C.M.: Impression creep of beta-tin single crystals. Mater. Sci. Eng. 39, 1 (1979).CrossRefGoogle Scholar
30Tabor, D.: The hardness of solids. Rev. Phys. Technol. 1, 145 (1970).Google Scholar
31Hill, R.: Similarity analysis of creep indentation tests. Proc. R. Soc. London, A (Math. Phys. Sci.) 436, 617 (1992).Google Scholar
32Jang, D. and Atzmon, M.: Grain-size dependence of plastic deformation in nanocrystalline Fe. J. Appl. Phys. 93, 9282 (2003).Google Scholar
33Li, H. and Ngan, A.H.W.: Indentation size effects on the strain-rate sensitivity of nanocrystalline Ni-25at.%Al thin films. Scripta Mater. 52, 827 (2005).CrossRefGoogle Scholar
34Shou-Yi, C., Yu-Shuien, L., and Ting-Kui, C.: Nanomechanical response and creep behavior of electroless deposited copper films under nanoindentation test. Mater. Sci. Eng., A (Struct. Mater.: Prop., Microstr. and Process.) 423, 52 (2006).Google Scholar
35Wen, S.P., Zeng, F., Gao, Y., and Pan, F.: Indentation creep behavior of nano-scale Ag/Co multilayers. Scripta Mater. 55, 187 (2006).Google Scholar
36Ashby, M.F. and Verrall, R.A.: Micromechanisms of flow and fracture and their relevance to the rheology of the upper mantle. Philos. Trans. R. Soc. London A (Math Phys. Sci.) 288, 59 (1978).Google Scholar
37Brownrigg, A., Spitzig, W.A., Richmond, O., Teirlinck, D., and Embury, J.D.: Influence of hydrostatic pressure on the flow stress and ductility of a spheroidized 1045 steel. Acta Metall. 31, 1141 (1983).Google Scholar
38Dorn, J.E., Goldberg, A., and Tietz, T.E.: Effect of thermal-mechanical history on strain hardening of metals. J. Met. 1(5, Sec 3), 325 (1949).Google Scholar
39Oliver, W.C. and Pharr, G.M.: Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).Google Scholar
40Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, UK, 1985), p. 452.CrossRefGoogle Scholar
41Poisl, W.H., Oliver, W.C., and Fabes, B.D.: The relationship between indentation and uniaxial creep in amorphous selenium. J. Mater. Res. 10, 2024 (1995).CrossRefGoogle Scholar
42Mulhearn, T.O.: Deformation of metals by Vickers-type pyramidal indenters. J. Mech. Phys. Solids 7, 85 (1959).CrossRefGoogle Scholar
43Samuels, L.E. and Mulhearn, T.O.: The deformation zone associated with indentation hardness impressions. J. Mech. Phys. Solids 5, 125 (1956).CrossRefGoogle Scholar
44Liu, L.F., Dai, L.H., Bai, Y.L., Wei, B.C., and Yu, G.S.: Strain rate-dependent compressive deformation behavior of Nd-based bulk metallic glass. Intermetallics 13, 827 (2005).CrossRefGoogle Scholar
45Mukai, T., Nieh, T.G., Kawamura, Y., Inoue, A., and Higashi, K.: Effect of strain rate on compressive behavior of a Pd40Ni40P20 bulk metallic glass. Intermetallics 10, 1071 (2002).Google Scholar
46Hao, L., Subhash, G., Xin-Lin, G., Kecskes, L.J., and Dowding, R.J.: Negative strain-rate sensitivity and compositional dependence of fracture strength in Zr/Hf based bulk metallic glasses. Scripta Mater. 49, 1087 (2003).Google Scholar