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Length-scale-based hardening model for ultra-small volumes

Published online by Cambridge University Press:  01 October 2004

J.M. Jungk ,
W.M. Mook ,
M.J. Cordill ,
M.D. Chambers ,
W.W. Gerberich ,
D.F. Bahr ,
N.R. Moody  and
J.W. Hoehn
J.M. Jungk*
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
W.M. Mook
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
M.J. Cordill
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
M.D. Chambers
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
W.W. Gerberich
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
D.F. Bahr
Affiliation:
Department of Mechanical and Materials Engineering, Washington State University, Pullman, Washington 99164
N.R. Moody
Affiliation:
Microsystems and Materials Mechanics, Sandia National Laboratories, Livermore, California, 94550
J.W. Hoehn
Affiliation:
Seagate Technology LLC, Minneapolis, Minnesota 55435
*
a) Address all correspondence to this author. e-mail: [email protected]
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Abstract

Understanding the hardening response of small volumes is necessary to completely explain the mechanical properties of thin films and nanostructures. This experimental study deals with the deformation and hardening response in gold and copper films ranging in thickness from 10 to 400 nm and silicon nanoparticles with particle diameters less than 100 nm. For very thin films of both gold and copper, it was found that hardness initially decreases from about 2.5 to 1.5 GPa with increasing penetration depth. Thereafter, an increase occurs with depths beyond about 5–10% of the film thickness. It is proposed that the observed minima are produced by two competing mechanisms. It is shown that for relatively deep penetrations, a dislocation back stress argument reasonably explains the material hardening behavior unrelated to any substrate composite effect. Then, for shallow contacts, a volume-to-surface length scale argument relating to an indentation size effect is hypothesized. A simple model based on the superposition of these two mechanisms provides a reasonable fit to the experimental nanoindentation data.

Keywords

Thin filmHardness
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 10 , October 2004 , pp. 2812 - 2821
Copyright
Copyright © Materials Research Society 2004

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References

REFERENCES

1Jacobs, H.O., Campbell, S.A. and Steward, M.G.: Approaching nanoxerography: The use of electrostatic forces to position nanoparticles with 100 nm scale resolution. Adv. Mater. 14, 1553 (2002).3.0.CO;2-9>CrossRefGoogle Scholar
2Jonsson, B. and Hogmark, S.: Hardness measurements of thin films. Thin Solid Films 114, 257 (1984).CrossRefGoogle Scholar
3Bhattacharya, A.K. and Nix, W.D.: Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates. Int. J. Solids Struct. 24, 1287 (1988).CrossRefGoogle Scholar
4Fabes, B.D. and Oliver, W.C.: Mechanical-properties of coatings and interfaces, in Thin Films: Stresses and Mechanical Properties II, edited by Doerner, M.F., Oliver, W.C., Pharr, G.M., and Brotzen, F.R. (Mater. Res. Soc. Symp. Proc. 188 Pittsburgh, PA, 1990) p. 127Google Scholar
5Gerberich, W.W., Tymiak, N.J., Grunlan, J.C., Horstemeyer, M.F. and Baskes, M.T.: Interpretations of indentation size effects. J. Appl. Mech. 69, 433 (2002).CrossRefGoogle Scholar
6Gerberich, W.W., Mook, W.M., Perrey, C.R., Carter, C.B., Baskes, M.T., Mukherjee, R., Godwani, A., Heberlein, J., McMurry, P.H. and Girshick, S.L.: Superhard silicon nanospheres. J. Mech. Phys. Solids 51, 979 (2003).CrossRefGoogle Scholar
7Gerberich, W.W., Mook, W.M., Cordill, M.J., Carter, C.B., Perrey, C.R., Heberlein, J.V., and Girshick, S.L.: Reverse plasticity in single crystal silicon nanospheres. Int. J. Plast. (2004, in press).Google Scholar
8Eshelby, J.D., Frank, F.C. and Nabarro, F.R.N.: The equilibrium of linear arrays of dislocations. Philos. Mag . 42, 351 (1951).CrossRefGoogle Scholar
9Zhang, T.Y. and Xu, W.H.: Surface effects on nanoindentation. J. Mater. Res. 17, 1715 (2002).CrossRefGoogle Scholar
10Gerberich, W.W., Jungk, J.M., Li, M., Volinsky, A.A., Hoehn, J.W. and Yoder, K.: Length scales for the fracture of nanostructures. Int. J. Fracture 119/120, 387 (2003).CrossRefGoogle Scholar
11Jungk, J.M., Cordill, M.J., Hoehn, J.W. and Gerberich, W.W.: Fracture and plasticity in tantalum thin films. Int. J. Fracture (in preparation).Google Scholar
12Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411 (1998).CrossRefGoogle Scholar
13Elmustafa, A.A., Ananda, A.A. and Elmahboub, W.M.: Dislocation mechanics simulations of the bilinear behavior in micro- and nanoindentation. J. Mater. Res. 19, 768 (2004).CrossRefGoogle Scholar
14Hirth, J.P. and Loethe, J.: Theory of Dislocations, 2nd ed. (J. Wiley and Sons, New York, 1982).Google Scholar
15Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
16Gerberich, W.W., Nelson, J.C., Lilleodden, E.T., Anderson, P. and Wyrobek, J.T.: Indentation induced dislocation nucleation: The initial yield point. Acta Mater . 44, 3585 (1996).CrossRefGoogle Scholar
17Kramer, D., Huang, H., Kriese, M., Robach, J., Nelson, J., Wright, A., Bahr, D. and Gerberich, W.W.: Yield strength predictions from the plastic zone around nanocontacts. Acta Mater. 47, 333 (1999).CrossRefGoogle Scholar
18Wei, Y. and Hutchinson, J.W.: Nonlinear delamination mechanics for thin films. J. Mech. Phys. Solids 45, 1137 (1997).CrossRefGoogle Scholar
19Volinsky, A.A., Moody, N.R. and Gerberich, W.W.: Interfacial toughness measurements for thin films on substrates. Acta Mater. 50, 441 (2002).CrossRefGoogle Scholar
20Volinsky, A.A., Vella, J.Adhihetty, I.S.Sarihan, V., Mercado, L.Young, B.H. and Gerberich, W.W.: Microstructure and mechanical properties of electroplated Cu thin films in Fundamentals of Nanoindentation and Nanotribology II, edited by Baker, S.P., Cook, R.F., Corcoran, S.G., and Moody, N.R.(Mater. Res. Soc. Symp. Proc. 649 Warrendale, PA, 2001) p. Q5.3.1.Google Scholar
21Tabor, D.: Hardness of Metals (Oxford University Press, Oxford, U.K., 1951) p. 67–76.Google Scholar