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Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations

Published online by Cambridge University Press:  31 January 2011

W. W. Gerberich ,
W. Yu ,
D. Kramer ,
A. Strojny ,
D. Bahr ,
E. Lilleodden  and
J. Nelson
W. W. Gerberich
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
W. Yu
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
D. Kramer
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
A. Strojny
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
D. Bahr
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
E. Lilleodden
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
J. Nelson
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
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A new method for evaluating modulus and hardness from nanoindentation load/ displacement curves is presented. As a spherical indenter penetrates an elastoplastic half-space, the elastic displacement above the contact line is presumed to diminish in proportion to the total elastic displacement under the indenter. Applying boundary conditions on the elastic and plastic displacements for elastic and rigid plastic contacts leads to an expression that can be best fit to the entire unloading curve to determine E*, the reduced modulus. Justification of the formulation is presented, followed by the results of a preliminary survey conducted on three predominantly isotropic materials: fused quartz, polycrystalline Al, and single crystal W. Diamond tips with radii ranging from 130 nm to 5 μm were used in combination with three different nanoindentation devices. Results indicate that the method gives property values consistent with accepted values for modulus and hardness. The importance of surface roughness and indentation depth are also considered.

Type
Articles
Information
Journal of Materials Research , Volume 13 , Issue 2 , February 1998 , pp. 421 - 439
Copyright
Copyright © Materials Research Society 1998

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References

REFERENCES

1.Hainsworth, S.V., Chandler, H.W., and Page, T. F., J. Mater. Res. 11, 1987 (1996).CrossRefGoogle Scholar
2.Loubet, J. L., Georges, J.M., and Meille, J., in Nanoindentation Techniques in Materials Science and Engineering, edited by Blau, P. T. and Lawn, B. R. (ASTM, Philadelphia, PA, 1986), pp. 7–89.Google Scholar
3.Hertz, H., J. Mathematik 92, 156 (1882).Google Scholar
4.Doerner, M. F. and Nix, W.D., J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
5.Oliver, W. C. and Pharr, G.M., J. Mater. Res. 7, 1580 (1992).CrossRefGoogle Scholar
6.Field, J. S. and Swain, M.V., J. Mater. Res. 8, 297 (1993).CrossRefGoogle Scholar
7.King, R.B., Int. J. Solids Structures 23, 1657 (1987).CrossRefGoogle Scholar
8.Gao, H., Chin, C-H., and Lee, J., Int. J. Solids Structures 29, 2471 (1992).Google Scholar
9.Stelmashenko, N.A., Walls, M.G., Brown, L.M., and Mil-man, Yu.V., Acta Metall. Mater. 41 (10), 2855 (1993).CrossRefGoogle Scholar
10.Wu, T.W., J. Mater. Res. 6, 407 (1991).CrossRefGoogle Scholar
11.Lilleodden, E. T., Bonin, W., Nelson, J., Wyrobek, J. T., and Gerberich, W.W., J. Mater. Res. 10, 2162 (1995).CrossRefGoogle Scholar
12.Sneddon, N. I., Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
13.Gerberich, W.W., Nelson, J. C., Lilleodden, E. T., Anderson, P., and Wyrobek, J. T., Acta Mater. 44 (9), 3585 (1996).CrossRefGoogle Scholar
14.Chou, T.C., Nieh, T.G., McAdams, S.D., and Pharr, G.M., Scripta Metall. et Mater. 25, 2203 (1991).CrossRefGoogle Scholar
15.Moody, N.R., Sandia Livermore National Laboratories, private communication.Google Scholar
16.Oliver, W. C. and McHargue, C. J., Thin Solid Films 161, 117 (1988).CrossRefGoogle Scholar
17.Greenwood, J.A. and Tripp, J.H., Trans. ASME, E., J. Appl. Mech. 34, 153 (1967).CrossRefGoogle Scholar
18.Johnson, K. L., Contact Mechanics (Cambridge University Press, Cambridge, 1985), pp. 405–421.CrossRefGoogle Scholar