Hostname: page-component-669899f699-8p65j Total loading time: 0 Render date: 2025-05-01T03:35:56.625Z Has data issue: false hasContentIssue false
  • English
  • Français

Dislocation Mechanics Simulations of the Bilinear Behavior in Micro- and Nanoindentation

Published online by Cambridge University Press:  03 March 2011

A.A. Elmustafa ,
A.A. Ananda  and
W.M. Elmahboub
A.A. Ananda
Affiliation:
NASA Langley Research Center-ConITS, Hampton, Virginia 23681-2199
W.M. Elmahboub
Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 23668
Get access

Abstract

The hardnesses of electropolished, polycrystalline α-brass, and aluminum were measured as functions of load using Vickers microindentation, and Berkovich nanoindentation. Data were compared with literature data for silver, copper, and tungsten. In all cases, the hardness was observed to increase with decreasing size. Theories in the literature based on strain gradient plasticity and the addition of statistically stored and geometrically stored dislocation densities predict that the square of the hardness should increase linearly with inverse size of the indent. Our data and the literature data agree with this prediction over a limited range of indent diameters represented by microhardness and deep nanohardness data, whereas for the shallow nanohardness data, a second linear behavior is observed. The linear behavior of the microhardness and deep nanohardness data together with the second linear behavior generated by the shallow nanohardness data constituted what we designate a bilinear behavior. An algorithm is developed to calculate the induced shear stresses in a circular Volterra dislocation loop from a line integral of the Peach–Koehler equation using dislocation mechanics and isotropic elasticity. The computed induced shear stresses when plotted versus depth of indentation produced curves that exhibited a bilinear behavior identical to the bilinear behavior resulted from experiments, and the curves collapsed to a single curve for the different materials simulated.

Keywords

Computer simulationMechanical propertiesNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 3 , March 2004 , pp. 768 - 779
Copyright
Copyright © Materials Research Society 2004

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

1Fleck, N.A. and Hutchinson, J.W., J. Mech. Phys. Solids 41, 1825 (1993).CrossRefGoogle Scholar
2Nix, W.D. and Gao, H., J. Mech. Phys. Solids 46, 411 (1998).CrossRefGoogle Scholar
3Gao, H., Huang, Y., Nix, W.D. and Hutchison, J.W., J. Mech. Phys. Solids 47, 1239 (1999).CrossRefGoogle Scholar
4Gao, H., Huang, Y. and Nix, W.D., Naturwissenschanften 86, 507 (1999).CrossRefGoogle Scholar
5Elmustafa, A.A. and Stone, D.S., Acta Mater. 50, 3641 (2002).CrossRefGoogle Scholar
6Hutchinson, J.W., Int. J. Solids Struct. 37, 225 (2000).CrossRefGoogle Scholar
7Gurtin, M.E., J. Mech. Phys. Solids 50, 5 (2002).CrossRefGoogle Scholar
8Elmustafa, A.A. and Stone, D.S. in Advanced Materials for the 21st Century, The 1999 Julia Weertman Symposium, edited by Chung, Y-W., Dunand, D.C., Liaw, P.K., and Olson, G.B. (The Mineral, Metals and Materials Society), p. 311.Google Scholar
9Elmustafa, A.A. and Stone, D.S., J. Mech. Phys. Solids 51, 357 (2003).CrossRefGoogle Scholar
10Xin, X.J., Daehn, G.S. and Wagoner, R.H., Acta Mater. 45, 1821 (1997).CrossRefGoogle Scholar
11Verecky’, S., Kratochvil, J. and Kroupa, F., Phys. Status Solidi 191, 418 (2002).3.0.CO;2-H>CrossRefGoogle Scholar
12Kassner, M.E., Pe’rez-Prado, M.-T., Vecchio, K.S. and Wall, M.A.Acta Mater. 48, 4254 (2000).CrossRefGoogle Scholar
13Tipplet, B., Bretschneider, J. and Hähner, P.Phys. Status Solidi 163, 11 (1997).3.0.CO;2-X>CrossRefGoogle Scholar
14Fisher, J.C., Hart, E.W. and Pry, R.H.Acta Metal. 1, 336 (1953).CrossRefGoogle Scholar
15Humphrey, F.J. and Hirsch, P.B., Proc. R. Soc. A318, 73 (1970).Google Scholar
16Ashby, M.F., Philos. Mag. 71, 399 (1970).CrossRefGoogle Scholar
17Brown, L.M. and Stobbs, W.M., Philos. Mag. 23, 1185 (1971).CrossRefGoogle Scholar
18Fleck, N.A. and Hutchinson, J.W., in Advances in Applied Mechanics, 33 edited by Hutchinson, J.W., and Wu, T.Y., editors (Academic Press, New York, 1997), pp. 295–361.Google Scholar
19Fleck, N.A. and Hutchinson, J.W., J. Mech. Phys. Solids 49, 2245 (2001).CrossRefGoogle Scholar
20Aifantis, E.C., Int. J. Fracture 95, 299 (1999).CrossRefGoogle Scholar
21Zbib, H. and Aifantis, E.C., Res. Mechanica 23, 261 (1989).Google Scholar
22Gryziecki, J. and Gdula, Z., J. Mater. Sci. Eng. 93, 99 (1987).CrossRefGoogle Scholar
23Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W., Acta Metall. Mater. 42, 475 (1994).CrossRefGoogle Scholar
24Poole, W.J., Ashby, M.F. and Fleck, N.A., Acta Metall. 34, 559 (1996).Google Scholar
25Ma, Q. and Clarke, D.R., J. Mater. Res. 10, 853 (1995).CrossRefGoogle Scholar
26Stone, D.S. and Yoder, K.B., J. Mater. Res. 9, 2524 (1994).CrossRefGoogle Scholar
27Elmustafa, A.A. Ph.D. Thesis, University of Wisconsin-Madison (1999).Google Scholar
28Qiu, X., Huang, Y., Nix, W.D., Hwang, K.C. and Gao, H., Acta Mater. 49, 3949 (2001).CrossRefGoogle Scholar
29Boyer, H.E. and Gall, T.L.Metals Handbook, Desk Edition (American Society for Metals, Metals Park, OH, 1985).Google Scholar
30Brammar, I.S. and Dewey, M.A.P., Specimen Preparation for Electron Metallography (Blackwell Scientific Publications, Oxford, U.K. 1966).Google Scholar
31Stone, D.S. and Yoder, K.B. in Thin Films: Stresses and Mechanical Properties IV, edited by Townsend, P.H., Weihs, T.P., Sanchez, J.E. Jr., and Børgensen, P. (Mater. Res. Soc. Symp. Proc. 308, Pittsburgh, PA, 1993), p. 121.Google Scholar
32Joslin, D.L. and Oliver, W.C., J. Mater. Res. 5, 123 (1990).CrossRefGoogle Scholar
33Stone, D.S., Yoder, K.B. and Sproul, W.D., J. Vac. Sci. Technol. A 9, 2543 (1991).CrossRefGoogle Scholar
34Huang, Y., Gao, H., Nix, W.D. and Hutchison, J.W., J. Mech. Phys. Solids 48, 99 (2000).CrossRefGoogle Scholar
35Lim, Y.Y. and Chaudhri, M.M., Philos. Mag. A. 79, 2979 (1999).CrossRefGoogle Scholar
36Acharya, A. and Bassani, J.L., J. Mech. Phys. Solids 48, 1565 (2000).CrossRefGoogle Scholar
37Sun, Y.Q., Hazzledine, P.M. and Hirsch, P.B., Phys. Rev. Lett. 88, 065503 (2002).CrossRefGoogle Scholar
38Khantha, M., Pope, D.P. and Vitek, V., Phys. Rev. Lett. 73, 684 (1994).CrossRefGoogle Scholar
39Khantha, M. and Vitek, V., Acta Mater. 45, 4675 (1997).CrossRefGoogle Scholar
40Khantha, M., Pope, D.P. and Vitek, V., Acta Mater. 45, 4687 (1997).CrossRefGoogle Scholar
41Goulddstone, A., Koh, H-J., Zeng, K-Y., Giannakopoulos, A.E. and Suresh, S., Acta Mater. 48, 2277 (2000).CrossRefGoogle Scholar
42Goulddstone, A., Krystyn, J., Van Vliet, J. and Suresh, S., Nature 411, 656 (2001).CrossRefGoogle Scholar
43Hirth, J.P. and Lothe, J.Theory of Dislocations, 2nd ed. (Krieger Publishing Company, Malabar, FL, 1992).Google Scholar
44Khraishi, T.A., Zbib, H.M., Hirth, J.P. and de La Rubia, T.D., Philos. Mag. A. 80, 95 (2000).Google Scholar