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Geometrical Critical Thickness Theory for the Size Effect at the Initiation of Plasticity

Published online by Cambridge University Press:  31 January 2011

Ting Zhu ,
Bruno Ehrler ,
Andy Bushby  and
Dave Dunstan
Ting Zhu
Affiliation:
t.zhu@qmul.ac.uk, Queen Mary University of London, Physics, London, United Kingdom
Bruno Ehrler
Affiliation:
bruno.ehrler@gmx.de, Queen Mary University of London, Physics, London, United Kingdom
Andy Bushby
Affiliation:
a.j.bushby@qmul.ac.uk, Queen Mary University of London, Materials, London, United Kingdom
Dave Dunstan
Affiliation:
d.j.dunstan@qmul.ac.uk, Queen Mary University of London, Physics, London, United Kingdom
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Abstract

Recently, size effects in the initiation of plasticity have been clearly observed and reported in different geometries; e.g., bending (Ehrler et al. Phil. Mag. 2008), twisting (Ehrler et al., MRS, Spring Meeting 2009) and indentation (Zhu et al. J. Mech. Phys. Sol. 56, 1170, 2008). Strain gradient plasticity theory is the principal approach for explaining size effects during plastic deformation in these geometries. However, it fails to account for any size effect at the initial yield. Geometrical critical thickness theory was proposed to explain the yield size effect in bending and torsion (Dunstan and Bushby, Proc. Roy. Soc. A460, 2781, 2004). The theory shows that the initial yield strength is scaled with the inverse square root of the characteristic length scale without requiring any free fitting parameters. Here, we extend the theory to describe the yield size effect in indentation. The theory agrees fairly well with experimental observations in micro-torsion (Ehrler et al., MRS, Spring Meeting 2009) and nanoindentation (Zhu et al., J. Mech. Phys. Solid, 2008).

Keywords

stress/strain relationshipdislocationsnano-indentation
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1185: Symposium II – Probing Mechanics at Nanoscale Dimensions , 2009 , 1185-II05-02
Copyright
Copyright © Materials Research Society 2009

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References

1. Zhu, T.T., Bushby, A.J. and Dunstan, D.J., Mater. Tech. 23 (4), 193 (2008).10.1179/175355508X376843Google Scholar
2. Hall, E.O., Proc. Phys. Soc. Lond. B, 64 (9), 747 (1951)10.1088/0370-1301/64/9/303Google Scholar
3. Lloyd, D. J., International Materials Reviews 39 (1), 1 (1994)10.1179/imr.1994.39.1.1Google Scholar
4. Greer, J.R., Oliver, W.C. and Nix, W.D., Acta Mater 53, 1821 (2005)10.1016/j.actamat.2004.12.031Google Scholar
5. Brenner, S.S., Science, 128, 568 (1956)Google Scholar
6. Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W., Acta Met. 42(2), 475 (1994)10.1016/0956-7151(94)90502-9Google Scholar
7. Ehrler, B. et al., Phys. Rev. Letter. submitted (2009)Google Scholar
8. Stölken, J. S., and Evans, A. G., Acta Metallurgica 46(14), 5109 (1998)Google Scholar
9. Ehrler, B., Bossis, R., Joly, S., P’ng, K., Bushby, A. and Dunstan, D., Phys. Rev. Letter., submitted.Google Scholar
10. Ma, Q. and Clark, D.R., J. Mater. Res. 10, 853 (1995)10.1557/JMR.1995.0853Google Scholar
11. Swadener, J.G., George, E.P., and Pharr, G.M., J. Mech. Phys. Solids 50, 681 (2002)10.1016/S0022-5096(01)00103-XGoogle Scholar
12. Zhu, T.T., Bushby, A.J. and Dunstan, D.J., J. Mech. Phys. Solids 56, 1170 (2008)10.1016/j.jmps.2007.10.003Google Scholar
13. Ashby, M.F., Phil. Mag. 21(170), 399 (1970)10.1080/14786437008238426Google Scholar
14. Huang, Y., Qu, S., Hwang, K.C., Li, M., and Gao, H., Int. J. Plasticity 20(4), 753 (2004)10.1016/j.ijplas.2003.08.002Google Scholar
15. Conrad, H., Feuerstein, S. and Rice, L., Mater. Sci. Eng. 2, 157 (1967)10.1016/0025-5416(67)90032-8Google Scholar
16. Bushby, A.J., Zhu, T.T. and Dunstan, D.J., J. Mater. Res., 24, 966 (2009)10.1557/jmr.2009.0104Google Scholar
17. Zhu, T.T., Bushby, A.J. and Dunstan, D.J., J. Mech. Phys. Solids., submittedGoogle Scholar
18. Frank, F.C. and Merwe, J. H.ven der, Proc Roy Soc (London): A198, 216 (1949)Google Scholar
19. Matthews, J. W., Philos. Mag., 1966, 13, 1207 (1974)Google Scholar
20. Dunstan, D.J., Young, S. and Dixon, R.H., J.Appl.Phys., 70, 3038 (1991)10.1063/1.349335Google Scholar
21. Dunstan, D.J.: Journal of Materials Science: Materials in Electronics, 8, 337 (1997)Google Scholar
22. Dunstan, D.J., and Bushby, A.J., J. Proc. R. Soc. Lond. A, 460, 2781, (2004).10.1098/rspa.2004.1306Google Scholar
23. Thompson, A. W., Acta Met., 23, 1337 (1973)10.1016/0001-6160(75)90142-XGoogle Scholar
24. Hill, R., The mathematical theory of plasticity, Oxford at the Clarendon Press., (1950).Google Scholar
25. Tabor, D.: The Hardness of Metals. Clarendon Press, Oxford, (1951)Google Scholar