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Geometrical Contribution to Yield Strength in Small Volumes

Published online by Cambridge University Press:  10 February 2011

D.J. Dunstan  and
A.J. Bushby
D.J. Dunstan
Affiliation:
Physics Department, Centre for Materials Research, Queen Mary, University of London, London, E1 4NS, England.
A.J. Bushby
Affiliation:
Materials Department
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Abstract

Critical thickness theory was developed to account for the ability of thin epitaxial metal and semiconductor layers to support high misfit or coherency strain. The thermodynamic equilibrium theory is correct, and is well approximated by a theory based on geometrical arguments. The latter theory is readily extended to arbitrary misfit strain profiles including linearly graded layers, for which a surface layer free of misfit dislocations. This result applies as well to linear strain gradients introduced by deformation, in which case the misfit dislocations are known as geometrically necessary dislocations. We show that a consequence of this surface layer is that the apparent yield strength of the material increases in small structures such as thin wires in torsion. Under large plastic deformation, even if the material is perfectly plastic, critical thickness theory also predicts an apparent work-hardening. The predictions of critical thickness theory are in excellent agreement with experimental data in the literature.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 778: Symposium U – Mechanical Properties Derived from Nanostructuring Materials , 2003 , U9.10
Copyright
Copyright © Materials Research Society 2002

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References

1. O'Reilly, E.P. and Adams, A.R., IEEE J. Quantum Electron. 30, 336 (1994).Google Scholar
2. Fitzgerald, E.A., Mat. Sci. Rep. 7, 87 (1991).Google Scholar
3. Frank, F.C. and Merwe, J.H. van der, Proc Roy. Soc. A198, 216 (1949).Google Scholar
4. Dunstan, D.J., J. Mat. Sci.: Mat Electron. 8, 337 (1997).Google Scholar
5. Willis, J.R., Jain, S.C. and Bullough, R., Phil. Mag. A62, 115 (1990).Google Scholar
6. Dunstan, D.J., Young, S. and Dixon, R.H., J. Appl. Phys. 70, 3038 (1991).Google Scholar
7. Downes, J.R., Dunstan, D.J. and Faux, D.A., Semicon. Sci. Tech. 9, 1265 (1994).Google Scholar
8. Beanland, R., J. Appl. Phys. 72, 4031 (1992).Google Scholar
9. Dixon, R.H. and Goodhew, P.J., J. Appl. Phys. 68, 3163 (1990).Google Scholar
10. Whitehouse, C.R., Barnett, S.J., Usher, B.E., Cullis, A.G., Keir, A.M., Johnson, A.D., Clark, G.F., Tanner, B.K., Spirkl, W., Lunn, B., Hagston, W.E. and Hogg, C., Inst. Phys. Conf. Ser. 134, 563 (1993).Google Scholar
11. Dunstan, D.J., Kidd, P., Beanland, R., Sacedón, A., Calleja, E., González, L., González, Y., and Pacheco, F.J., Mater. Sci. Tech. 12, 181 (1996).Google Scholar
12. Tersoff, J., Appl. Phys. Lett. 62, 693 (1993).Google Scholar
13. Dunstan, D.J., Phil. Mag. A73, 1323 (1996).Google Scholar
14. Fleck, N.A., Muller, G.M., Ashby, M.F., and Hutchinson, J.W., Acta Metall. Mater. 42, 475 (1994).Google Scholar
15. Stölken, J.S. and Evans, A.G., Acta Mater. 46, 5109 (1998).Google Scholar
16. Dunstan, D.J., Spary, I.J. and Bushby, A.J., Proc. Roy. Soc. A (2003) (submitted).Google Scholar
17. Spary, I.J., Bushby, A.J., Jennett, N.M. and Pharr, G.M., this volume.Google Scholar