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The Mechanics of a Free-Standing Strained Film / Compliant Substrate System

Published online by Cambridge University Press:  15 February 2011

L. B. Freund
L. B. Freund*
Affiliation:
Division of Engineering, Brown University, Providence, RI 02912
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Abstract

The deformation of film/substrate systems due to a through-the-thickness distribution of mismatch strain is discussed for cases when the layers are thin, compliant and freestanding. The connection between substrate curvature and mismatch strain is reviewed within the framework of small strains and small deflections. These results are applied to determine the second-order correction to the Stoney formula and to note the connection between mismatch strain distribution and curvature history. Then, for small strains but large deflections, it is observed that a symmetric system with equi-biaxial mismatch strain can undergo a bifurcation in deformation mode. It is also shown that the bifurcation response is sensitive to system imperfections. Finally, the critical condition for introduction of an interface misfit dislocation in an epitaxial system is established, thereby extending the Matthews-Blakeslee criterion to the case of free-standing compliant systems.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 436: Symposium CC – Thin Films Stresses and Mechanical Properties VI , 1996 , 393
Copyright
Copyright © Materials Research Society 1997

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References

1. Freund, L. B., J. Crystal Growth 132, 341 (1993).Google Scholar
2. Kroupa, F., Knesl, Z. and Valach, J., Acta Tech. CSAV 38, 29 (1993).Google Scholar
3. Wittrick, W. H., Quart. J. Mech. Appl. Math. 6, 15 (1953).Google Scholar
4. Masters, C. B. and Salamon, N. J., Int. J. Engrg. Sci. 31,915 (1993).Google Scholar
5. Hyer, M. W., J. Compos. Mater. 16, 318 (1982).Google Scholar
6. Finot, M. and Suresh, S., J. Mech. Phys. Solids 44, 683 (1996).Google Scholar
7. Matthews, J. W. and Blakeslee, A. E., J. Cryst. Growth 27, 118 (1974).Google Scholar
8. Flinn, P. A., in Thin Films: Stresses and Mechanical Properties, edited by Bravman, J. C., Nix, W. D., Barnett, D. M. and Smith, D. A. (Mater. Res. Soc. Proc. 130, Pittsburgh, PA, 1989), pp. 041–51.Google Scholar
9. Stoney, G. G., Proc. Roy. Soc. (London) A82, 172 (1909).Google Scholar
10. Spaepen, F., J. Mech. Phys. Solids 44, 675 (1996).Google Scholar
11. Freund, L. B., J. Mech. Phys. Solids 44, 723 (1996).Google Scholar
12. Freund, L. B. and Nix, W. D., submitted for publication, (1996).Google Scholar
13. Nix, W. D., Metall. Trans. 20A, 2217 (1989).Google Scholar
14. Freund, L. B., J. Appl. Mech. 54, 553 (1987).Google Scholar