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Practical Application of a Geometrically Nonlinear Stress-Curvature Relation

Published online by Cambridge University Press:  22 February 2011

Christine B. Masters  and
N. J. Salamon
Christine B. Masters
Affiliation:
The Pennsylvania State University, Department of Engineering Science and Mechanics, University Park, PA 16802
N. J. Salamon
Affiliation:
The Pennsylvania State University, Department of Engineering Science and Mechanics, University Park, PA 16802
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Abstract

A recently developed geometrically nonlinear stress-curvature relation based on a minimization of the total strain energy, which predicts a bifurcation in shape as the magnitude of intrinsic film stress increases, is discussed in this paper. It is compared with the linear theories of Stoney and Brenner & Senderoff for a thin molybdenum film on silicon substrates with various thicknesses. Although the ratio of film to substrate elastic modulus is only 2, Stoney's equation generates significant error for this film/substrate system and the Brenner & Senderoff relation should be used for calculating initial film stress when plate deflections are small. When deflections exceed approximately half the substrate thickness the Brenner & Senderoff equation produces over 10% error and consequently, the nonlinear stress-deflection relation should be used to relate plate curvatures to initial film stress.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 239: Symposium D – Thin Films: Stresses and Mechanical Properties III , 1991 , 293
Copyright
Copyright © Materials Research Society 1992

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References

REFERENCES

[1] Hoffman, R.W., Surface and Interface Analysis 3 (1), 62–67 (1981).Google Scholar
[2] D'Heurle, R.M. and Harper, J.M.E., Thin Solid Films, 81–92 (1989).CrossRefGoogle Scholar
[3] Stoney, G.G., Proc. Roy. Soc. [A] 82, London, pp 172–175 (1909).Google Scholar
[4] Brenner, A. and Senderoff, S., National Bureau of Standards No. RP1954 42, February, 105–123 (1949).Google Scholar
[5] Morton, V.M., Corrosion Science 9, 261–270 (1969).Google Scholar
[6] Masters, C.B., Salamon, N.J., and Fahnline, D.E. in Thin Films: Stresses and Mechanical Properties II (Mater. Res. Soc. Proc. 188, Pittsburgh, PA, 1990) pp. 21–27.Google Scholar
[7] Harper, B.D. and Wu, C.P., Int. J. Solids Structures 26 (5/6), 511–525 (1990).Google Scholar
[8] Fahnline, D.E., Masters, C.B., and Salamon, N.J., J. Vacuum Science and Technology A9, 2483–2487 (1991).Google Scholar
[9] Ugural, A.C., Stresses in Plates and Shells, McGraw-Hill Book Company, New York, NY (1981).Google Scholar
[10] Glang, R., Holmwood, R.A., and Rosenfeld, R.L., The Review of Scientific Instruments 36 (1), 7–10 (1965).Google Scholar