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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

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