Geometrically nonlinear stress-deflection relations for thin film/substrate systems with a finite element comparison

Christine Masters, N. J. Salamon

Research output: Contribution to conferencePaper

1 Citation (Scopus)

Abstract

A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film/substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixth-order polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.

Original languageEnglish (US)
Pages1-7
Number of pages7
StatePublished - Dec 1 1994
EventProceedings of the 1994 International Mechanical Engineering Congress & Exhibition, of the Winter Annual Meeting - Chicago, IL, USA
Duration: Nov 6 1994Nov 11 1994

Other

OtherProceedings of the 1994 International Mechanical Engineering Congress & Exhibition, of the Winter Annual Meeting
CityChicago, IL, USA
Period11/6/9411/11/94

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Thin films
Substrates
Polynomials

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

Masters, C., & Salamon, N. J. (1994). Geometrically nonlinear stress-deflection relations for thin film/substrate systems with a finite element comparison. 1-7. Paper presented at Proceedings of the 1994 International Mechanical Engineering Congress & Exhibition, of the Winter Annual Meeting, Chicago, IL, USA, .
Masters, Christine ; Salamon, N. J. / Geometrically nonlinear stress-deflection relations for thin film/substrate systems with a finite element comparison. Paper presented at Proceedings of the 1994 International Mechanical Engineering Congress & Exhibition, of the Winter Annual Meeting, Chicago, IL, USA, .7 p.
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abstract = "A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film/substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixth-order polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.",
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Masters, C & Salamon, NJ 1994, 'Geometrically nonlinear stress-deflection relations for thin film/substrate systems with a finite element comparison' Paper presented at Proceedings of the 1994 International Mechanical Engineering Congress & Exhibition, of the Winter Annual Meeting, Chicago, IL, USA, 11/6/94 - 11/11/94, pp. 1-7.

Geometrically nonlinear stress-deflection relations for thin film/substrate systems with a finite element comparison. / Masters, Christine; Salamon, N. J.

1994. 1-7 Paper presented at Proceedings of the 1994 International Mechanical Engineering Congress & Exhibition, of the Winter Annual Meeting, Chicago, IL, USA, .

Research output: Contribution to conferencePaper

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N2 - A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film/substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixth-order polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.

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Masters C, Salamon NJ. Geometrically nonlinear stress-deflection relations for thin film/substrate systems with a finite element comparison. 1994. Paper presented at Proceedings of the 1994 International Mechanical Engineering Congress & Exhibition, of the Winter Annual Meeting, Chicago, IL, USA, .