GEOMETRICALLY NONLINEAR STRESS DEFLECTION RELATIONS FOR THIN-FILM SUBSTRATE SYSTEMS WITH A FINITE-ELEMENT COMPARISON

Citation
Cb. Masters et Nj. Salamon, GEOMETRICALLY NONLINEAR STRESS DEFLECTION RELATIONS FOR THIN-FILM SUBSTRATE SYSTEMS WITH A FINITE-ELEMENT COMPARISON, Journal of applied mechanics, 61(4), 1994, pp. 872-878
Citations number
22
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanics
Journal title
ISSN journal
0021-8936
Volume
61
Issue
4
Year of publication
1994
Pages
872 - 878
Database
ISI
SICI code
0021-8936(1994)61:4<872:GNSDRF>2.0.ZU;2-I
Abstract
A new higher order geometrically nonlinear relation is developed to re late the deflection of a thin film/substrate system to the intrinsic f ilm 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 secon d-order polynomial and midplane normal strains by sixth-order polynomi als. Several plate deflection configurations arise in an isotropic sys tem: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increas es, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress a pproaches infinity, the ellipsoidal configurations develop into cylind rical plate curvatures about either one of the two axes. Curvatures pr edicted by this new relation are significantly more accurate than prev ious theories when compared to curvatures calculated from three-dimens ional nonlinear finite element deflection results. Furthermore, the fi nite element results display significant transverse stresses in a smal l boundary region near the free edge.