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Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: Analysis for obtaining film stress from non-local curvature information

Ngo, D. and Feng, X. and Huang, Y. and Rosakis, A. J. and Brown, M. A. (2007) Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: Analysis for obtaining film stress from non-local curvature information. International Journal of Solids and Structures, 44 (6). pp. 1745-1754. ISSN 0020-7683. http://resolver.caltech.edu/CaltechAUTHORS:20100924-103650164

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Abstract

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis and co-workers [Huang, Y., Ngo, D., Rosakis, A.J., 2005. Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures. Acta Mech. Sin. 21, 362–370; Huang, Y., Rosakis A.J., 2005. Extension of Stoney’s Formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry. J. Mech. Phys. Solids 53, 2483–2500; Ngo, D., Huang, Y., Rosakis, A. J., Feng, X. 2006. Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between non-uniform film stresses and system curvatures. Thin Solid Films (in press)] established methods for film/substrate system subject to non-uniform misfit strain and temperature changes. The film stresses were found to depend non-locally on system curvatures (i.e., depend on the full-field curvatures). The existing methods, however, all assume uniform film thickness which is often violated in the thin film/substrate system. We extend these methods to arbitrarily non-uniform film thickness for the thin film/substrate system subject to non-uniform misfit strain. Remarkably the stress-curvature relation for uniform film thickness still holds if the film thickness is replaced by its local value at the point where the stress is evaluated. This result has been experimentally validated in Part II of this paper.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.ijsolstr.2006.10.016DOIArticle
http://www.sciencedirect.com/science/article/pii/S0020768306004215PublisherArticle
Additional Information:© 2007 Elsevier. Received 20 July 2006; received in revised form 10 October 2006 Available online 20 October 2006.
Group:GALCIT
Subject Keywords:Thin films; Non-uniform misfit strain; Non-uniform film thickness; Non-local stress-curvature relations; Interfacial shears
Record Number:CaltechAUTHORS:20100924-103650164
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100924-103650164
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20125
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:24 Sep 2010 19:27
Last Modified:07 Jan 2017 00:46

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