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Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures

Huang, Yonggang and Ngo, D. and 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 Mechanica Sinica, 21 (4). pp. 362-370. ISSN 0567-7718. http://resolver.caltech.edu/CaltechAUTHORS:20170408-142840770

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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. By considering a circular thin film/substrate system subject to non-uniform, but axisymmetric misfit strain distributions in the thin film, we derived relations between the film stresses and the misfit strain, and between the plate system’s curvatures and the misfit strain. These relations feature a "local" part which involves a direct dependence of the stress or curvature components on the misfit strain at the same point, and a "non-local" part which reflects the effect of misfit strain of other points on the location of scrutiny. Most notably, we also derived relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary radial non-uniformities. These relations also feature a "non-local" dependence on curvatures making a full-field measurement a necessity. Finally, it is shown that the interfacial shear tractions between the film and the substrate are proportional to the radial gradients of the first curvature invariant and can also be inferred experimentally.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s10409-005-0051-9DOIArticle
https://link.springer.com/article/10.1007%2Fs10409-005-0051-9PublisherArticle
http://rdcu.be/rwAnPublisherFree ReadCube access
Additional Information:© Springer-Verlag 2005. Received: 12 May 2005 / Accepted: 16 May 2005 / Revised: 17 May 2005 / Published online: 13 August 2005
Group:GALCIT
Subject Keywords:Non-uniform misfit strain · Non-uniform wafer curvatures · Stress-curvature relations · Non-local effects · Interfacial shears
Record Number:CaltechAUTHORS:20170408-142840770
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170408-142840770
Official Citation:Huang, Y., Ngo, D. & Rosakis, A. ACTA MECH SINICA (2005) 21: 362. doi:10.1007/s10409-005-0051-9
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75951
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:21 Apr 2017 20:50
Last Modified:21 Apr 2017 20:50

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