Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: The relation between non-uniform film stresses and system curvatures

D. Ngo, Y. Huang*, A. J. Rosakis, X. Feng

*Corresponding author for this work

Research output: Contribution to journalArticle

15 Scopus citations

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 arbitrarily non-uniform misfit strain distributions, we derive 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 derive relations between 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 non-uniformities. These relations also feature a "non-local" dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. Finally, it is shown that the interfacial shear tractions between the film and the substrate are related to the gradients of the first curvature invariant and can also be inferred experimentally.

Original languageEnglish (US)
Pages (from-to)2220-2229
Number of pages10
JournalThin Solid Films
Volume515
Issue number4
DOIs
StatePublished - Dec 5 2006

Keywords

  • Interfacial shears
  • Non-local stress-curvature relations
  • Non-uniform misfit strain
  • Thin films

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Surfaces and Interfaces
  • Surfaces, Coatings and Films
  • Metals and Alloys
  • Materials Chemistry

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