Stresses in a multilayer thin film/substrate system subjected to nonuniform temperature

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to uniform film stress and system curvature states over the entire system of a single thin film on a substrate. By considering a circular multilayer thin film/substrate system subjected to nonuniform temperature distributions, we derive relations between the stresses in each film and temperature, and between the system curvatures and temperature. These relations featured a "local" part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a "nonlocal" part, which reflects the effect of temperature of other points on the location of scrutiny. We also derive relations between the film stresses in each film and the system curvatures, which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a "nonlocal" dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. The interfacial shear tractions between the films and between the film and substrate are proportional to the gradient of the first curvature invariant, and can also be inferred experimentally.

Original languageEnglish (US)
Pages (from-to)210221-210227
Number of pages7
JournalJournal of Applied Mechanics, Transactions ASME
Issue number2
StatePublished - Mar 2008


  • Interfacial shears
  • Multilayer thin films
  • Nonlocal stress-curvature relations
  • Nonuniform film temperatures and stresses
  • Nonuniform system curvatures

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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