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Research Papers

Stresses in a Multilayer Thin Film/Substrate System Subjected to Nonuniform Temperature

[+] Author and Article Information
X. Feng

Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, P.R. China

Y. Huang1

Department of Civil/Environmental Engineering and Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208y-huang@northwestern.edu

A. J. Rosakis

Graduate Aeronautical Laboratory, California Institute of Technology, Pasadena, CA 91125

1

Corresponding author.

J. Appl. Mech 75(2), 021022 (Feb 27, 2008) (7 pages) doi:10.1115/1.2755178 History: Received April 27, 2007; Revised June 06, 2007; Published February 27, 2008

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.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

A schematic diagram of a multilayer thin film/substrate system, showing the cylindrical coordinates (r,θ,z)

Grahic Jump Location
Figure 2

A schematic diagram of the nonuniform shear traction distribution at the film/film and film/substrate interfaces

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