The Effects of In-Plane Stress on Waves in Thin Films

  • George C. Johnson
  • Shih-Emn Chen

Abstract

The application of acoustoelasticity for the nondestructive evaluation of residual stress has, for the most part, been limited to waves which may be classified as being of short wavelength. For many thin films, whose thicknesses may be on the order of 1 μm or less, the frequency required to obtain a “short wavelength” is well into the gigahertz regime. Thus, for acoustoelasticity to be applicable to such thin films, an improved understanding of the effect of stress on the wave response in the intermediate to long wavelength regimes must be available. This paper considers the effect of stress on the response of waves propagating in plate-like structures. The frequency equation is derived in the context of three-dimensional elastodynamics in which a small disturbance is superposed on a finite deformation of the nonlinearly elastic plate. Particular attention is directed toward the lowest order antisymmetric (flexural) mode which exhibits membrane response in the long wavelength limit. Results showing the details of the transition from the long wavelength limit to the short wavelength limit (bulk wave response) are presented for this mode.

Keywords

Residual Stress Wave Speed Rayleigh Wave Velocity Change Biaxial Tension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nix, W. D., Met. Trans., 20A, 2217–2245 (1989).Google Scholar
  2. 2.
    Segmueller, A. and M. Murakami, “X-ray Diffraction Analysis of Strains and Stresses in Thin Films,” in Treatise in Materials Science and Technology, 19A, ed. by H. Herman (Academic Press, New York, 1988) pp. 143–200.Google Scholar
  3. 3.
    Rickerby, D. S, B. A. Bellamy, and A. M. Jones, Surface Engineering, 3, 138–146 (1987).Google Scholar
  4. 4.
    Flinn, P. A., Mat. Res. Soc. Symp., Proc. Vol. 130, 41–51 (1989).CrossRefGoogle Scholar
  5. 5.
    Mehregany, M., R. T. Howe, and S. D. Senturia, J. Appl. Phys., 62, 3579–3584 (1987).CrossRefGoogle Scholar
  6. 6.
    Guckel, H., T. Randazzo, and D. W. Burns, J. Appl. Phys., 57, 1671–1675 (1985).CrossRefGoogle Scholar
  7. 7.
    Howe, R. T., Thin Solid Films, 181, 235–243 (1989).CrossRefGoogle Scholar
  8. 8.
    Meeks, S. W., D. Peter, D. Home, K. Young and V. Novotny, Appl. Phys. Lett., 55, 1835–1837 (1989).CrossRefGoogle Scholar
  9. 9.
    Pao, Y. H., W. Sachse and H. Fukuoka, in Physical Acoustics: Principles and Methods, 17, ed. by W. P. Mason and R. N. Thurston, (Academic Press, New York, 1984) pp. 61–143.Google Scholar
  10. 10.
    Kino, G. S., J. B. Hunter, G. C. Johnson, A. R. Selfridge, D. M. Barnett, G. Herrmann, and C. R. Steele, J. Appl. Phys., 50, 2607–2612 (1979).CrossRefGoogle Scholar
  11. 11.
    Dike, J J. and G. C. Johnson, J. Appl. Mech., 57, 12–17 (1990).CrossRefGoogle Scholar
  12. 12.
    Hsu, N. N., Experimental Mechanics, 14, 169–176 (1974).CrossRefGoogle Scholar
  13. 13.
    Thompson, R. B., S. S. Lee, and J. F. Smith, J. Acoust. Soc. Am., 80, 921–931 (1986).CrossRefGoogle Scholar
  14. 14.
    Man, C. S. and W. Y. Lu, J. Elasticity, 17, 159–182 (1987).CrossRefGoogle Scholar
  15. 15.
    Husson, D., J. Appl. Phys., 57, 1562–1567 (1985).CrossRefGoogle Scholar
  16. 16.
    Liang, K., S. D. Bennett, B. T. Khuri-Yakub, and G. S. Kino, Appl. Phys. Lett., 41, 1124–1126 (1982).CrossRefGoogle Scholar
  17. 17.
    Chen, S. E., “The Influence of Stress on the Dynamic Response of Elastic Layers,” Ph. D. Dissertation, University of California, Berkeley (1989).Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • George C. Johnson
    • 1
  • Shih-Emn Chen
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

Personalised recommendations