Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T13:30:31.667Z Has data issue: false hasContentIssue false
  • English
  • Français

Interaction of Elastic Waves with Dislocations

Published online by Cambridge University Press:  21 February 2012

Agnes Maurel ,
Fernando Lund ,
Felipe Barra  and
Vincent Pagneux
Agnes Maurel
Affiliation:
LOA/Institut Langevin, Paris, France.
Fernando Lund
Affiliation:
DFI and CIMAT, FCFM, Universidad de Chile, Santiago, Chile.
Felipe Barra
Affiliation:
DFI and CIMAT, FCFM, Universidad de Chile, Santiago, Chile.
Vincent Pagneux
Affiliation:
LAUM, Le Mans, France.
Get access

Abstract

The theory of the interaction of elastic waves with dislocations is reviewed, as is the extent to which it has been tested by experiment. There are two essential ingredients to the wave-dislocation interaction: one is that, when a wave hits a dislocation, the latter will respond by moving in some fashion. The other is that, when a dislocation moves, it generates (“radiates”) elastic waves. For a linearly elastic solid continuum, both phenomena can be described by equations that are linear outside the dislocation core. One is a linear elastic wave equation with a right-hand-side term that is localized at the dislocation position. The other is a linear equation for the vibrations of a string (that is coincident with the dislocation), with an external loading provided by the wave. This provides the basic mechanism for the scattering of elastic waves by dislocations, and it can be worked out in considerable detail for pinned dislocation segments and prismatic dislocation loops in infinite media, as well as for the scattering of surface (Rayleigh) elastic waves by subsurface dislocation segments.

The results for the scattering by a single dislocation can be used as input in a multiple scattering formalism to study the properties of a coherent wave propagating in a solid with many dislocations present. Expressions for the effective velocity of propagation, and for the disorder-induced (as distinct from the internal losses) attenuation can be found. They test successfully with Resonant Ultrasound Spectroscopy (RUS) experimental measurements.

Open problems, possible further applications and current efforts are discussed.

Keywords

dislocationselastic propertiesacoustic
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1404: Symposium W – Phonons in Nanomaterials–Theory, Experiments and Applications , 2012 , mrsf11-1404-w02-05
Copyright
Copyright © Materials Research Society 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Koehler, J., in Imperfections in Nearly Perfect Crystals, edited by Smoluchowski, R. (Wiley, New York, 1952).Google Scholar
2. Hirth, J. P. and Lothe, J., Theory of Dislocations (Wiley, New York, 1982).Google Scholar
3. Mura, T., Philos. Mag. 8, 843 (1963).Google Scholar
4. Lund, F., J. Mater. Res. 3, 280 (1988).Google Scholar
5. Kausel, E., Fundamental Solutions in Elastodynamics: A Compendium (Cambridge University Press, 2006).Google Scholar
6. Eshelby, J. D., Phil. Trans. Roy. Soc. London A 244, 87 (1951).Google Scholar
7. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Phys. Rev. B 72, 174110 (2005).Google Scholar
8. Rodríguez, N., Maurel, A., Pagneux, V., Barra, F. and Lund, F., J. Appl. Phys. 106, 054910 (2009).Google Scholar
9. Masters, B. C., Philos. Mag. 11, 881 (1965).Google Scholar
10. Eyre, B. L. and Bartlett, A. F., Philos. Mag. 12, 261 (1965); J. Nucl. Mater. 47, 143(1973).Google Scholar
11. Bullough, T. J., English, C. A., and Eyre, B. L., Proc. R. Soc. London, Ser.A 534, 85 (1991).Google Scholar
12. Kawanishi, H., Ishino, S., and Kuramoto, E., J. Nucl. Mater. 141–143, 899 (1986).Google Scholar
13. Horton, L. L. and Farrell, K, J. Nucl. Mater. 122, 684 (1984).Google Scholar
14. Shilo, D. and Zolotoyabko, E., Phys. Rev. Lett. 91, 115506 (2003).Google Scholar
15. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Phys. Rev B 75, 224112 (2007).Google Scholar
16. Zolotoyabko, E. and Shilo, D., Phys. Rev. B 80, 136101 (2009).Google Scholar
17. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Phys. Rev B 80, 136102 (2009).Google Scholar
18. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Phys. Rev. B 72, 174111 (2005).Google Scholar
19. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Int. J. Bifurc. Chaos 19, 2765 (2009).Google Scholar
20. Granato, V. and Lücke, K., J. Appl. Phys. 27, 583 (1956); 27, 789(1956).Google Scholar
21. Ogi, H., Tsujimoto, A., Mirao, H. and Ledbetter, H., Acta Mater. 47, 3745 (1999).Google Scholar
22. Ledbetter, H. M. and Fortunko, C., J. Mater. Res. 10, 1352 (1995):Google Scholar
23. Ogi, H., Nakamura, N., Hirao, M. and Ledbetter, H., Ultrasonics 42, 183 (2004).Google Scholar
24. Ogi, H., Ledbetter, H. M., Kim, S. and Hirao, M., J. Acoust. Soc. Am. 106, 660 (1999).Google Scholar
25. Barra, F., Caru, A., Cerda, M. T., Espinoza, R., Jara, A., Lund, F. and Mujica, N., Int. J. Bifurc. Chaos 19, 3561 (2009).Google Scholar