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Interaction of Elastic Waves with Dislocations

  • Agnes Maurel (a1), Fernando Lund (a2), Felipe Barra (a2) and Vincent Pagneux (a3)


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.



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1. Koehler, J., in Imperfections in Nearly Perfect Crystals, edited by Smoluchowski, R. (Wiley, New York, 1952).
2. Hirth, J. P. and Lothe, J., Theory of Dislocations (Wiley, New York, 1982).
3. Mura, T., Philos. Mag. 8, 843 (1963).
4. Lund, F., J. Mater. Res. 3, 280 (1988).
5. Kausel, E., Fundamental Solutions in Elastodynamics: A Compendium (Cambridge University Press, 2006).
6. Eshelby, J. D., Phil. Trans. Roy. Soc. London A 244, 87 (1951).
7. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Phys. Rev. B 72, 174110 (2005).
8. Rodríguez, N., Maurel, A., Pagneux, V., Barra, F. and Lund, F., J. Appl. Phys. 106, 054910 (2009).
9. Masters, B. C., Philos. Mag. 11, 881 (1965).
10. Eyre, B. L. and Bartlett, A. F., Philos. Mag. 12, 261 (1965); J. Nucl. Mater. 47, 143(1973).
11. Bullough, T. J., English, C. A., and Eyre, B. L., Proc. R. Soc. London, Ser.A 534, 85 (1991).
12. Kawanishi, H., Ishino, S., and Kuramoto, E., J. Nucl. Mater. 141143, 899 (1986).
13. Horton, L. L. and Farrell, K, J. Nucl. Mater. 122, 684 (1984).
14. Shilo, D. and Zolotoyabko, E., Phys. Rev. Lett. 91, 115506 (2003).
15. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Phys. Rev B 75, 224112 (2007).
16. Zolotoyabko, E. and Shilo, D., Phys. Rev. B 80, 136101 (2009).
17. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Phys. Rev B 80, 136102 (2009).
18. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Phys. Rev. B 72, 174111 (2005).
19. Maurel, A., Pagneux, V., Barra, F. and Lund, F., Int. J. Bifurc. Chaos 19, 2765 (2009).
20. Granato, V. and Lücke, K., J. Appl. Phys. 27, 583 (1956); 27, 789(1956).
21. Ogi, H., Tsujimoto, A., Mirao, H. and Ledbetter, H., Acta Mater. 47, 3745 (1999).
22. Ledbetter, H. M. and Fortunko, C., J. Mater. Res. 10, 1352 (1995):
23. Ogi, H., Nakamura, N., Hirao, M. and Ledbetter, H., Ultrasonics 42, 183 (2004).
24. Ogi, H., Ledbetter, H. M., Kim, S. and Hirao, M., J. Acoust. Soc. Am. 106, 660 (1999).
25. Barra, F., Caru, A., Cerda, M. T., Espinoza, R., Jara, A., Lund, F. and Mujica, N., Int. J. Bifurc. Chaos 19, 3561 (2009).



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