Wave propagation through a random array of pinned dislocations: Velocity change and attenuation in a generalized Granato and Luecke theory

Journal Article · Tue Nov 01 00:00:00 EST 2005 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PhysRevB.72.174111· OSTI ID:20719778

Maurel, Agnes ^[1]; Pagneux, Vincent ^[2]; Barra, Felipe ^[3]; Lund, Fernando ^[3]

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1. Laboratoire Ondes et Acoustique, UMR CNRS 7587, Ecole Superieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75005 Paris (France)
2. Laboratoire d'Acoustique de l'Universite du Maine, UMR CNRS 6613 Avenue Olivier Messiaen, 72085 Le Mans Cedex 9 (France)
3. Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Casilla 487-3, Santiago (Chile)

A quantitative theory of the elastic wave damping and velocity change due to interaction with dislocations is presented. It provides a firm theoretical basis and a generalization of the Granato and Luecke model [J. Appl. Phys. 27, 583 (1956)]. This is done considering the interaction of transverse (T) and longitudinal (L) elastic waves with an ensemble of dislocation segments randomly placed and randomly oriented in an elastic solid. In order to characterize the coherent wave propagation using multiple scattering theory, a perturbation approach is used, which is based on a wave equation that takes into account the dislocation motion when forced by an external stress. In our calculations, the effective velocities of the coherent waves appear at first order in perturbation theory while the attenuations have a part at first order due to the internal viscosity and a part at second order due to the energy that is taken away from the incident direction. This leads to a frequency dependence law for longitudinal and transverse attenuations that is a combination of quadratic and quartic terms instead of the usual quadratic term alone. Comparison with resonant ultrasound spectroscopy (RUS) and electromagnetic acoustic resonance (EMAR) experiments is proposed. The present theory explains the difference experimentally observed between longitudinal and transverse attenuations [Ledbetter, J. Mater. Res. 10, 1352 (1995)].

• OSTI ID: 20719778
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 72, Issue 17; Other Information: DOI: 10.1103/PhysRevB.72.174111; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
36 MATERIALS SCIENCE
ATTENUATION
COMPARATIVE EVALUATIONS
DAMPING
DISLOCATION PINNING
DISLOCATIONS
DISTURBANCES
FREQUENCY DEPENDENCE
MULTIPLE SCATTERING
PERTURBATION THEORY
RANDOMNESS
RESONANCE
SOLIDS
SPECTROSCOPY
STRESSES
VELOCITY
VISCOSITY
WAVE EQUATIONS
WAVE PROPAGATION