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

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 explainsmore » the difference experimentally observed between longitudinal and transverse attenuations [Ledbetter, J. Mater. Res. 10, 1352 (1995)].« less

[1]  A. Maurel,et al.  Interaction between an elastic wave and a single pinned dislocation , 2005 .

[2]  A. Maurel,et al.  Elastic wave propagation through a distribution of dislocations , 2005 .

[3]  H. Ogi,et al.  Acoustic damping characterization and microstructure evolution in nickel-based superalloy during creep , 2005 .

[4]  S. Kalidindi,et al.  Dynamic elastic hysteretic solids and dislocations. , 2005, Physical review letters.

[5]  A. Maurel,et al.  Elastic wave propagation through a random array of dislocations , 2004 .

[6]  A. Maurel,et al.  Scattering of an elastic wave by a single dislocation , 2004 .

[7]  S. Andrews.  Using Rotational Averaging To Calculate the Bulk Response of Isotropic and Anisotropic Samples from Molecular Parameters , 2004 .

[8]  H. Ogi,et al.  Determination of elastic, anelastic, and piezoelectric coefficients of piezoelectric materials from a single specimen by acoustic resonance spectroscopy. , 2004, Ultrasonics.

[9]  D. Shilo,et al.  Stroboscopic X-ray imaging of vibrating dislocations excited by 0.58 GHz phonons. , 2003, Physical review letters.

[10]  Shant Kenderian,et al.  Ultrasonic monitoring of dislocations during fatigue of pearlitic rail steel , 2003 .

[11]  R. E. Green,et al.  Ultrasonic Attenuation and Velocity in Pearlitic Rail Steel During Fatigue Using Longitudinal Wave Probing , 2003 .

[12]  D. Shilo,et al.  Visualization of surface acoustic wave scattering by dislocations. , 2002, Ultrasonics.

[13]  E. M. Nadgorny,et al.  Combined model of dislocation motion with thermally activated and drag-dependent stages , 2001 .

[14]  D. Shilo,et al.  X-ray imaging of acoustic wave interaction with dislocations , 2001 .

[15]  H. Ogi,et al.  Ultrasonic attenuation peak during fatigue of polycrystalline copper , 2000 .

[16]  H. Ogi,et al.  Stress-dependent recovery of point defects in deformed aluminum: an acoustic-damping study , 1999 .

[17]  Hirotsugu Ogi,et al.  Contactless mode-selective resonance ultrasound spectroscopy: Electromagnetic acoustic resonance , 1999 .

[18]  H. Ogi,et al.  Noncontact ultrasonic spectroscopy on deforming polycrystalline copper: Dislocation damping and acoustoelasticity , 1998 .

[19]  Zhenping Zhu,et al.  Sensitivity of Ultrasonic Attenuation and Velocity Change to Cyclic Deformation in Pure Aluminum , 1998 .

[20]  W. Johnson.  Ultrasonic damping in pure aluminum at elevated temperatures , 1998 .

[21]  Hirotsugu Ogi,et al.  Noncontact measurement of ultrasonic attenuation during rotating fatigue test of steel , 1997 .

[22]  Hirotsugu Ogi,et al.  Ultrasonic attenuation and grain‐size evaluation using electromagnetic acoustic resonance , 1995 .

[23]  C. Fortunko,et al.  Elastic constants and internal friction of polycrystalline copper , 1995 .

[24]  Ping Sheng,et al.  Scattering And Localization Of Classical Waves In Random Media , 1990 .

[25]  F. Lund.  Response of a stringlike dislocation loop to an external stress , 1988 .

[26]  A. Granato,et al.  Effect of independent and coupled vibrations of dislocations on low-temperature thermal conductivity in alkali halides , 1982 .

[27]  A. Granato,et al.  Simplified theory of dislocation damping including point-defect drag. I. Theory of drag by equidistant point defects , 1981 .

[28]  H. Ledbetter.  Sound velocities and elastic-constant averaging for polycrystalline copper , 1980 .

[29]  T. Ninomiya.  Frictional Force Acting on a Dislocation – Fluttering Mechanism – , 1974 .

[30]  W. P. Mason,et al.  Phonon and Electron Drag Coefficients in Single-Crystal Aluminum , 1966 .

[31]  A. Ikushima,et al.  Acoustic attenuation studies of the frictional force on a fast moving dislocation , 1964 .

[32]  Toshio Mura,et al.  Continuous distribution of moving dislocations , 1963 .

[33]  A. Granato,et al.  Overdamped resonance of dislocations in copper , 1962 .

[34]  A. Granato,et al.  Application of Dislocation Theory to Internal Friction Phenomena at High Frequencies , 1956 .

[35]  A. Granato,et al.  Theory of Mechanical Damping Due to Dislocations , 1956 .

[36]  A. Granato,et al.  Sensitivity of Ultrasonic Attenuation and Velocity Changes to Plastic Deformation and Recovery in Aluminum , 1956 .

[37]  M. Lax.  MULTIPLE SCATTERING OF WAVES. II. THE EFFECTIVE FIELD IN DENSE SYSTEMS , 1952 .

[38]  M. Lax.  Multiple Scattering of Waves , 1951 .

[39]  M. Peach,et al.  THE FORCES EXERTED ON DISLOCATIONS AND THE STRESS FIELDS PRODUCED BY THEM , 1950 .

[40]  L. Foldy,et al.  The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers , 1945 .

[41]  John A. Scales,et al.  Resonant Ultrasound Spectroscopy: theory and application , 2002 .