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Title: Dislocation drag from phonon wind in an isotropic crystal at large velocities

Abstract

The anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force $vB$ $(ν, T, ρ)$ on the dislocation. In early studies the drag coefficient B was computed and experimentally determined only for dislocation velocities v much less than transverse sound speed, $$c_T$$ . In this paper we derive analytic expressions for the velocity dependence of B up to $$c_T$$ in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to B in the range 1%–90% $$c_T$$ for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as $$ν → c_T$$ , whereas B is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements.

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1604033
Report Number(s):
LA-UR-19-25851
Journal ID: ISSN 1478-6435
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Philosophical Magazine (2003, Print)
Additional Journal Information:
Journal Name: Philosophical Magazine (2003, Print); Journal Volume: 100; Journal Issue: 5; Journal ID: ISSN 1478-6435
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
Dislocations in crystals; drag coefficient; phonon wind

Citation Formats

Blaschke, Daniel N., Mottola, Emil, and Preston, Dean L. Dislocation drag from phonon wind in an isotropic crystal at large velocities. United States: N. p., 2019. Web. doi:10.1080/14786435.2019.1696484.
Blaschke, Daniel N., Mottola, Emil, & Preston, Dean L. Dislocation drag from phonon wind in an isotropic crystal at large velocities. United States. doi:10.1080/14786435.2019.1696484.
Blaschke, Daniel N., Mottola, Emil, and Preston, Dean L. Wed . "Dislocation drag from phonon wind in an isotropic crystal at large velocities". United States. doi:10.1080/14786435.2019.1696484.
@article{osti_1604033,
title = {Dislocation drag from phonon wind in an isotropic crystal at large velocities},
author = {Blaschke, Daniel N. and Mottola, Emil and Preston, Dean L.},
abstractNote = {The anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force $vB$ $(ν, T, ρ)$ on the dislocation. In early studies the drag coefficient B was computed and experimentally determined only for dislocation velocities v much less than transverse sound speed, $c_T$ . In this paper we derive analytic expressions for the velocity dependence of B up to $c_T$ in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to B in the range 1%–90% $c_T$ for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as $ν → c_T$ , whereas B is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements.},
doi = {10.1080/14786435.2019.1696484},
journal = {Philosophical Magazine (2003, Print)},
number = 5,
volume = 100,
place = {United States},
year = {2019},
month = {12}
}

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Works referenced in this record:

Mobility of Dislocations in Aluminum
journal, February 1969

  • Gorman, J. A.; Wood, D. S.; Vreeland, T.
  • Journal of Applied Physics, Vol. 40, Issue 2
  • DOI: 10.1063/1.1657472

Dislocation kinematics: a molecular dynamics study in Cu
journal, December 2016

  • Oren, E.; Yahel, E.; Makov, G.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 25, Issue 2
  • DOI: 10.1088/1361-651X/aa52a7

Thermodynamics of Crystals
journal, November 1972

  • Wallace, Duane C.; Callen, Herbert
  • American Journal of Physics, Vol. 40, Issue 11
  • DOI: 10.1119/1.1987046

Analytic model of the remobilization of pinned glide dislocations from quasi-static to high strain rates
journal, July 2015


Dynamic Peierls-Nabarro equations for elastically isotropic crystals
journal, January 2010


Averaging of elastic constants for polycrystals
journal, October 2017

  • Blaschke, Daniel N.
  • Journal of Applied Physics, Vol. 122, Issue 14
  • DOI: 10.1063/1.4993443

Acoustic attenuation studies of the frictional force on a fast moving dislocation
journal, November 1964


Dislocation Mobility in Copper
journal, August 1967

  • Greenman, W. Frank; Vreeland, Thad; Wood, David S.
  • Journal of Applied Physics, Vol. 38, Issue 9
  • DOI: 10.1063/1.1710178

Dislocation Mobility in Pure Copper at 4.2 °K
journal, October 1973


The energetics of dislocations accelerating and decelerating through the shear-wave speed barrier
journal, January 2009

  • Markenscoff, Xanthippi; Huang, Surong
  • Applied Physics Letters, Vol. 94, Issue 2
  • DOI: 10.1063/1.3072351

Dislocation theory
journal, September 1958


Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions
journal, January 2016


Analysis for a screw dislocation accelerating through the shear-wave speed barrier
journal, June 2008

  • Markenscoff, Xanthippi; Huang, Surong
  • Journal of the Mechanics and Physics of Solids, Vol. 56, Issue 6
  • DOI: 10.1016/j.jmps.2008.01.005

Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys
journal, March 2005

  • Olmsted, David L.; HectorJr, Louis G.; Curtin, W. A.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 13, Issue 3
  • DOI: 10.1088/0965-0393/13/3/007

Dislocation Contributions to the Modulus and Damping in Copper at Megacycle Frequencies
journal, February 1961

  • Alers, G. A.; Thompson, D. O.
  • Journal of Applied Physics, Vol. 32, Issue 2
  • DOI: 10.1063/1.1735992

New estimates of the third-order elastic constants for isotropic aggregates of cubic crystals
journal, April 1997


Third-Order Constants of a Cubic Quasi-Isotropic Solid
journal, June 1990


Overdamped resonance of dislocations in copper
journal, April 1962


Finite Deformations of an Elastic Solid
journal, April 1937

  • Murnaghan, F. D.
  • American Journal of Mathematics, Vol. 59, Issue 2
  • DOI: 10.2307/2371405

Second- and third-order elastic coefficients in polycrystalline aluminum alloy AMg6
journal, November 2015


Uniformly Moving Dislocations
journal, May 1949


Dislocation dynamics and mechanical properties of crystals
journal, January 1988


Properties of Dislocation Drag from Phonon Wind at Ambient Conditions
journal, March 2019


Sound Waves in Deformed Perfectly Elastic Materials. Acoustoelastic Effect
journal, February 1961

  • Toupin, R. A.; Bernstein, B.
  • The Journal of the Acoustical Society of America, Vol. 33, Issue 2
  • DOI: 10.1121/1.1908623

High dislocation velocities and the structures of slip bands in shock loaded high purity lithium fluoride
journal, January 1964


Theory of Dislocation Mobility in Pure Slip
journal, June 1962


Supersonic Dislocation Kinetics from an Augmented Peierls Model
journal, January 2001


A multiscale strength model for extreme loading conditions
journal, April 2011

  • Barton, N. R.; Bernier, J. V.; Becker, R.
  • Journal of Applied Physics, Vol. 109, Issue 7
  • DOI: 10.1063/1.3553718

Stress and temperature dependence of screw dislocation mobility in α -Fe by molecular dynamics
journal, November 2011


Velocity dependent dislocation drag from phonon wind and crystal geometry
journal, January 2019


Elastic precursor wave decay in shock-compressed aluminum over a wide range of temperature
journal, January 2018

  • Austin, Ryan A.
  • Journal of Applied Physics, Vol. 123, Issue 3
  • DOI: 10.1063/1.5008280

Line tension of a dislocation moving through an anisotropic crystal
journal, June 2018


Anharmonicity Contributions to Dislocation Drag
journal, April 1972

  • Brailsford, A. D.
  • Journal of Applied Physics, Vol. 43, Issue 4
  • DOI: 10.1063/1.1661329

Plastic deformation under high-rate loading: The multiscale approach
journal, July 2010


Probing the character of ultra-fast dislocations
journal, November 2015

  • Ruestes, C. J.; Bringa, E. M.; Rudd, R. E.
  • Scientific Reports, Vol. 5, Issue 1
  • DOI: 10.1038/srep16892

Dislocation mobility in potassium and iron single crystals
journal, March 1975


Dislocation Mobility in Aluminum
journal, July 1972

  • Parameswaran, V. R.; Urabe, N.; Weertman, J.
  • Journal of Applied Physics, Vol. 43, Issue 7
  • DOI: 10.1063/1.1661644

Supersonic Dislocations Observed in a Plasma Crystal
journal, July 2007


Aspects of the Theories of Dislocation Mobility and Internal Friction
journal, February 1960


Third‐Order Elastic Constants of Single‐Crystal and Polycrystalline Columbium
journal, June 1968

  • Graham, L. J.; Nadler, H.; Chang, Roger
  • Journal of Applied Physics, Vol. 39, Issue 7
  • DOI: 10.1063/1.1656726

Response of copper to shock-wave loading at temperatures up to the melting point
journal, August 2013

  • Zaretsky, E. B.; Kanel, G. I.
  • Journal of Applied Physics, Vol. 114, Issue 8
  • DOI: 10.1063/1.4819328