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Dynamic Peierls-Nabarro equations for elastically isotropic crystals

Abstract : The dynamic generalization of the Peierls-Nabarro equation for dislocations cores in an isotropic elastic medium is derived for screw, and edge dislocations of the `glide' and `climb' type, by means of Mura's eigenstrains method. These equations are of the integro-differential type and feature a non-local kernel in space and time. The equation for the screw differs by an instantaneous term from a previous attempt by Eshelby. Those for both types of edges involve in addition an unusual convolution with the second spatial derivative of the displacement jump. As a check, it is shown that these equations correctly reduce, in the stationary limit and for all three types of dislocations, to Weertman's equations that extend the static Peierls-Nabarro model to finite constant velocities.
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https://hal-cea.archives-ouvertes.fr/cea-00412985
Contributor : Yves-Patrick Pellegrini <>
Submitted on : Wednesday, September 2, 2009 - 6:59:38 PM
Last modification on : Friday, April 24, 2020 - 10:28:04 AM

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Yves-Patrick Pellegrini. Dynamic Peierls-Nabarro equations for elastically isotropic crystals. Physical Review B: Condensed Matter and Materials Physics, American Physical Society, 2010, 81, pp.024101. ⟨10.1103/PhysRevB.81.024101⟩. ⟨cea-00412985⟩

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