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arXiv · 0908.2371

Dynamic Peierls-Nabarro equations for elastically isotropic crystals

Yves-Patrick Pellegrini
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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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Yves-Patrick Pellegrini. 2010-02-24. Dynamic Peierls-Nabarro equations for elastically isotropic crystals. https://doi.org/10.1103/physrevb.81.024101

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