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Derivation of Orowan's law from the Peierls-Nabarro model

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Abstract

In this paper we consider the time dependent Peierls-Nabarro model in dimension one. This model is a semi-linear integro-differential equation associated to the half Laplacian. This model describes the evolution of phase transitions associated to dislocations. At large scale with well separated dislocations, we show that the dislocations move at a velocity proportional to the effective stress. This implies Orowan's law which claims that the plastic strain velocity is proportional to the product of the density of dislocations by the effective stress.

Most cited references8

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Fractal First-Order Partial Differential Equations

(2006)
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Nonlinear diffusion of dislocation density and self-similar solutions

(2008)
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.
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Dislocation group dynamics III. similarity solutions of the continuum approximation

(2006)
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Author and article information

Journal
1207.4412

Analysis