  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.
