On the statistical origin of disorientations in dislocation structures

The formation of disorientations in dislocation structures during plastic deformation is considered as a random accumulation process of excess dislocations in the dislocation boundaries. For a single slip system the assumption of a Gaussian white noise for the bias of dislocation fluxes leads to a Gaussian distribution for the disorientation angles with a vanishing mean value. The corresponding standard deviation is determined by the dependence of the cell size on plastic strain, if the number of mobile dislocations of one sign of the Burgers vector at the same time present in a dislocation cell can be described by a Poisson distribution. For a constant cell size the square root dependence of the mean disorientation angle on plastic strain-as previously proposed by Argon and Haasen and derived by Nabarro-is confirmed simultaneously showing the intrinsic restriction of this dependence to a constant cell size. The necessary modifications for symmetrical double slip as well as for a non-constant cell size are presented. (C) 1998 Acta Metallurgica Inc.