The formation of misorientations in dislocation structures during plastic deformation was attributed to the random accumulation of excess dislocations in the dislocation boundaries. For a single-slip system, the assumption of Gaussian white noise as a bias in the dislocation fluxes led to a Gaussian distribution, for the misorientation angles, with a vanishing mean value. The corresponding standard deviation was determined by the dependence of the cell size upon plastic strain, if the number of mobile dislocations with Burgers vectors of one sign, present in a dislocation cell at a given time, could be described by a Poisson distribution. For a constant cell size, the square-root dependence of the mean misorientation angle upon plastic strain was confirmed, and this also demonstrated the intrinsic restriction of this dependence to the condition of constant cell-size.

On the Statistical Origin of Disorientations in Dislocation Structures W.Pantleon: Acta Materialia, 1998, 46[2], 451-6