On the evolution of disorientations in dislocation cell structures during plastic deformation

The distribution function for disorientation angles across dislocation boundaries is calculated taking into account the random accumulation processes of excess dislocations. For a single set of straight and parallel dislocations a Gaussian distribution for the disorientation angles can be obtained. In the case of an equivalent contribution of two inclined sets with a Gaussian distribution for each of the elementary dislocation systems a universal function is derived which depends only slightly on the inclination of the contributing dislocation sets. The resulting theoretical disorientation distributions are in good agreement with the experimentally determined histograms and support the experimentally observed scaling behaviour.