A local pinning model was formulated for the description of the kinetics of dislocation self-immobilisation due to random cross-slip events. An exact solution to the corresponding statistical problem was presented, which involved the distributions of displacements along the dislocation line, and super-kink heights. The detailed knowledge of the characteristics of the dislocation arrangement suggested the existence of a new type of dislocation-velocity versus applied-stress relationship. This yielded a positive temperature dependence for the flow stress; thus explaining the well-known anomalous behaviour.

Statistical Model of the Local Pinning of Dislocations due to Cross-Slip Events. B.V.Petukhov: Materials Science and Engineering A, 2001, 309-310, 345-7