Statistical model of the local pinning of dislocations due to cross-slip events

A local pinning model is formulated describing kinetics of dislocation self-immobilisation due to random cross slip events. An exact solution to a corresponding statistical problem is presented, which operates with the distributions of displacements along the dislocation line and superkink heights. The knowledge of such detailed characteristics of the dislocation arrangement allows to suggest a new type of dislocation velocity-applied stress relation, which yields the positive temperature dependence of the flow stress, thus explaining the anomalous behaviour of material plasticity.