On the physics of the Portevin-Le Châtelier effect part 1: The statistics of dynamic strain ageing

Based on the temporal evolution of an ageing time distribution function, a statistical theory of discontinuous glide of non-interacting dislocations in a dynamic strain ageing (DSA) alloy is presented. DSA is shown to lead to retardation effects that are due to a redistribution of ageing times accompanying a change of the deformation path. A first-order approximation in terms of a relaxator equation is given. Moreover, a general linear response theory is developed, in order to describe, for instance, abrupt changes of the imposed strain rate. The results differ from former theories, since DSA is found to be insufficient to explain the occurrence of negative strain-rate sensitivities, unless collective effects due to dislocation interactions are also taken into account. A generalized theory of the combined influence of DSA and dislocation interactions is developed in Part 2.