Theory of plasticity and anelasticity due to dislocation creep through a multi-scale hierarchy of obstacles

The creep of a dislocation on its glide plane is essentially controlled by three different stress fields: the external applied stress, the internal stress field due to a multi-scale hierarchy of different obstacles (the structural defects acting on the dislocation by short- or long-range interactions) and the thermal stress field due to thermal fluctuations. The dislocation glide dynamics involves solution of a string equation, which can be written as a Langevin equation. In this paper, it is shown that general analytical solutions of this equation can be found, allowing calculation of the plastic strain rate and the amplitude-dependent internal friction (ADIF), by using simple assumptions concerning the multi-scale hierarchy of obstacles and the mechanisms of Brownian dislocation creep through the different kinds of interacting obstacles. It is also shown that several experimental observations are well explained by this approach.