Dislocation link-length statistics and elevated temperature deformation of crystals

Abstract

A new theory of elevated temperature deformation, based on the statistics of the distribution of dislocation link lengths, is developed. The distribution consists of a sessile region ( L < L c) in which network growth, or recovery, occurs by a coarsening process, and a glissile region ( L > L c) in which dislocation links are long enough to glide— L c is a critical link length determined by the applied stress. New partial differential equations governing the evolution of the distribution of link lengths are derived for a model that assumes gliding links collide only with network links and produce only new network links. New equations which constrain the behavior of the distribution are formulated; the theory is shown to be self-consistent with respect to these equations. A proper expression for the strain rate is developed, which, with no ad hoc assumptions, automatically includes the contributions of network growth and dislocation glide. Using simple expressions for the rates of link growth in the sessile and glissile regions, equations describing the dislocation kinetics and the strain rate are derived. It is shown that these equations are consistent with experimentally observed transient creep behavior. An equation for the steady state creep rate is also presented which includes a ‘microstructural parameter’ that depends upon constants derivable from the distribution of dislocation link lengths. It is argued that the conventional notions of recovery-controlled and glide-controlled creep are most meaningful during transient deformation. During steady state deformation, however, these concepts have significance only with respect to whether the fraction of mobile dislocation links in the distribution produces the majority of the strain.