The theory of dislocation-based crystal plasticity

Abstract

Abstract An overview of the low-energy dislocation structure (LEDS) theory of low-temperature, that is non-creep, dislocation-based crystal plasticity is presented, as systematically developed over the past 35 years. It is ultimately based on G. I. Taylor's 1934 theory of work hardening wherein he assumed that stress application causes the essentially instantaneous athermal generation of dislocation structures which are in equilibrium with the applied stress and which on stress release and reversal are stable up to the previously highest stress magnitude. As will be shown, at least in principle even though many details are still lacking, the following phenomena of crystal plasticity are readily explained by means of the LEDS theory: (1) the four stages of work hardening; (2) the shape of the stress-strain curve; (3) the temperature dependence of work hardening; (4) the low-temperature strain rate dependence of the flow stress; (5) the difference between ‘planar’ and ‘wavy’ glide materials (as exemplified by α-brass and copper respectively); (6) the empirical relationship D = KGb/T between dislocation cell size and flow stress; (7) grain-boundary hardening; (8) alloy hardening including solid-solution, precipitation and phase-boundary hardening; (9) slip lines and slip bands; (10) the evolution of the dislocation structures from stages I to IV; (11) deformation texture evolution; (12) work softening; (13) the thermodynamics of dislocation storage; (14) recovery, creep and recrystallization; (15) the development of dislocation structures in fatigue. All these are explained effortlessly on the basis of only the known properties of glide dislocations and the second law of thermodynamics, as expressed in the LEDS hypothesis, to wit that, among the structures which are in equilibrium with the applied tractions and accessible to the dislocations, those are formed which most nearly minimize the stored energy. (See Note added in proof at end of this paper.) The alternative ‘self-organizing dislocation’ model of crystal plasticity assumes plastic deformation to be due to individual thermally activated processes, which are treatable by the thermodynamics of energy-flow-through systems. It can be traced back to the early theory by R. Becker in 1925 and 1926 and still has to yield significant results.