The theory of dislocation-based crystal plasticity

An overview of the low-energy dislocation structure (LEDS) theory of low-te mperature, that is non-creep, dislocation-based crystal plasticity is prese nted, 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 th at stress application causes the essentially instantaneous athermal generat ion of dislocation structures which are in equilibrium with the applied str ess and which on stress release and reversal are stable up to the previousl y highest stress magnitude. As will be shown: at least in principle even th ough many derails are still lacking, the following phenomena of crystal pla sticity are readily explained by means of the LEDS theory: (1) the four sta ges of work hardening; (2) the shape of the stress-strain curve; (3) the te mperature dependence of work hardening; (4) the low-temperature strain rate dependence of the Bow stress; (5) the difference between 'planar' and 'wav y' glide materials las exemplified by alpha-brass and copper respectively); (6) the empirical relationship D=KGb/tau between dislocation cell size and flow stress; (7) grain-boundary hardening; (8) alloy hardening including s olid-solution, precipitation and phase-boundary hardening; (9) slip lines a nd 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 recrystall ization; (15) the development of dislocation structures in fatigue. All the se are explained effortlessly on the basis of only the known properties of glide dislocations and the second law of thermodynamics, as expressed in th e LEDS hypothesis, to wit that. among the structures which are in equilibri um with the applied tractions and accessible to the dislocations, those are formed which most nearly minimize the stored energy. (See Note added in pr oof at end of this payer.) The alternative 'self-organizing dislocation' mo del of crystal plasticity assumes plastic deformation to be due to individu al 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 1925 and still has to yield significant results.