Deformation bands, the LEDS theory, and their improtance in texture development: Part II.Theoretical conclusions

摘要

The facts regarding "regular" deformation bands(DBs) outlined in Part I of this series of articles are related to thelow-energy dislocation structure (LEDS) theory of dislocation-based plasticity. They prompt an expansion of the theory byincluding the stresses due to strain gradients on account ofchanging selections of slip systems to the previously knowndislocation driving forces. This last and until now neglecteddriving force is much smaller than the components consideredhitherto, principally due to the applied stress and to mutualstress-screening among neighbor dislocations. As a result, itpermits a near-proof of the LEDS hypothesis, to wit that amongall structures which, in principle, are accessible to thedislocations, that one is realized which has the lowest freeenergy. Specifically, the temperature rises that would result fromannihilating the largest DBs amount to only several millidegreesCentigrade, meaning that they, and by implication the entiredislocation structures, are close to thermodynamical equilibrium.This is in stark contrast to the assumption of the presentlywidespread self-organizing dislocation structures (SODS)modeling that plastic deformation occurs far from equilibriumand is subject to Prigogine's thermodynamics of energy-flow-through systems. It also holds out promise for future rapidadvances in the construction of constitutive equations, since theLEDS hypothesis is the principal basis of the LEDS theory ofplastic deformation and follows directly from the second law ofthermodynamics in conjunction with Newton's third law. Bycontrast, all other known models of metal plasticity are inconflict with the LEDS hypothesis. In regard to texturemodeling, the present analysis shows that Taylor's criterion ofminimum plastic work is incorrect and should be replaced by thecriterion of minimum free energy in the stressed state. Last, theLEDS hypothesis is but a special case of the more general low-energy structure (LES) hypothesis, applying to plasticdeformation independent of the deformation mechanism. It isthus seen that plastic deformation is one of nature's means togenerate order, as a byproduct of the entropy generation whenmechanical work is largely converted into heat.