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

The facts regarding "regular" deformation bands (DBs) outlined in Part I of this series of articles are related to the low-energy dislocation structur e (LEDS) theory of dislocation-based plasticity. They prompt an expansion o f the theory by including the stresses due to strain gradients on account o f changing selections of slip systems to the previously known dislocation d riving forces. This last and until now neglected driving force is much smal ler than the components considered hitherto, principally due to the applied stress and to mutual stress-screening among neighbor dislocations. as a re sult, it permits a near-proof of the LEDS hypothesis, to wit that among all structures which, in principle, are accessible to the dislocations, that o ne is realized which has the lowest free energy. Specifically, the temperat ure rises that would result from annihilating the largest DBs amount to onl y several millidegrees Centigrade, meaning that they, and by implication th e entire dislocation structures, are close to thermodynamical equilibrium. This is in stark contrast to the assumption of the presently widespread sel f-organizing dislocation structures (SODS) modeling that plastic deformatio n occurs far from equilibrium and is subject to Prigogine's thermodynamics of energy-flow-through systems. It also holds out promise for future rapid advances in the construction of constitutive equations, since the LEDS hypo thesis is the principal basis of the LEDS theory of plastic deformation and follows directly from the second law of thermodynamics in conjunction with Newton's third law. By contrast, all other known models of metal plasticit y are in conflict with the LEDS hypothesis. In regard to texture modeling, the present analysis shows that Taylor's criterion of minimum plastic work is incorrect and should be replaced by the criterion of minimum free energy in the stressed state. Last, the LEDS hypothesis is but a special case of the more general low-energy structure (LES) hypothesis, applying to plastic deformation independent of the deformation mechanism. It is thus seen that plastic deformation is one of nature's means to generate order, as a bypro duct of the entropy generation when mechanical work is largely converted in to heat.