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

Abstract

The facts regarding “regular” deformation bands (DBs) outlined in Part I of this series of articles are related to the low-energy dislocation structure (LEDS) theory of dislocation-based plasticity. They prompt an expansion of the theory by including the stresses due to strain gradients on account of changing selections of slip systems to the previously known dislocation driving forces. This last and until now neglected driving force is much smaller than the components considered hitherto, principally due to the applied stress and to mutual stress-screening among neighbor dislocations. As a result, it permits a near-proof of the LEDS hypothesis, to wit that among all structures which, in principle, are accessible to the dislocations, that one is realized which has the lowest free energy. Specifically, the temperature rises that would result from annihilating the largest DBs amount to only several millidegrees Centigrade, meaning that they, and by implication the entire dislocation structures, are close to thermodynamical equilibrium. This is in stark contrast to the assumption of the presently widespread self-organizing dislocation structures (SODS) modeling that plastic deformation 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 hypothesis 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 plasticity 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 byproduct of the entropy generation when mechanical work is largely converted into heat.