On a joint quantized and mechanical description for the Chernov-L\"uders macroband of localized deformation

Abstract

We suggest a quantum procedure, based on our recent statistical theory of flow stress in polycrystalline materials under quasi-static plastic deformations, with the intention to approach a theoretical description of the Chernov-L\"uders shear macroband of localized deformation, exhibited by some Fe-containing materials with a second phase beyond the yield-strength point on the stress-strain curve {\sigma}={\sigma}({\epsilon}). The procedure makes substantial use of a quasi-particle interpretation for the minimal portion of mechanical energy in a given single-mode polycrystalline aggregate that is necessary for the thermal-fluctuation mechanism to create a 0D-defect nanopore as the initial zone of a localized deformation under external loading. Using a quasi-particle description, we obtain analytic expressions both for the scalar density of dislocations, given the size of grains, the temperature, the most probable sliding system, and for the dependence {\sigma} ={\sigma}({\epsilon}) itself. A two-level system, which characterizes the mechanism of absorption and emission of such quasi-particles (dislocons) by the crystal lattice of any grain under quasi-static loading provides an effective physical description for the emergence and propagation of the Chernov-L\"uders shear macroband. An enhancement of acoustic emission observed in experiments and accompanied by the macroband phenomenon justifies the interpretation of a dislocon as a composite short-lived particle consisting of acoustic phonons. A more realistic three-level system within a two-phase model with third (with dispersion particles) phase presence for actual polycrystalline samples is also produced.