On combined quantized and mechanical descriptions of the Chernov-Luders macroband of localized deformation

We suggest the quantized approach, based on the recently proposed statistical theory of flow stress for the polycrystalline materials under quasi-static plastic deformation, in order to theoretically describe the Chernov-Luders shear macroband of localized deformation, which is manifested in a number of Fe-containing materials with the second phase presence beyond the yield strength point on the stress-strain curve, σ=σ(ϵ). The procedure essentially uses the quasi-particle interpretation for the part of the minimal mechanical energy for given single-mode polycrystalline aggregate to be necessary to create, according to thermal-fluctuation mechanism, the 0D-defect - nanopore as the initial zone of localized deformation under external loading. With help of the quasi-particles description the analytical expressions both for the scalar density of dislocations for given grain sizes, temperature, the most probable sliding system and for the σ=σ(ϵ) dependence 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 permits to effectively describe the physics of the appearance and propagation of the Chernov-Luders shear macroband. The experimentally observed enhancement of the acoustic emission, accompanying the phenomenon, justifies the interpretation of the dislocon as the composite short-lived particle consisting of acoustic phonons. The case of more realistic three-level system within two-phase model for real polycrystalline samples is suggested as well.