Plastic Flow Macrolocalization: Autowave and Quasi-Particle

Abstract

A new approach is proposed to describe the autowave processes responsible for plastic deformation localization in metals and alloys. The existence of a quasi-particle, which corresponds to a localized plastic flow autowave, is postulated and its characteristics are determined. The above postulate leads to a number of corollaries and quantitative assessments that are considered herein. The deformation processes occurring on the macro-and micro-scale levels are found to be directly related.

Overall Model of Plasticity and Failure of Metals

“…The main findings of this study show that the plastic flow tends to localize at all the scale levels [1]. For a researcher in plasticity physics the macro-scale level is obviously the most convenient one since it serves to provide a unified explanation for a variety of plastic flow localization phenomena with striking regularities which are usually left unexplained.…”

“…The latter dependence is determined by the viscous drag of dislocations due to the occurrence of phonon and electron gases in metals [1].…”

“…[7]. To test the validity of this idea, m aw values were calculated from (3), using the autowave characteristics obtained for a number of metals and alloys [1] Then the volume was calculated as Ω = m aw /ρ (here m aw is the effective mass and ρ is metal density), hence the effective size d Ω = Ω 1/3 . The ratios d Ω /d ion listed in the Table suggest that the volumes and ion radii calculated for the studied metals [8] are close in magnitude.…”

“…As is seen from Fig. 3, equation (1) can be brought to canonical form by the substitution of ω = ω 0ω and k = k 0 +k (sgnαα/ω 0 ) −1/2 to giveω = 1 ±k 2 (hereω is the dimensionless frequency,k is the dimensionless wave number and sgnα is a signum function of the coefficient α. Thus we obtain the appropriate dispersion relation of quadratic form, which satisfies the Schrödinger non- linear equation [5] and is descriptive of self-organization processes in nonlinear media.…”

“…Thus it is found that (i) the plastic flow would exhibit a localization behavior from yield point to failure, (ii) each flow stage is characterized by the emergence of a specific localization pattern, (iii) the occurrence of localization patterns is explained as due to the generation of autowaves (self-excited waves), (iv) the latter waves are associated in turn with the processes of self-organization of defects. The kinematic observations were carried on with the aid of a specially developed technique related to speckle photography [1]. A typical example of autowave patterns occurring in the deforming medium is shown in Fig 1. The propagation velocity, wavelength and frequency were defined experimentally for the autowaves in question.…”