Current Instability of Hardening of a Deformable Medium Element as a Reason of the Neck Propagation

The effect of the current instability of hardening of a deformable medium element on the strain localization at different scale levels has been studied. The current instability term has been taken from the characteristic of the current instability of the electrical conductivity of semiconductors in strong electric fields with a specific I‒V curve [1]. A similar shape of the σ‒ε curve of hardening of a deformable medium element has been considered to be the cause of the strain localization. The strain localization phenomena caused by the current instability of different types have been discussed and modeled. It is shown that the plastic flow scenario under the current instability at the level of a microelement of a medium can manifest itself at the macroscale plastic flow level in the form of localizations of various types. The simulation within a two-level finite element model proposed previously in [2] has been carried out. The cases of a stable neck or neck propagation at the macrolevel under the uniaxial tension of a sample have been observed, depending on the shape of the hardening curves of the unit volume of a deformed sample similar the current instability curves.