Localization of plastic strain and isothermal superplasticity

Plastic strain localization in the course of the transition from a strain-hardening state to strain softening at the stage preceding fracture of the material is investigated. The solutions describing the structure of strain-localization bands are obtained in two models-elastoviscoplastic and nonlocal elastoplastic. This approach is shown to provide an adequate mathematical description of strain localization. Detailed analysis of the solution allows isothermal superplasticity to be accounted for. As the small parameters of the problem, related to nonlocality or strain rate, approach zero, localization bands give way to lines of discontinuity, which differs qualitatively from that appearing in phase transitions or ultrasonic shock waves.