On the Properties of a Deformable Medium Element as a Factor of the Superplasticity of Metallic Materials

A theoretical study of the phenomenon of the superplasticity of metallic materials is carried out. Numerical calculations are performed on the basis of a two-level finite-element model of an elastic–plastic medium. The plastic properties of the deformable-medium element, at which deformation by uniaxial tension in the superplasticity mode occurs, are found. It is shown that depending on the shape of the stress–strain curve (σ–ε) of the medium element, various types of plastic-flow localizations are observed at the macroscale level. The nonmonotonic dependence σ–ε of a deformable-medium element with a single maximum is determined as the condition for the appearance of a stable necking. In the case when the dependence σ–ε, which is characterized by the hardening of the elementary volumes, has two maxima, a propagating (running) neck is observed, then a second (counter) neck appears, while further tension leads to the appearance of a third stable neck in which fracture occurs. In the case of a more complex oscillating shape of the σ–ε curve, multiple propagating necks are observed. The movement of multiple necks propagating along the sample leads, ultimately, to a uniform pattern of deformation and makes it possible to achieve the strain values observed in the superplasticity mode.