Multilevel Model for the Description of Plastic and Superplastic Deformation of Polycrystalline Materials

Superplastic forming is promising for the manufacturing of complex-shaped metal parts and components. Superplastic conditions allow one to produce unwelded parts, to reduce the number of technological operations and forming forces, and thus to reduce tool wear. Optimal processing modes can be determined using mathematical models based on constitutive equations. However, there are serious difficulties in describing even the simplest uniaxial tests with superplastic behavior because of a very complex deformation scenario, which involves several interacting physical mechanisms with changing roles and significant structure evolution of the material. A similar situation is observed in technological processes involving superplasticity. The search for better technologies requires the mathematical models of material deformation that are able to describe changes in the structure and structure-dependent physicomechanical properties. The most promising in this respect is a multilevel crystal plasticity approach based on the introduction of internal variables and an explicit description of the material structure and physical deformation mechanisms. Here we propose a multilevel model for describing the behavior of polycrystalline metals and alloys with account for key plastic and superplastic deformation mechanisms, such as intragranular dislocation slip, crystal lattice rotation, and grain structure evolution. Special attention is paid to the description of grain boundary sliding, which is the leading mechanism in superplastic deformation, and accompanying accommodation mechanisms, such as grain boundary diffusion and dynamic recrystallization. When describing grain boundary sliding, viscous-to-plastic transitions along crystallite boundaries are considered explicitly, and the submodel is attributed to a separate structural level. The model takes into account the interaction between grain boundary sliding and intragranular slip. The influx of intragranular dislocations into the boundary increases the amount of defects in it (making it nonequilibrium), increases the boundary energy, and promotes grain boundary sliding. On the other hand, grain boundary sliding reduces the number of grain boundary defects and hence the resistance to intragranular slip. The obtained numerical results agree well with experimental data, showing that the proposed multilevel model is suitable for describing various inelastic deformation modes and transitions between them.