Microstructural constitutive model for polycrystal viscoplasticity in cold and warm regimes based on continuum dislocation dynamics

Viscoplastic flow of polycrystalline metallic materials is the result of motion and interaction of dislocations, line defects of the crystalline structure. In the microstructural/physics-based constitutive model presented in this paper, the main underlying microstructural processes influencing viscoplastic deformation and mechanical properties of metals in cold and warm regimes are statistically described by the introduced sets of postulates/axioms for continuum dislocation dynamics (CDD). Three microstructural (internal) state variables (MSVs) are used for statistical quantifications of different types/species of dislocations by the notion of dislocation density. Considering the mobility property of dislocations, they are categorized to mobile and (relatively) immobile dislocations. Mobile dislocations carry the plastic strain (rate), while immobile dislocations contribute to plastic hardening. Moreover, with respect to their arrangement, dislocations are classified to cell and wall dislocations. Cell dislocations are those that exist inside cells/subgrains, and wall dislocations are packed in (and consequently formed) the subgrain walls/boundaries. Therefore, the MSVs incorporated in this model are cell mobile, cell immobile and wall immobile dislocation densities. The evolution of these internal variables is calculated by means of adequate equations that characterize the dislocation processes dominating material behavior during cold and warm monotonic viscoplastic deformation. The constitutive equations are then numerically integrated; and the constitutive parameters are determined/fitted for a widely used ferritic-pearlitic steel (20MnCr5).