Methods of Accounting for Temperature and Strain Rate Variation in Multilevel Constitutive Models of Metal Deformation (Analytical Review)

Technological metal forming processes involving hot and superplastic deformation are sensitive to temperature and strain rate. This is because inelasticity mechanisms operate in different ways under different conditions, leading to the formation of different structures and therefore different effective physical and mechanical properties of the material. Optimal temperature and strain rate conditions for the forming process which provide improved performance of the resulting products with acceptable energy consumption (or, conversely, minimum energy consumption with acceptable performance characteristics) can be most effectively determined by mathematical modeling. The key elements of the latter are constitutive models for describing the behavior of the material (physical equations), which account for the influence of temperature and strain rate on various mechanisms of inelastic deformation. Such constitutive models can be most effectively developed using a multilevel approach based on the introduction of internal variables, crystal plasticity, and an explicit description of the material structure and physical deformation mechanisms. There are many works that propose multilevel mathematical models of metals that somehow explicitly account for the temperature and strain rate effects on inelastic deformation. Based on physical considerations, this analytical review defines the most promising approach to constructing multilevel constitutive models with comprehensive consideration of the temperature and strain rate effects.