Multilevel models of materials are the instrument allowing one to take into consideration micro- and nanomechanics in the description of technological processes at a macroscale level. The advantage of such models is an explicit description of physical mechanisms, evolution of material structure, and physical and mechanical properties in inelastic deformation. This allows one to apply models to improve the existing technologies of mechanical treatment (including the ones for submicrocrystalline and nanocrystalline materials) and develop some new ones. Corresponding boundary-value problems should be considered for the general case of large displacement gradients, the main problem is the formulation of the kinematic and constitutive relations. A widely recognized approach, based on the use of objective stress corotational rate, is briefly analyzed in the paper. A multiplicative representation of the deformation gradient with explicitly separated motion of the moving coordinate system at the mesolevel is proposed. The linear elastic law is satisfied in the moving coordinate system (just as within formulations with corotational derivatives). The moving coordinate system is associated with the elements of crystallite symmetry (crystallographic direction and plane). The constitutive elastoviscoplastic relations in the finite and rate forms, equivalent to each other are formulated in terms of the unloaded configuration. There is no hysteresis of stresses and no energy dissipation along closed elastic cycles. The approximate relations in the current configuration are represented in the rate form. They can be used in the description of the technological treatment of metals.

Grain boundary sliding is an important deformation mechanism, and therefore its description is essential for modeling different technological processes of thermomechanical treatment, in particular the superplasticity forming of metallic materials. For this purpose, we have developed a three-level statistical crystal plasticity constitutive model of polycrystalline metals and alloys, which takes into account intragranular dislocation sliding, crystallite lattice rotation and grain boundary sliding. A key advantage of our model over the classical Taylor-type models is that it also includes a consideration of grain boundaries and possible changes in their mutual arrangement. The constitutive relations are defined in rate form and in current configuration, which makes it possible to use additive contributions of intragranular sliding and grain boundary sliding to the strain rate at the macrolevel. In describing grain boundary sliding, displacements along the grain boundaries are considered explicitly, and changes in the neighboring grains are taken into account. In addition, the transition from displacements to deformation (shear) characteristics is done for the macrolevel representative volume via averaging, and the grain boundary sliding submodel is attributed to a separate structural level. We have also analyzed the interaction between grain boundary sliding and intragranular inelastic deformation. The influx of intragranular dislocations into the boundary increases the number of defects in it and the boundary energy, and promotes grain boundary sliding. The constitutive equation for grain boundary sliding describes boundary smoothing caused by diffusion effects. The results of the numerical experiments are in good agreement with the known experimental data. The numerical simulation demonstrates that analysis of grain boundary sliding has a significant impact on the results, and the multilevel constitutive model proposed in this study can be used to describe different inelastic deformation regimes, including superplasticity and transitions between conventional plasticity and superplasticity.

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...

Multilevel models of materials give an explicit description of the physical mechanisms, evolution of material structure, and physical and mechanical properties in inelastic deformation. This allows one to apply such models to improve the existing technologies of mechanical treatment (including the ones for submicrocrystalline and nanocrystalline materials) and develop some new ones. A key point in multilevel modeling of polycrystalline metals and alloys is the formulation of kinematic and constitutive relations at the mesolevel (the level of individual crystallites), which would apply to large displacement gradients peculiar to most processes of thermomechanical treatment of metals and alloys. Various formulations of the constitutive mesolevel models used in multilevel models of polycrystalline metals and alloys are considered. These are the relations in the unloaded configuration in the finite form, which are based on the motion decomposition with an explicit separation of the motion of the moving coordinate system, and the relations written in the rate form in the current configuration. The relationships used in these formulations to describe the rotations of the crystallite lattices are analyzed and compared. The analysis reveals the equivalence or closeness (in the sense of the response to be estimated) of the spins under consideration (with the exception of the logarithmic spin). The results of numerical calculations carried out for a polycrystal under arbitrarily chosen kinematic impacts lend support to the analytical conclusions.

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.