Multilevel models of crystal plasticity and viscoplasticity in multiphase polycrystalline materials

The paper considers the problem of modelling the processes of inelastic deformation of polycrystalline materials with regard to microstructure, physical mechanisms and their carriers. At present physical approach based on an explicit introduction of variables (responsible for these mechanisms) into the mathematical model is widely spread. It is necessary to consider deeper scale levels than a macroscopic one for description of such models. That is why this type of model can be considered as a multilevel model. Classification features in multilevel models based on the physical theory of plasticity may be: hypothesis transition between scale levels, the number of the scale levels involved in the consideration and physical model lying in the low level. The fact that physical laws of meso- and microlevel are quite universal, this class of models can be used to analyze a wide range of materials and processes, and their scope is constantly increasing. To be more exact, these are multiphase materials, both widely used and newly developed and implemented in production, for example, steel and titanium alloys. Analysis of meso-and microstructure shows the dependence of the response of the material at the macro level on its current state. The peculiarity of such materials is a high degree of heterogeneity of stress and strain fields arising due to the physical heterogeneity of the individual phases of polycrystal. The present paper provides a review of multilevel models of plasticity theory based on the explicit consideration of carriers and mechanisms of inelastic deformation. The review contains different aspects of application of various modifications of multilevel physical models for description of behavior of multiphase materials that are widely used in industry. Special attention is paid to critical analysis of models.