The problem of constructing the multilevel physical model of inelastic deformation in steels allowing to take into consideration diffusionless solid-state phase (martensitic) transitions is considered. The model structure includes three scale levels with the closed system of equations offered for them. Explicit internal variables reflecting the evolution of the material structure (both the defect structure and the grain one) are introduced at the lower scale levels of the model. The distinctive feature of the developed model is consideration of the lower scale level in such a way that a homogeneous element of this level completely turns into a new phase at a high speed (relative to the kinematic quasi-static loading), that is close to the speed of sound in the crystal medium. Based on the principles of classical thermodynamics the phase transformation criterion is written. According to this criterion, the choice of a transformational system under the martensitic transition is made. The algorithm of the model is developed and its realization features are described in connection with the high-rate restructuring of the face-centered cubic lattice to the body-centered tetragonal one. The result of this restructuring is a severe change in the physic-mechanical properties of the material.
As both self-consistent and direct multilevel models (suggesting solution of boundary value problems at the meso-level) are extremely resource intensive, nowadays statistical crystal plasticity models are supposed to be the most promising ones for modeling technological processes of thermo-mechanical treatment of materials. The statement of a boundary value problem at the current configuration in the rate form is preferable, as it is convenient for applying numerical methods. In this case, step-by-step solution with redefining the computational domain configuration (including contacting surfaces) is possible. The two-level (macro- and meso-level) statistical constitutive model for describing deformation of polycrystalline metals and alloys, being formulated in terms of the actual configuration in the rate form, is proposed. The flexible coordinate system at the meso-level is connected with the symmetry elements of the crystallites, which determines appropriate choice of the corotational derivative in the constitutive relation. The approximate model for describing grain structure refinement on the basis of considering the amount of accumulated inelastic deformation as an integral characteristic of the defect structure state is included into the model. The results of the test calculations for describing loading processes, being relevant for equal-channel angular pressing, are given.
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