Abstract
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.
Highlights
A dvanced high-strength steels have a wide range of applications in industry and technology, which is constantly increasing due to the excellent combination of their plastic and durability properties [1,2]
Constitutive and kinematic equations describing the irreversible deformation at the meso-level due to the slip of dislocations, phase transitions, the evolution equations for critical shear stresses, description of rotation for the crystallites, the influence of the temperature changing and the attached stresses on the evolution of the defect structure are included into consideration
The multilevel crystal plasticity model for describing inelastic deformation of polycrystalline materials taking into account the evolving internal material structure is formulated within the paper
Summary
A dvanced high-strength steels have a wide range of applications in industry and technology, which is constantly increasing due to the excellent combination of their plastic and durability properties [1,2]. From the point of mathematical modeling and solid mechanics a phase is understood as a certain sub-region inside a material which behavior under deformation is described by the constitutive relations of the fixed type with a specified (determined from the solution of some auxiliary subtasks) set of properties being defined by the parameters and the current value of internal variables.
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