Motion decomposition, frame-indifferent derivatives, and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling

Трусов, П. В.; Shveykin, A. I.; Yanz, A. Yu.

doi:10.1134/s1029959917040014

Cited by 31 publications

(11 citation statements)

References 16 publications

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“…Belonging to a particular phase determines the basic properties of the meso-II element, including the type of its crystal lattice. Orientation of the axes of the moving coordinate system [18][19] is considered as known for each meso-II element. This orientation changes during a deformation process (as a result of rotation for the meso-II element or as a result of the transformation the element lattice after the realized phase transition).…”

Section: The Structure Of Multi-scale Model With Phase Transformationsmentioning

confidence: 99%

“…As the model is intended to describe the processes of thermo-mechanical treatment being characterized by large displacement gradients, geometrically nonlinear kinematic and constitutive relations are used in its structure [18][19]. The rate statement of the problem is done in the current configuration and the following constitutive relations are used [20][21]:…”

Section: The Model Constitutive Relations For a Meso-ii Elementmentioning

confidence: 99%

“…where Π is the tensor of elastic properties for the meso-II element, defined by the constant components in the basis of the crystallographic coordinate system of the current phase in the initial configuration;   l v is the transposed velocity gradient for the material particles of the meso-II element in the current configuration, transmitted from the meso-I; , ρ are the densities of the meso-II element's material in the initial (unloaded) and current configurations (the density depends on the phase the element at the considered moment is in); σ is the Cauchy stress tensor of the meso-II element; ω is the spin tensor of the meso-II element (to define it, any physically based model of rotation can be used, for example, it can be the Teylor's model of turning in a fully constrained conditions [22] or the model of lattice rotation [18]). Wherein, at each moment of the process, the rotation of the rigid moving coordinate system's axes of the meso-II element, connected with the lattice of the element in its current phase, is considered.…”

Section: The Model Constitutive Relations For a Meso-ii Elementmentioning

confidence: 99%

See 2 more Smart Citations

Multi-level model describing phase transformations of polycrystalline materials under thermo-mechanical impacts

Kondratev

Трусов

Makarevich³

2019

Frattura Ed Integrità Strutturale

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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.

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Section: The Structure Of Multi-scale Model With Phase Transformationsmentioning

confidence: 99%

Section: The Model Constitutive Relations For a Meso-ii Elementmentioning

confidence: 99%

Section: The Model Constitutive Relations For a Meso-ii Elementmentioning

confidence: 99%

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Multi-level model describing phase transformations of polycrystalline materials under thermo-mechanical impacts

Kondratev

Трусов

Makarevich³

2019

Frattura Ed Integrità Strutturale

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“…The crystallite orientation distributions are obtained with the help of the two-level crystal elasto-visco-plasticity model discussed in [54]. The equations for the co-rotational spins, ω (m) , of the crystallites are taken from [77]:…”

Section: Changes In Elastic Symmetry Of Polycrystals During Inelasticmentioning

confidence: 99%

On Elastic Symmetry Identification for Polycrystalline Materials

Трусов¹,

Ostapovich²

2017

Symmetry

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Abstract:The products made by the forming of polycrystalline metals and alloys, which are in high demand in modern industries, have pronounced inhomogeneous distribution of grain orientations. The presence of specific orientation modes in such materials, i.e., crystallographic texture, is responsible for anisotropy of their physical and mechanical properties, e.g., elasticity. A type of anisotropy is usually unknown a priori, and possible ways of its determination is of considerable interest both from theoretical and practical viewpoints. In this work, emphasis is placed on the identification of elasticity classes of polycrystalline materials. By the newly introduced concept of "elasticity class" the union of congruent tensor subspaces of a special form is understood. In particular, it makes it possible to consider the so-called symmetry classification, which is widely spread in solid mechanics. The problem of identification of linear elasticity class for anisotropic material with elastic moduli given in an arbitrary orthonormal basis is formulated. To solve this problem, a general procedure based on constructing the hierarchy of approximations of elasticity tensor in different classes is formulated. This approach is then applied to analyze changes in the elastic symmetry of a representative volume element of polycrystalline copper during numerical experiments on severe plastic deformation. The microstructure evolution is described using a two-level crystal elasto-visco-plasticity model. The well-defined structures, which are indicative of the existence of essentially inhomogeneous distribution of crystallite orientations, were obtained in each experiment. However, the texture obtained in the quasi-axial upsetting experiment demonstrates the absence of significant macroscopic elastic anisotropy. Using the identification framework, it has been shown that the elasticity tensor corresponding to the resultant microstructure proves to be almost isotropic.

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“…The model was formulated in the rate form in the current configuration, which made it possible to apply the hypothesis of additive contributions of IDS and GBS to strain rate at the macroscale level. In a series of works [51][52][53][54], the choice of this approach for formulating geometrically nonlinear equations was justified. It turned out that, in the absence of GBS, the model offers the results, which agree well with the data obtained using other mesoscale models, including those with the most popular formulation of constitutive equations in terms of the unloaded configuration [28,55].…”

Section: Introductionmentioning

confidence: 99%

Statistical Crystal Plasticity Model Advanced for Grain Boundary Sliding Description

2020

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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.

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Motion decomposition, frame-indifferent derivatives, and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling

Cited by 31 publications

References 16 publications

Multi-level model describing phase transformations of polycrystalline materials under thermo-mechanical impacts

Multi-level model describing phase transformations of polycrystalline materials under thermo-mechanical impacts

On Elastic Symmetry Identification for Polycrystalline Materials

Statistical Crystal Plasticity Model Advanced for Grain Boundary Sliding Description

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