Multilevel Models of Polycrystalline Metals: Application for Cyclic Loading Description

Трусов, П. В.; Volegov, Pavel S.; Shveykin, A. I.; Gribov, Dmitry S.

doi:10.4028/www.scientific.net/ssp.243.155

Cited by 3 publications

(8 citation statements)

References 11 publications

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“…The model is focused to describe the deformation process at large displacement gradients. Therefore, for the mesolevel elements, the decomposition of the motion into quasi-rigid and deformation components is applied [26,44]. The corotational moving coordinate system with an orthonormal basis k i , i = 1, 3, linked with one of the axes and one plane of the crystal lattices, is responsible for the quasi-rigid motion; the rotation rate of this coordinate system is determined by the spin ω (the crystallite numbers are omitted).…”

Section: Structure and Basic Relations Of The Three-level Elastovisco...mentioning

confidence: 99%

“…γ (k) are calculated through the dislocation velocities and dislocation current densities at EM2. The evolution of mesolevel-1 internal variables is described by the following system of equations (for all crystallites) [26]:…”

Section: Structure and Basic Relations Of The Three-level Elastovisco...mentioning

confidence: 99%

“…Since the macro-phenomenological theories have some disadvantages mentioned above, such as the constitutive models being based on the introduction of internal variables [21,22], a multilevel approach [23][24][25][26][27][28][29][30][31] has become increasingly popular in recent decades. Because the formulation of constitutive models of this type is based on the physical laws and mechanisms characteristic of entire classes of materials, they have significant universality.…”

Section: Introductionmentioning

confidence: 99%

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Application of a Three-Level Elastoviscoplastic Model for Describing Complex Loading Processes

Trusov,

Gribov,

Kurmoyartseva

2023

Crystals

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It is known that the meso- and microstructures of metals determine the physical, mechanical and operational properties of their final products. Scientific and technological progress of recent decades has given impetus to the elaboration and use of models capable of describing the evolving structure of materials. The most promising are multilevel models that include internal variables and are based on physical theories of elastoplasticity (elastoviscoplasticity). This paper presents the structure and basic relationships of a three-level (macro-, meso-1 and meso-2 levels) elastoviscoplastic model. The developed model operates on such internal variables as dislocation densities on slip systems, barriers on split dislocations and sources of edge dislocations. The model describes the mechanisms of production, annihilation, formation of barriers and sources of dislocations. The law of hardening directly takes into account the densities of dislocations and barriers. The mechanism of inelastic deformation is the gliding of edge dislocations along slip systems. Special emphasis is placed on the influence of split dislocations (prone to forming hard Lomer–Cottrell and Hirth barriers) on the deformation of the material. The model is used to describe the behavior of an elastoviscoplastic polycrystalline aggregate with an FCC lattice. Geometric nonlinearity is taken into account by utilizing decomposition of the crystallite motion into quasi-rigid and deformation components. For this purpose, a rigid moving coordinate system for the crystal lattice is introduced. Examples of the application of the model for analyzing the simple and complex deformation mechanisms of materials with different stacking fault energies and, consequently, with different tendencies toward the decomposition of dislocations and barrier formation are given.

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Section: Structure and Basic Relations Of The Three-level Elastovisco...mentioning

confidence: 99%

Section: Structure and Basic Relations Of The Three-level Elastovisco...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of a Three-Level Elastoviscoplastic Model for Describing Complex Loading Processes

Trusov,

Gribov,

Kurmoyartseva

2023

Crystals

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“…Since the experimental research methods are expensive, this generates a need to use mathematical modeling methods for studying this problem [ 16 , 20 , 21 ]. Physically based mathematical modeling that relies on a multilevel approach with internal variables is an effective tool for solving this complicated problem [ 22 , 23 ]. Multilevel physical models involving the explicit consideration of the material structure evolution are used extensively to describe dynamic recrystallization [ 24 , 25 , 26 , 27 ].…”

Section: Introductionmentioning

confidence: 99%

“…Certain variables and parameters were introduced in these models to describe the material structure and the mechanisms governing the formation of recrystallization nuclei and the migration of grain boundaries [ 19 , 25 , 28 , 29 ]. In the context of a physical approach, three main classes of multilevel models [ 22 ] are widely met: statistical [ 27 , 30 ], self-consistent [ 26 , 31 ] and direct [ 32 , 33 ]. Direct models explicitly consider the topology of grains and, during numerical implementation they are oriented towards the use of a finite element method.…”

Section: Introductionmentioning

confidence: 99%

A Multilevel Physically Based Model of Recrystallization: Analysis of the Influence of Subgrain Coalescence at Grain Boundaries on the Formation of Recrystallization Nuclei in Metals

et al. 2023

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This paper considers the influence of subgrain coalescence at initial high-angle boundaries on the initiation and growth of recrystallization nuclei (subgrains) under thermomechanical treatment. With certain processing regimes, adjacent subgrains in polycrystalline materials can be assembled into clusters during coalescence. Subgrain clusters at high-angle boundaries are the preferred potential nuclei of recrystallization. Coalescence is one of the dynamic recovery mechanisms, a competing process to recrystallization. When intensive coalescence develops on both sides of the grain boundary, recrystallization slows down or even stops. The problem formulated is solved using a multilevel modeling apparatus with internal variables. Application of the statistical multilevel model modified to take into account the local interaction between crystallites makes it possible to explicitly describe dynamic recrystallization and recovery. The results of modeling the behavior of a copper sample are presented and the effects of temperature, deformation velocity and subgrain structure on the formation and growth of recrystallization nuclei at arbitrary and special grain boundaries during coalescence are analyzed.

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Consideration of Softening Near Free Surface in the Direct Model of Crystal Plasticity

Viatkin,

Ostanina,

Trusov

2023

BULLETIN OF PERM UNIVERSITY. Mathematics. Mechanics. Computer S

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Current industrial demands require the improvement of existing technologies and the creation of new ones that allow the production of parts and structures with advanced performance properties. Es-pecially important are the issues of design and analysis of thermomechanical treatment of metals and al-loys by intensive inelastic deformation methods. The study of manufacturing processes for miniaturized parts deserves special attention. The boundary value problems arising in this case belong to the class of physically and geometrically nonlinear problems of the mechanics of deformable solids, for the solution of which it is necessary to develop appropriate mathematical models. Most classical models are based on the macrophenomenological theory of elastoplasticity. However, in the processes under consideration, significant structural changes occur at the meso- and microscale that have a significant influence on the physical and mechanical characteristics of the processed materials and the performance characteristics of the products. These changes are not described by the mentioned theories. An effective approach to de-scribe these processes is to use multilevel models of crystal plasticity. Despite the tendency to miniaturize products, the parameters of such models are usually determined from the results of experiments on mac-rosamples. The question arises whether such parameters are valid for the analysis and modeling of real structures with typical length scales below 500 μm, where the internal and external boundaries of crystal-lites play a special role. In this study, the influence of the free surface on the mechanical properties of single crystalline and polycrystalline materials is considered. Modification of the basic direct crystal plas-ticity model of elastoviscoplasticity to account for the softening of slip systems near free boundaries due to easier exit of dislocations to the surface is proposed.

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Multilevel Models of Polycrystalline Metals: Application for Cyclic Loading Description

Cited by 3 publications

References 11 publications

Application of a Three-Level Elastoviscoplastic Model for Describing Complex Loading Processes

Application of a Three-Level Elastoviscoplastic Model for Describing Complex Loading Processes

A Multilevel Physically Based Model of Recrystallization: Analysis of the Influence of Subgrain Coalescence at Grain Boundaries on the Formation of Recrystallization Nuclei in Metals

Consideration of Softening Near Free Surface in the Direct Model of Crystal Plasticity

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