Two-scale models of polycrystals: Macroscale motion decomposition

Трусов, П. В.; Volegov, Pavel S.; Yanz, A. Yu.

doi:10.1134/s1029959914020039

Cited by 8 publications

(22 citation statements)

References 6 publications

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“…6b) with the velocity of 30 о per 1% of cumulative strain. It is obvious that the process image made in LF depends on the rigid motion applied which confirms the results previously obtained by theoretical researches [11] conducted by the authors of this article.…”

Section: Numerical Results and Analyses Under Complex Loadingssupporting

confidence: 93%

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Two‐level models of polycrystalline elastoviscoplasticity: Complex loading under large deformations

2015

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Key words Polycrystal, multilevel models, geometrical nonlinear models, matching of constitutive relations, quasi-rigid motion, loading process image, complex loading, material memory, vector property lagging. This paper considers the application of multilevel mathematical models describing processes of severe inelastic deformations of monocrystals and polycrystals that requires the usage of geometrically and physically nonlinear constitutive relations. In order to describe the behavior of a representative macrovolume, a two-level model based on the physical theory of elastoviscoplasticity is used. The motion of rigid corotating frame describing quasi-rigid motion is determined by a macrolevel motion decomposition hypothesis. The following macrolevel hypotheses are considered: (1) the representative volume total motion is a deformational one; (2) the motion is decomposed into a deformational and a rigid ones with a spin being determined by an averaging of the mesolevel spins; (3) quasi-solid and deformational motions are determined by corresponding skew-symmetrical and symmetrical parts of the macrolevel displacement velocity gradient. In order to describe experimentally known effects observed under complex loading the questions related to the application of monoand poly-crystals inelastic deformation multilevel models based on crystal plasticity theories are discussed. In particular, a polycrystalline metals inelastic deformation of the two-level model is used to consider the scalar and vector properties lagging effects arising during deformation path breakage within the Ilyushin's space: the isotropy postulate fulfillment is discussed and a possible explanation for the effects based on physical consideration is provided.

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Section: Numerical Results and Analyses Under Complex Loadingssupporting

confidence: 93%

“…However, when we create a loading process image by method PI3, we take the hypothesis describing the quasi-rigid motion on the macrolevel through tensor of W of continuum spin, which, as demonstrated in [11], strictly limits the mesolevel spin, i.e. the selection of crystallite rotation model.…”

Section: Numerical Results and Analyses Under Complex Loadingsmentioning

confidence: 99%

Two‐level models of polycrystalline elastoviscoplasticity: Complex loading under large deformations

2015

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“…In the overwhelming majority of papers, quasi-rigid motion (more precisely, its rotational component) is assumed to be defined by vorticity tensor W (as a rule, no mention is made of motion decomposition, and quasi-rigid motion is chosen implicitly by using the Jaumann derivative). However, as was shown elsewhere [5], the assumption of this hypothesis in two-scale models makes it impossible to independently choose a lattice rotation model for describing real physical interactions at lower scales.…”

Section: Introductionmentioning

confidence: 98%

“….urther consideration is performed for first-order materials [6]; consequently, the stress-strain state and quasirigid motion characteristics of the representative macrovolume are assumed to be homogeneous. The following hypotheses of motion decomposition for the representative macrovolume are considered [5]:…”

Section: Introductionmentioning

confidence: 99%

“…Any decomposition method implies the introduction of a co-rotational derivative, which yields both different values of the stress state measure (Cauchy stress tensor) and different physical meaning of obtained nonholonomic strain state measures, as was shown in [5]. Paper [5] provides full mathematical problem statements in terms of different ways of motion decomposition on the macroscale and the procedure of matching different-scale constitutive equations.…”

Section: Introductionmentioning

confidence: 99%

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Two-scale models of polycrystals: Independence of the loading process image of a representative macrovolume

2014

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The paper considers variants of constructing the process image introduced by A.A. Ilyushin for loading of a representative macrovolume of polycrystalline metal with high displacement gradients. Analysis is performed to clarify whether the loading process image in the variants under study depends on the rigid rotation imposed on the entire representative volume (or on the choice of a reference frame). It is found that with high displacement gradients, the loading process image is rather difficult to construct. Possible ways of decomposing the motion into quasi-rigid and strain-induced motions are investigated. The behavior of the representative macrovolume is described using a two-scale model based on the physical theory of elasto-viscoplasticity. The motion of rigid coordinate systems descriptive of quasi-rigid motion is defined by a specific hypothesis of motion decomposition on the macroscale. The hypotheses under consideration are the following: (i) the whole motion of the representative volume is strain-induced motion; (ii) the motion is decomposed into strain-induced motion and quasi-rigid motion whose spin is determined by averaging mesoscale spins calculated from a certain general lattice rotation model; and (iii) the quasi-rigid and strain-induced motions are defined respectively by the antisymmetric and symmetric parts of the macroscale displacement velocity gradient. It is shown that with the first hypothesis, the loading process image depends on the rigid rotation imposed on the representative volume as a whole; with the other two hypotheses, the process image does not depend on the choice of the reference frame. At the same time, the third hypothesis makes it impossible to determine the lattice rotations independently of macroscale kinematic relations which, in fact, are determined by micro-and mesoscale physical interactions.

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To the description of martensitic transformations in polycrystalline alloys: Multilevel models, transformation criteria

Трусов

Makarevich

Podsedertsev

et al. 2020

28th Russian Conference on Mathematical Modelling in Natural Sciences

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Two-scale models of polycrystals: Macroscale motion decomposition

Cited by 8 publications

References 6 publications

Two‐level models of polycrystalline elastoviscoplasticity: Complex loading under large deformations

Two‐level models of polycrystalline elastoviscoplasticity: Complex loading under large deformations

Two-scale models of polycrystals: Independence of the loading process image of a representative macrovolume

To the description of martensitic transformations in polycrystalline alloys: Multilevel models, transformation criteria

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