Two-scale models of polycrystals: Analysis of complex loading

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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“…The dive is a short reduction of stresses with the following restoration. This effect is also found in the numerical simulations [62].…”

Section: Figsupporting

confidence: 81%

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

2015

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“…Here ρ is a material density, c v is a heat capacity at the constant volume, β is a coefficient of the heat output; 9 is the additivity hypothesis of the critical shear rate stress of k-th slip system. Here is the part of the critical shear rate stress describing the interaction of the mobile dislocations with the forest dislocations [12],…”

Section: High Technology: Research and Applicationsmentioning

confidence: 99%

Crystal Plasticity Modeling of Duplex Steels at High Temperatures

Трусов

Kondratev

2014

AMR

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The paper considers physical approach to the description of inelastic deformation of two-phase polycrystalline materials – duplex steels. Such approach is based on the introduction the key mechanisms of inelastic deformation in explicit way. The main mechanism of plastic deformation is slipping of edge dislocations. The structure of duplex steel consists of austenite and ferrite phases. At high temperatures ferrite reveals dynamic recovery (DRV) and austenite ability to undergo dynamic recrystallization (DRX). The way to describe DRV and DRX processes within the multilevel approach of elastoviscoplastic modeling is proposed. Obtained results of numerical experiments of uniaxial compression deformation at different temperatures have good qualitative agreement with experimental data.

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“…The evolution of the vector-momentum associated with the couple stress tensor and determines from the analysis of the incompatibility of dislocation motion on the boundary of the crystallites by equation (4 5 ). Based on the input of the couple stresses may be used for description of fragmentation [7].…”

Section: Two-level Constitutive Model For Inelastic Deformations Of Pmentioning

confidence: 99%

Polycrystals multilevel models using crystal plasticity: consistency of constitutive equations at different scale levels

Shveykin

Трусов

Volegov

2014

J. Phys.: Conf. Ser.

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Abstract. Two-level models of different polycrystalline metal's inelastic deformation based on crystal plasticity and describing viscoplastic intragranular dislocations slip, lattice rotation with an explicit consider of dislocation slip incompatibility in neighboring grains, and fragmentation of crystallites are developed. The homogenization of constitutive equations at various scale levels is used, which allows to connect the same type of characteristics of different scale levels and leads to an unambiguous description of geometric nonlinearity on the macro level by specifying the corotational derivative of Cauchy stress tensor. An algorithm for solving boundary value problems in FEM package Abaqus with using proposed models to describe the behavior of the material is developed, corresponding computational modules are created. Numerical investigation of different loading of samples from various polycrystalline metals with a description of the evolving internal structure is done. IntroductionNumerous theoretical and experimental studies show that the performance of the internal material structure determines the behavior of the material at the macro level and its performance characteristics. During intensive plastic deformation the internal structure of the material is significantly restructured: the grain and dislocation structures are changing, crystallites lattice is rotated; it is widely used to produce materials with unique properties: submicrocrystalline, nanocrystalline, textured materials and materials, which are capable of superplastic deformation.At the time, the construction of models capable of describing the change of the internal structure of polycrystalline materials, a growing acceptance of the approach based on an explicit introduction to the structure of the constitutive relations parameters reflecting the state and evolution of meso-and microstructure evolution and the kinetic equations for these parameters (so-called internal variables) [1]. In particular, recent decades, a very wide development of crystal plasticity based models, which built in the framework of this approach and explicitly describing the material structure and the mechanisms of inelastic deformation at the crystallite level, is observed; this models allows a natural way to describe the structure evolution at deep plastic strain.Based on the crystal plasticity models can be divided into three classes [2,3]: statistics, selfconsistent and direct. Models of the last two classes require inaccessible currently computing resources, so for modeling of real processes statistical constitutive model are more popular.The paper briefly discusses the general structure of the two-level models of polycrystalline metals inelastic deformation developed by the authors, explains how to homogenize the constitutive equations

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Two-scale models of polycrystals: Analysis of complex loading

Cited by 10 publications

References 7 publications

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

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

Crystal Plasticity Modeling of Duplex Steels at High Temperatures

Polycrystals multilevel models using crystal plasticity: consistency of constitutive equations at different scale levels

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