Three-Level Dislocation-Based Model for Describing the Deformation of Polycrystals: Structure, Implementation Algorithm, Examples for Studying Nonproportional Cyclic Loading

A three-level constitutive model is proposed for describing the deformation of polycrystalline materials, which is based on crystal elasto-viscoplasticity and the introduction of internal variables. The structure, mathematical formulation, and implementation algorithm of the model are discussed. The...

Full description

Saved in:
Bibliographic Details
Published inPhysical mesomechanics Vol. 25; no. 6; pp. 557 - 567
Main Authors Gribov, D. S., Trusov, P. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2022
Springer Nature B.V
Subjects
Online AccessGet full text
ISSN1029-9599
1990-5424
DOI10.1134/S102995992206008X

Cover

Abstract A three-level constitutive model is proposed for describing the deformation of polycrystalline materials, which is based on crystal elasto-viscoplasticity and the introduction of internal variables. The structure, mathematical formulation, and implementation algorithm of the model are discussed. The element of the upper structural-scale level is the representative macrovolume. The elements of mesolevels 1 and 2, which are identical in scale, are crystallites (grains, subgrains, fragments, depending on the required element size). The description at mesolevel 1 is performed in terms of thermomechanical variables (stresses, strains, strain rates). The behavior of meso-2 elements is described in terms of dislocation densities and velocities. Particular attention is paid to the formation of barriers on split dislocations. As an example, the model is applied to study proportional and nonproportional cyclic loading of samples with substantially different stacking fault energies. It is shown that barriers are more readily formed in materials with low stacking fault energy, leading to their additional cyclic hardening under nonproportional loading.
AbstractList A three-level constitutive model is proposed for describing the deformation of polycrystalline materials, which is based on crystal elasto-viscoplasticity and the introduction of internal variables. The structure, mathematical formulation, and implementation algorithm of the model are discussed. The element of the upper structural-scale level is the representative macrovolume. The elements of mesolevels 1 and 2, which are identical in scale, are crystallites (grains, subgrains, fragments, depending on the required element size). The description at mesolevel 1 is performed in terms of thermomechanical variables (stresses, strains, strain rates). The behavior of meso-2 elements is described in terms of dislocation densities and velocities. Particular attention is paid to the formation of barriers on split dislocations. As an example, the model is applied to study proportional and nonproportional cyclic loading of samples with substantially different stacking fault energies. It is shown that barriers are more readily formed in materials with low stacking fault energy, leading to their additional cyclic hardening under nonproportional loading.
Author Trusov, P. V.
Gribov, D. S.
Author_xml – sequence: 1
  givenname: D. S.
  surname: Gribov
  fullname: Gribov, D. S.
  organization: Perm National Research Polytechnic University
– sequence: 2
  givenname: P. V.
  surname: Trusov
  fullname: Trusov, P. V.
  email: tpv@matmod.pstu.ac.ru, tpv@pstu.ru
  organization: Perm National Research Polytechnic University
BookMark eNp9Uc1O3DAQtioqQYEH4GapV0Jtx_lxb3SBgrS0lZZK3CKvM941cuKt7SDyULwjDqmE1Kr1xZ75fuaT5wPa610PCJ1QckZpzj-tKGFCFEIwRkpC6vt36IAKQbKCM76X3gnOJnwfHYfwQNLJmeBEHKDnu60HyJbwCBZfmGCdktG4PvsiA7T41rWpr53HFxCUN2vTb3DcQipTs3ulYqfxD2dH5ccQpQ2f8Sr6QcXBwym-6XYWOujjTD23G-dN3Han-PJJTlh4dV_FoR0n72-u33m3c36iS4sXo7JG4aWTbYKP0HudJsDx7_sQ_by6vFtcZ8vvX28W58tMMV7GrNRtqYuyhrplRMt1XVEKrK4r4DlpK8oTQHOSy7LSwBlRbS4UrdZUUCqYzvND9HH2TVl-DRBi8-AGn_KEhlW8rouiEEVi0ZmlvAvBg2523nTSjw0lzbSY5q_FJE31h0aZ-W-il8b-V8lmZUhT-g34t0z_Fr0AwB-l3w
CitedBy_id crossref_primary_10_3390_ma16196459
crossref_primary_10_3390_cryst13121682
crossref_primary_10_1134_S1029959924040027
Cites_doi 10.1016/j.mechrescom.2015.06.00
10.1016/J.PMATSCI.2010.12.001
10.1080/14786445108561065
10.1134/S1029959919040052
10.1108/eb023742
10.1016/0029-5493(89)90112-x
10.3390/ma15030760
10.1016/S1566-1369(03)80022-5
10.1016/0956-7151(93)90325-M
10.1016/j.ijplas.2010.02.008
10.1063/1.1711937
10.1016/0022-5096(71)90010-X
10.1016/0025-5416(86)90281-8
10.1557/jmr.2018.333
10.1080/14786444108561385
10.1134/S1029959917040026
10.1016/0001-6160(85)90154-3
10.1016/j.ijplas.2005.02.004
10.1016/S0022-5096(01)00134-X
10.1016/j.ijplas.2016.12.004
10.1088/0959-5309/52/1/303
10.1016/j.jmatprotec.2019.04.029
10.1007/978-94-009-3439-9_1
10.1007/978-90-481-2687-3_4
10.1016/j.matchemphys.2022.125997
10.1115/1.2897188
ContentType Journal Article
Copyright Pleiades Publishing, Ltd. 2022
Pleiades Publishing, Ltd. 2022.
Copyright_xml – notice: Pleiades Publishing, Ltd. 2022
– notice: Pleiades Publishing, Ltd. 2022.
DBID AAYXX
CITATION
DOI 10.1134/S102995992206008X
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList

DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Physics
EISSN 1990-5424
EndPage 567
ExternalDocumentID 10_1134_S102995992206008X
GroupedDBID --K
-EM
06D
0R~
123
1B1
29~
30V
4.4
5VS
71M
96X
AAAVM
AACDK
AAEDT
AAHNG
AAIAL
AAJBT
AAJKR
AALRI
AANZL
AAQFI
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAXUO
AAYIU
AAYQN
AAYTO
AAZMS
ABAKF
ABDZT
ABECU
ABFTV
ABJNI
ABJOX
ABKCH
ABMQK
ABQBU
ABTEG
ABTHY
ABTKH
ABTMW
ABWVN
ABXPI
ACAOD
ACCUX
ACDTI
ACGFS
ACHSB
ACIWK
ACKNC
ACMLO
ACOKC
ACPIV
ACREN
ACRPL
ACZOJ
ADHHG
ADHIR
ADINQ
ADKNI
ADKPE
ADMUD
ADNMO
ADRFC
ADURQ
ADYFF
ADYOE
ADZKW
AEBTG
AEFQL
AEGNC
AEJHL
AEJRE
AEKER
AEMSY
AENEX
AEOHA
AEPYU
AETCA
AEVLU
AEXYK
AFBBN
AFLOW
AFQWF
AFWTZ
AFYQB
AFZKB
AGAYW
AGDGC
AGJBK
AGMZJ
AGQMX
AGRTI
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHSBF
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AITUG
AJBLW
AJRNO
AKLTO
ALFXC
ALMA_UNASSIGNED_HOLDINGS
AMKLP
AMTXH
AMXSW
AMYLF
AMYQR
ANMIH
ASPBG
AUKKA
AVWKF
AXYYD
BGNMA
CS3
DNIVK
DPUIP
DU5
EBLON
EBS
EIOEI
EJD
EO8
EO9
EP2
EP3
ESBYG
FDB
FEDTE
FERAY
FIGPU
FINBP
FNLPD
FNPLU
FRRFC
FSGXE
FYJPI
GGCAI
GGRSB
GJIRD
GQ7
HMJXF
HRMNR
HVGLF
HZ~
I0C
IHE
IKXTQ
IWAJR
J-C
JBSCW
JZLTJ
KOV
LLZTM
M41
M4Y
N9A
NPVJJ
NQ-
NQJWS
NU0
O9-
O9J
OZT
P2P
PT4
RIG
RLLFE
ROL
RPZ
RSV
SDG
SHX
SJYHP
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
TSG
UG4
UOJIU
UTJUX
UZXMN
VFIZW
W48
ZMTXR
AAYXX
ABDBE
ABFSG
ABRTQ
ACSTC
AEZWR
AFDZB
AFHIU
AFOEB
AFOHR
AHPBZ
AHWEU
AIXLP
ATHPR
CITATION
VCL
VIT
~HD
ID FETCH-LOGICAL-c246t-6fd6f568e8d20fab8711e2887e430d714e8d1303a67fe420cd39c17b191192f33
IEDL.DBID AGYKE
ISSN 1029-9599
IngestDate Thu Sep 25 00:51:01 EDT 2025
Wed Oct 01 02:09:14 EDT 2025
Thu Apr 24 23:06:24 EDT 2025
Fri Feb 21 02:43:55 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 6
Keywords split dislocations
dislocation barriers
multilevel model
hardening
nonproportional cyclic loading
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c246t-6fd6f568e8d20fab8711e2887e430d714e8d1303a67fe420cd39c17b191192f33
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 2748855595
PQPubID 2044192
PageCount 11
ParticipantIDs proquest_journals_2748855595
crossref_primary_10_1134_S102995992206008X
crossref_citationtrail_10_1134_S102995992206008X
springer_journals_10_1134_S102995992206008X
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2022-12-01
PublicationDateYYYYMMDD 2022-12-01
PublicationDate_xml – month: 12
  year: 2022
  text: 2022-12-01
  day: 01
PublicationDecade 2020
PublicationPlace Moscow
PublicationPlace_xml – name: Moscow
– name: Heidelberg
PublicationTitle Physical mesomechanics
PublicationTitleAbbrev Phys Mesomech
PublicationYear 2022
Publisher Pleiades Publishing
Springer Nature B.V
Publisher_xml – name: Pleiades Publishing
– name: Springer Nature B.V
References Malinin, N.N., Applied Theory of Plasticity and Creep, Moscow: Mashinostroenie, 1968.
BishopJ.F.HillR.Philos. Mag. Ser. 719514241442710.1080/14786445108561065
BeyerleinI.KnezevicM.J. Mater. Res.201833371137382018JMatR..33.3711B10.1557/jmr.2018.333
BenallalA.Le GalloP.MarquisD.Nucl. Eng. Design198911434535310.1016/0029-5493(89)90112-x
Orlov, A.N., Introduction to the Theory of Defects in Crystals, Moscow: Vyssh. Shkola, 1983.
OrowanE.Proc. Phys. Soc.1940521926194810.1088/0959-5309/52/1/303
Rogovoy, A.A., Formalized Approach to the Construction of Solid Mechanics Models. Part 1. Basic Equations of Continuum Mechanics, Moscow: Institute of Computer Science, 2021.
VasinR.A.Itogi Nauk. Tekhn. Mekh. Deform. Tv. Tela. VINITI199021375
Maugin, G.A., Mechanics of Electromagnetic Solids, Norwell: Kluwer Academic Publishers, 2003.
Horstemeyer, M.F., Multiscale Modeling: A Review, in Practical Aspects of Computational Chemistry, Leszczynski, J. and Shukla, M.K., Eds., Heidelberg: Springer, 2009, pp. 87–135. https://doi.org/10.1007/978-90-481-2687-3_4
TaylorG.I.J. Inst. Met.193862307324
ColemanB.D.GurtinM.E.J. Chem. Phys.1967475976131967JChPh..47..597C10.1063/1.1711937
FranciosiP.Acta Metall.1985331601161210.1016/0001-6160(85)90154-3
RiceJ.R.J. Mech. Phys. Solids1971194334551971JMPSo..19..433R10.1016/0022-5096(71)90010-X
McDowellD.L.Int. J. Plasticity2010261280130910.1016/j.ijplas.2010.02.008
Physical Mesomechanics of Heterogeneous Media and Computer-Aided Design of Materials, Panin, V.E., Ed., Cambridge: Cambridge Interscience Publishing, 1998.
LiangQ.WengS.FuT.HuS.PengX.Mater. Chem. Phys.202228212599710.1016/j.matchemphys.2022.125997
ArsenlisA.ParksD.M.J. Mech. Phys. Solids200250197920092002JMPSo..50.1979A10.1016/S0022-5096(01)00134-X
Trusov, P.V. and Shveikin, A.I., Multilevel Models of Single- and Polycrystalline Materials: Theory, Algorithms, Application Examples, Novosibirsk: Izd-vo SO RAN, 2019.
Trusov, P.V. and Shveikin, A.I., Theory of Plasticity, Perm: Izd-vo PNRPU, 2011.
MauginG.A.Mech. Res. Commun.201569798610.1016/j.mechrescom.2015.06.00
AubinV.QuaegebeurP.DegallaixS.Eur. Struct. Integr. Soc.20033140142210.1016/S1566-1369(03)80022-5
BishtA.KumarL.SubburajJ.JagadeeshG.SuwasS.J. Mater. Process. Technol.201927156858310.1016/j.jmatprotec.2019.04.029
LiP.LiS.X.WangZ.G.ZhangZ.F.Progr. Mater. Sci.20115632837710.1016/J.PMATSCI.2010.12.001
Krivtsov, A.M., Deformation and Fracture of Solids with Microstructure, Moscow: FIZMATLIT, 2007.
ChoJ.MolinariJ.-F.AnciauxG.Int. J. Plasticity201790667510.1016/j.ijplas.2016.12.004
Ilyushin, A.A., Plasticity: Fundamentals of General Mathematical Theory, Moscow: AN SSSR, 1963.
XiaZ.EllyinF.J. Appl. Mech.1991583173251991JAM....58..317X10.1115/1.2897188
RomanovaV.A.BalokhonovR.R.BatukhtinaE.E.EmelyanovaE.S.SergeevM.V.Phys. Mesomech.20192229630610.1134/S1029959919040052
BenallalA.MarquisD.Eng. Comput.1988524124710.1108/eb023742
Roters, F., Advanced Material Models for the Crystal Plasticity Finite Element Method: Development of a General CPFEM Framework, Aachen: RWTH Aachen, 2011.
Pozdeev, A.A., Trusov, P.V., and Nyashin, Yu.I., Large Elastoplastic Deformations: Theory, Algorithms, Applications, Moscow: Nauka, 1986.
AshikhminV.N.VolegovP.S.TrusovP.V.PNRPU Bull. Mat. Modelir. Sistem Protsess.2006141126
Kachanov, L.M., Foundations of the Theory of Plasticity, North-Holland Pub. Co., Amsterdarm, 1971.
Trusov, P.V. and Gribov, D.S., The Three-Level Elastoviscoplastic Model and Its Application to Describing Complex Cyclic Loading of Materials with Different Stacking Fault Energies, Materials, 2022, vol. 15(3). https://doi.org/10.3390/ma15030760
LairdC.CharsleyP.MughrabiH.Mater. Sci. Eng.19868143345010.1016/0025-5416(86)90281-8
Kocks, U.F., Constitutive Behavior Based on Crystal Plasticity, in Unified Constitutive Equations for Creep and Plasticity, Miller, A.K., Ed., Dordrecht: Springer, 1987, pp. 1–88. https://doi.org/10.1007/978-94-009-3439-9_1
Sokolovskii, V.V., Theory of Plasticity, Moscow: Vyssh. Shkola, 1969.
DoquetV.Acta Metall. Mater.1993412451245910.1016/0956-7151(93)90325-M
Shtremel, M.A., Strength of Alloys. Part I. Lattice Defects, Moscow: MISIS, 1999.
Cottrell, A.H., Dislocations and Plastic Flow in Crystals, Oxford University Press, New York, 1953.
TrusovP.V.ShveykinA.I.Phys. Mesomech.20172037739110.1134/S1029959917040026
ZhangJ.JiangY.IJOP2005212191221110.1016/j.ijplas.2005.02.004
BishopJ.F.W.HillR.Philos. Mag. Ser. 71951421298130710.1080/14786444108561385
1199_CR28
J.R. Rice (1199_CR27) 1971; 19
1199_CR24
P. Franciosi (1199_CR39) 1985; 33
1199_CR25
Q. Liang (1199_CR21) 2022; 282
J. Cho (1199_CR18) 2017; 90
C. Laird (1199_CR6) 1986; 81
V.N. Ashikhmin (1199_CR29) 2006; 14
A. Benallal (1199_CR40) 1988; 5
Z. Xia (1199_CR42) 1991; 58
J.F. Bishop (1199_CR11) 1951; 42
P.V. Trusov (1199_CR32) 2017; 20
1199_CR9
R.A. Vasin (1199_CR7) 1990; 21
1199_CR4
P. Li (1199_CR17) 2011; 56
1199_CR5
1199_CR2
1199_CR3
E. Orowan (1199_CR33) 1940; 52
1199_CR1
A. Bisht (1199_CR20) 2019; 271
I. Beyerlein (1199_CR23) 2018; 33
J.F.W. Bishop (1199_CR12) 1951; 42
1199_CR13
1199_CR35
A. Benallal (1199_CR41) 1989; 114
1199_CR14
1199_CR15
1199_CR37
1199_CR16
1199_CR38
V.A. Romanova (1199_CR19) 2019; 22
A. Arsenlis (1199_CR36) 2002; 50
V. Doquet (1199_CR8) 1993; 41
G.I. Taylor (1199_CR10) 1938; 62
G.A. Maugin (1199_CR31) 2015; 69
J. Zhang (1199_CR44) 2005; 21
V. Aubin (1199_CR43) 2003; 31
D.L. McDowell (1199_CR22) 2010; 26
1199_CR34
B.D. Coleman (1199_CR26) 1967; 47
1199_CR30
References_xml – reference: Maugin, G.A., Mechanics of Electromagnetic Solids, Norwell: Kluwer Academic Publishers, 2003.
– reference: OrowanE.Proc. Phys. Soc.1940521926194810.1088/0959-5309/52/1/303
– reference: FranciosiP.Acta Metall.1985331601161210.1016/0001-6160(85)90154-3
– reference: Trusov, P.V. and Shveikin, A.I., Multilevel Models of Single- and Polycrystalline Materials: Theory, Algorithms, Application Examples, Novosibirsk: Izd-vo SO RAN, 2019.
– reference: TrusovP.V.ShveykinA.I.Phys. Mesomech.20172037739110.1134/S1029959917040026
– reference: Shtremel, M.A., Strength of Alloys. Part I. Lattice Defects, Moscow: MISIS, 1999.
– reference: LairdC.CharsleyP.MughrabiH.Mater. Sci. Eng.19868143345010.1016/0025-5416(86)90281-8
– reference: BenallalA.MarquisD.Eng. Comput.1988524124710.1108/eb023742
– reference: AubinV.QuaegebeurP.DegallaixS.Eur. Struct. Integr. Soc.20033140142210.1016/S1566-1369(03)80022-5
– reference: MauginG.A.Mech. Res. Commun.201569798610.1016/j.mechrescom.2015.06.00
– reference: ZhangJ.JiangY.IJOP2005212191221110.1016/j.ijplas.2005.02.004
– reference: BishopJ.F.W.HillR.Philos. Mag. Ser. 71951421298130710.1080/14786444108561385
– reference: ChoJ.MolinariJ.-F.AnciauxG.Int. J. Plasticity201790667510.1016/j.ijplas.2016.12.004
– reference: BishtA.KumarL.SubburajJ.JagadeeshG.SuwasS.J. Mater. Process. Technol.201927156858310.1016/j.jmatprotec.2019.04.029
– reference: BeyerleinI.KnezevicM.J. Mater. Res.201833371137382018JMatR..33.3711B10.1557/jmr.2018.333
– reference: ColemanB.D.GurtinM.E.J. Chem. Phys.1967475976131967JChPh..47..597C10.1063/1.1711937
– reference: ArsenlisA.ParksD.M.J. Mech. Phys. Solids200250197920092002JMPSo..50.1979A10.1016/S0022-5096(01)00134-X
– reference: Cottrell, A.H., Dislocations and Plastic Flow in Crystals, Oxford University Press, New York, 1953.
– reference: Kachanov, L.M., Foundations of the Theory of Plasticity, North-Holland Pub. Co., Amsterdarm, 1971.
– reference: VasinR.A.Itogi Nauk. Tekhn. Mekh. Deform. Tv. Tela. VINITI199021375
– reference: Kocks, U.F., Constitutive Behavior Based on Crystal Plasticity, in Unified Constitutive Equations for Creep and Plasticity, Miller, A.K., Ed., Dordrecht: Springer, 1987, pp. 1–88. https://doi.org/10.1007/978-94-009-3439-9_1
– reference: DoquetV.Acta Metall. Mater.1993412451245910.1016/0956-7151(93)90325-M
– reference: Physical Mesomechanics of Heterogeneous Media and Computer-Aided Design of Materials, Panin, V.E., Ed., Cambridge: Cambridge Interscience Publishing, 1998.
– reference: Horstemeyer, M.F., Multiscale Modeling: A Review, in Practical Aspects of Computational Chemistry, Leszczynski, J. and Shukla, M.K., Eds., Heidelberg: Springer, 2009, pp. 87–135. https://doi.org/10.1007/978-90-481-2687-3_4
– reference: TaylorG.I.J. Inst. Met.193862307324
– reference: Trusov, P.V. and Shveikin, A.I., Theory of Plasticity, Perm: Izd-vo PNRPU, 2011.
– reference: RomanovaV.A.BalokhonovR.R.BatukhtinaE.E.EmelyanovaE.S.SergeevM.V.Phys. Mesomech.20192229630610.1134/S1029959919040052
– reference: McDowellD.L.Int. J. Plasticity2010261280130910.1016/j.ijplas.2010.02.008
– reference: RiceJ.R.J. Mech. Phys. Solids1971194334551971JMPSo..19..433R10.1016/0022-5096(71)90010-X
– reference: Pozdeev, A.A., Trusov, P.V., and Nyashin, Yu.I., Large Elastoplastic Deformations: Theory, Algorithms, Applications, Moscow: Nauka, 1986.
– reference: LiangQ.WengS.FuT.HuS.PengX.Mater. Chem. Phys.202228212599710.1016/j.matchemphys.2022.125997
– reference: XiaZ.EllyinF.J. Appl. Mech.1991583173251991JAM....58..317X10.1115/1.2897188
– reference: Rogovoy, A.A., Formalized Approach to the Construction of Solid Mechanics Models. Part 1. Basic Equations of Continuum Mechanics, Moscow: Institute of Computer Science, 2021.
– reference: Krivtsov, A.M., Deformation and Fracture of Solids with Microstructure, Moscow: FIZMATLIT, 2007.
– reference: Roters, F., Advanced Material Models for the Crystal Plasticity Finite Element Method: Development of a General CPFEM Framework, Aachen: RWTH Aachen, 2011.
– reference: Ilyushin, A.A., Plasticity: Fundamentals of General Mathematical Theory, Moscow: AN SSSR, 1963.
– reference: BenallalA.Le GalloP.MarquisD.Nucl. Eng. Design198911434535310.1016/0029-5493(89)90112-x
– reference: Malinin, N.N., Applied Theory of Plasticity and Creep, Moscow: Mashinostroenie, 1968.
– reference: BishopJ.F.HillR.Philos. Mag. Ser. 719514241442710.1080/14786445108561065
– reference: Orlov, A.N., Introduction to the Theory of Defects in Crystals, Moscow: Vyssh. Shkola, 1983.
– reference: AshikhminV.N.VolegovP.S.TrusovP.V.PNRPU Bull. Mat. Modelir. Sistem Protsess.2006141126
– reference: LiP.LiS.X.WangZ.G.ZhangZ.F.Progr. Mater. Sci.20115632837710.1016/J.PMATSCI.2010.12.001
– reference: Sokolovskii, V.V., Theory of Plasticity, Moscow: Vyssh. Shkola, 1969.
– reference: Trusov, P.V. and Gribov, D.S., The Three-Level Elastoviscoplastic Model and Its Application to Describing Complex Cyclic Loading of Materials with Different Stacking Fault Energies, Materials, 2022, vol. 15(3). https://doi.org/10.3390/ma15030760
– volume: 69
  start-page: 79
  year: 2015
  ident: 1199_CR31
  publication-title: Mech. Res. Commun.
  doi: 10.1016/j.mechrescom.2015.06.00
– ident: 1199_CR9
– volume: 56
  start-page: 328
  year: 2011
  ident: 1199_CR17
  publication-title: Progr. Mater. Sci.
  doi: 10.1016/J.PMATSCI.2010.12.001
– volume: 62
  start-page: 307
  year: 1938
  ident: 1199_CR10
  publication-title: J. Inst. Met.
– ident: 1199_CR14
– ident: 1199_CR37
– volume: 42
  start-page: 414
  year: 1951
  ident: 1199_CR11
  publication-title: Philos. Mag. Ser. 7
  doi: 10.1080/14786445108561065
– volume: 22
  start-page: 296
  year: 2019
  ident: 1199_CR19
  publication-title: Phys. Mesomech.
  doi: 10.1134/S1029959919040052
– ident: 1199_CR35
– ident: 1199_CR16
– volume: 5
  start-page: 241
  year: 1988
  ident: 1199_CR40
  publication-title: Eng. Comput.
  doi: 10.1108/eb023742
– volume: 114
  start-page: 345
  year: 1989
  ident: 1199_CR41
  publication-title: Nucl. Eng. Design
  doi: 10.1016/0029-5493(89)90112-x
– ident: 1199_CR25
  doi: 10.3390/ma15030760
– volume: 31
  start-page: 401
  year: 2003
  ident: 1199_CR43
  publication-title: Eur. Struct. Integr. Soc.
  doi: 10.1016/S1566-1369(03)80022-5
– volume: 41
  start-page: 2451
  year: 1993
  ident: 1199_CR8
  publication-title: Acta Metall. Mater.
  doi: 10.1016/0956-7151(93)90325-M
– volume: 26
  start-page: 1280
  year: 2010
  ident: 1199_CR22
  publication-title: Int. J. Plasticity
  doi: 10.1016/j.ijplas.2010.02.008
– ident: 1199_CR2
– ident: 1199_CR4
– volume: 47
  start-page: 597
  year: 1967
  ident: 1199_CR26
  publication-title: J. Chem. Phys.
  doi: 10.1063/1.1711937
– ident: 1199_CR28
– volume: 19
  start-page: 433
  year: 1971
  ident: 1199_CR27
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/0022-5096(71)90010-X
– volume: 81
  start-page: 433
  year: 1986
  ident: 1199_CR6
  publication-title: Mater. Sci. Eng.
  doi: 10.1016/0025-5416(86)90281-8
– volume: 33
  start-page: 3711
  year: 2018
  ident: 1199_CR23
  publication-title: J. Mater. Res.
  doi: 10.1557/jmr.2018.333
– ident: 1199_CR24
– volume: 42
  start-page: 1298
  year: 1951
  ident: 1199_CR12
  publication-title: Philos. Mag. Ser. 7
  doi: 10.1080/14786444108561385
– volume: 20
  start-page: 377
  year: 2017
  ident: 1199_CR32
  publication-title: Phys. Mesomech.
  doi: 10.1134/S1029959917040026
– volume: 33
  start-page: 1601
  year: 1985
  ident: 1199_CR39
  publication-title: Acta Metall.
  doi: 10.1016/0001-6160(85)90154-3
– ident: 1199_CR38
– volume: 21
  start-page: 2191
  year: 2005
  ident: 1199_CR44
  publication-title: IJOP
  doi: 10.1016/j.ijplas.2005.02.004
– volume: 50
  start-page: 1979
  year: 2002
  ident: 1199_CR36
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/S0022-5096(01)00134-X
– ident: 1199_CR30
– ident: 1199_CR13
– volume: 90
  start-page: 66
  year: 2017
  ident: 1199_CR18
  publication-title: Int. J. Plasticity
  doi: 10.1016/j.ijplas.2016.12.004
– volume: 52
  start-page: 1926
  year: 1940
  ident: 1199_CR33
  publication-title: Proc. Phys. Soc.
  doi: 10.1088/0959-5309/52/1/303
– volume: 271
  start-page: 568
  year: 2019
  ident: 1199_CR20
  publication-title: J. Mater. Process. Technol.
  doi: 10.1016/j.jmatprotec.2019.04.029
– ident: 1199_CR34
  doi: 10.1007/978-94-009-3439-9_1
– ident: 1199_CR15
  doi: 10.1007/978-90-481-2687-3_4
– ident: 1199_CR1
– volume: 282
  start-page: 125997
  year: 2022
  ident: 1199_CR21
  publication-title: Mater. Chem. Phys.
  doi: 10.1016/j.matchemphys.2022.125997
– ident: 1199_CR3
– ident: 1199_CR5
– volume: 21
  start-page: 3
  year: 1990
  ident: 1199_CR7
  publication-title: Itogi Nauk. Tekhn. Mekh. Deform. Tv. Tela. VINITI
– volume: 58
  start-page: 317
  year: 1991
  ident: 1199_CR42
  publication-title: J. Appl. Mech.
  doi: 10.1115/1.2897188
– volume: 14
  start-page: 11
  year: 2006
  ident: 1199_CR29
  publication-title: PNRPU Bull. Mat. Modelir. Sistem Protsess.
SSID ssj0000329409
Score 2.27374
Snippet A three-level constitutive model is proposed for describing the deformation of polycrystalline materials, which is based on crystal elasto-viscoplasticity and...
SourceID proquest
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 557
SubjectTerms Algorithms
Classical Mechanics
Constitutive models
Crystallites
Cyclic loads
Deformation
Dislocation density
Materials Science
Mathematical models
Nonproportional loads
Physics
Physics and Astronomy
Polycrystals
Solid State Physics
Stacking fault energy
Viscoplasticity
Title Three-Level Dislocation-Based Model for Describing the Deformation of Polycrystals: Structure, Implementation Algorithm, Examples for Studying Nonproportional Cyclic Loading
URI https://link.springer.com/article/10.1134/S102995992206008X
https://www.proquest.com/docview/2748855595
Volume 25
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVLSH
  databaseName: SpringerLink Journals
  customDbUrl:
  mediaType: online
  eissn: 1990-5424
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000329409
  issn: 1029-9599
  databaseCode: AFBBN
  dateStart: 20120101
  isFulltext: true
  providerName: Library Specific Holdings
– providerCode: PRVAVX
  databaseName: SpringerLINK - Czech Republic Consortium
  customDbUrl:
  eissn: 1990-5424
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000329409
  issn: 1029-9599
  databaseCode: AGYKE
  dateStart: 20040101
  isFulltext: true
  titleUrlDefault: http://link.springer.com
  providerName: Springer Nature
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3fb9MwED5BJyR44McA0TEmP_AE83Bsx0l5a8fKBKNCWieVpyhx7FEtS6amkyj_E_8jZydZYfyQ9hg5thKdc9938d13AC-DIItSpSUyN6koIp6gKWcxVaGJkT9kVmpXKPxpog5P5IdZOGvruOsu2707kvSeuuk7It8cIxQ6cawB5wxROp7dhg0vt9WDjeH7Lx_Xv1aY4APpkzvcFOrmtOeZf13nd0Ra08xrJ6MecMYPYNo9apNncrZ3ucz29PdrKo43fJeHcL8loGTY7JhHcMuUm3DvF1nCTbjj00J1_Rh-TNHUhh65zCLybl475HOWpCMEv5y4RmoFQdpLMHxF94NR9ilBRomXV0WRpLLkc1Ws9GKFRLSo35JjL1l7uTC7xGsTn7flTyUZFqfVYr78er5LDr6lbqz2q7tkR1eORSZVeeHaOiyaP5hkf6WLuSZHla8EeAIn44Pp_iFtGzxQzaVaUmVzZUMVmzjnzKYZBm-B4ej2jBQsjwKJAw5jUxVZIznTuRjoIMowxkRiaoV4Cr2yKs0zIHEmogy9l7ZSSGPDAWcyDYVVaciZUXkfWGfkRLfq564JR5H4KEjI5A-b9OHV1ZSLRvrjfzdvdzsnab1AnWDEH8chxmxhH153G2E9_M_Ftm5093O4y11Nhs-x2YYeGtG8QKa0zHbwyxiPRpOd9gv5CR6-Cn0
linkProvider Springer Nature
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1db9MwFL0anRDwwGCAKAzwA08wj8R2nHRvZWwU1lVI66TuKUoce6uWJVPTSZT_xH_ctZOsMD6kPUaOrUTXueec-H4AvPX9NEykEsjchKSIeJwmzIuoDHSE_CE1QtlE4YORHByJr5Ng0uRxV220e3sk6Tx13XdEfDhEKLTFsXqMeYjS0eQOrArUJ6wDq_3Px_vLXyseZz3hgjvsFGrnNOeZf13nd0Ra0swbJ6MOcPbWYNw-ah1ncrZ1OU-31I8bVRxv-S6P4GFDQEm_3jGPYUUX6_Dgl7KE63DXhYWq6gn8HKOpNR3ayCLyaVpZ5LOWpB8R_DJiG6nlBGkvQfmK7gdV9glBRomX10mRpDTkW5kv1GyBRDSvtsmhK1l7OdObxNUmPm_SnwrSz0_K2XR-er5Jdr8ndqxyq9tgR5uORUZlcWHbOszqP5hkZ6HyqSLD0mUCPIWjvd3xzoA2DR6oYkLOqTSZNIGMdJQxzyQpijdfM3R7WnAvC32BAxZjExkaLZinMt5TfpiixkRiajh_Bp2iLPRzIFHKwxS9lzKCC22CHvNEEnAjk4B5WmZd8Fojx6qpfm6bcOSxU0FcxH_YpAvvrqdc1KU__nfzRrtz4sYLVDEq_igKULMFXXjfboTl8D8Xe3Gru9_AvcH4YBgPv4z2X8J9ZvMzXLzNBnTQoPoVsqZ5-rr5Sq4AO00L4A
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwELagFQgOPAqoCwV84AR169iOk-W2tF0KXVaV2krLKSSOXVZNk9UmlVj-E_-RseN0oTwkxDHyQ4lmMvONPfMNQi-CIItSqQQgNyEJeDxOUkZjIkMdA37IjFC2UPjDWO6fiPeTcOL7nNZdtnt3JdnWNFiWprLZnuXG9yAR20fgFi1RVp8xCh47nlxHqxCZRKDoq4O3Hw-WxyyUs75wiR52CbFr_N3mb_f52TstIeeVW1LnfIZ30afutduck7OtiybbUl-vMDr-x3fdQ3c8MMWDVpPuo2u6XEO3f6ArXEM3XLqoqh-gb8egApqMbMYR3p3W1iNaCZM34BRzbBusFRjgMIawFswSRN-nGJAmPF4WS-LK4MOqWKj5AgBqUb_GR47K9mKuN7HjLD73ZVElHhSn1XzafD7fxHtfUjtWu91tEqQt08LjqpzZdg_z9mQT7yxUMVV4VLkKgYfoZLh3vLNPfOMHopiQDZEmlyaUsY5zRk2aQVAXaAbmUAtO8ygQMGB9byojowWjKud9FUQZxJ4AWA3nj9BKWZV6HeE441EGVk0ZwYU2YZ9RkYbcyDRkVMu8h2gn8ER5VnTbnKNIXHTERfKLTHro5eWSWUsJ8rfJG50WJd461AmLwGyGEMuFPfSqU4rl8B83e_xPs5-jm4e7w2T0bnzwBN1itmzDpeFsoBWQp34KYKrJnvkf5jsG-xTE
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Three-Level+Dislocation-Based+Model+for+Describing+the+Deformation+of+Polycrystals%3A+Structure%2C+Implementation+Algorithm%2C+Examples+for+Studying+Nonproportional+Cyclic+Loading&rft.jtitle=Physical+mesomechanics&rft.au=Gribov%2C+D+S&rft.au=Trusov%2C+P+V&rft.date=2022-12-01&rft.pub=Springer+Nature+B.V&rft.issn=1029-9599&rft.eissn=1990-5424&rft.volume=25&rft.issue=6&rft.spage=557&rft.epage=567&rft_id=info:doi/10.1134%2FS102995992206008X&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1029-9599&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1029-9599&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1029-9599&client=summon