by Andrea M. Jokisaari

192 Pages·2016·10.62 MB·English

MULTIPHYSICS PHASE FIELD MODELING OF HYDROGEN
DIFFUSION AND δ-HYDRIDE PRECIPITATION IN
α-ZIRCONIUM
by
Andrea M. Jokisaari
Adissertationsubmittedinpartialfulfillment
oftherequirementsforthedegreeof
DoctorofPhilosophy
(MaterialsScienceandEngineering)
intheUniversityofMichigan
2016
DoctoralCommittee:
ProfessorKatsuyoS.Thornton,Chairperson
ProfessorJohnE.Allison
ProfessorMichaelThouless
ProfessorGaryS.Was
(cid:13)c Andrea M. Jokisaari 2016
AllRightsReserved
DEDICATION
To my family, friends, and scientists of the past and the future.
ii
ACKNOWLEDGMENTS
Iwould liketoexpress mysincere appreciation tomy advisor,Dr. KatsuyoThornton, for
her continuous support of my doctoral research. She gave me an opportunity to work
in computational and theoretical materials science, an area in which I had little prior
expertise. I would also like to thank the rest of my thesis committee: Dr. John Allison,
Dr. GaryWas,andespeciallyDr. MichaelThouless,fortheirencouragement,insightful
comments, and hard questions. I would also like to thank my fellow group members
fortheirsupportandfellowshipthroughoutmygraduatecareer,particularlyDr. Larry
Aagesen, Dr. Susan Gentry, Dr. Candace Gilet, and Dr. David Montiel. I also express
mydeepestgratitudetomymentorsandcollaborators,especiallyDr. OlleHeinonen,Dr.
MichaelTonks,andCodyPermann,fortheirsupport.
Iwouldliketoacknowledgethecomputationresourcesusedinpursuitofthisresearch,
namely the High Performance Computing Center at Idaho National Laboratory. I also
wish to express my gratitude to the MOOSE team at Idaho National Laboratory for
their generous help and support. This research was supported by the Consortium for
AdvancedSimulationofLightWaterReactors(www.casl.gov),anEnergyInnovationHub
(http://www.energy.gov/hubs)forModelingandSimulationofNuclearReactorsunder
U.S.DepartmentofEnergyContractNo. DE-AC05-00OR22725.
Wordscannotexpressmyloveandappreciationformyhusband,Jake,whoencouraged
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me to come to University of Michigan so many years ago and has been by my side
throughoutitall. Iwouldliketothankmyfriendsforenrichingmylife,andEdHuebner
andChristineKelleyfortheirinvaluablepersonalsupportandguidance.
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TABLE OF CONTENTS
DEDICATION ii
ACKNOWLEDGMENTS iii
LISTOFFIGURES ix
LISTOFTABLES xviii
ABSTRACT xix
ChapterI.Introduction 1
1.1 Generalintroductiontonuclearelectricitygeneration . . . . . . . . . . . . . 1
1.2 Fuelcladdinganditsdegradation . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Characteristicsofzirconiumhydrideinfuelcladding . . . . . . . . . . . . . 6
1.4 Existingmodelsofhydridinginzirconium . . . . . . . . . . . . . . . . . . . 14
1.5 Researchobjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Dissertationoutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
ChapterII.Background: PhysicsandNumericalMethods 19
2.1 IntroductiontothePhaseFieldModel . . . . . . . . . . . . . . . . . . . . . . 19
v
2.1.1 Freeenergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.2 Governingequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Multiphysicsphasefieldmodel . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.1 Freeenergyformulation . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.2 Governingequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.3 Solidmechanicsmodel . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.4 Nucleationmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.5 Nondimensionalizationoftheequations . . . . . . . . . . . . . . . . 43
2.3 Numericalmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.1 Mathematicalformulationofthefiniteelementmethod . . . . . . . . 45
2.3.2 MOOSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.3.3 Hyrax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.4 Chaptersummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
ChapterIII.GeneralMethodforIncorporatingCALPHADFreeEnergiesofMixing
intoPhaseFieldModels: Applicationtothe α-Zirconium/δ-HydrideSystem 63
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2.1 Generalcoupledconserved-nonconservedphasefieldmodel . . . . 66
3.2.2 GenericCALPHADfreeenergyapproximation . . . . . . . . . . . . 68
3.2.3 The α-zirconium/δ-hydridemodel . . . . . . . . . . . . . . . . . . . 71
3.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Chapter IV. A Nucleation Algorithm for the Coupled Conserved-Nonconserved
vi
PhaseFieldModel 88
4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1.1 Phasefieldmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1.2 Explicitnucleationalgorithm . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.3 Order-parameter-only nucleation algorithm and implementation
details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.1.4 Simulationconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2.1 OPOnucleusevolution . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2.2 ValidationofOPOnucleationandgrowth . . . . . . . . . . . . . . . 106
4.2.3 Effectofadaptivityonconcurrentnucleationandgrowthsimulations110
4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
ChapterV.PreliminaryWorkandFutureWork 117
5.1 Preliminarywork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.1.1 Sensitivityofthevolumetricnucleationrate . . . . . . . . . . . . . . 118
5.1.2 Spatialdistributionofthevolumetricnucleationratearoundapre-
cipitate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.1.3 Concurrentnucleationandgrowthsimulations . . . . . . . . . . . . 134
5.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.2.1 Terminalsolidsolubilityhysteresisofhydrogenin α-zirconium . . . 139
5.2.2 Interfacialenergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.2.3 Thermodiffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.2.4 Plasticityandirradiation . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
vii
ChapterVI.Conclusions 150
Bibliography 153
viii
LIST OF FIGURES
1.1.1 AveragecapacityfactorofnuclearpowerplantsintheUnitedStates,1973-
2011[5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 APWRfuelassemblyschematic,reproducedfromRef.[10]. . . . . . . . . . 4
1.3.1 Phasediagramofthezirconium-hydrogensystem. FromRef.[23]. . . . . . 8
1.3.2 A compilation of TSSd and TSSp data of a-zirconium alloys (zirconium,
Zircaloy-2, and Zircaloy-4), labeled by the first author. Experimental
techniquesincludesynchrotronX-raydiffraction(Barrow,Zircaloy-2[33],
Zanellato, Zircaloy-4 [32], Colas, Zircaloy-2 [20]); differential scanning
calorimetry (McMinn, Zircaloy-2 and 4 [30], Une, Zircaloy-2 (2003) [31],
Une, zirconium (2004) [41], Tang, Zircaloy-4 [42]); dilatometry (Erickson,
zirconium[29],Slattery,Zircaloy-4[43]);anddiffusioncoupling(Kearns,
zirconium[44]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.3 The macroscale hydride structure of irradiated Zircaloy-4 fuel cladding.
Thehydridesarepresentasdarkgraycircumferentiallines. Reproduced
fromRef.[48]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.4 Themicrostructureofasinglehydrideprecipitate. (a)BrightfieldTEM;the
hydrideappearsasonemassiveparticle. (b)DarkfieldTEM;theindividual
platesinthehydrideareapparent. ReproducedfromRef.[22]. . . . . . . . . 11
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