Complete Simulation Models to Describe the Ductile-to-Brittle Transition of Steels for Arctic Applications A Beremin-Gurson Approach Henrik Andre Scheide Master of Science in Mechanical Engineering Submission date: May 2018 Supervisor: Odd Magne Akselsen, MTP Co-supervisor: Antonio Alvaro, SINTEF Bård Nyhus, SINTEF Norwegian University of Science and Technology Department of Mechanical and Industrial Engineering Preface The master’s thesis is published at the Department of Mechanical and Industrial Engi- neeringattheNorwegianUniversityofScienceandTechnology(NTNU)incooperation withSINTEFIndustry(SINTEFMaterialsandChemistryupuntil01/2018),andtheArc- ticMaterialsProject. Themaster‘sthesiscompletesTMM4960EngineeringDesignand Materials,Master’sThesisandequals30ECTSCredits. TheresearchandtheworkconductedhavebeenunderthesupervisionofAntonioAlvaro. Additional guidance and co-supervising have been provided by Odd Magne Akselsen, VidarOsenandBa˚rdNyhus, allfromSINTEFIndustry. Thethesisworkwasconducted betweenJanuaryandJune2018andisanextensionofapreliminarystudyfromthecourse TMM4560EngineeringDesignandMaterials,SpecializationProject. [126] The specialisation project was conducted prior to the master’s thesis and discloses two ductile-to-brittle transition models. Both models are based on the combination of The Complete Gurson Model and the RKR Criterion as a post-processing routine based oncriticalopeningstressesovercharacteristicdistancestovisualisetheductile-to-brittle transition regions. The project thesis with its constitutive simulation scheme and model improvementdiscussionsarethefundamentalbasisforthemaster’sthesis. [126] Most of the time was spent on doing extensive research on fracture mechanics, bi- modalgrainsizedistribution,andexistingsimulationsmodelswiththeirconstitutivecom- putational implementation methods. A lot of time and focus were also spent on compu- tationalsimulationsandmodellinginABAQUStogetaccurateandrepresentativeresults. TheprimaryfocusaddressestheWeibull-basedBereminmodelanditsadaptabilitytodif- ferent steels, constraint levels, and laboratory testing requirements. Additional attention issettotheWeibullparameterswhichareshowntobethemostcomplicatedpartsofthe simulation scheme to adequately describe the abrupt fracture toughness transition. The fracture mechanical data collection was highly time-consuming due to the ambiguity of the SINTEF material database with its constitutive AM1-TP8 project and a more recent testseriesconductedtogetcharacteristicresistancecurvesintheductileregion. Firstofall, IwouldliketothankmysupervisorAntonioAlvaroatSINTEFwhohas provided me with continuous feedback, fruitful discussions and support throughout the entire duration of the project and master’s thesis endeavor. My outright gratitude to my co-supervisorsOddMagneAkselsen, VidarOsenandBa˚rdNyhuswhohavecontributed withvaluableinputandprofoundscientificdiscussions. Ithasbeenaprivilegetowritethe master’sthesisatSINTEFIndustrywhichmaderoomforpersonaldevelopment,freedom ofresearch,andanutmostinspiringatmosphere. 11-06-2018,Trondheim HenrikA.Scheide Abstract Thetoughnessofcommonstructuralsteelsisoftenaffectedbytemperaturechangeswhere lowservicetemperaturesfrequentlypromotebrittlematerialcharacteristics. Lowservice temperaturesoftenoccurintheArcticregions,andunexpectedcatastrophicfailuresmay occur due to inadequate material characterisation. It is crucial to have a model with the highestlevelofaccuracytomitigatetheriskofsuddenbrittlefailurewhichinturncanpre- cisely capture the material behaviour at shifting temperatures. The primary objective of themaster‘sthesisisthustodevelopamodelwhichisabletodescribethetemperaturede- pendenceoffracturetoughnessinsteels. Theaimistoreducethelaboratoryworkneeded to characterise the ductile-to-brittle transition regions. At lower temperatures, steels ex- hibitbrittlebehaviourandbecomesusceptibletosuddenbrittlefracturewithoutwarning. Higher temperatures yield ductile behaviour with mechanisms such as void nucleation, voidgrowthandvoidcoalescencepromotingductiletearingandcontrolledductilefailure. The transition between the ductile and brittle regions exhibit both ductile and brittle be- haviourandiscrucialwhensteelsareutilisedinfluctuatingandlowservicetemperatures wheresuddencleavagefracturemayoccur. TwoGurson-RKRmodelsareinitiallydevelopedinapreliminarystudytodescribethe completeductile-to-brittletransitionandtovisualisetheductile, transitionandbrittlere- gions. [126]TheRKRCriterionisapost-processingroutinefortheductileGursonmodel and is used to predict brittle failure by considering critical stresses along the crack liga- mentwiththecriticalopeningstressaheadofthecracktipasbothtemperaturedependent andindependent.TheCombinedGurson-RKRModelwithtemperatureindependentopen- ingstresscandescribetheductile-to-brittletransitionbydemonstratingincreasingfracture toughness with increasing temperature. However, the results are somewhat conservative asthecombinedmodelhighlyoverestimatesthesteel’sbrittlenessathighertemperatures. TheCombinedGurson-RKRModelwithtemperaturedependentcriticalopeningstresscan visualisetheductile-to-brittleregionswheretheupperandlowerboundarylimitscapture alltheexperimentalfracturetoughnessfrom-60◦C to21◦C. Nevertheless,theopening stresstemperatureapproximationcannotbeconcludedwithoutfurthertesting,andseveral material fitting parameters remain uncertain and questionable. Hence, further improve- mentsofthecurrentmodelisnecessaryinordertodevelopasufficientmodeltodescribe theductile-to-brittletransitionofsteelswithlimitedlaboratorytesting. Thus,amorecomprehensivemodelisdevelopedtodescribetheductile-to-brittletran- sitionbyintroducingastatisticalandmechanismsbasedmodelfollowingtheweakest-link principle;instabilityofonesinglemicrocrackinanarbitraryvolumeelementmayleadto completespecimenfailure. AWeibull-basedcriterionsubstitutesthedistance-basedRKR Criterionwhichinturnprovidesaframeworkfortheconnectionbetweenthedrivingforces onamicro-scalelevelandmacro-scalemodelsforcleavagefracture. TheWeibull-based Bereminmodelisusedasapost-processingroutinecombinedwithTheCompleteGurson Modelandconstitutesacompletegeneralisationoftheprobabilityofbrittlefractureand ductile damage control while concurrently accounting for and supporting different crack configurations, geometry constraints, and loading modes. The two Beremin model pa- rametersfittedinthebrittleregionarecalibratedfromexperimentalandtheoreticalresults and respectively characterises the flaw distribution and the scaling factor of the Weibull distributionutilisedtocalculatetheprobabilityofbrittlefracturethroughouttheDBT. TheWeibullstressalongwiththecalibratedWeibullparameterscanbeusedtocom- pute the probability of brittle failure by considering the aggregate sum of the maximum principalstressesinallthevolumeelementsexceedingaparticularcriticalstress. Asthe Beremin model largely underestimates the rupture energies in the transition region, The CompleteGursonModelisutilisedtosimulateductiledamagemechanismstodescribethe shiftingstressstateinthetransitionregion.TheWeibull-basedBereminModelisthenused asapost-processingroutinetocalculatetheprobabilityofbrittlefailureconcurrentlywith thecompetingductilemechanismsintegratedbyTheCompleteGursonModel.Hence,the Gurson model is independently fitted to the experimental results at the highest tempera- ture in the ductile region to accurately describe ductile mechanisms and crack extension throughouttheductile-to-brittletransition. TheGursonmodelcansimulateaccuratecrack extensionthroughouttheDBTforthehighconstraintgeometrywhenutilisingtemperature independentGursonparameters. However,thesameGursonparametersareonlytosome extentabletocharacterisetheapplicableresistancecurvesforthelowconstraintgeometry. TheWeibull-basedBereminmodelcanconstraint-correctandcharacterisethefracture toughness to the specimens in the brittle region but is only to some extent able to de- scribetheDBTasitoverestimatesthesteel’sbrittlenessinthetransitionregion. AGurson user-definedmaterial(UMAT)withconstitutiveductilemechanismequationsisthenused to characterise typical material behaviour in the transition region. The Beremin-Gurson model with temperature independent Weibull parameters fitted at the lowest temperature in the brittle region can constraint-correct the fracture geometries and describe the frac- ture toughness throughout the brittle region. However, the model is unable to capture the lower bound transition at higher temperatures but can capture the applicable upper bound transition in the ductile-to-brittle transition which evidently supports temperature dependentWeibullparameters. Thus, toughnessscalingandconstraint-correctionoftwo fracture geometries with different constraint levels are conducted to find the appropriate temperaturedependentWeibullparameters.TheBeremin-Gursonmodelwithtemperature dependent Weibull parameters can accurately constraint-correct the fracture geometries anddescribetherelevantfracturetoughnessvaluesthroughouttheductile-to-brittletran- sition. The Weibull modulus defining the flaw distribution and the slope of the Weibull cumulative distribution function is constant in the brittle region and increases when en- tering the transition region where it remains relatively constant throughout the transition region. Thescaleparameterdefiningtheresistancetobrittlefailurefollowstheopposite trendaslargeWeibullmoduluspromotesmallscaleparametersandviceversa. The current Beremin-Gurson model needs further improvements as several material parameters remain questionable and uncertain. The Weibull stress calculation program, LINKpfat must be further enhanced to represent the weakest-link principles in the con- stitutiveBereminmodel. Thus,athoroughevaluationoftheWeibullstresscalculationis necessary.AnotherweldsimulatedsteelmustbeevaluatedtoconcludetheWeibullparam- etertemperaturetrends,andathirdconstraintlevelmustbeintegratedtoinfertheaccuracy oftheconstraint-correction. Sammendrag Seighetentilvanligestrukturellesta˚leroftepa˚virketavtemperaturendringerhvorlaveop- erasjonstemperatureroftefremmersprømaterialegenskaper. Laveoperasjonstemperaturer oppsta˚r ofte i arktiske regioner, og uventede katastrofale brudd kan oppsta˚ pa˚ grunn av utilstrekkeligmaterialkarakterisering. Fora˚ redusererisikoenforplutseligesprøbrudder detviktiga˚ haenmodellmedhøyestmulignøyaktighet, ogsomeristandtila˚ nøyaktig beskrivematerialetsoppførselvedskiftendetemperaturer.Hovedma˚lettilmasteroppgaven er dermed a˚ utvikle en modell som er i stand til a˚ beskrive temperaturavhengigheten til sta˚letsbruddseighet. Ma˚letera˚reduserelaboratoriearbeidetsomtrengsfora˚karakterisere regioneneiovergangenfraduktiltilsprøoppførsel.Vedlaveretemperaturerharsta˚letsprø oppførsel og kan bli utsatt for plutselige sprøbrudd uten forvarsel. Høyere temperaturer girduktiloppførselmedmekanismersomkjernedannelseavtomrom,vekstitomromog sammenvoksing av tomrom som fremmer duktil sprekkvekst og kontrollerte duktilitets- brudd. Overgangsregionenmellomdeduktileogsprø regioneneharba˚deduktilogsprø oppførsel, og er avgjørende na˚r sta˚l brukes i svingende- og lave operasjonstemperaturer derplutseligespaltningsbruddkanforekomme. To Gurson-RKR-modeller er i første omgang utviklet i en innledende studie for a˚ beskriveovergangen fraduktiltil sprø oppførsel, og fora˚ visualisere deduktileog sprø regionene samt overgangsregionen. [126] RKR-kriteriet er en etterbehandlingsrutine for denduktileGurson-modellen,ogbrukestila˚forutsisprøbruddveda˚vurderekritiskespen- ninger langs midtsprekken hvor den kritiske a˚pningsspenningen foran sprekkspissen blir testetsomba˚detemperaturavhengigog-uavhengig. DenkombinerteGurson-RKRmod- ellen med temperaturuavhengig a˚pningsspenning er i stand til a˚ beskrive den duktile til sprø overgangen som demonstrerer økende bruddseighet med stigende temperatur. Imi- dlertid er resultatene noe konservative da den kombinerte modellen overestimerer sta˚lets sprøhet ved høye temperaturer. Den kombinerte Gurson-RKR modellen med temperat- uravhengig kritisk a˚pningsspenning er i stand til a˚ visualisere regionene i overgangen fra duktil til sprø oppførsel der de øvre og nedre grenseverdiene fanger alle de eksperi- mentellbruddseighetenefra-60◦C til21◦C. Likevelkantemperaturapproksimasjonenav a˚pningspenningen ikke konkluderes uten videre testing, og flere materialparametere for- blirusikreogtvilsomme. Videreforbedringavgjeldendemodellerderfornødvendigfor a˚ utvikleentilstrekkeligmodelltila˚ beskrivedenduktiletilsprøovergangenavsta˚lmed begrensetlaboratorietesting. Dermederenmeromfattendemodellutvikletfora˚ beskrivedenduktiletilsprøover- gangen ved a˚ innføre en statistisk og mekanismebasert modell som følger svakeste-ledd prinsippet; ustabilitet av en enkel mikrosprekk i et vilka˚rlig volumelement kan føre til fullstendigprøvestavbrudd.DetavstandsbaserteRKR-kriterietererstattetmedetWeibull- basertkriteriumsomgiretrammeverkforsammenhengenmellomdrivkraftenpa˚etmikro- skala-niva˚ og makroskala-modeller for spaltningsbrudd. Den Weibull-baserte Beremin- modellenbenyttessomenetterbehandlingsrutinekombinertmedDenKompletteGurson- modellen, og gir en fullstendig generalisering av sannsynligheten for sprøbrudd og duk- til skadekontroll samtidig som den tar hensyn til og støtter ulike sprekk-konfigurasjoner, geometri constraint og laster. Beremin-modellen er innledningsvis tilpasset i den sprø regionen hvor to Weibull-parametere er kalibrert fra eksperimentelle og teoretiske resul- tater. Weibull-parameternekanhenholdsviskarakteriseredefektdistribusjonenogskaler- ingsfaktoren til Weibull-fordelingen brukt til a˚ beregne sannsynligheten for sprøbrudd i heleovergangenfraduktiltilsprøoppførsel. Weibull-spenningene sammen med de kalibrerte Weibull-parameterne kan brukes til a˚ beregne sannsynligheten for sprøbrudd ved a˚ ta den samlede summen av de høyeste hovedspenningene i alle volumelementer som overstiger en viss kritisk spenning. Et- tersom Beremin-modellen i stor grad overvurderer rupturkreftene i overgangsregionen er Den Komplette Gurson-modellen brukt til a˚ simulere duktilskademekanismer for a˚ beskrive den skiftende spenningstilstanden i overgangsregionen. Den Weibull-baserte Beremin-modellenbrukessa˚somenetterbehandlingsrutinefora˚beregnesannsynligheten for sprøbrudd samtidig som de konkurrerende duktile mekanismene integreres med Den Komplette Gurson-modellen. Derfor er Gurson-modellen uavhengig tilpasset de eksper- imentelleresultateneveddenhøyestetemperaturenidenduktileregionenfora˚ nøyaktig beskrive de duktile mekanismene og sprekkutvidelsen gjennom hele den duktile til sprø overgangen. Gurson-modellen er i stand til a˚ simulere nøyaktig sprekkforlengelse gjen- nom hele den duktile til sprø overgangen for prøvestavene med høyt constraint-niva˚ ved brukavtemperaturuavhengigeGurson-parametere. LikevelerGurson-parameternekuntil envissgradistandtila˚ karakteriseredeaktuellemotstandskurveneforprøvestavenemed lavtconstraint-niva˚. DenWeibull-baserteBeremin-modelleneristandtila˚ constraint-korrigereogkarak- terisere bruddseigheten til prøvestavene i den sprø regionen, men er bare til en viss grad i stand til a˚ beskrive den duktile til sprø overgangen ettersom den overvurderer sta˚lets sprøhet i overgangsregionen. Et Gurson-brukerdefinert materiale (UMAT) med grunn- leggende ligninger for duktile mekanismer brukes sa˚ til a˚ karakterisere den representa- tivematerialeadferdeniovergangsregionen. Beremin-Gurson-modellenmedtemperaturu- avhengige Weibull-parametere tilpasset ved den laveste temperaturen i det sprø omra˚det er i stand til a˚ constraint-korrigere bruddgeometriene og beskrive bruddseigheten i hele den sprø regionen. Modellen er imidlertid ikke i stand til a˚ fange den nedre grenseover- gangenvedhøyeretemperaturer, meneristandtila˚ fangedenaktuelleøvregrenseover- gangen i den duktile til sprø overgangen, noe som tydelig støtter temperaturavhengige Weibull-parametere. Dermed er seighetsskalering og constraint-korreksjon av to brud- dgeometrier med forskjellige constraint-niva˚er utført for a˚ finne de aktuelle temperatu- ravhengige Weibull-parameterne. Beremin-Gurson-modellen med temperaturavhengige Weibull-parametereklarera˚ nøyaktigconstraint-korrigerebruddgeometriene,ogbeskrive deaktuellebruddseighetsverdienegjennomheledenduktiletilsprøovergangen. Weibull- modulen som definerer defektfordelingen og helningen pa˚ den Weibull-kumulative dis- tribusjonsfunksjonenforblirkonstantidensprøregionen,ogøkerna˚rdenga˚rinniover- gangsregionen hvor den igjen forblir relativt konstant gjennom hele overgangsregionen. Skaleringsparameteren som definerer motstanden til sprøbrudd følger den motsatte tren- denhvorstorWeibull-modulfremmersma˚ skaleringsparametere,ogomvendt. Den na˚værende Beremin-Gurson-modellen trenger ytterligere forbedringer ettersom flerematerialparametereforblirtvilsommeogusikre. ProgrammetforWeibull-spennings- beregning, LINKpfat ma˚ forbedres ytterligere for a˚ fa˚ en mer nøyaktig representasjon av svakeste-leddprinsippene til Beremin-modellen, og dermed ma˚ en grundig evaluering av beregningene av Weibull-spenningene bli gjennomført. Et annet sveisesimulert sta˚l ma˚ vurderes for a˚ konkludere temperaturtrendene til Weibull-parameterne, og et tredje constraint-niva˚ma˚integreresfora˚konkluderenøyaktighetenavconstraint-korreksjonene. Nomenclature Thislistdescribestheconstitutivesymbolsandacronymsusedwithinthebodyofthepaper. A = Amplitude ACMOD = AreaundertheForce-CMODcurve pl B = ThicknessofaSENBspecimen C = Diameterofasecond-phaseparticle 0 C = MaterialdependentRamberg-Osgoodconstant E = Young’smodulus E’ = Elasticmodulusunderplainstrain J = LineJ-integral J = LineJ-IntegralofmodeIcrack I J = CriticalJ IC I K = Stressintensityfactor K = StressintensityfactorofmodeIcrack I K = CriticalK forcleavagefractureinitiation IC I P = Cumulativeprobabilityoffailure F P = Survivalprobability(reliability) S Q = Maximumstressintensificationfactor max T = Peaktemperature p V = ElementaryvolumeofV (referencevolume) 0 p V = Volumeofthefractionprocesszone(FPZ) p W = WidthofaSENBspecimen α = Numericalconstantfunctionofthecrackshape ∆a = Crackgrowth ∆t = Weldcoolingtimebetween800-500◦C 8/5 Γ = Minimumworkofseparationforcleavage 0 γ = Effectivesurfaceenergy p γ = Specificsurfaceenergy s δ = Cracktipopeningdisplacement(CTOD) δ = CriticalCTOD c δ = Initialcrackopening 0 (cid:15) = Plasticstraintensor p (cid:15) = EquivalentvonMisesplasticstraintensor eq (cid:15) = EquivalentvonMisesplasticstrain v (cid:15) ,(cid:15) ,(cid:15) = Principalstrains 1 2 3 λ = Weibullscaleparameter(CTOD) σ = Initialtensileyieldstrength 0 σ = Openingstress 22 σ = Ultimatetensilestrength UTS σ = Criticalstress c σ = Temperaturedependentcriticalopeningstress cTD σ = Temperatureindependentcriticalopeningstress cTID Φ = Gursonyieldfunction σ = Decohesionstress d σ = Effectivestress e σ = EquivalentvonMisesstress eq σ = Fracturestress f σ = Meanstress m σ = Weibullscaleparameter u σ = Weibullstress w σ = Uniaxialyieldstrength y σ = Yieldstrength ys σ = Openingstress yy σ = Maximumopeningstress yymax σ ,σ ,σ = Principalstresses 1 2 3 σ = Stresstensor ij θ = Anglefromcracktiptostressfield a = Halfthelengthofaninternalcrack a = Criticalcrackdepth c a = Initialcrackdepth 0 d = Averagegraindiameter f = Voidvolumefraction f = Grainsizeareafraction area f∗ = Artificiallyacceleratedvoidgrowth f = Criticalvoidvolumefraction c f = Voidvolumefractionattheendofcoalescence F f = Initialvoidvolumefraction 0 f andg = Dimensionlessfunctionsofθ ij ij i = Ranknumber k = Weibullshapeparameter(CTOD) l = Meshelementlength c m = Weibullmodulus n = Strainhardeningexponent q = Heatinput(duringwelding) q = VonMisesstress vm q = ConstantGursonfactor(=1.5) 1 q = ConstantGursonfactor(=1.0) 2 r = Distancefromcracktiptostressfield r¯ = Currentvoidradius r = Initialvoidradius 0 r = Rotationalfactor(equalto0.44) p t = Surfacetraction v = Poisson’sratio x = Characteristicdistance c .cmd = Commandoscript .dat = Outputfile .inp = Inputfile .odb = ABAQUSdatabasefile .pfp = LINKpfatsimulationfile CDF = CumulativeDistributionFunction CE = CarbonEquivalent CMOD = CrackMouthOpeningDisplacement CGHAZ = Course-GrainedHeatAffectedZone CTOD = CrackTipOpeningDisplacement CVN = CharpyV-Notch DBT = Ductile-to-BrittleTransition DBTT = Ductile-to-BrittleTransitionTemperature EDM = ElectricalDischargeMachining FE = FiniteElement FEA = FiniteElementAnalysis FEM = FiniteElementMethod FGHAZ = Fine-GrainedHeatAffectedZone FPZ = FractureProcessZone GTN = Gurson,TvergaardandNeedleman HAZ = HeatAffectedZone LSQ = LeastSquare ML = MaximumLikelihood MLE = MaximumLikelihoodEstimation MOTE = MinimumOfThreeEquivalent M-A = Martensite-Austenite RKR = Ritchie-Knott-Rice SDV = State-DependentVariable SENB = SingleEdgeNotchedBend SENB02 = SENBspecimenwith a =0.2 W SENB05 = SENBspecimenwith a =0.5 W SENT = SingleEdgeNotchedTension SP = Specimen SSY = Small-ScaleYielding TD = TemperatureDependent TID = TemperatureIndependent UFG = Ultrafine-Grained UMAT = User-DefinedMaterial