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GuidanceDocumentGD35-2023

ChinaClassificationSociety

GuidelinesforFatigueStrengthAssessmentBasedonFractureMechanicsMethodology

Effectivefrom1January2024Beijing

PAGE

10

TableofContents

Section1General 3

Application 3

Definition 3

Symbols 4

FatigueFailureMode 5

FatigueAssessmentMethodology 5

FatigueLoadingConditions 5

FatigueLoadCases 5

Section2FatigueEvaluation 6

General 6

Structuraldetailstobeassessed 6

UniqueCrackGrowthRateCurveModel 6

FatigueStressRangeSpectrum 7

FailureAssessmentMethodology 7

FatigueLifeCalculation 8

FatigueCrackGrowthAssessmentProcedure 8

Section3InitialDefectSizeCharacterizationsandStressIntensityFactorSolutions 11

General 11

InteractionRulesforCoplanarCracks 11

StressIntensityFactorSolutions 12

Section4EquivalentDesignWaveMethodology 17

General 17

FatigueStressRangeSpectrum 17

StressRange 18

Section5SpectralAnalysisMethodology 19

General 19

HydrodynamicAnalysis 19

FiniteElementAnalysis 19

FatigueStressRangeSpectrum 19

FatigueStressRangeSpectrumProcedure 21

Section6FailureAssessmentMethodology 23

General 23

FailureAssessmentLine 23

FractureParameterforFatigueCrackGrowth 24

PlasticCollapseParameterforFatigueCrackPropagation 24

Appendix1StressIntensityFactorforTypicalCrack 26

StressIntensityFactorforEmbeddedEllipticalCrack 26

StressIntensityFactorforSurfaceCrackatWeldToe 26

Section1General

Application

TheGuidelinesspecifythefatiguestrengthassessmentofhullstructurebasedonfracturemechanicsmethodology.Theloadistypicallycalculatedbymeansoftheequivalentdesignwavemethodorthespectralanalysismethod.TheGuidelinesareapplicabletoshipsthataresubjecttofatiguestrengthassessmentbasedonfracturemechanicsmethodologydefinedaccordingtorulesorguidelinessetforthbyChinaClassificationSociety(hereinafterreferredtoasCCS),andalsoapplicabletoshipsforwhichclassnotationsasspecifiedinSection1[1.1.2]arevoluntarilyapplied,orshipsforwhichCCSdeemsitnecessarytoconsidertheeffectsofcrackgrowth.

UponthecompletionofthefatiguestrengthassessmentinaccordancewiththeGuidelinesandcompliancewiththerequirements,aclassnotationFFM(XX,YY)willbeappended,whereXXreferstotheenvironmentalconditions(e.g.NAforNorthAtlantic,whichscatterdiagramdefinedaccordingtoIACSRec.34),andYYreferstothedesignlife(inyear).

ForshipssubjecttofatiguestrengthassessmentinaccordancewiththeGuidelines,theirstructuraldesign,constructionprocedureandconstructionqualityshallmeettherequirementsoftheRulesforClassificationofSea-goingSteelShipsortheRulesforMaterialsandWeldingofCCSorotherrelevantstandardsacceptedbyCCS.

Definition

Initialdefect

Itreferstoslaginclusionsandporositygeneratedinthesmeltingandmanufacturingprocedureofactualstructures,toolmarksandgroovesgeneratedduringprocessing,cracks,incompletepenetration,porosity,undercuts,overburningandslaginclusionsgeneratedduringwelding,shrinkagecavitiesandloosenessincastings,aswellasstresscorrosioncracksandfatiguecracksgeneratedduringtheuseofthestructureindifferentenvironments.Thetypesofdefectsincludethroughthicknesscracks,edgecracks,embeddedcracksandsurfacecracks.ThespecificschematicdiagramofeachtypeisshowninSection3,[3.3].

Fatiguestressrangespectrum

Itreferstoastressrangespectrumconsistingoffatiguestressrangesthatmeettherequirementsofthedistributionfunction,whereeachvalueservesasthestressrangeforthepredictioncalculationofdetailfatiguecrackgrowth.

EquivalentDesignWavemethodology

ThecalculationofthefatiguestressrangespectrumisbasedontheEquivalentDesignWavemethod,suchasthestressrangecalculationmethodgiveninPart9-1,Chapter9oftheRulesforClassificationofSea-goingSteelShips,ortheGuidelinesforFatigueStrengthofShipStructureofCCS.

SpectralAnalysismethodology

FatiguestressrangespectrumcalculationisbasedontheSpectralAnalysismethodology,suchasthestressrangecalculationmethodgivenintheGuidelinesforSpectrumBasedFatigueAssessmentofHullStructureofCCS.

FailureAssessmentDiagramMethod(FAD)

Itreferstoamethodforassessingtheintegrityofstructurescontainingplanardefects,forwhichallpossiblefailuremodes,frombrittlefracturetoplasticcollapse,areconsidered.ThecalculationmethodsaredescribedinSection6.

Nominalstress

Itreferstostresscalculatedinastructural,onlytakingintoaccountthegeometriceffectofthestructure,butdisregardingthestressconcentrationduetostructuraldiscontinuityandwelds.Tensilestressispositiveandcompressivestressisnegative.

Symbols

?σn:Nominalstressrange,inN/mm2;thevariationrangeofalternatingstressresultinginstructuralfatigue,calculatedbythefollowingformula:

nmaxmin

Where:

σmax:Algebraicmaximuminanominalstresscycle,inN/mm2;σmin:Algebraicminimuminanominalstresscycle,inN/mm2.

σref:Referencestress,inN/mm2,usedintheFADtoassessthestressresultinginplasticfractureofthestructure,calculatedaccordingtoSection6Table6.4.1.

σmean:Meannominalstress,N/mm2,calculatedbythefollowingformula:

mean

maxmin

2

,N/mm2.

K:Stressintensityfactor,inMPa√??,reflectingthephysicalquantityofelasticstressfieldstrengthatcracktip,inrelationtocracktype,cracksize,geometricsizeofstructureandstressmagnitude,asdescribedinSection3,[3.3].

?K:Stressintensityfactorrange,inMPa√??,thedifferencebetweenthemaximumandminimumstressintensityfactorsinanalternatingstresscycle,asdescribedinSection2,[2.3].

?Keq0:Equivalentstressintensityfactorrange,inMPa√??,takingintoaccounttheinfluenceofload(stress)ratio.

R:Load(stress)ratio,referringtotheratiooftheminimumstresstothemaximumstressinafatigueload(stress)cycle.

?Kth0:Thresholdstressintensityfactorrange,inMPa√??,characterizingthecriticalpointatwhichcrackgrowthoccurs,i.e.whenthevalueisgreaterthanthisthreshold,crackpropagates;otherwise,crackdoesnotpropagate.Forhullstructuressteels,therecommendedthresholdis2MPa√??.

C:Materialconstantinfatiguecrackgrowthlaw,takenastheParisLaw’sparameter.Therecommendvalueforsteelisfollowed

C=1.6510-11.

m:Materialconstantinfatiguecrackgrowthlaw,takenastheParisLaw’sparameter.Therecommendvalueforsteelism=3.

KIC:Planestrainfracturetoughness,inMPam.Underplanestrainconditions,thethresholdstressintensityfactorfortheunstablegrowthofModeI(i.e.openingmode)cracksinsteelshallcomplywithrelevantprovisionsinPart1,Chapter2oftheRulesforMaterialsandWeldingofCCS.

da/dN:Crackgrowthrate,inm/cycle,aphysicalquantitydescribingthecrackgrowthspeedandtheamountofcrackgrowthineachcycle.

Kr:Fractureparameter,theratioofstressintensityfactortofracturetoughness,asdescribedinSection6,[6.3].

Lr:Plasticcollapseparameter,ameasureoftheappropriatedstressslevelandtobecontrolledbyplasticcollapseconsideration,asdescribedinSection6,[6.4].

Ntotal:Totalnumberofcycles,thetotalnumberoffatigueloadcyclesduringthedesignfatiguelife.

NF:Failurenumberofcycles,thenumberoffatigueloadcyclesexperiencedbeforethefatiguefailureofthestructure.

ReH:Materialyieldstrength,inN/mm2,whichshallcomplywiththerequirementsinPart2,Chapter1,Section3oftheRulesforClassificationofSea-goingSteelShipsofCCS.

Rm:Materialtensilestrength,inN/mm2,whichshallcomplywithrelevantprovisionsinPart1,Chapter3oftheRulesforMaterialsandWeldingofCCS.

Note:Fortheconstantsin1.3.8-1.3.10,ifothervaluesareused,theyshallbeapprovedbyCCS.

FatigueFailureMode

TheGuidelinesmainlydescribethefollowingtwofatiguecrackfailuremodes:

Fatiguecracksinitiatingfromsmalldefectsorundercutsattheweldtoeandpropagatingintothebasematerial;

Fatiguecracksinitiatingfromtheedgeofanon-weldeddetails(cut,grooveorsmallsurfacedefect/irregularityinstructure)

FatigueAssessmentMethodology

Thetheoreticalbasisforfatigueassessmentistheuniquecurvemodelofcrackgrowthrateequationbasedonfracturemechanicsmethodology,andthespecificcalculationmethodisdescribedinSection2,[2.3.1].

Forfatigueassessment,theequivalentdesignwavemethodorspectralanalysismethodisusedfordifferentdetailpositionsrespectively,asdescribedinSection2,[2.2].

FatigueLoadingConditions

WhentheassessmentisperformedusingtheEquivalentDesignWavemethod,theloadingconditionsandfractionoftimeineachloadingconditionforfatigueassessmentshallcomplywiththerelevantrequirementsoftheRulesforClassificationofSea-GoingSteelShipsortheGuidelinesforFatigueStrengthofShipStructureofCCS.

WhentheassessmentisperformedusingtheSpectralAnalysismethod,theloadingconditionsandfractionoftimeineachloadingconditionforfatigueassessmentshallcomplywiththerelevantrequirementsoftheRulesforClassificationofSea-goingSteelShipsortheGuidelinesforSpectrumBasedFatigueAssessmentofHullStructureofCCS.

FatigueLoadCases

TheloadcasesforfatigueassessmentbytheEquivalentDesignWavemethodshallcomplywiththerelevantrequirementsoftheRulesforClassificationofSea-GoingSteelShipsortheGuidelinesforFatigueStrengthofShipStructureofCCS.

TheloadcasesforfatigueassessmentbytheSpectralAnalysismethodshallcomplywiththerelevantrequirementsoftheRulesforClassificationofSea-GoingSteelShipsortheGuidelinesforSpectrumBasedFatigueAssessmentofHullStructureofCCS.

Section2FatigueEvaluation

General

ThefatiguestrengthassessmentintheGuidelinesisbasedonthecalculationoffatiguecrackgrowthandthefailureassessmentprinciples.Thefatiguestress(range)usedinthecalculationisthenominalstress(range).

ThecalculatedfatiguelifeTFistocomplywiththefollowingformula:

TF≥TDF

where:

TDF :Designfatiguelife,inyear.

ThedesignfatiguelifeTDFofthehullstructureshallbeinaccordancewiththeRulesforClassificationofSea-GoingSteelShips,theGuidelinesforFatigueStrengthofShipStructureortheGuidelinesforSpectrumBasedFatigueAssessmentofHullStructureofCCS.

Structuraldetailstobeassessed

TheGuidelinesapplytothefatigueassessmentofweldtoesandfreeedgesofbasematerial,andtheassessmentdetailsareasspecifiedinPart9-1,Chapter9oftheRulesforClassificationofSea-GoingSteelShips,theGuidelinesforFatigueStrengthofShipStructureortheGuidelinesforSpectrum-basedFatigueAssessmentofHullStructure.

UniqueCrackGrowthRateCurveModel

ThecrackgrowthlawistheUniqueCrackGrowthRateCurveModelexpressedasfollows:

daCK

mK

m

dN

where:

eq0

th0

C :Crackgrowthconstant;

m :Crackgrowthconstant;

?Kth0:Thresholdstressintensityfactorrange;

?Keq0:Equivalentstressintensityfactorrange,calculatedbythefollowingformula:

Keq0MRK

△K:Stressintensityfactorrange,calculatedbythefollowingformula:

m

KKmaxKmin,MPa

MR:Correctionfactorofload(stress)ratio,calculatedbythefollowingformula:

MR

1R1

1R

R0

0R0.5

1.051.4R0.6R2 0.5R1

R :Load(stress)ratio,calculatedbythefollowingformula:

RKmin+Kres

Kmax+Kres

Kmin:Theminimumstressintensityfactor,inMPa√??,calculatedaccordingtoSection3,[3.3];Kmax:Themaximumstressintensityfactor,inMPa√??,calculatedaccordingtoSection3,[3.3];Kres:Stressintensityfactorofresidualstress,inMPa√??,calculatedaccordingtoSection3,[3.3];

β,β1:Parametersdependingonmaterialsandserviceenvironment,takenas:

β=0.3,β1=0.7;

Note:Whenothervaluesareused,theyshallbeapprovedbyCCS.

FatigueStressRangeSpectrum

Theloadforthecalculationoffatiguecrackgrowthisobtainedfromasteppedstressrangespectrum,andthestandardsteppedstressrangespectrumiscalculatedbythefollowingformula:

lgN

1/

i1 i

max lgNtotal

where:

?σmax:ThemaximumdesignfatiguestressrangecorrespondingtothetotalnumberofcyclesNtotal;Ni :Numberofstressrangecyclesofstressrangespectrumblocki;

?σi :FatiguestressrangecorrespondingtothenumberofcyclesNi;

ξ :Weibulldistributionshapeparameter,withreferencetoPart2oftheRulesforClassificationofSea-GoingSteelShipsortheGuidelinesforFatigueStrengthofShipStructureofCCS;

Ntotal:Totalnumberoffatigueloadcycles.

FailureAssessmentMethodology

Thefailureassessmentcalculationforstructuraldetails,takingintoaccountinitialdefects,isusedofFailureAssessmentDiagram(hereinafterreferredtoasFAD).

AtypicalFADisshowninFig.2.5.2,withtheplasticcollapseparameterLrplottedontheabscissaandthefracturecoefficientKrontheordinate.Thefailureassessmentcurvedividestheassessmentdiagramintotwoareas:safeandunsafe.Iftheassessmentpointonthefatiguecrackgrowthcurveisbelowthefailureassessmentcurve,itindicatesthatthestructurecontainingcracksissafe;otherwise,itisunsafe.

Fig.2.5.2TypicalFailureAssessmentDiagram

ThecalculationmethodoffailureassessmentcurveiscalculatedaccordingtoSection6,[6.3].

ThecalculationmethodsoffractureandplasticcollapsefactorsforfatiguecrackgrowtharegiveninSection6,[6.3]and[6.4].

Theintersectionofthefailureassessmentcurveandfatiguecrackgrowthcurveisthefailurepointofthestructuraldetail,andthecorrespondingnumberofloadcyclesinthefatiguestressrangeisthenumberoffailurecyclesNF.

FatigueLifeCalculation

Thefatiguefailurelifeofstructureshallbecalculatedbythefollowingformula:

TF

NF

Ntotal

TDF

where:

TDF :Designfatiguelife,inyear;

NF :Totalnumberoffatiguecyclesbeforefailure;

Ntotal:TotalnumberoffatigueloadcycleswithinthedesignfatiguelifeTDF.

FatigueCrackGrowthAssessmentProcedure

Fatiguecrackgrowthcalculationandfailureassessmentcalculationmainlyconsistofthefollowingsteps.

Step1:Determinationofinitialparameters

Geometricsizesofdetails:platethicknessandwidth,withparametersdefinedaccordingtoSection3,[3.3];Equivalentinitialdefectsizeofdetail:withparametersdefinedaccordingtoSection3,[3.1.2];

Materialproperties:fracturetoughness,yieldstrengthandtensilestrength,withparametersdefinedaccordingtoSection1,[1.3.11],[1.3.17]and[1.3.18];

Materialcrackgrowthconstant:withparametersdefinedaccordingtoSection1,[1.3.8]-[1.3.10].

Step2:Generationoffatiguestressrangespectrum

FortheEquivalentDesignWavemethod,thelong-termprobabilitydistributionforthecalculationofstress

rangeistakenasWeibulldistributionfunction,withparametersdefinedaccordingtoSection4;

FortheSpectralAnalysismethod,theshort-termprobabilitydistributionforthecalculationofstressrangeistakenasRayleighdistributionfunction,withparametersdefinedaccordingtoSection5;

Thesteppedspectrumblocksoffatiguestressrangeandthecorrespondingnumberofcyclesaregeneratedaccordingtotheprobabilitydistributionfunctionofstressrange.

Step3:Normalizationofinitialdefectsizeandcalculationofstressintensityfactor

Calculatethestressintensityfactor(range)atthefatiguehotspotofthestructurebyequivalentnormalizationofinitialdefectsdefinedaccordingtoSection3.

Step4:Calculationoffatiguecrackgrowth

CalculatetheincrementdaforeachcyclicloadcalculatedaccordingtoSection2.

Step5:Failureassessment

ConstructtheFADbycalculatingthefailureassessmentcurveandfatiguecrackgrowthcurve;determinewhetherthecrackexceedsthefailurecriterionbasedonthefailureconditionsdefinedaccordingtoSection6:Ifthefailurecriterionissatisfied,thecalculationends;otherwise,repeatthecalculationdefinedaccordingtoSteps3to5.

TheprocedureforthecalculationoffatiguecrackgrowthisshowninFig.2.7.2.ThecalculationmethodofequivalentstressintensityfactorrangeintheflowchartisdefinedaccordingtoSection2.3"EquivalentStressIntensityFactorRange?Keq0".

Fig.2.7.2FlowchartforFatigueCrackGrowthAssessmentProcedure

Section3InitialDefectSizeCharacterizationsandStressIntensityFactorSolutions

General

IntheGuidelines,itisassumedthatstructuraldetailsactuallyhaveinitialdefectsduringtheprocedureofmetallurgicalfabrication,machiningandwelding.

Fornewlybuiltships,themodesofcracksrelatedtoinitialdefectsincludeedgecracksandsurfacecracks.Thecracksizecanbedeterminedbasedontheresultsfromconventionalnondestructivetestingmethods.ThesizesofinitialcracksshowninTable3.1.2maybeusedduringthedesignstageorattheunavailabilityofreliabledetectiondata.

FittedInitialCrackSizesforabsenceofNon-DestructiveTesting Table3.1.2

CrackType

CrackSize,m

EdgeCrack

a=0.1x10-3

-

SurfaceCrack

a=0.5x10-3

2c=10x10-3

Note:Foredgecracks,aisthecracklength;

Forsurfacecracks,aisthecrackdepthandcisthehalfofthecracklength.

Forshipsinoperation,themodesandsizesofcracksrelatedtoinitialcracksshallbedeterminedbasedonthenondestructivetestingresults,andtheequivalentsizeshallbesimplifiedasspecifiedinSection3,[3.2].Theembeddedcrackissimplifiedasanellipticalcrack,andthesurfacecrackissimplifiedasasemi-ellipticalcrack.

ThebasematerialinthisSectionreferstoflatsteelplatesubjectedtouniformtensilestress,andthecrackmodeunderconsiderationisModeIcrack,alsoknownasopeningcrack.Forthismodeofcrack,thecracktipopensundertheappliedstressperpendiculartothecrackplane,andthecrackgrowsinadirectionperpendiculartothestress.

InteractionRulesforCoplanarCracks

Coplanarcracksrefertomultiplecracksexistingonthesameplane.Fortwoormorecoplanarcracks,interactionshallbecarriedoutaccordingtothecriteriashowninTable3.2.1.

InteractionRulesforCoplanarCracks Table3.2.1

SchematicCracks

CriteriaforInteraction

EffectiveDimensionsafterInteraction

1

Coplanarsurfacecracks

s≤max(0.5a1,0.5a2) a1/Band/ora2/B≤0.5s≤max(a1,a2) a1/Banda2/B>0.5

amaxa1,a2

2c2c12c2s

2

Coplanarembeddedcracks(interactioninthicknessdirection)

sa1a2

2a2a12a2s

2cmax2c1,2c2

3

Coplanarembeddedcracks(interactioninwidthdirection)

smax(a1,a2)

2amax(2a1,2a2)2c2c12c2s

4

Coplanarembeddedcracks(interactioninthicknessandwidthdirection)

s1max(a1,a2)

s2a1a2

2c2c12c2s1

2a2a12a2s2

5

Coplanarsurfacecracks(interactioninthicknessdirection)

sa1a2

a2a1a2s

2cmax2c1,2c2

6

Coplanarsurfacecracks(interactioninthicknessandwidthdirection)

s1max(0.5a1,a2)

s2a1a2

aa12a2s2

2c2c12c2s1

StressIntensityFactorSolutions

Thissectioncontainsstressintensityfactorsolutionsforarangeofcracktypesthatincludethrough-thicknesscrack,edgecrack,embeddedcrackandsurfacecrackatweldtoes.Itisalsogiventhestressintensityfactorsolutionsforsurfacecrackunderweldingresidualstressatweldtoe.tisgiventhestressintensityfactorsolutionsforsurfacecrackunderweldingresidualstressatweldtoe.

m

ThestressintensityfactorKofthethroughthicknesscrackonplateunderuniformtensioniscalculatedbythefollowingformula:

where:

Kn

aYa

MPa

σn :Nominalstress,inN/mm2;

a :Halfofcracklength,inm,asshowninFig.3.3.2;

Y(a):Calculatedbythefollowingformula:

secaw

2a2 2a4

Ya10.25w0.06w

W :Widthofplate,inm,asshowninFig.3.3.2.

Fig.3.3.2Through-thicknessCrack(t:thicknessofplate,inm)

m

ThestressintensityfactorKofthefreeedgecrackonplateunderuniformtensioniscalculatedbythefollowingformula:

a

KY(a)n

MPa

where:

σn :Nominalstress,inN/mm2;

a :Cracklength,inm,asshowninFig.3.3.3;

Y(a):Calculatedbythefollowingformula:

Y(a)

a a2

a3 a4

1.120.231(w)10.55(w)

21.72()

w

30.39()

w

w :Widthofplate,inm,asshowninFig.3.3.3.

Fig.3.3.3EdgeCrack(t:thicknessofplate,inm)

ThestressintensityfactorKoftheembeddedcrackonplateunderuniformtensioniscalculatedbythefollowingformula:

KFa,a,c,

an

m

MPa

ctw

where:

σn :Nominalstress,inN/mm2;

a :Halfcracklengthofminoraxis,inm,asshowninFig.3.3.4;

Φ :CalculatedaccordingtoAppendix1,[1.1.1];

Faac

:CalculatedaccordingtoAppendix1,[1.1.1];

,,,

ctw

c :Halfcracklengthofmajoraxis,inm,asshowninFig.3.3.4;

t' :Equivalentthickness,inm,calculatedbythefollowingformula:

t'=2a+2p

:Distancefromminoraxisplaneofcracktoplateplane,inm,asshowninFig.3.3.4;

w :Widthofplate,inm,asshowninFig.3.3.4;

θ :Eccentricangleofellipse,inradian.

Fig.3.3.4EmbeddedCracks(t:thicknessofplate,inm)

Note:ThecalculationmethodinthisSectionisbasedontheassumptionthatembeddedcracksareelliptical,andcrackparametersshallmeetthefollowingconditions:

0≤a/2c≤1,2c/w<0.5,-π<φ≤π,andat0≤a/2c≤0.1,(a/t')<0.625·(0.6+a/c)

m

ThestressintensityfactorKofthesurfacecrackattheweldtoeiscalculatedbythefollowingformula:

KMT

MBH

aFa,a,c,

MPa

Km K b Φ

ctw

where:

σm :Nominalmembranestress,inN/mm2;

σb :Nominalbendingstress,inN/mm2;

H:CalculatedaccordingtoAppendix1,[1.1.2];A:Crackdepth,inm,asshowninFig.3.3.5(1);Φ:CalculatedaccordingtoAppendix1,[1.1.2];

Faac

:CalculatedaccordingtoAppendix1,[1.1.2];

,,,

ctw

c :Halfcracklengthofmajoraxis,inm,asshowninFig.3.3.5(1);

t :Platethickness,inm,asshowninFig.3.3.5(1);

w :Platewidth,inm,asshowninFig.3.3.5(1);

θ :Eccentricangleofellipse,inradian;

M

K

T :Stressintensitymagnificationfactorofweldedstructureundertensilestress;

M

K

B :Stressintensitymagnificationfactorofweldedstructureunderbendingstress;

Whenthedefectorcrackislocatedinalocalstressconcentrationarea,refertoFig.3.3.5(2);

MT,MBshallbecalculatedbythefollowingformula:

K

au

v

(MT1.0)

K

t

MT(B) K

1 (MT1.0)

K

v,u:asshowninTable3.3.5.

L :Lengthofweldtoe,inm,asshowninFig.3.3.5(2).

Fig.3.3.5(1) SurfaceCrack

Fig.3.3.5(2) ButtWeld

Valuesofvanduforaxialandbendingloading Table3.3.5

TypeofLoad

L/t

a/t

v

u

Axial

≤2

≤0.05(L/t)0.55

>0.05(L/t)0.55

0.51(L/t)0.27

0.83

-0.31

-0.15(L/t)0.46

>2

≤0.073

>0.073

0.615

0.83

-0.31

-0.20

Bending

≤1

≤0.03(L/t)0.55

>0.03(L/t)0.55

0.45(L/t)0.21

0.68

-0.31

-0.19(L/t)0.21

>1

≤0.03

>0.03

0.45

0.68

-0.31

-0.91

Note:ThecalculationmethodinthisSectionisbasedontheassumptionthatthesurfacecrackissemi-elliptical,andthecrackparametersshallmeetthefollowingconditions:

0≤a/c≤1.0,0≤a/t≤1.0,2c/w≤0.5,0≤φ≤π

ares

m

ThestressintensityfactorKresforweldingresidualstressesattheweldtoeiscalculatedbythefollowingformula:

K Faac

MPa

res

,, ,

where:

ctw

σres :Weldingresidualstress,inN/mm2,calculatedbythefollowingformula:

res0.3ReH

ReH :Yieldstrengthofmaterial,inN/mm2.OthersymbolsaredefinedinSection3,[3.3.5].

Section4EquivalentDesignWaveMethodology

General

TheEquivalentDesignWavemethodisapplicableforthefatigueassessmentoftypicaldetailsinhullstructures,wheretheinitialcracksaregenerallyfoundattheweldtoeofweldeddetailoratthefreeedgeofplate.

ThefatiguestressrangefortheEquivalentDesignWavemethodisdeterminedaccordingtothefatigue-relatedrequirementsintheRulesforClassificationofSea-GoingSteelShipsortheGuidelinesforFatigueStrengthofShipStructure.

Appropriatestressintensityfactorsareselectedforthecalculationofcrackpropagationaccordingtothetypicaldetailconnectionformandposition.

FatigueStressRangeSpectrum

TheGuidelinesrecommendthemethodofdeterminingthefatiguestressrangespectrumbasedonthelong-termdistributionfunctionoffatiguestressrange.OthermethodsofdeterminingthefatiguestressrangespectrumshallbeapprovedbyCCS.

AsteppedstressrangespectrumfollowingthedistributionisgeneratedusingtheshapeparameterξandscaleparameterqofWeibulldistribution.Thestressrangevalueofeachspectrumblockistakenasthestressrange?σnforcalculatingthefatiguelifewithrespecttothecrackgrowthofstructure,andthemaximumandminimumstressesareσmax=?σn/2+σmeanandσmin=?σn/2+σmeanrespectively.

Theprobabilitydensityfunctionofthelong-termdistributionofstressrangeisrepresentedbyatwo-parameterWeibulldistribution,anditsprobabilitydensityiscalculatedbythefollowingformula:

1

fWeibullqq

expq

0

where:

?σ :Stressrange,inN/mm2;

ξ :Weibulldistributionshapeparameter,withreferencetoPart2oftheRulesforClassificationofSea-GoingSteelShipsortheGuidelinesforFatigueStrengthofShipStructureofCCS;

:EquivalentscaleparameterofWeibulldistribution,calculatedbythefollowingformula:

qkqk

k

ak :Fractionoftimeofloadingconditionk,asdescribedinSection1,[1.6.1];

qk :Weibulldistributionscaleparameterofloadingconditionk,calculatedbythefollowingformula:

q n,k

k

lnnk

1/

?σn,k:Nominalstressrangeofloadingconditionkcorrespondingto10-8probabilitylevelofexceedance,inN/mm2;

nk :Numberofloadcyclesunderloadingconditionkcorrespondingto10-8probabilitylevelofexceedance,calculatedbythefollowingformula:

nk

kNtotal

Ntotal:Totalnumberoffatigueloadcycleswithinthedesignfatiguelife,withreferencetotheRulesforClassificationofSea-GoingSteelShipsortheGuidelinesforFatigueStrengthofShipStructureofCCS.

StressRange

Thefatiguedesignstressrange?σn,kforloadingconditionkshallbecalculatedbythefollowingequation:

n,ik

n,kmax( )

N/mm2

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