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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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