IN DEGREE PROJECT TECHNOLOGY AND LEARNING,SECOND CYCLE, 30 CREDITS
, STOCKHOLM SWEDEN 2017
Reduced variation in design and analysis of lightweight welded structureIn collaboration with Bromma and Volvo CE
CHUNYING LI
KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT
Acknowledge
Firstofall,IamgratefulformysupervisorZuheirBarsoumwhohasameetingwithourproject
groupeverysecondweek.Zuheirisaveryniceprofessorwhoalwayscarefullyandpatiently
explainedeveryquestionthat Iraisedup.Meanwhile, Igotfamiliarwithvariousdetailsof
welding and designing requirements from SD2420 Advanced design of welded structures
coursetaughtbyZuheirBarsoum.
Secondly, my co-supervisor Joakim Hedegård and Mansoor Khurshid also gave me large
amount of beneficial suggestions. Joakim Hedegård is familiar with different welding
technologyandheprovidedmesomepractical information.MansoorKhurshidworked in
Brommaandtookpartinthesameprojectwithus.HewasaPhDstudentofZuheirBarsoum
beforeandhealwayshelpedmesolveproblemsactively.
Thirdly, Iwould like togive sincere thanks tomyexaminerArneMelanderwhohas close
collaborationwithmysupervisorZuheirBarsoum.
Fourthly, IalsohadgoodcommunicationandcooperationwithmypartnerPeterHaglund
whoisaPhDstudent.Sincemymasterthesisisapartoftwo-yearproject,Peterwilldomore
analysisonspecimensandImostlyfocusontheoryresearch.Hewillalsodofatiguetestsin
thefuture.
GreatthankswillbealsosenttomyfriendJinchaoZhuandCarlLjungwhoareinthesame
officewithmeandwehelpedeachotheralot.
Last but not least, Iwould like to givemy appreciation tomy family for their continuous
supportandencouragementofmylife.
ChunyingLi
KTH,August2017
Abstract
The subject of this master thesis is about reduced variation in design and analysis of
lightweightweldedstructures.TheprojectisacollaborationwithVolvo,BrommaandKTH.
Withtechnologydevelopment,lightweightstructuresarebecomemoreandmorepopular.
In manufacturing factories, improving fatigue life in lightweight welded structures is
necessary and essential. This thesis is about reduced variation in design and analysis of
lightweightweldedstructures.Differentmethodthatarelinearelasticfracturemechanics,
effectivenotchstressandnominalstressareimplementedtoanalysisofloadcarryingand
non-loadcarryingcases.Meanwhile,variouscodesIIW,Eurocode3andCranestandardare
compared.ForIIW,allthreemethodsareincluded.However,onlynominalstressmethodis
usedforEurocode3andCranestandard.Insimpleloadingandnon-loadcarryinggeometrical
models,changingplatethicknessandpenetrationwillresultindifferenteffectonfatiguelife.
ThelatterpartofthesisisfocusedintheevaluationofVolvostandards.Effectivenotchstress
method is applied toobtain stress values and then calculate fatigue life. Several typesof
imperfectioncasesareanalyzedforbothloadcarryingandnon-loadcarryingcases.Allfatigue
lifevaluesarecomparedtothereferencefatiguelifevaluewhichis2millioncyclessothatall
statisticsarepresentedinclearpercentages.
Thestudyshowsthatvariedplatethicknessandpenetrationwillinfluencefatiguelife.Various
methodsandcodeswill affect fatigue lifediversely in loadcarryingandnon-loadcarrying
cases.ThevariationofwelddefectsinVolvostandardcasesalsohavedifferentimpacton
loadcarryingandnon-loadcarryingcases.
Keywords:Fatigue,weldquality,FEM,nominalstress,effectivenotchmethod, lightweight
structures,linearelasticfracturemethod
AbstraktDetta examensarbete handlar omminskad variation i design och analys av lätta svetsadestrukturer.ExamensarbetetharutförtsinomettsamarbetemellanVolvo,BrommaochKTH.Medteknologiskutvecklingblirlättastruktureralltmerpopulära.Vidtillverkningavfabrikerärdetnödvändigtochviktigtatt förbättrautmattningslivslängd i lättasvetsadestrukturer.Detta examensarbete handlar omminskad variation i design och analys av lätta svetsadestrukturer. Tre olika metoder, linjär elastisk brottmekanik, effektivanvisningsspänningsmetod och nominell spänningsmetod implementeras för analys avlastbärande och icke-lastbärande fall. Samtidigt jämförs olika koder IIW, Euro code 3 ochLyftkransstandard. För IIW ingår alla tre metoder. Emellertid används endast nominellspänningsmetod för Euro Code 3 och Lyftkransstandard. För enkla lastbärande och icke-lastbärandegeometriskamodellerkommerändradplåttjocklekochpenetrationattresulteraiolikaeffekterpåutmattningslivslängden.Den senare delen av examensarbetet är inriktad på utvärderingen av Volvos standarder.Effektivanvisningsspänningsmetodtillämpasföratterhållastressvärdenochsedanberäknautmattningslivslängd. Flera typer av diskontinuiteter analyseras för både lastbärande ochicke-lastbärande fall. Alla värden för utmattningslivslängd jämförs medreferensutmattningsvärdetsomär2miljonercyklersåattallstatistikpresenterassomtydligaprocentandelar.Studien visar att varierad plåttjocklek och penetration kommer att påverkautmattningslivslängden.Olikametoderochstandarderpåverkarutmattningslivslängdenolikailastbärandeochicke-lastbärandefall.VariationenavsvetsdefekteriVolvosstandardfallharocksåolikainverkanpålastbärandeochicke-lastbärandefall.
TableofContents
Acknowledge..........................................................................................................................................2
Abstract..................................................................................................................................................3
Listoffigures.................................................................................................................................6
Listoftables..................................................................................................................................7
1Introduction...............................................................................................................................81.1Background......................................................................................................................................8
1.2Problemdescription.........................................................................................................................8
1.3Objective..........................................................................................................................................8
1.4Layoutofthereport.........................................................................................................................8
1.5Overviewofmethodandcodes.......................................................................................................8
1.5.1Linearelasticfacturemechanics(LEFM)...................................................................................9
1.5.2Effectivenotchstress(ENS).......................................................................................................9
1.5.3Nominalstress(NS).................................................................................................................10
1.5.4Eurocode3.............................................................................................................................10
1.5.5Cranestandard........................................................................................................................10
2Loadcarryingcruciformcase..................................................................................................112.1TheInternationalInstituteofWelding(IIW)...................................................................................11
2.1.1Applicationoflinearelasticfracturemechanics(LEFM).........................................................11
2.1.2Applicationofeffectivenotchstressmethod(ENS)................................................................13
2.1.3Applicationofnominalstress(NS)..........................................................................................14
2.2Eurocode3application..................................................................................................................15
2.3Cranestandardapplication............................................................................................................15
3Non-loadcarryingcruciformcase...........................................................................................163.1TheInternationalInstituteofWelding(IIW)....................................................................................16
3.1.1Applicationoflinearelasticfracturemechanics(LEFM).........................................................16
3.1.2Applicationofeffectivenotchstressmethod(ENS)................................................................17
3.1.3Applicationofnominalstress(NS)..........................................................................................18
3.2Eurocode3application..................................................................................................................19
3.3Cranestandardapplication............................................................................................................19
4Comparisonbetweenmethodsandcodes.............................................................................20
5SpecificcasesofVolvostandards............................................................................................215.1VolvostandardcaseNo.106...........................................................................................................21
5.2VolvostandardcaseNo.108...........................................................................................................22
5.3VolvostandardcaseNo.202...........................................................................................................24
5.4VolvostandardcaseNo.203...........................................................................................................26
5.5VolvostandardcaseNo.204...........................................................................................................27
5.6VolvostandardcaseNo.211...........................................................................................................28
6SummaryofwelddefectsinVolvostandardcases.................................................................29
7Demonstrator..........................................................................................................................30
8Conclusions..............................................................................................................................31
9Futurework.............................................................................................................................32
10References.............................................................................................................................33
AppendixA-Effectivenotchfatigueresistanceforsteel...........................................................34
AppendixB-LoadcarryingweldedjointsofEurocode3..........................................................34
AppendixC-VolvostandardNo.203..........................................................................................35
AppendixD-VolvostandardNo.204..........................................................................................36
AppendixE-VolvostandardNo.211..........................................................................................37
Listoffigures
Figure1.Fractureinmodes I, II, and III..................................................................................9Figure2.Recommendedroundingofweldtoesandfilletweldroots[2]..............................10
Figure3.Loadcarryingcruciformstructure...........................................................................11
Figure4.Loadcarryingwithpenetrationof2mminFRANC2D.............................................12
Figure5.FatiguelifeofdifferentplatethicknessinloadcarryingcaseforLEFMmethod....13
Figure6.FatiguelifeofdifferentpenetrationinloadcarryingcaseforLEFMmethod.........13
Figure7.Loadcarryingcase,penetrationof2mm.................................................................13
Figure8.FatiguelifeofdifferentplatethicknessinloadcarryingcaseforENSmethod.......14
Figure9.FatiguelifeofdifferentpenetrationinloadcarryingcaseforENSmethod............14
Figure10.Non-loadcarryingcruciformstructure..................................................................16
Figure11.Non-loadcarryingwithpenetrationof2mminFRANC2D...................................16
Figure12.Fatiguelifeofdifferentplatethicknessinnon-loadcarryingforLEFMmethod...17
Figure13.Fatiguelifeofdifferentpenetrationinnon-loadcarryingforLEFMmethod........17
Figure14.Non-loadcarryingcase,penetrationof2mm.......................................................18
Figure15.Fatiguelifeofdifferentplatethicknessinnon-loadcarryingforENSmethod.....18
Figure16.FatiguelifeofdifferentpenetrationinloadcarryingforENSmethod..................18
Figure17.ComparisonofIIWmethods..................................................................................21
Figure18.ComparisonbetweenIIW,EurocodeandCranestandard...................................21
Figure19.Legdeviationanalysis............................................................................................22
Figure20.Fatiguelifeforthelegdeviationcase...................................................................22
Figure21.Badfit-uploadcarrying,gapheighth=3mm.........................................................23
Figure22.Badfit-upnon-loadcarrying,gapheighth=3.......................................................23
Figure23.Fatiguelifeofdifferentgapheightsinnon-loadcarrying.....................................24
Figure24.Loadcarryingcase,weldqualityC,r=2mm...........................................................25
Figure25.Non-loadcarryingcase,weldqualityC,r=2mm....................................................25
Figure26.Fatiguelifeofdifferenttransitionradiusinnon-loadcarrying.............................26
Figure27.Loadcarryingcase,undercutA=1.5mm................................................................26
Figure28.Non-loadcarryingcase,undercutA=1.5mm.........................................................27
Figure29.Fatiguelifeofdifferentundercutinnon-loadcarrying.........................................27
Figure30.Fatiguelifeofdifferentthroatthicknessinnon-loadcarrying..............................28
Figure31.Loadcarryingα=105°.............................................................................................28Figure32.Non-loadcarryingα=105°.....................................................................................29Figure33.Fatiguelifeofdifferentanglesinnon-loadcarrying.............................................29
Figure34.Simplifiedstructureofthedemonstrator.............................................................30
Listoftables
Table1.Materialproperties...................................................................................................12
Table2.Fatigueresistancesvaluesforcruciformjointsand/orT-joints...............................14
Table3.Fatiguestrengthofconstructionaldetailsforcranestandard.................................15
Table4.Fatigueresistancevaluesfornon-loadcarryingattachmentsNo.511[2]................18
Table5.Detailcategoriesofconstructionaldetailsinnon-loadcarryingforEurocode3.....19
Table6.Fatiguestrengthofconstructionaldetailsinnon-loadcarryingforcranestandard20
Table7.VolvostandardNo.106requirementdetails[8].......................................................22
Table8.VolvostandardNo.108requirementdetails[8].......................................................23
Table9.VolvostandardNo.202requirementdetails[8].......................................................24
1Introduction
1.1BackgroundLightweight structures reduce the environmental impact by decreased fuel consumption,
materialusage,andproductionresourcesused.Aknownandpossiblyreducedvariationin
theentirevaluestreamwillincreasethecontrolofsafetymarginshenceenablingreduced
leadtimeandincreasedflexibility.Theintroductionoflightweightstructuresisconnectedto
thepossibilitytousehighstrengthsteel(HSS).Highqualityrequirementsonweldedjoints
areseldomusedwhichlimittheintroductionofmoreHSSmaterialinindustrialmanufacturing
process.Theweightofstructurescanbereduced20%byimprovedtechnologies,meanwhile
theproductioncostisreduced.Withareducedscatterinproduction,loadestimation,and
structuralstrengthabetterutilizationofHSSispossiblewiththegreatpotentialoflightweight
structures.
In this master thesis, different of variation will be studied and mapped. High quality
requirementsonwelded jointsareseldomusedwhich limit the introductionofmoreHSS
heavierthanwhat ispossible.Thereferencefatiguelifevaluesare2millioncycles.Allthe
fatiguelifevaluesarecomparedwiththereferencefatiguelifesoalltheresultsareshown
veryclearly.
1.2ProblemdescriptionAlargecontributoroftheslowintroductionofHSSisduetothelargescatterintheproduction
processwhichresultsinvariationinthefactorsthataffectthefatigueproperties,forexample,
weldqualityandresidualstresses.
1.3ObjectiveThegoalofthethesisworkistomapandstudyvariationinthedesignandFEanalysisprocess
oftheproductdevelopmentinfabricationofweldedstructures.
1.4LayoutofthereportInthebeginningofthereport,thegeneralideasofthismasterthesisaredescribed.Different
concepts of methods and codes are introduced. Then, two basic cases of load carrying
cruciformandnon-load carrying cruciformare specified. The correspondingmethods and
codesareimplementedintothetwocasesandarecompared.Chapter5isaboutanalysisof
failureandimperfectionofVolvostandardcases.Chapter6isthesummaryinapedagogical
waythemagnitudeofeffectofdifferentwelddefects.Intheend,conclusionandfuturework
areclarified.
1.5OverviewofmethodandcodesLinearelasticfracturemechanics(LEFM),Effectivenotchstress(ENS)andnominalstress(NS)
are three fatigue assessmentmethods to analysis. Different codes and standards such as
InternationalInstituteofWelding(IIW),Eurocode3(EC3)andCranestandard(CrandSTD)will
beusedtostudythevariationinlifeassessment.
1.5.1Linearelasticfacturemechanics(LEFM)Linearelasticfracturemechanicsmethodisusedtopredictthebehaviorofcracksinsolids
subjectedtofatigueloading.TherearethreebasictypesofloadcasethatisshowninFigure
1.ModeIisanopenmode.ModeIIisaslidingorshearingmode.ModeIIIisatearingmode.
In order to predict fatigue crack propagation, numerous empirical or semi-empirical
equationshavebeenproposedtorelatefatiguecrackgrowthratedatatotheparameterΔ#[1].NumericalintegrationofParislawisusedinfatiguelifeassessment,thatis
$%
$&= ( ∙ Δ#*
.
Where+, / +. is the crack growth rate per cycle, C and m are material specific input
parameters. Cmeans fatigue crack growth coefficient andmmeans fatigue crack growth
exponent.
Figure1.Fractureinmodes I, II, and III.
Inthisthesis,FRANC2Dsoftwareisusedtoanalysisthecrackpropagationprocess.Thestress
intensityfactorscanbeobtainedautomaticallyinFRANC2D.Then, exporttheSIFhistorytocomputecyclesinExcelwhichistheExcelsheetshownonCornellFractureGroupwebsite[3].
1.5.2Effectivenotchstress(ENS)Thetotalstressacquiredassuminglinear-elasticmaterialbehavioriseffectivenotchstress.
Forstructuralsteelsandaluminumalloysaneffectivenotchrootradiusofr=1mmhasbeen
verified to give consistent results if plate thickness is equal or bigger than 5mm [4]. This
methodassessesweldedjointsrestrictedlywithrespecttopotentialfatiguefailuresfromthe
weldrootorweldtoe.Thefatigueassessmentisassociatedfatigueclass(FAT)forthebase
material. In thispaper, thematerial is steel and the correspondingFATvalue is225 from
AppendixA.RecommendedroundingofweldtoesandfilletweldrootsisshowninFigure2.
Figure2.Recommendedroundingofweldtoesandfilletweldroots[2]
1.5.3Nominalstress(NS)Nominal stress is the stress that is calculated in the sectional area under consideration,
containingthestressraisingeffectsofthemacro-geometricshapeofthecomponentnearthe
joint,ignoringthelocalstressraisingeffectsoftheweldedjoint.
Inmost simple cases, the nominal stress can be calculated using elementary theories of
structuralmechanicswhichisbasedonlinear-elasticbehavior.Nominalstressistheaverage
stressintheweldthroatorintheplateattheweldtoeasindicatedinthetablesofstructural
details[4].ThecalculationofnominalstressiscomparedwithaFAT-value.Selectedfroma
catalogue of details, the geometry most closely resembling the actual welded detail.
Meanwhile, small misalignments are covered in the FAT values, also residual stresses.
NominalstressmethodcouldbeusedifFAT-valueandloadingareconsistentwiththefatigue
class.Usually,forcomplexstructuresisnoteasytodefinenominalstress.
1.5.4Eurocode3Eurocodes,EN1993-1-9isusedforfatiguestrengthinstructuralsteels. Thefatiguestrengthfornominalstressrangesisrepresentedbyaseriesof(log∆01)-(logN)curvesand(log∆21)- (log N) curves (S-N-curves), which correspond to typical detail categories. Each detail
categoryisdesignatedbyanumberwhichrepresents, inN/334,thereferencevalue∆01 and∆21 forthefatiguestrengthat2millioncycles[5].
Thefatigue lifeassessmentshouldbecarriedoutwiththeuseofnominalstressrangefor
detailsshown inthetables.Thevalueof thestressrange∆05 correspondingtoavalueof.5=2millioncycleswerecalculatedfora75%confidencelevelof95%probabilityofsurvival
forlogN,meanwhile,thestandarddeviationandthesamplesizeandresidualstresseffects
aretakenintoconsideration.
1.5.5CranestandardCrane standard deals only with the nominal stress method. The stresses are calculatedaccordingwiththenominalstressconcept.Anominalstressisastressinthebasematerial
adjacenttoapotentialcracklocation,calculatedinaccordancewithsimpleelasticstrength
ofmaterialstheory,excludinglocalstressconcentrationeffects[6].Thecharacteristicfatigue
strengthvaluescontaintheeffectsoflocalstressconcentrationduetotheshapeofthejoint
andtheweldgeometry,thestressdirection,residualstresses,theweldingprocess,etc.
Thelimitdesignstressofaconstructionaldetailischaracterizedbythecharacteristicfatigue
strength, that is the value of∆05 . The representation of∆05 is the fatigue strength at
2×10:cyclesunderconstantstressrange loadingandwithaprobabilityofsurvival97.7%.Thevaluesof∆05dependontheweldqualitylevels.
2LoadcarryingcruciformcaseFirstbasicmodelisloadcarryingcruciformcaseinwhichtheupperpartisnotfullpenetration
andlowerpartisfullpenetrationsothatthismodelcanbeconsideredasT-joint.Theplate
thicknessinthisstudyis6mm,12mmand21mm.Andthepenetrationinthisstudyis1mm,
2mm,3mmand4mm.Thestressrangeisaconstant,thatis100Mpa.Thegeometrymodelis
showninFigure3.
Figure3.Loadcarryingcruciformstructure
2.1TheInternationalInstituteofWelding(IIW)The International Institute ofWelding was found in 1948 by the welding institute of 13
countrieswhofeltimportanttomakemorerapidscientificandtechnicalprogress.
ThetechnicalareaofIIWencompassesthejoining,cuttingandsurfacetreatmentofmetallic
andnon-metallicmaterialsbysuchprocessesaswelding,bracing,soldering,thermalcutting,
thermalspraying,adhesivebondingandmicrojoining.IIWworkalsoembracesalliedfields
includingqualityassurance,non-destructivetesting,standardization,inspection,healthand
safety,education,training,qualification,designandfabrication[4].
2.1.1Applicationoflinearelasticfracturemechanics(LEFM)HerearesomebasicstepswhicharedoneinFranc2D.Inthebeginning,somepreliminary
work shouldbedone.UseAnsysAPDL to createabasicT-jointmodel,makemeshesand
archivethefilein*.cdbfile.Thentranslate*.cdbfileto*.inpfilebytranslator.
Inputthe*.infileandruntheFRAND2Dprogram.First,inPRE-PROCESS,choosePlanstress
inPROBLEMTYPE.Then,selecttheMATERIALoption,thismodelismadeofsteel.SelectE
andwritetheYong’smodulusof210000MPa.
t[mm] Platethickness 10
H[mm] Leglength 9.9
2a[mm] Weldrootgap 8
S[MPa] Nominalstressrange 100
Materialdata:
-Basic:Steel:DOMEX550MC
Yieldstrength=550Mpa
Ultimatestrength=700Mpa
E-modulus=210GPa,n=0.3-FractureandFatigue:��m=3�C=5.0E-12(unitsinMPaandmeter)
R=0(stressratio)�K<==120MPa√m(fracturetoughness)
∆K>?=2MPa√m(thresholdvalue)
Table1.Materialproperties
Inloadcarryingcase,thecrackspropagatefromtherootsides.Extractstressintensityfactors
computedwithinFRANC2Dtogetfatiguelife.
Figure4.Loadcarryingwithpenetrationof2mminFRANC2D
When three different plate thicknessmodels are compared, the penetration is kept as a
constant1mm.Allthroatthicknessis0.7timesplatethickness.Adeclinetrendthatasthe
platethicknessincreases,thefatiguelifewilldecreaseisshownclearly.
0.00%
40.00%
80.00%
120.00%
160.00%
200.00%
240.00%
6 12 21
Percentageofreferencelife
Platethickness[mm]
!"/(2E+6)
Figure5.FatiguelifeofdifferentplatethicknessinloadcarryingcaseforLEFMmethod
Whentheplatethickness issetasaconstantthat is12mm,weldpenetrationwillmakea
differenceonfatiguelife.Thecorrespondingfatiguelifewillincreasewiththeincreaseofthe
penetration.
Figure6.FatiguelifeofdifferentpenetrationinloadcarryingcaseforLEFMmethod
2.1.2Applicationofeffectivenotchstressmethod(ENS)
Figure7.Loadcarryingcase,penetrationof2mm
Herethreeplatethicknesseswhichare6mm,12mmand21mmarechoseninthestudy.All
throatthicknessis0.7timesplatethickness.Whenthepenetrationiskeptasaconstantwhich
is1mm,thefatiguelifevalueswilldecreaseastheplatethicknessincrease.
0.00%
40.00%
80.00%
120.00%
160.00%
200.00%
240.00%
1 2 3 4
Percentageofreferencelife
Penetration [mm]
!"/(2E+6)
Figure8.FatiguelifeofdifferentplatethicknessinloadcarryingcaseforENSmethod
Whentheplate thickness iskeptasaconstantwhich is12mm, the fatigue lifevalueswill
increaseaccordingtheincreaseofpenetration.
Figure9.FatiguelifeofdifferentpenetrationinloadcarryingcaseforENSmethod
2.1.3Applicationofnominalstress(NS)
Table2.Fatigueresistancesvaluesforcruciformjointsand/orT-joints
Innominalstress,theassociatedfatigueclassisrelativelylow(FAT36-FAT40),definingthe
characteristic fatigue strength of the design S-N curve at 2 million cycles for a survival
probability of 97.7%. The reasons for the low fatigue class are that a very sharp notch is
presentandthatthenominalstressinthewelddisregardsanylocalbendingeffects[7].
FAT:=36Mpa,∆0@ =A
4%∙ ∆0* +
A
:%∙ ∆0C=71.4Mpa,.D:=2∙ 10
: ∙ (FGH
∆IJ)L=2.56E+5cycles
0.00%
30.00%
60.00%
90.00%
120.00%
150.00%
180.00%
6 12 21
Percentageofreferencelife
Plate thickness [mm]
!"/(2E+6)
0.00%
30.00%
60.00%
90.00%
120.00%
150.00%
1 2 3 4
Percentageofreferencelife
Penetration [mm]
!"/(2E+6)
However, if plate thickness t is kept as a constant, throat thickness a is decreased, FAT:
=40Mpa,.D:=2∙ 10: ∙ (
FGH
∆IJ)L=3.52E+5cycles,fatiguelifewillincrease.
2.2Eurocode3applicationFromtheappendixB,detailcategoriesforconstructionaldetailsareshown.
Detailcategory:=36Mpa,∆σN =>
4O∙ ∆σP +
>
:O∙ ∆σQ=71.4Mpa,
NS:=2∙ 10: ∙ (
$UA%VWX%AUYZ[\
∆]^)L=2.56E+5cycles
Themisalignmentoftheload-carryingplatesshouldnotexceed15%oftheplatethicknessoftheintermediateplate[5].
Theminimumvalue:∆σN =}~.�ÄÅO
~~Ç%= 62.09Mpa, NS:=2∙ 10
: ∙ ($UA%VWX%AUYZ[\
∆]^)L=3.9E+5
cycles,fatiguelifewillincrease.
Themaximumvalue:∆σN =}~.�ÄÅO
àÇ%= 84Mpa, NS:=2∙ 10
: ∙ ($UA%VWX%AUYZ[\
∆]^)L=1.6E+5
cycles,fatiguelifewilldecrease.
2.3Cranestandardapplication
Table3.Fatiguestrengthofconstructionaldetailsforcranestandard
Here,∆0X,∆2Xarethecharacteristicfatiguestrengths.Stressinweldthroat,FAT:=45Mpa,∆σN=F/(2×,×ℓ)=F/(2×0.7×ç×ℓ)=71.4Mpa
NS:=2∙ 10: ∙ (
éèê
∆]^)L=5.01E+5cycles.
InTable3,itisshownthecharacteristicfatiguestrengthsforweldqualitylevelCandlevelB.
WeldqualitylevelC,FAT:=63Mpa,NS:=2∙ 10: ∙ (
éèê
∆]^)L=5.01E+5cycles.
WeldqualitylevelB,FAT:=71Mpa,NS:=2∙ 10: ∙ (
éèê
∆]^)L=7.16E+5cycles,.Dincrease
3Non-loadcarryingcruciformcaseAnotherbasicmodelisnon-loadcarryingcruciformcaseinwhichboththeupperpartandthe
lowerpartisnotfullpenetration.Theplatethicknessinthisstudyis6mm,12mmand21mm.
Andthepenetrationinthisstudyis1mm,2mm,3mmand4mm.Thestressrangeisaconstant,
thatis100Mpa.TheweldqualityforthiscaseismainlyVE,VDandVC.Thegeometrymodel
isshowninFigure10.
Figure10.Non-loadcarryingcruciformstructure
3.1TheInternationalInstituteofWelding(IIW)3.1.1Applicationoflinearelasticfracturemechanics(LEFM)
Figure11.Non-loadcarryingwithpenetrationof2mminFRANC2D
Innon-loadcarryingcase,thecrackspropagatefromtheedgeoftoe.IneverymodelofFRANC
2D,aninitialcrackof0.38mmwhichisacasualvaluebutissmallandgoodenoughisformed
inthebeginning.Theninthesimulation,thecrackpropagatesautomaticallyandthecrack
endswiththecracklengthof5.38mm.Thefinalcracklength5.38mmischosenarbitrarily.All
thestressintensityfactorvaluescanbeobtainedinstressintensityhistory.Inputallthese
valuesintotheExcelsheetshownonCornellFractureGroupwebsitetogetthefatiguelife.
Astheplatethicknessincrease,thefatiguelifewilldecrease.
Figure12.Fatiguelifeofdifferentplatethicknessinnon-loadcarryingforLEFMmethod
However,thechangeofpenetrationwillnotaffectfatigue life.Theaveragepercentageof
fatiguelifeisaround83%whichcanbeseeninfigure13.
Figure13.Fatiguelifeofdifferentpenetrationinnon-loadcarryingforLEFMmethod
3.1.2Applicationofeffectivenotchstressmethod(ENS)TheFEManalysiswhenthepenetrationis2mminnon-loadcarryingisshowninFigure14.
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
6 12 21
Percentageofreferencelife
Plate thickness [mm]
!"/(2E+6)
Figure14.Non-loadcarryingcase,penetrationof2mm
Ineffectivenotchmethod,ifpenetrationiskeptasaconstant1mm,fatiguelifedecreasewith
the increase of the plate thickness.When the plate thickness is 6mm, the percentage of
fatiguelifeis148.91%.However,whentheplatethicknessis21mm,thepercentageoffatigue
lifeisonly19.78%.ThestatisticsareshowninFigure15.
Figure15.Fatiguelifeofdifferentplatethicknessinnon-loadcarryingforENSmethod
Whentheplatethicknessiskeptasaconstantwhichis12mm,fatiguelifevalueswillnothave
largevariationwiththechangeofpenetration.
Figure16.FatiguelifeofdifferentpenetrationinloadcarryingforENSmethod
3.1.3Applicationofnominalstress(NS)
Table4.Fatigueresistancevaluesfornon-loadcarryingattachmentsNo.511[2]
0.00%
30.00%
60.00%
90.00%
120.00%
150.00%
180.00%
6 12 21
Percentageofreferencelife
Platethickness[mm]
!"/(2E+6)
FAT:=80Mpa,∆0@=100Mpa.Thiscaseanangularmisalignmentcorrespondingto#*=1.2isconsideredsothatthelimitvalue∆0* =100/#*=83.33Mpa.
.D:=2∙ 10: ∙ (
FGH
∆Ië)L=1.77E+6cycles
However,ifthestructureischangedfromcruciformtotwosidesfilletsorweldtoeisground,
thesituationwillchange.ThenFAT:=100Mpa,∆0@=100Mpa,∆0*=100/#*=83.33Mpa,.D:
=2∙ 10: ∙ (FGH
∆IJ)L=3.46E+6cycles,fatiguelifewillincrease.Inproductionprocess,moreafter-
workshouldbedonesoproductioncostwillalsoincrease.
3.2Eurocode3application
Table5.Detailcategoriesofconstructionaldetailsinnon-loadcarryingforEurocode3
Inthiscase,theplatethicknessisalwayssmallerthan50mm.FromTable13shownabove,
detailcategoryis80withcorrespondingtotheplatethicknesslessthan50mm.
FAT:=80Mpa,∆0@ = 100Mpa,.D:=2∙ 10: ∙ (
FGH
∆IJ)L=1.02E+6cycles
Increaseplatethicknesslandkeeptherangefrom50mmto80mm,FAT:=71Mpa,
.D:=2∙ 10: ∙ (
FGH
∆IJ)L=7.16E+5cycles,.Dincrease.
3.3Cranestandardapplication
Table6.Fatiguestrengthofconstructionaldetailsinnon-loadcarryingforcranestandard
FatiguestrengthvaluesarevariedwithweldqualitylevelBandqualitylevelC[6].Meanwhile,
inthisthesis,thestudiedstructureisdoublefilletweld.FromTable6,
WeldqualitylevelC,FAT:=90Mpa,∆σN = 100Mpa,NS:=2∙ 10: ∙ (
éèê
∆]^)L=1.46E+6cycles
WeldqualitylevelB,FAT:=100Mpa,∆σN = 100Mpa,NS:=2∙ 10: ∙ (
éèê
∆]^)L=2E+6cycles
4ComparisonbetweenmethodsandcodesComparingthreedifferentmethodsofIIWcode,somevaluesaresetasconstant.Theplate
thicknessis12mm,thestressrangeis100Mpa,throatthicknessis0.7timesofplatethickness
andthepenetrationis3mm.
FromFigure17,wecanseethatforbothloadcarryingandnon-loadcarrying,themethodof
linear elastic fracturemechanicswould always reach thehighest percentageof reference
fatiguelife.
12.80%
81.38%
118.70%
51.20%
73.88% 84.63%
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
140.00%
NS ENS LEFM
Percentageofreferencelife
ComparisonofIIWmethods
load-carrying nonload-carrying
Figure17.ComparisonofIIWmethods
When three codes IIW, Euro code 3 and Crane standard are in comparison, the control
conditions of plates are the same as above. In addition, some misalignment values are
considered in some specific codes. Thenon-load carrying caseof IIW is coveredwith the
maximumangularmisalignmentcorrespondingto#*=1.2whichmeansthatthelimitvalue
∆0* =100/#* =83.33Mpa. The load carrying case of Euro code 3 includes that themaximummisalignmentoftheload-carryingplatesis15%oftheplatethicknessoftheintermediateplate.
Figure18.ComparisonbetweenIIW,EurocodeandCranestandard
5SpecificcasesofVolvostandardsOverall,variationsthateffectsfatigue lifeofweldedstructureshavebeenclearlyclarified.
Thensomescattersareconsidered intoVolvostandard181-0004tostudyvariousspecific
cases.InVolvostandards,severalspecificcaseswhichcovermisalignmentandfailuresare
usedtoanalysisfatiguelifebyeffectivenotchstressmethodwhichshowsgeometrymodels
clearly.AllthemodelsarecreatedinAnsysbyinputtingcodesintoit,meshing,solving,etc.
Differentweldclassaredescribedtofulfillvariousproductionrequirement.VSisweldclass
for static strength. VE, VD, VC, VB are weld classes for fatigue strength from lowest
requirementtohighestrequirement.
5.1VolvostandardcaseNo.106ThecaseofVolvostandardNo.106isaboutlegdeviationshowninTable7.Sincetheplate
thicknessis10mm,themaximumdeviationdistanceis3.4mmforalltheweldrequirements
VE,VD,VCandVB.Meanwhile,thedeviationisalwaysinthesamedirectionalongwiththe
loading direction. In this study, the referencemodelswhich don’t have leg deviation are
comparedwithmodelswhichhave themaximum legdeviation.The stressanalysisof the
geometrymodelswithdeviation3.4mmareshowninFigure19.
12.80% 19.50%
25.05%
88.50%
51.20%
73.00%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
IIW Eurocode3 Cranestandard
Percentageofreferencelife
Comparisionofcodes
load-carrying nonload-carrying
Table7.VolvostandardNo.106requirementdetails[8]
Figure19.Legdeviationanalysis
Fromthestaticsshownbelow,bothforloadcarryingandnon-loadcarrying,percentageof
referencefatiguelifewillincreaseaslegdeviationoccurs.ThisisshowninFigure20.
Figure20.Fatiguelifeforthelegdeviationcase
5.2VolvostandardcaseNo.108Thiscaseisaboutbadfit-upwhichmeansthattwoplateshaveagapdistance.Thisisshown
inTable8.Forallweldqualities,iftheplatethicknessis10mm,maximumgapheightis3mm.
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
0 3.4
Percentageofreferencelife
Leg deviation A [mm]
loadcarrying nonload carrying
!"/(2E+6)
Here, four conditions inwhichgapheight are0mm,1mm,2mmand3mmare taken into
consideration.
Table8.VolvostandardNo.108requirementdetails[8]
Figure21.Badfit-uploadcarrying,gapheighth=3mm
Inloadcarryingcases,gapheightswill influencethefatiguelife.Thegeometrymodelwith
gapheighth=3mminbadfit-uploadcarryingcaseisshowninFigure21.Whenthegapheight
is2mm,thefatiguelifevalueisthemostandwhenthegapheightis3mm,thefatiguelife
valueistheleast.ThisisshowninFigure23.
Figure22.Badfit-upnon-loadcarrying,gapheighth=3
Innon-loadcarryingcases,gapheightsdon’thaveimpactonthefatiguelife.Asthegapheight
changes from 0 to 3mm, the average fatigue life is around 3.13E+06 cycles. The average
percentageofreferencefatiguelifeis156.5%.
Figure23.Fatiguelifeofdifferentgapheightsinnon-loadcarrying
5.3VolvostandardcaseNo.202VolvostandardNo.202 isabout requirementsofouter transitionradiusshown inTable9.
Welding requirement VE doesn’t have requirements. The outer transition of weld
requirement VD should be equal to or bigger than 0.3mm. The outer transition ofweld
requirement VC should be equal to or bigger than 1 mm. The outer transition of weld
requirementVBshouldbeequaltoorbiggerthan4mm.Hence,thenotchradiusforCE,VD,
VCandVBareseparately1mm,1.3mm,2mmand5mm.
Table9.VolvostandardNo.202requirementdetails[8]
0.00% 20.00% 40.00% 60.00% 80.00%
100.00% 120.00% 140.00% 160.00% 180.00%
0 1 2 3
Percentageofreferencelife
Gap height h [mm]
loadcarrying nonload carrying
!"/(2E+6)
Figure24.Loadcarryingcase,weldqualityC,r=2mm
Forloadcarrying,fatiguelifevariesalittleasthetransitionradiuschange.Whentheweld
qualityisVB,thereferenceoffatiguelifeisthemost.However,whentheweldqualityisVC,
thereferenceoffatiguelifeisthe79%andistheleast.Thegeometrymodelwithtransition
radius2mmisshowninFigure24.
Figure25.Non-loadcarryingcase,weldqualityC,r=2mm
Fatiguelifewillincreasefastasthetransitionradiusincreasesfornon-loadcarrying.When
theweldqualityisVB,thepercentageofreferencefatiguelifecanreach197%.Thegeometry
modelwithtransitionradius2mminnon-carryingcaseisshowninFigure25.
Figure26.Fatiguelifeofdifferenttransitionradiusinnon-loadcarrying
5.4VolvostandardcaseNo.203VolvostandardNo.203isaboutundercutandtheanalysisofthisthesis isfocusedonfillet
welding.AppendixCshowsspecificrequirementsfordifferentweldqualities.Fortheweld
requirementVE,VDandVC,themaximumundercutis1.5mm.FortheweldrequirementVE
andVD,A≤0,1t,thatisA≤1mmsincetheplatethicknessforthiscaseis10mm.Andforthe
weldrequirementVC,A≤0,08t,thatisA≤0.8mm.
Figure27.Loadcarryingcase,undercutA=1.5mm
Figure27showsthegeometrymodelwithundercutA=1.5mminloadcarryingcase.Undercut
doesn’thaveabiginfluenceonfatiguelifeinloadcarryingcases.
0.00%
50.00%
100.00%
150.00%
200.00%
250.00%
300.00%
350.00%
1 1.3 2 5
Percentageofreferencelife
Transition radius r [mm]
loadcarrying nonload carrying
!"/(2E+6)
Figure28.Non-loadcarryingcase,undercutA=1.5mm
Figure28showsthegeometrymodelwithundercutA=1.5mminnon-loadcarryingcase.In
non-loadcarryingcases,theresultswillbeincontrastthatdeeperundercutwillcauselower
percentage of reference fatigue life. If there’s no undercut, the percentage of reference
fatigue life is 155.59%. However, if the undercut is 1.5mm, the percentage of reference
fatiguelifeisonly23%.ThiscanbeseeninFigure29.
Figure29.Fatiguelifeofdifferentundercutinnon-loadcarrying
5.5VolvostandardcaseNo.204Volvo standard No.204 is under passed throat dimension from Appendix D. If the plat
thickness is10mm,thepermission forminimumthroat is larger than0.9a, that is6.3mm.
Meanwhile,deviationnotexceed-2mm.Hence,threethroatthicknesseswhichare5mm,6.3
and7mmareconsidered.
Inloadcarryingcase,biggerthroatthicknesscausehigherfatiguelife.Innon-loadcarrying
case,throatthicknessdoesn’thavebiginfluenceonfatiguelife.Alittledeclinetrendisshown
withtheincreaseofthroatthickness.ThisisshowninFigure30.
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
140.00%
160.00%
180.00%
0 0.8 1 1.5
Percentageofreferencelife
A [mm]
loadcarrying nonload carrying
!"/(2E+6)
Figure30.Fatiguelifeofdifferentthroatthicknessinnon-loadcarrying
5.6VolvostandardcaseNo.211ThefailureofVolvostandardNo.211 isabout incorrectweldtoe.Theanglesbetweenthe
weldingfaceandtheplatesformabnormalangles.ItshowsindetailsfromAppendixE.Here
theanalysisisthroughfourangleswhichare90°,105°,120°and135°.Whentheangleis105°,
themodelisshowninFigure31.
Figure31.Loadcarryingí=105°
Asthevaluesshownbelowaboutloadcarryingcases,comparingallothersangleswiththe
reference angle 135°, the fatigue life will decrease gradually and slowly when the angle
decreasesfrom90°to135°.ThisisshowninFigure33.
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
5 6.3 7
Percentageofreferencelife
Throat thickness a [mm]
loadcarrying nonload carrying
!"/(2E+6)
Figure32.Non-loadcarryingí=105°
Whentheangleis105°innon-loadcarrying,themodelisshowninFigure32.Asthevalues
shownbelowaboutthenon-loadcarryingcases,anglesdon’thavegreateffectonfatiguelife.
Astheanglevariesfromthereferenceangle135°to120°,fatiguelifeincreasealittle.But
whentheanglevariedfrom120°to90°,fatiguelifedecreasealittle.Themodeledgeometry
thattheangleis105°isshowninFigure33.
Figure33.Fatiguelifeofdifferentanglesinnon-loadcarrying
6SummaryofwelddefectsinVolvostandardcasesInloadcarryingcases,ifthevariatesoflegdeviation,underpassedthroatandincorrectweld
toeincrease,thecorrespondingfatiguelifewillincrease.Thevariationofundercutdoesn’t
influencefatiguelife.Innon-loadcarryingcases,ifthevariatesoflegdeviationandtransition
radiusrise,thecorrespondingfatiguelifewillincrease.Ifthevariatesofundercutandunder
passedthroatreduce,thefatiguelifewilldecrease.Thevariationofbadfit-updoesn’thave
animpactonfatiguelife.
0.00% 20.00% 40.00% 60.00% 80.00%
100.00% 120.00% 140.00% 160.00% 180.00%
90° 105° 120° 135°
Percentageofreferencelife
α
loadcarrying nonload carrying
!"/(2E+6)
7Demonstrator
Acommonrepresentativecomponentwhichcoversmostaspectsofvariationinanalysisand
designwillbesuggestedbytheparticipatingcompanies,whichthestudents(andengineers
at the different companies) will carry out design and analysis on the demonstrator. The
simplifiedstructureofthedemonstratorisshowninFigure34.Thespecimensareprovided
fromBrommacompany.PeterHaglundwhoisaPhDstudentfrommysupervisorZuheirwill
continueallthespecimensresearch.
Figure34.Simplifiedstructureofthedemonstrator
8Conclusions
Reducingvariationindesignandanalysisofweldedstructureswillmakeconvenienceforthe
researchofimprovingfatiguelife.Thevariationofpenetrationandplatethicknessarestudied
inloadcarryingandnon-loadcarryingcases.Thecomparisonwithdifferentmethodsoflinear
elasticfracturemechanics,effectivenotchstressandnominalstressshowsthatlinearelastic
fracturemechanicsmethodwillobtainhighestfatiguelifeforbothloadcarryingandnon-load
carryingcases.VariouscodesofIIW,Eurocode3andCranestandardarecomparedtoshow
thediversity.Thestudyofdifferentmethodsandcodeswillprovidethereferencefor the
researchofspecimens.
TheanalysisofimperfectionweldmodelsinVolvostandardcasesprovethevariationofweld
analysis. Imperfectionsof legdeviation,gapheight, transition radius,underpassed throat
thickness,undercutandincorrectweldtoehavedifferenteffectonloadcarryingandnon-
load carrying cases. Fatigue life research of analyzing misalignment and failure in Volvo
standardswillencouragetheweldingdevelopmentinmanufacturingprocess.
9Futurework
In the future, there are still some further research to be done. For example, if different
misalignments and failure occur simultaneously on the models, fatigue life will change
differently. Meanwhile, that kind of cases would be much more complicated. For Volvo
standardcaseNo.203,theundercutheightisconsideredinthisstudy,butinfact,thebottom
radius of the hole is also a considerable factor. There are still someother cases in Volvo
standardwhichcanbeanalyzedbyothermethods.
Fatiguetestsofspecimenswouldbedonesothatrealvaluescouldbeobtainedtocompare
withresearchvalues.Thedifferenceofresearchvaluesandrealisticvalueswouldexit.
Volvowouldmodifysomestandardssubjectedtodifferentweldqualities.Theestimatedtime
tostartisthebeginningof2018.Improvingweldingqualitytoimprovefatiguelifeisagreat
objectiveformanyfactories.
10References
[1]T.Nykänen,G.Marquis, T.Björk, July2006, Fatigueanalysisofnon-load-carrying fillet
weldedcruciformjoints,EngineeringFractureMechanics74(2007)399-415
[2] John B. Wachtman,W. Roger Cannon and M. John Matthewson, September 2009, MechanicalPropertiesofCeramics,SecondEdition, DOI:10.1002/9780470451519.ch5,P71[3]Website:http://cfg.cornell.edu/software/
[4] A.F. Hobbacher, 2014, Recommendations for Fatigue Design of welded joints and
components,SecondEdition,IIW-2259-15
[5]Eurocode3:Designofsteelstructures-Part1-9:Fatigue,2005,Authority:TheEuropean
UnionPerRegulation305/2011,Directive98/34/EC,Directive2004/18/EC
[6] Cranes-GeneralDesign-Part3-1:LimitStatesandproofcompetenceofsteelstructure,
July2013,EuropeanCommitteeforStandardization
[7]Wolfgang Fricke, June 2012, IIW Guideline for the Assessment ofWeld Root Fatigue,
WeldingintheWorld,IIW-Doc.XII-2380r3-11/XV-1383r3-11,Revision3
[8]VolvoGroupStandard,April2013,STD181-004
AppendixA-Effectivenotchfatigueresistanceforsteel
AppendixB-LoadcarryingweldedjointsofEurocode3
AppendixC-VolvostandardNo.203
AppendixD-VolvostandardNo.204
AppendixE-VolvostandardNo.211
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