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Effect of material grade on fatiguestrength and residual stresses in

high strength steel welds

WASIM ASGHER

Master of Science Thesis in Lightweight Structures

Dept of Aeronautical and ehicle EngineeringStoc!holm" Sweden #$%#


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EFFECT OF MATERIAL GRADE ON FATIGUESTRENGTH AND RESIDUAL STRESSES IN HIGH

STRENGTH STEEL WELDS

Wasim Asgher

A Master Thesis Report written in collaboration withDepartment of Aeronautical and Vehicle Engineering

Royal Institute of TechnologyStocholm! Sweden

AndVol"o #onstruction E$uipment

%ra&s! Sweden

April! '()'


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Preface

This thesis wor was performed at Vol"o #E! %ra&s and di"ision of lightweightstructures! "ehicle and aeronautical engineering department! *T+! Stocholm,

I am greatly thanful to my super"isors Dr, -uheir %arsoum .*T+/ and %ertil0onsson .V#E/ for their continuous support and guidance during the thesis wor,Especially! I am highly indebted to Dr, -uheir %arsoum for teaching me a lot andspending his precious time, I would also lie to than Ru 1eng and Annethe %illeniusfrom 2in3ping 4ni"ersity for pro"iding assistance in measurement of residualstresses,

2astly! I want to than my parents who ha"e been a great source of moral support andencouragement to me during this wor,

Stockholm, April 2012

Wasim Asgher,


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Abstract.

This thesis wor is concerned with effect of material grade on fatigue strength ofwelded 5oints, 6atigue strength e"aluation of welded 5oints in as welded and post weldtreated condition was carried out with effecti"e notch method, Results of pea stressmethod ha"e also been compared with those of effecti"e notch method for as welded5oints, In addition! using the results of effecti"e notch method! the effect of important

weld and global geometry factors on notch stress concentration factor has beenstudied with '7le"el design of e8periment and a mathematical relation among stressconcentration factor and the geometric factors has been proposed, 9"erall! thicnessof the base plate and toe radius is found to be the most important factors determiningfatigue strength of the 5oint,

Welding induced residual stresses ha"e also been predicted using 'D and :D 6EManalysis to see their effect on fatigue strength of the 5oints, Also! trans"ersal residualstresses were measured using ;7ray diffraction method to assess the accuracy ofpredicted results, %ased on simulation results! effect of geometric factors onma8imum "alue of trans"ersal residual stress was also in"estigated,

Keywr!s. 6atigue Strength! 6illet Welded 0oints! Effecti"e


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Tab"e f C#te#ts

1reface 'Abstract, :*eywords, :

Table of #ontents =Table of 6igures >) I RE6ERE


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Tab"e f F$%&res

Figure 1 *itigawa diagram B An illustration of the effect of material grade onfatigue strength,.................................................................................. ....................... 4

Figure 2 - Schematic illustration of the relation between accuracy! comple8ity andwor effort re$uired for fatigue analysis of welded structures FrefG.............................. 5

Figure 3 An illustration of creating effecti"e notches.......................................... 6Figure 4

Model of the fillet 5oint................................................. ....................... 7

Figure 5 Modeling with effecti"e notch method................................................. 7Figure 6 Modelling with pea stress method......................................... ............. 8Figure 7 6EM model for residual stress simulations, a/ 'D Model with boundary

conditions, b/ boundary conditions for :D model for first weld, c/ boundary conditionfor weld on other side,........................................................................................... .... 9

Figure 8 Mo"ing heat source for :D analysis.................................................. .... 9Figure 9 Temperature dependent material properties, a/ conducti"ity and specific

heat b/ yield stress! tangent modulus and thermal e8pansion coefficient FrefG............ 10Figure 10 Distribution of first principal stress in the 5oint................................ 11Figure 11 6irst principal stress along longitudinal direction.............................. 11Figure 12 Illustration of different load lengths................................................. 12Figure 13 6atigue li"es of the 5oints mapped on pea stress scatter bands........ 13Figure 14 Influence of main factors on stress concentration factor.................. 14Figure 15 Influence of main factors on stress concentration factor for post weld

treated 5oints,................................................................................................ ........... 15Figure 16 Temperature distribution in molten Hone, a/ +A- Hone b/

Temperature history........................................................ ......................................... 15Figure 17 - Stresses in 6mm5oints, S87Trans"ersal! Sy7A8ial! SH72ongitudinal,..... 16Figure 18 Measurement of trans"ersal residual stresses, a/ 6mm 5oints b/ 10mm

5oints....................................................................................................................... 17Figure 19 Trans"ersal residual stress.............................................................. .. 18Figure 20 - #omparisonof measurements with 6EM results............................... 19Figure 21 6actors affecting pea "alue of trans"ersal residual stress, a/ Main

factors b/ Interaction of parameters....................................................................... .. 20


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' INTRODUCTION'.' (ac)%r!

Vol"o construction e$uipment is one of the largest manufacturers of construction e$uipment in theworld, In Sweden! articulated haulers and wheel loaders are manufactured where welding is usedprimarily for 5oining steel structures, According to many regulations of fatigue in welded structures!high strength steels offer no ad"antage for fatigue loaded welded structures, This is because of craclie imperfections formed by welding processes which go"ern the fatigue life of the 5oint to a greatere8tent, It is howe"er recently established by the researchers that a comparati"ely higher fatigue life canbe obtained by using high strength steels for fatigue loaded welded structures pro"ided that weld$uality is controlled, The same is suggested by a typical *itigawa diagram! see figure 1, Therefore it isre$uired to formulate an acceptability criterion for defect siHe so that high strength steels can be usedfor achie"ing better fatigue life in as welded conditions,

Figure 1 *itigawa diagram B An illustration of the effect of material grade on fatigue strength,

'.* Wr) A++rac,The wor is di"ided in two sections

1. Fatigue assessment Life prediction ith F!" and parametric anal#sis.

6atigue life assessment of fillet welded 5oints was carried out with effecti"e notch stress method andpea stress method, A design of e8periment was performed to identify the factors ha"ing ma5or

influence on fatigue strength, #onse$uently a mathematical model of stress concentration factor wasproposed through regression analysis,

2. $esidual Stresses "easurement and F!" simulations

Trans"ersal residual stresses induced by welding process were measured using ;7ray diffractionmethod, 6inite element modeling and se$uentially coupled thermo7mechanical analysis of the welded5oints was performed to predict the residual stress state, 6urthermore a comparison of 6EM results

was made with e8perimental measurements and effect of different parameters on residual stresses wasstudied through finite element simulations,


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* LITERATURE RE-IEW*.' Fat$%&e Assesse#t f We"!e! /$#ts

Apart from e8perimental in"estigation! a number of methods ha"e been de"eloped for fatiguee"aluation of welded 5oints, %ased on their approach! they are categoriHed as global method or localmethod, lobal methods lie nominal stress method and structural hot spot method do not tae intoaccount the stress concentration effects due to notches produced by welds and therefore are not goodfor critical e"aluations, 9n the other hand! local methods e.g.effecti"e notch stress method and linearelastic fracture mechanics .2E6M/ address these issues "ery well and gi"e comparati"ely accurateresults, +owe"er woring effort for these methods is relati"ely greater and is usually a trade7offbetween accuracy of the results and comple8ity of the structure! see figure 2, A detailed description ofthese can be found in F)G,

Figure 2 - Schematic illustration of the relation between accuracy! comple8ity and wor effortre$uired for fatigue analysis of welded structures F=G

uite recently another method! called pea stress method! has been proposed for fatigue assessmentof welded 5oints, This is an efficient method in terms of calculation time howe"er it is restricted inapplications, In this thesis wor fatigue assessment of fillet welded 5oints was performed witheffecti"e notch stress method and pea stress method,

Effect$0e Ntc, Stress Met,!

Effecti"e notch stress method was introduced by International Institute of Welding .IIW/ in )CC>,

According to +obbacher F'G! the stress at the root of the notch! obtained by assuming linear elasticmaterial beha"ior represents effecti"e notch stress, The statistical "ariation of weld shape and non7linear material beha"ior at the notch is accounted for by replacing the actual notch with an effecti"enotch of 1mmradius as shown in figure %,


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Figure 3 An illustration of creating effecti"e notches

Pea) Stress Met,!

1ea stress method is based on notch stress intensity factor approach and can be utiliHed for fatigue

assessment of welded 5oints by using the scatter bands proposed by Meneghetti F? J >G, The scatterbands ha"e been "alidated on a number of different types of welded 5oints for steel and aluminiumstructures and are termed as uni$ue based on their consistency to gi"e sufficiently accurate results fordifferent geometries and loading conditions, This method is much more efficient than othercontemporary methods of fatigue assessment because it re$uires significantly less computationalresources, +owe"er this efficiency has come with certain limitations on its applicability, It is currently

"alid for sharp notches restricted to an opening angle of 1%&degrees and therefore canKt be used forfatigue assessment of post weld treated 5oints, 6urthermore it has only been "alidated for fillet 5oints,

*.* Res$!&a" StressesDue to rapid heating and cooling of welds! residual stresses are produced in the 5oints, Depending

upon weld shape and boundary conditions these stresses may be tensile or compressi"e in the weld,While compressi"e residual stresses may be good for fatigue loaded structures! tensile stresses aredetrimental and may significantly reduce the endurance limit of the structure, It has beendemonstrated in se"eral te8ts that residual stresses due to welding can be of the order of material yieldstrength,


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1 METHODS1.' M!e" Descr$+t$#Model consists of a fillet welded T75oint! see figure =, The trans"ersal dimension of the 5oint is taenlong so that important residual stresses are present in the 5oint, It was howe"er! limited by theen"elope of the fatigue testing machine with a ma8imum load capacity of 2&0'(in dynamic loading,

Figure 4 Model of the fillet 5oint

Two le"els were chosen for base plate thicness! t1and stiffener plate thicness! t2with magnitudes 6mm and 10 mm, 2ength of both plates .out of plane dimension/ was selected to be 1%0 mm, 9therparameters in the figure )and are defined below

Width of base plate L 1L %00 mmWidth of stiffener plate L 2L &0 mm

Material properties of steel were used for fatigue life calculations i.e.oungKs modulus! * 20& +aand 1oisson ratio - L (,:, 6or residual stress analysis! thermal and temperature dependent mechanical

properties were also used for three different material grades corresponding to yield strength %&0! 00and /60 "a, These properties are outlined in section %.%and appendi8 F)G,

1.* Fat$%&e L$fe Ca"c&"at$#sA 'D parametric analysis was performed with different weld geometry parameters for fatigue lifecalculation of the selected model using effecti"e notch stress method and pea stress method, Theseparameters were selected for as welded and post weld treated 5oints and are outlined in section ).2.

Effect$0e Ntc, Met,!

Due to symmetry! half of the geometry was modeled with plain strain condition, 6inite element meshwas generated with $uadratic $uadrilateral elements and sufficiently refined mesh at notches! seefigure &, A 10'(load was applied in four point bending arrangement with a load span of 100mm,

Figure 5 Modeling with effecti"e notch method

Symmetry

Mesh at Root Mesh at Toe


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6atigue li"es were calculated using the following relation

+ere and m are material parameters and represents stress range, is calculated usingrecommended 6AT "alue of ''?"aat 2million cycles F'G,

Pea) Stress Met,!

9nly half of geometry was modelled due to symmetry with 12AG and notch stress intensity factor '3was calculated using

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+ere is the stress intensity factorN d is element siHe and represents stress at weld toe

determined through pea stress method, and are constants which depend on element type!

mesh siHe and the software used, 6atigue life was estimated by using the lower scatter band asreference cur"e.6igure 6shows mesh and loading condition,

Figure 6 Modelling with pea stress method

1.1 Res$!&a" Stresses 2 Pre!$ct$# a#! Meas&ree#tIt is well established from e8periments that fatigue crac at weld toes usually propagate into basemetal under tensile or bending loads, Therefore trans"ersal residual stresses in the selected T75ointmodel become important, Residual stress analysis of the 5oint was performed with finite elementbased uncoupled thermal and mechanical analysis to study the stress state in the 5oint, Moreo"er!eeping in "iew the failure location suggested by fatigue calculations! trans"ersal residual stresses were

measured in the 5oints to see the actual stresses and "erify the predicted results,Test S+ec$e#s

T75oints were constructed from D9ME; steels with yield strength :??! @(( and C>("a, eometryof the 5oints is described in section %.1, The specimens were MA welded! manually! in a single passon each side with following welding conditions

Tab"e 'B Welding condition for T75oints,

Welding 1rocess #urrent

FAG

Voltage

F4G

Welding speed

Fcm5minG

6iller wire diameter

FmmG

MA 'C( :(,? ?( ),=

Weld toe is shared by only twoelements, See Meneghetti FrefG,

Symmetry


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Pre!$ct$# f Res$!&a" Stresses

Welding simulations were performed in 'D and :D by a se$uentially uncoupled thermal andmechanical analysis, The temperature distribution predicted by transient thermal analysis was used as

load for subse$uent mechanical analysis to estimate stresses due to welding, Same mesh was used formechanical analysis as was used in thermal analysis and is shown in the figure ,

%oundary conditions shown in figure were used, Since base plate was tac welded on the bottom sidebefore welding of stiffener plate! it was held fi8ed for first weld and stiffener plate was allowed todeform, 6or welding on the other side! boundary conditions on the base plate were remo"ed andstiffener plate was constrained instead,

Figure 7 6EM model for residual stress simulations, a3'D Model with boundary conditions, b3

boundary conditions for :D model for first weld, c3boundary condition for weld on other side,

+eat source modeling described by %arsoum F)( J ))G was used for 'D simulations while a mo"ingheat source with constant "olume flu8 was implemented for :D analysis, Mo"ing heat source wasimplemented by di"iding the weld "olume into a finite number of "olumes and then se$uentiallyacti"ating elements contained by each "olume during welding, It was assumed that heat distributiondue to welding arc was uniform and arc stayed on each "olume for a specific time before mo"ing onto ne8t "olume,

Figure 8 Mo"ing heat source for :D analysis

a

b c


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Temperature dependent material properties were used for the simulations and are shown in figure /for D9ME;:?(, Material properties for other material grades were taen from 0mat1ro,

Figure 9 Temperature dependent material properties, a3conducti"ity and specific heat b3yieldstress! tangent modulus and thermal e8pansion coefficient F)(G

Meas&ree#t f Tra#s0ersa" Res$!&a" Stresses

Symmetrical distribution of trans"ersal residual stress was assumed based on restraint conditionsduring welding and measurements were taen only on one side of the stiffener, ;7ray diffractionmethod was used and measurements were taen on top surface of base plate, Measurements were alsocompared with results obtained through finite element simulations,


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4 RESULTS AND DISCUSSION4.'

Fat$%&e Stre#%t, E0a"&at$#

6atigue e"aluation was carried out on the basis of first principle stress whose ma8imum "alue occursat load carrying weld toe for all 5oints and mars the position of fatigue failure! see figure 10, :Danalysis also gi"es the same results and is shown in figure 10.

Figure 10 Distribution of first principal stress in the 5oint


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It was further in"estigated whether this longitudinal distribution of ma8imum principal stress could beaffected by different lengths of applied load and boundary condition! as shown in figure 12.Resultsshow that longitudinal distribution of first principal notch stress remains nearly indifferent withdifferent load lengths as modeled with parameter Ld! table 2,

Figure 12 Illustration of different load lengths

Table 2 Distribution of first principal stress in longitudinal direction for different load lengths,

L!5'6.. L!516..

L!576.. L!586..


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C+ar$s# betwee# Effect$0e Ntc, Met,! a#! Pea) Stress Met,!

6atigue strength data obtained through effecti"e notch stress method has been mapped on scatterbands for steel! proposed by pea stress method F? J >G, The plot in figure 1%shows that pea stressmethod is more conser"ati"e than effecti"e notch method for prediction of fatigue life for welded5oints, This method is more efficient than other contemporary methods of fatigue assessment for

welded 5oints because it re$uires significantly less computational resources, +owe"er this efficiencyhas come with certain limitations on its applicability, 6or instance! it is currently "alid for sharpnotches restricted to an opening angle of 1%& degrees and therefore canKt be used for fatigueassessment of post weld treated 5oints,

Figure 13 6atigue li"es of the 5oints mapped on pea stress scatter bands

4.* I#f"&e#ce f Geetr$c Factrs # Fat$%&e Stre#%t,


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Tab"e 4 2Weld parameters for post weld treated 5oints,

1arameter Symbol 2ow le"el +igh le"el

Toe radiusP FmmG r = ?

Throat thicness FmmG a = >

6lan Angle FdegG Q =? >(

PToe radius here indicates effecti"e notch radius,

As We"!e! /$#ts

Stress concentration factor 'twas calculated for different simulated cases and the effect of differentgeometric factor on stress concentration factor is shown in the plots below

Figure 14 Influence of main factors on stress concentration factor

The plot shows that weld toe radius and base plate thicness are the most dominating factorsaffecting fatigue strength of the load carrying 5oint, While a higher toe radius tends to reduce thestress concentration factor significantly! thicness of the base plate does the opposite, Therefore athinner fatigue loaded 5oint would be safer compared to a thicer one pro"ided that nominal stress in

the 5oint is same, This is because of thicness effect and has its e8planation in sharp stress gradientsassociated with plate thicness FCG,

9ther factors and their interactions ha"e a little impact on ! as indicated by figure 1), %ased on

these obser"ation! following mathematical model establishes a relationship among and differentgeometric factors for as welded 5oints

1.5075 + 0.017! + 0.05151"# 0.0$33 !"+ 0.00$7%&

Pst We"! Treate! /$#ts

Design of e8periment in"estigation for post weld treated 5oints show results similar to those of aswelded 5oints, +owe"er! one notable thing is that the effect of weld geometry parameters! particularly

weld toe radius becomes less pronounced, The relationship of with geometric factors! for postweld treated 5oints is

21

2.1

2.0

1.9

1.8

1.7

106 106

64

2.1

2.0

1.9

1.8

1.7

6045

Toe Radius

Mean

Base Plate Thickness Stiffner Thiick ness

Throat Thickness lank !n"le

Main Effects Plot for Stress Concentration Factor, Kt#ata $eans


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1.0'35$ # 0.01373! 0.0'$7"# 0.005% !"

Figure 15 Influence of main factors on stress concentration factor for post weld treated 5oints,

4.1 We"!$#% Res$!&a" StressesS$&"at$# f We"!$#% Res$!&a" Stress

During thermal analysis! "olume heat flu8 was ad5usted with a body factor to obtain a reasonable siHeof molten weld pool F)(G and is shown in figure 16, Temperature history of a point )?mm away from

weld toe is also shown,

Figure 16 Temperature distribution in molten Hone, a/ +A- Hone b/ Temperature history

6ollowing diagrams show different stresses in 6mmthic 5oints, Results show that longitudinal stressescan be of the order of material yield strength or e"en more howe"er trans"ersal and a8ial stressesdonKt,

54

1.45

1.40

1.%5

1.%0

1.25

106 106

64

1.45

1.40

1.%5

1.%0

1.25

6045

Toe Radius

Mean

Base Plate Thickness Stiffner Thick ness

Throat Thickness lank !n"le

Main Effects Plot for Stress Concentration Factor, Kt#ata $eans

a b


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Figure 17 - Stresses in 6mm5oints, S87Trans"ersal! Sy7A8ial! SH72ongitudinal,


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Meas&ree#t f Tra#s0ersa" Res$!&a" Stress

6ollowing figure show the measurements for trans"ersal residual stress

Figure 18 Measurement of trans"ersal residual stresses, a/ 6mm5oints b/ 10mm5oints

The results show that trans"ersal residual stresses ha"e a pea "alue near weld toe and tend to rela8

sharply, %eing tensile in nature! this can be detrimental for fatigue loaded 5oints, It can also been seenfrom the plots that irrespecti"e of material yield strength and plate thicness! trans"ersal residualstresses ha"e a pea "alue at the same distance from toe and tend to rela8 at a same distance for all5oints, This indicates that distribution of residual stresses is independent of mechanical properties anddepends solely on thermal properties of the material,

Measurements on both sides of stiffener were also performed on another set of specimens and areshown in figure 1, They show nearly symmetrical distribution of trans"ersal stress on both sides, 6orthe second sample of /60"a steel! plot shows a big "ariation which is possibly due to a differentconstraint condition during welding,

a

b

:??t> represents the 5oint withmaterial yield strength %&&",aandthicness 6mm, Same applies toother legends,


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Figure 19 Trans"ersal residual stress

9177t:

9177t'6

9;:6t:

9


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C+ar$s# f FEM Res&"ts w$t, Meas&ree#ts

6igure 1/shows comparison of measurements with 6EM results for 6mm 5oints, 6EM results agree"ery well for :?(M1a 5oint, They donKt agree well for other 5oints! howe"er show similar distribution

pattern,

Figure 20 - #omparisonof measurements with 6EM results

Se Factrs I#f"&e#c$#% Pea) 0a"&e f Tra#s0ersa" Res$!&a" Stress

A design of e8periment in"estigation was carried out to study different factors that may ha"e an effecton pea "alue of trans"ersal residual stresses, 6actors studied include yield strength! plate thicnessand throat thicness and are described in table 6,

Table 5 1arameters for DoE in"estigation of Trans"ersal Residual Stress

1arameter 2ow 2e"el Intermediate le"el +igh le"el

ield Strngth F"aG %&& @(( C>(

1late thicness FmmG 6 7 )(

Throat Thicness FmmG = ? >

1ea "alue of trans"ersal stress for described boundary condition was! obtained through 6EMsimulations! was used as response, 6ollowing results were obtained

9177t: 9


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a b

Figure 21 6actors affecting pea "alue of trans"ersal residual stress, a/ Main factors b/Interaction of parameters

1lots show that only yield strength of the material has a significant effect on pea "alue of trans"ersalresidual stress, With higher yield strength! pea "alue of residual stress increases! figure 1a! and theeffect is more pronounced as thicness of the 5oint is increased! figure 1, It should be noted!howe"er! that these results are "alid for a particular set of parameters and a specific boundarycondition and does not represent fillet welded 5oints in general,

%21

%20

280

240

200

%21

21

%20

280

240

200

&ield St ress

Mean

Throat

Plate Thickness

Main Effects Plot for Peak Stress#ata $eans

%21 21

400

%00

200

400

%00

200

Yield Stress

Throat

Plate Thickness

1

2

%

Stress

&ield

1

2

%

Throat

Interaction Plot for Peak Stress#ata $eans


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7 CONCLUSIONSBased on above results, following conclusions can be made:

[1] Fatigue strength of fillet welded joints is considerably affected by plate thickness and toe radius. Otherweld geometry parameters dont play an important role for fatigue life enhancement.

[2] Notch stress, as calculated by effective notch method, remains almost constant along longitudinaldirection of the joint and therefore no distinct failure point can be assumed.

[3] Longitudinal stresses due to welding can be of the order of material yield strength or even morehowever transversal and axial stresses remain much below yield limit.

[4] Transversal residual stresses tend to have peak value at same distance from toe location irrespective ofmaterial yield strength and plate thickness. They also tend to relax at same distance from toe.

[5] Material yield strength as well as constraint conditions during welding govern the peak valueof transversal residual stresses in the joint.


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: REFERENCES[1] Radaj D. and Sonsino C.M., Fatigue assessment of welded joints with local approaches, Abington

publishing, Cambridge, 1998.

[2] Hobbacher A., Fatigue design of welded joints and components, IIW doc. XIII-1539-96, 1996.[3] Fricke W., Guidelines for the fatigue assessment by notch stress analysis for welded structures , IIW

Doc. XIII-WG3-03r6-08, 2008.

[4] Barsoum Z.,Residual stress analysis and fatigue assessment of welded structure, Ph.D. thesis, Dept. ofAeronautical and Vehicle Engineering, KTH, Sweden, 2005.

[5] Barsoum Z. and Samuelsson J., Fatigue assessment of cruciform joints with different methods, SteelResearch International 77, No. 12, 2006.

[6] Barsoum Z. and Jonsson B, Fatigue assessment and LEFM analysis of cruciform welded jointsfabricated with different welding processes, IIW, 2007.

[7] Meneghetti G., The peak stress method applied to fatigue assessment of steel and aluminum filletwelded joints subjected to Mode-I loading, Fatigue and Fracture of Engineering Materials and

structures, 2008.

[8] Meneghetti G. and Lazzarin P., The use of peak stress method for fatigue strength assessments ofwelded lap joints and cover plates with toe and root failures, Engineering Fracture Mechanics, 2011.

[9] Mats G.,A study of thickness effect on fatigue in thin welded high strength steel joints, Steel ResearchInternational, ISSN 1611-3683, 2006.

[10] Barsoum Z. and Lunbck A., Simplified FE Welding simulation of fillet welds 3D effects on theformation of residual stresses, Engineering Failure Analysis, 2009.

[11] Barsoum Z.and Barsoum I., Residual stress effects on fatigue life of welded structures using LEFM,Engineering Failure Analysis, 2009.

[12] Martinsson J., Fatigue assessment of complex welding structures, Ph.D. thesis, Dept. of Aeronauticaland Vehicle Engineering, KTH, Sweden, 2005.[13] Hansen J.L., Numerical modeling of welding induced stresses, Ph.D. thesis, Technical university of

Denmark, ISBN 87-90855-52-3, 2003.

[14] Barsoum Z.,Residual stress analysis and fatigue of multipass welded tubular structures, EngineeringFailure Analysis, 2008.

[15] ANSYS guide,Ansys Release 13.0, Swanson analysis systems: Housten.


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