me als
A icle
Fa igue Pe o mance o Thin Lase Bu Welds in HSLA S eel
Pa icio G. Rio ío1, Fe nando An unes 2,* , JoséFe ei a 2, An ónio Cas anhola Ba is a 3
and Ca los Capela 2,4


Ci a ion: Rio ío, P.G.; An unes, F.;
Fe ei a, J.; Ba is a, A.C.; Capela, C.
Fa igue Pe o mance o Thin Lase
Bu Welds in HSLA S eel. Me als
2021,11, 1499. h ps://doi.o g/
10.3390/me 11101499
Academic Edi o : Koh-ichi Sugimo o
Recei ed: 24 June 2021
Accep ed: 31 July 2021
Published: 22 Sep embe 2021
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
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ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
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A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
1
DECEM, Depa amen o de Ciencias de la Ene gía y Mecánica, Uni e sidad de las Fue zas A madas-ESPE, A .
Gene al Rumiñahui S/N, Sangolquí171103, Ecuado ; [email p o ec ed]
2CEMMPRE, Depa men o Mechanical Enginee ing, Uni e si y o Coimb a, 3030-788 Coimb a, Po ugal;
[email p o ec ed] (J.F.); [email p o ec ed] (C.C.)
3CFisUC, Depa men o Physics, Uni e si y o Coimb a, 3004-516 Coimb a, Po ugal; [email p o ec ed]
4ESTG, Depa men o Mechanical Enginee ing, Ins i u o Poli écnico de Lei ia, Mo o do Lena—Al o Viei o,
2400-901 Lei ia, Po ugal
*Co espondence: [email p o ec ed]; Tel.: +351-9347-98913
Abs ac :
This wo k is ocused on unde s anding he signi ican ac o s a ec ing he a igue s eng h
o lase -welded bu join s in hin high-s eng h low-alloy (HSLA) s eel. The e ec s o he weld p o ile,
impe ec ions, ha dness, and esidual s esses we e conside ed o explain he esul s ound in he S-N
cu es o ou welded se ies. The esul s showed accep able a igue s eng h al hough he welded
se ies p esen ed mul iple-impe ec ions. The analysis o a igue beha io a low s ess le els h ough
he s ess-concen a ing e ec explained he in luence o each ac o on he S-N cu es o he welded
se ies. The a igue limi s o he welded se ies p edic ed h ough he s ess-concen a ing e ec and by
he ela ionship p oposed by Mu akami showed good ag eemen wi h he expe imen al esul s.
Keywo ds: a igue s eng h; lase bu weld; HSLA s eel; a igue limi p edic ion
1. In oduc ion
High-s eng h s eels ha e high a igue esis ance o c ack ini ia ion, as his damage
mechanism dec eases wi h he inc ease o he ma e ial’s ensile s eng h. The welding o
hese ma e ials may be done using lase welding due o low hea inpu s, small hea -a ec ed
zones, and less so ening o he ma e ial. Howe e , educ ions o up o 40% in he a igue
limi , low a ios o he a igue limi o he ul ima e s eng h o he base me al (BM), and
a igue limi s ha do no exceed 175 MPa we e epo ed in [
1
–
3
] when hin high s eng h
s eels we e lase welded.
The ele an ac s ha comp ise he di e ences be ween welded join s and elemen s
wi h no ches o o he de ec s, a e he p esence o c ack-like impe ec ions and he changes
in oduced by he hea inpu (HI) in o he BM. This has led o he a igue ini ia ion pe iod
being neglec ed [
4
,
5
] and o he applica ion o he ac u e mechanics app oach, conside ing
only he pe iod o c ack g ow h o he assessmen o he a igue li e [
6
]. Howe e , o
small sized c acks and o low s ess le els, he ini ia ion s age is conside ed [7,8].
The con en ional app oach used o p edic he a igue limi in no ched elemen s
based on s ess concen a ion and s ess g adien models is also used in welded join s [
9
].
In [10,11],
se e al adi ional models o sensi i i y o no ches and new models we e ana-
lyzed o he p edic ion o he a igue limi o elemen s wi h small impe ec ions and o
he applica ion in welded join s. Based on ac u e mechanics, Mu akami [
12
] p oposed
an exp ession o a igue limi p edic ions o ma e ials con aining small de ec s o c acks
as a unc ion o he ha dness and he size o de ec s, and Åman e al. [
13
] modi ied he
men ioned exp ession o conside he e ec o he no ch oo on he small de ec s and
sugges ed he applica ion o he welded join s.
Se e al ac o s a ec ing a igue s eng h in weldmen s a e highligh ed in [
4
,
6
,
14
],
howe e , hey can be summa ized in he ollowing: weld quali y, esidual s esses, ma e ial,
Me als 2021,11, 1499. h ps://doi.o g/10.3390/me 11101499 h ps://www.mdpi.com/jou nal/me als
Me als 2021,11, 1499 2 o 22
and size e ec s. Al hough i has been shown ha he weld quali y con ol [
15
] o he use
o pos -weld ea men s [
16
–
19
] in welded join s wi h high-s eng h s eels inc eases he
a igue s eng h by educing he se e i y o i s inhe en impe ec ions, his is ecognized in
design guides, allowing he inc ease o a igue class cu e (FAT) when he impe ec ions
we e e i ied wi h nondes uc i e es ing (NDT) o when an imp o emen me hod was
used [
5
]; he e is no di e en ia ion in he inc ease acco ding o he mechanical s eng h
o he ma e ials. The o egoing has been explained due o he ac ha he g ow h o
c acks domina es he a igue li e o he welded join s and because he a igue c ack g ow h
a e (FCGR) is insensi i e o he mechanical s eng h o he ma e ial [
20
]. Howe e , as
coun e pa , i was shown ha when he weld quali y is high, o high-s eng h s eels,
a igue s eng h is posi i ely co ela ed o mechanical s eng h [21].
Mic os uc u al ea u es such as phases and ha dness a e ac o s in luencing he
a igue beha io o he welded join s. Due o he welding p ocess, he mic os uc u es
o he hea -a ec zone (HAZ), usion zone (FZ), and BM a e di e en and since, in mos
cases, he a igue s a s and pa hs a e in he HAZ o FZ, he p ope ies o hese zones a e
impo an . Thus, he ha dness is used ins ead o hose o he BM, imp o ing he esul s o
a igue p edic ions as shown by Kucha czyk e al. [
22
]. In [
23
], i is shown ha he inc ease
o he p opo ion o ma ensi e in he mic os uc u e dec eases he FCGR and inc eases he
c ack g ow h h eshold. In welded join s, he size e ec s e e o he dec ease in a igue
s eng h when he hickness o he pla es inc eases [
4
]. Fo his eason, a igue s eng h
educ ion ac o s a e applied when 25 mm o hickness is exceeded [
5
]. Al hough he e is
e idence ha he opposi e e ec occu s o hin hicknesses [
7
], his is no conside ed in
he design guides.
The gene al e ec o no ches and esidual s esses on a igue s eng h o welded join s
is well known. In a ious s udies, hei combined e ec s we e s udied and a ela i e
e ec was obse ed. Wa anabe e al. [
24
] epo ed ha he a igue s eng h is domina ed
by s ess concen a ion ac o (SCF) when his is high and by he esidual s esses when
SCF is small. Ha a i e al. [
25
] concluded ha he esidual s esses ha e a la ge in luence
han he weld oe geome y, meanwhile, Nguyen e al. [
26
] es ablished ha o ensile
esidual s esses o low magni ude o o comp essi e s esses, he e ec o an unde cu is
dominan . Shiozaki e al. [
27
] epo ed ha due o he equali y o esul s in he S-N cu es
be ween he as-welded and hea - ea ed specimens, he e ec o esidual s ess should
no be conside ed. In almos all p e ious wo ks, ela i ely hick pla es and con en ional
welding p ocesses we e used.
The e a e ew s udies on he main ac o s in luencing a igue s eng h and on he
applica ion o he ac u e mechanics app oach o he e alua ion o a igue limi s o hin
s eel pla es in lase welded join s. In he wo k [
28
], o bu join s o 3 mm hickness in
S enx
®
700MCE s eel welded by lase , he weld bead geome y, he impe ec ions, and
he quali y le el o he welds acco ding o he ISO 13919-1 [
29
] s anda d we e de e mined.
The a igue s eng h o he men ioned welded join s was e alua ed in his s udy. Fo his,
local p ope ies such as ha dness and esidual s esses in he HAZ and FZ and a mo e
ealis ic weld p o ile will be conside ed. The ac ual p o ile o he weld beads, including
impe ec ions, is comple ely modeled o de e mine he SCFs by FEM. The esidual s esses
a e measu ed by X- ay echnique. Th ough he ailu e analysis o ac u ed su aces and
using he s ess-concen a ing e ec , he in luence o he main ac o s on a igue beha io
a low s ess le els is explained. P edic ions o he a igue limi s o he welded se ies a e
also ende ed bo h by he s ess-concen a ing e ec and by he ela ionship p oposed by
Mu akami.
2. Ma e ial and P ocedu es
2.1. Ma e ial and Lase Welding
Bu weld join s we e c ea ed wi h 3 mm hick high-s eng h low-alloy (HSLA) s eel
pla e S enx
®
700MCE [
30
]. This s eel has he chemical composi ion and ensile mechanical
p ope ies shown in Tables 1and 2[
31
], espec i ely. I p esen s a ine-g ain e i ic-baini ic
Me als 2021,11, 1499 3 o 22
mic os uc u e. The yield s ess is close o he ensile s eng h, which indica es ha his
ma e ial keeps he elas ic beha io almos un il inal ac u e.
Table 1. Base me al chemical composi ion (w %).
C Mn Si P S C V Nb Ni Cu Al Mo Ti Co Fe
0.07 1.69 0.01 0.012 0.006 0.03 0.02 0.046 0.04 0.011 0.044 0.016 0.117 0.016
balance
Table 2. Mechanical p ope ies o he base me al.
Yield S eng h (MPa) Tensile S eng h (MPa) Elonga ion (%)
808 838 15.0
Fi e se ies we e welded conside ing he welding pa ame e s shown in Table 3. The
S1, S2, S3, and S4 se ies a e single-welded join s while he S5 se ies is double-welded join .
Fo his las se ies, he welding speed o he weld pass on he op side was di e en o
each sample (1.75, 1.80, 1.90, 1.95, and 2.00 m/min), while he weld pass on he bo om
side was cons an o all samples (2.50 m/min). These pa ame e s we e selec ed based on a
p e ious s udy o he e ec o pa ame e s on de ec s and ensile p ope ies [
31
]. The hea
inpu s used in welding we e de ined in o de o achie e di e en alues o ha dness in
he welded se ies, bu simul aneously main aining small HAZs, low so ening, and ensile
mechanical p ope ies simila o he BM, as shown in [
31
]. A disk lase equipmen T ump
T uDisk 2000 wi h: lase maximum ou pu , 2000 W; beam wa eleng h, 1020 nm; beam
pa ame e p oduc , 2 mm-m ad; and ibe diame e , 200
µ
m was used in con inuous mode.
A gon (99.996%) shielding gas was supplied only on he op side o he weld a a low a e
o 20 L/min. Figu e 1a shows he size o pla es used in he welding p ocess.
Table 3. Welding pa ame e s used in he expe imen al wo k.
Se ies Lase Powe (kW) Welding Speed (m/min) Hea Inpu (J/mm)
S1 2.00 1.60 75.0
S2 1.75 1.60 65.6
S3 2.00 2.00 60.0
S4 1.75 2.00 52.5
op side weld pass
1.75 1.75–2.00 52.5–60.0
S5 bo om side weld pass
1.25 2.50 30.0
In wo k [
28
], acco ding o he welding quali y s anda d ISO 13919-1, a B quali y le el
o he S1, S2, and S3 welded se ies and a D quali y le el o he S5 welded se ies, we e
epo ed and acco ding o he impe ec ion sizes epo ed, hese can be conside ed as c ack-
like impe ec ions (see he impe ec ions sizes in Table 6). In he a o emen ioned wo k, he
impe ec ions we e measu ed using a p o ilome e wi h a pi ch o 1
µ
m and a mic oscope
equipped wi h digi al mic o-me e s. Since he S4 se ies did no each ull pene a ion, i
will be omi ed in he nex sec ions. The e o e, his se ies de ines app oxima ely he lowe
bounda y o he hea inpu s in o de o ob ain ull pene a ion o he welding in he 3 mm
hick specimens.
Me als 2021,11, 1499 4 o 22
Me als 2021, 11, x FOR PEER REVIEW 3 o 22
2. Ma e ial and P ocedu es
2.1. Ma e ial and Lase Welding
Bu weld join s we e c ea ed wi h 3 mm hick high-s eng h low-alloy (HSLA) s eel
pla e S enx® 700MCE [30]. This s eel has he chemical composi ion and ensile mechan-
ical p ope ies shown in Tables 1 and 2 [31], espec i ely. I p esen s a ine-g ain e i -
ic-baini ic mic os uc u e. The yield s ess is close o he ensile s eng h, which indica es
ha his ma e ial keeps he elas ic beha io almos un il inal ac u e.
Table 1. Base me al chemical composi ion (w %).
C Mn Si P S C V Nb Ni Cu Al Mo Ti Co Fe
0.07 1.69 0.01 0.012 0.006 0.03 0.02 0.046 0.04 0.011 0.044 0.016 0.117 0.016 balance
Table 2. Mechanical p ope ies o he base me al.
Yield S eng h (MPa) Tensile S eng h (MPa) Elonga ion (%)
808 838 15.0
Fi e se ies we e welded conside ing he welding pa ame e s shown in Table 3. The
S1, S2, S3, and S4 se ies a e single-welded join s while he S5 se ies is double-welded
join . Fo his las se ies, he welding speed o he weld pass on he op side was di e en
o each sample (1.75, 1.80, 1.90, 1.95, and 2.00 m/min), while he weld pass on he bo om
side was cons an o all samples (2.50 m/min). These pa ame e s we e selec ed based on
a p e ious s udy o he e ec o pa ame e s on de ec s and ensile p ope ies [31]. The
hea inpu s used in welding we e de ined in o de o achie e di e en alues o ha dness
in he welded se ies, bu simul aneously main aining small HAZs, low so ening, and
ensile mechanical p ope ies simila o he BM, as shown in [31]. A disk lase equipmen
T ump T uDisk 2000 wi h: lase maximum ou pu , 2000 W; beam wa eleng h, 1020 nm;
beam pa ame e p oduc , 2 mm-m ad; and ibe diame e , 200 µm was used in con inu-
ous mode. A gon (99.996%) shielding gas was supplied only on he op side o he weld
a a low a e o 20 L/min. Figu e 1a shows he size o pla es used in he welding p ocess.
Figu e 1. (a) Ske ch o pla es (dimensions in mm) o he welding and loca ion o specimens, (b)
dimensions (in mm) o specimens used in a igue es s.
Figu e 1.
(
a
) Ske ch o pla es (dimensions in mm) o he welding and loca ion o specimens, (
b
) dimensions (in mm) o
specimens used in a igue es s.
2.2. Fa igue Tes ing and Analysis
The a igue specimens we e p epa ed and es ed acco ding o he guidelines o he
ASTM E466-15 s anda d [
32
]. Figu e 1a illus a es he loca ion o he specimens in he
welded pla es, which we e ob ained by lase cu , meanwhile, Figu e 1b shows specimens’
dimensions. The a igue specimens we e es ed in h ee condi ions: no -welded (BM),
as-welded, and bo om side- emo ed. Fo his las condi ion, he excess weld me al and
unde cu s we e p og essi ely elimina ed in o de o ob ain a smoo h ansi ion be ween
he weld and he pla e, hus minimizing he s ess concen a ion. The specimens we e
ca e ully g ound o a inal polish wi h sandpape # 220, pa icula ly he edges and he
welding su aces. The o al elimina ion o he unde cu s was e i ied using he op ical
mic oscope wi h 20×magni ica ion powe .
The es ing was pe o med using DARTEC INSTRON se o-hyd aulic machine. The
a igue specimens we e axially loaded wi h cons an ampli ude a a s ess a io R = 0 and
a a equency o 15 Hz. The specimens we e es ed up o he inal ac u e a a ious s ess
le els; howe e , when a a ce ain s ess le el in which he li e o he specimens exceeded
2
×
10
6
cycles, he es s we e s opped ( un-ou s). A e he ac u e o he specimens,
hei su aces we e analyzed wi h a s e eo-mic oscope in o de o de e mine he si e, s a ,
impe ec ion, pa h, and shape o he a igue su ace.
A powe law ela ionship was assumed o he S-N cu es:
log (N) = log (C) −m log (∆σ), (1)
whe e he nominal s ess ange
∆σ
is he independen a iable, he numbe o cycles N a
which he ailu e occu s is he dependen a iable and C, m a e pa ame e s ha cha ac e ize
he cu es. Th ough linea eg ession, he S-N da a we e analyzed acco ding o he ASTM
E739-10 s anda d [
33
] o de e mine he pa ame e s (C, m) o he S-N ela ionships, he
median S-N cu e, and i s 95% con idence band. The es ing o adequacy o he linea
model was also e i ied acco ding o he men ioned s anda d. Fo compa ison, he FAT100
cu e (slope m = 3,
∆σ
= 100 MPa a wo million cycles) was also plo ed in he S-N g aphs.
This FAT100 cu e, sugges ed in he a igue design ecommenda ions o he In e na ional
Ins i u e o Welding (IIW) o bu join s when impe ec ions (unde cu s and po osi y) a e
e alua ed [
5
], was chosen because i s equi emen s closely ma ch (di e s in he hickness
Me als 2021,11, 1499 5 o 22
and he po osi y o one o he se ies) he impe ec ion sizes and quali y le el ound in
welded se ies, as epo ed in [28].
2.3. Measu emen o Residual S esses
The esidual s ess analysis was pe o med by X- ay di ac ion using P o o iXRD
equipmen in he longi udinal and ans e se di ec ions o he lase welds and on bo h sides
( op and bo om su aces) o he specimens. La ice de o ma ions o he {211} di ac ion
planes (2
θ≈
156
◦
) we e measu ed using C -K
α
X- ay adia ion, wi h 11
β
angles in he
ange
±
30
◦
(22
ψ
angles in he ange
±
42
◦
), an acquisi ion ime o 30 s by peak, and
±
2
◦
oscilla ions in
ψ
. An ape u e leng h o 0.5 mm
×
3 mm in he ans e se and longi udinal
di ec ions, espec i ely, was used. The esidual s esses we e e alua ed wi h an ellip ical
eg ession o sin
2ψ
using he X- ay elas ic cons an s o 5.83
×
10
−6
(MPa)
−1
o
1
2S{211}
2
and
−
1.28
×
10
−6
(MPa)
−1
o
S{211}
1
. Fo he analyzed ma e ial and conside ing he adia ion
used, he a e age pene a ion dep h o he X- ays was abou 5 µm.
The measu emen o he esidual s esses was pe o med in he middle o he wid h o
he a igue specimen a poin s loca ed along he ho izon al line (hl), see Figu e 1b. A 32 mm
ex ension was co e ed wi h a sepa a ion be ween poin s ha was p og essi ely educed
when app oaching he welded zone, hese sepa a ions we e: 4 mm, 2 mm, 1 mm, and
0.5 mm.
Figu e 1b shows he di ec ions o he longi udinal (L) and ans e se (T) esidual
s esses.
3. Resul s and Discussion
3.1. S-N Cu es
Figu e 2shows he S-N expe imen al esul s o bo h he welded se ies and he BM. The
mean and he 95% con idence band cu es o he BM a e also p esen ed along wi h FAT100
cu e, which is a e e ence o welded join s. The BM shows a linea beha io in log-log
scale wi h small sca e . The nominal s ess ange a ied be ween 600 and 800 MPa, which
co esponds o 74% and 99% o he ma e ial’s yield s ess, espec i ely. The modi ica ions
in oduced by lase welding on mic os uc u e signi ican ly changed he posi ion o he S-N
cu es. A signi ican dec ease o s ess ange o he same a igue li e is e iden , namely
o lowe load anges, i.e., o longe a igue li es. The sca e inc eased signi ican ly and
compa a i ely o he BM. Bo h he S-N cu es o he BM and o he welded join s p esen ed
he cha ac e is ic “knee poin ” ha iden i ies he s ess le el o he a igue limi , which,
in his wo k, will be assumed as he a igue s eng h o un-ou s a wo million cycles.
E en ually, he se ies S2 may be conside ed o ha e a highe limi . The FAT100 cu e is
clea ly below he expe imen al esul s ob ained o he welded se ies, which is a good
indica ion o he quali y o lase welding.
Figu e 3p esen s he esul s o each se ies and a pho o-mac og aph showing he
ypical c oss-sec ion o he weld bead. The s ess le els co esponding o he a igue limi
a e also indica ed. The dispe sion o he en i e da a se is educed when each se ies is
conside ed sepa a ely, and he dispe sion o each se ies is simila o ha o he BM. In he
case o he S5 se ies, because wo specimens (named as S5-F9) showed conside ably highe
a igue s eng h han he es o specimens, hey we e no conside ed wi hin he S5 se ies.
The FAT100 is clea ly below he expe imen al esul s o all he se ies.
Table 4p esen s log C and m pa ame e s o S-N cu es. The e is a limi ed in luence
o welded se ies on hese alues, wi h he excep ion o S2 se ies. The m alues a e close
o FAT100 cu e slope. The ela i ely high m alue ob ained o he BM indica es ha
he ini ia ion is dominan o e he p opaga ion. Con e sely, he ela i ely low alue o
m o he welded join s indica es he p edominance o p opaga ion o e ini ia ion. The
a igue limi s shown in Table 4, which we e assumed o be he maximum s ess ange
alues eached by he specimens ha exceeded wo million cycles, a e be ween 30% and
57% o he a igue limi o he BM. As can be seen in Figu e 3, all se ies had a a igue li e
o e he FAT100 cu e. F om he esul s ob ained, he con idence F- es o all welded
se ies and BM did no ejec he hypo hesis o linea model.

Me als 2021,11, 1499 6 o 22
Me als 2021, 11, x FOR PEER REVIEW 6 o 22
Figu e 2. S-N cu es o all welded se ies and BM.
Figu e 3. S-N cu es o each welded se ies.
Figu e 2. S-N cu es o all welded se ies and BM.
Me als 2021, 11, x FOR PEER REVIEW 6 o 22
Figu e 2. S-N cu es o all welded se ies and BM.
Figu e 3. S-N cu es o each welded se ies.
Figu e 3. S-N cu es o each welded se ies.
Me als 2021,11, 1499 7 o 22
Table 4. S-N cu es pa ame e s and a igue limi s.
Se ies Linea Model F Tes
F0.95 Fcalcula ed
log C m Fa igue Limi s
(MPa)
S1 6.59 0.27 (no ejec ed) 13.46 3.23 180
S2 9.28 7.86 (no ejec ed) 16.21 4.25 270
S3 3.97 1.62 (no ejec ed) 13.25 3.12 210
S5 3.69 1.57 (no ejec ed) 13.47 3.21 215 (340) 1
BM 3.70 0.44 (no ejec ed) 30.64 9.00 600
1The alue 340 MPa co esponds o S5-F9 specimens.
3.2. Fa igue Failu e Modes
Based on he analysis o he ac u ed su aces o all he specimens, mainly ou ailu e
modes we e ound in he welded se ies. These a e designa ed as FM1, FM2, FM3, and
FM4. Table 5p esen s he p incipal ea u es o each ailu e mode: he se ies in which
he ailu e mode was p esen ; he si e, impe ec ion, and side o he weld bead whe e
a igue s a ed; de ails o he impe ec ions; he shape o he ac u ed su ace; and ema ks.
Table 5includes ep esen a i e pho og aphs showing he ac u e su aces, he a igue
ini ia ion si es, and de ails o he impe ec ions ha caused he a igue. Fo each mode,
he pho og aphs o wo ac u ed specimens a e p esen ed wi h he excep ion o he FM4
mode, o which only he pho og aphs a e p esen ed o one specimen.
Table 5. Failu e modes ea u es.
Failu e Mode
(Se ies)
Fa igue S a
Si e-Impe ec ion
(Side)
De ails App oxima e Shape o
F ac u ed Su ace Rema ks
FM1 (S1, S3) oo -unde cu s (bo om
side)
(a)
long and deep
unde cu s, one o
wo e y close
(b)
se e al unde cu s
ac oss he wid h
(a)
big semi-ellip ical
(b)
ending o
ec angula by
coalescence o small
semi-ellip ical
in some cases,
mic ode ec s close o
unde cu s
Me als 2021, 11, x FOR PEER REVIEW 7 o 22
Table 4 p esen s log C and m pa ame e s o S-N cu es. The e is a limi ed in luence
o welded se ies on hese alues, wi h he excep ion o S2 se ies. The m alues a e close o
FAT100 cu e slope. The ela i ely high m alue ob ained o he BM indica es ha he
ini ia ion is dominan o e he p opaga ion. Con e sely, he ela i ely low alue o m o
he welded join s indica es he p edominance o p opaga ion o e ini ia ion. The a igue
limi s shown in Table 4, which we e assumed o be he maximum s ess ange alues
eached by he specimens ha exceeded wo million cycles, a e be ween 30% and 57% o
he a igue limi o he BM. As can be seen in Figu e 3, all se ies had a a igue li e o e he
FAT100 cu e. F om he esul s ob ained, he con idence F- es o all welded se ies and
BM did no ejec he hypo hesis o linea model.
Table 4. S-N cu es pa ame e s and a igue limi s.
Se ies Linea Model F Tes
F
0.95
F
calcula ed
log C m Fa igue Limi s
(MPa)
S1 6.59 0.27 (no ejec ed) 13.46 3.23 180
S2 9.28 7.86 (no ejec ed) 16.21 4.25 270
S3 3.97 1.62 (no ejec ed) 13.25 3.12 210
S5 3.69 1.57 (no ejec ed) 13.47 3.21 215 (340)
1
BM 3.70 0.44 (no ejec ed) 30.64 9.00 600
1
The alue 340 MPa co esponds o S5-F9 specimens.
3.2. Fa igue Failu e Modes
Based on he analysis o he ac u ed su aces o all he specimens, mainly ou
ailu e modes we e ound in he welded se ies. These a e designa ed as FM1, FM2, FM3,
and FM4. Table 5 p esen s he p incipal ea u es o each ailu e mode: he se ies in which
he ailu e mode was p esen ; he si e, impe ec ion, and side o he weld bead whe e a-
igue s a ed; de ails o he impe ec ions; he shape o he ac u ed su ace; and e-
ma ks. Table 5 includes ep esen a i e pho og aphs showing he ac u e su aces, he
a igue ini ia ion si es, and de ails o he impe ec ions ha caused he a igue. Fo each
mode, he pho og aphs o wo ac u ed specimens a e p esen ed wi h he excep ion o
he FM4 mode, o which only he pho og aphs a e p esen ed o one specimen.
Table 5. Failu e modes ea u es.
Failu e Mode
(Se ies)
Fa igue S a
Si e-Impe ec ion
(Side)
De ails App oxima e Shape o
F ac u ed Su ace Rema ks
FM1 (S1, S3) oo -unde cu s
(bo om side)
(a) long and deep
unde cu s, one o wo e y
close
(b) se e al unde cu s ac oss
he wid h
(a) big semi-ellip ical
(b) ending o ec angula by
coalescence o small
semi-ellip ical
in some cases,
mic ode ec s close o
unde cu s
Me als 2021, 11, x FOR PEER REVIEW 8 o 22
FM2
(S2, S1, S3)
oo -excess weld
(bo om side)
mul iple s a s in
mic o-impe ec ions (po es,
ca i ies, shallow c ack-like)
ac oss he wid h
ending o a ec angula
s ipe ac oss he wid h
semi-ellip ical o ms
we e no obse ed in
weld oo
FM3
(S5)
(S1,S2,S3)
ace-unde ill
(bo om side)
( op side)
mul iple s a s in wa es and
sha p ipples wi h
mic ode ec s
small semi-ellipses o ending
o a big semi-ellipse by
coalescence
in many cases, unde ill
a bo de
Me als 2021,11, 1499 8 o 22
Table 5. Con .
Failu e Mode
(Se ies)
Fa igue S a
Si e-Impe ec ion
(Side)
De ails App oxima e Shape o
F ac u ed Su ace Rema ks
FM2 (S2, S1, S3) oo -excess weld
(bo om side)
mul iple s a s in
mic o-impe ec ions
(po es, ca i ies, shallow
c ack-like) ac oss he
wid h
ending o a ec angula
s ipe ac oss he wid h
semi-ellip ical o ms
we e no obse ed in
weld oo
Me als 2021, 11, x FOR PEER REVIEW 8 o 22
FM2
(S2, S1, S3)
oo -excess weld
(bo om side)
mul iple s a s in
mic o-impe ec ions (po es,
ca i ies, shallow c ack-like)
ac oss he wid h
ending o a ec angula
s ipe ac oss he wid h
semi-ellip ical o ms
we e no obse ed in
weld oo
FM3
(S5)
(S1,S2,S3)
ace-unde ill
(bo om side)
( op side)
mul iple s a s in wa es and
sha p ipples wi h
mic ode ec s
small semi-ellipses o ending
o a big semi-ellipse by
coalescence
in many cases, unde ill
a bo de
Me als 2021, 11, x FOR PEER REVIEW 8 o 22
FM2
(S2, S1, S3)
oo -excess weld
(bo om side)
mul iple s a s in
mic o-impe ec ions (po es,
ca i ies, shallow c ack-like)
ac oss he wid h
ending o a ec angula
s ipe ac oss he wid h
semi-ellip ical o ms
we e no obse ed in
weld oo
FM3
(S5)
(S1,S2,S3)
ace-unde ill
(bo om side)
( op side)
mul iple s a s in wa es and
sha p ipples wi h
mic ode ec s
small semi-ellipses o ending
o a big semi-ellipse by
coalescence
in many cases, unde ill
a bo de
FM3 (S5) (S1, S2,
S3) ace-unde ill (bo om
side) ( op side)
mul iple s a s in wa es
and sha p ipples wi h
mic ode ec s
small semi-ellipses o
ending o a big
semi-ellipse by coalescence
in many cases, unde ill
a bo de
Me als 2021, 11, x FOR PEER REVIEW 8 o 22
FM2
(S2, S1, S3)
oo -excess weld
(bo om side)
mul iple s a s in
mic o-impe ec ions (po es,
ca i ies, shallow c ack-like)
ac oss he wid h
ending o a ec angula
s ipe ac oss he wid h
semi-ellip ical o ms
we e no obse ed in
weld oo
FM3
(S5)
(S1,S2,S3)
ace-unde ill
(bo om side)
( op side)
mul iple s a s in wa es and
sha p ipples wi h
mic ode ec s
small semi-ellipses o ending
o a big semi-ellipse by
coalescence
in many cases, unde ill
a bo de
Me als 2021, 11, x FOR PEER REVIEW 9 o 22
FM4
(S5, S1, S2, S3)
cen e -po osi y
(la e al side)
single po e o se e al on o
nea he su ace
app oaching he middle o a
semi-ellip ical
in some cases
in luenced by unde ill
close o co ne
The FM1 ailu e mode was due o he unde cu s a weld oo o he S1 and S3 se ies;
he e was gene ally mo e han one unde cu ha gene a ed semi-ellip ical c acks. In he
FM2 ailu e mode, mul iple impe ec ions along he weld oo caused ailu es, especially
in he S2 se ies. In hese cases, he p esence o semi-ellip ical c acks was no e iden . The
FM3 ailu e mode was p esen in p ac ically all he welded se ies and he a igue s a s
we e loca ed in he unde ill and he ipples. The ipples co esponding o he S5 se ies
we e smalle ; see Table 5. The FM4 ailu e mode e e s o ailu e due o he p esence o
po es ha we e p esen in all se ies bu in g ea e numbe s in he S5 se ies. The po es
caused a igue ailu es a he la e al side o he specimens gene ally when hey we e lo-
ca ed nea o on he su ace. This ailu e can also be in luenced by he unde ill a he
bo de o he elemen , as illus a ed in Table 5.
I should be no ed ha in app oxima ely 44% o he ac u ed specimens, a leas wo
ailu e modes we e obse ed (as illus a ed in FM2 mode, S3 se ies in Table 5), howe e ,
in mos cases, only one mode was decisi e o a igue ailu e. The a igue pa h was gen-
e ally s aigh om he weld oo h ough hickness o he unde ill o ice e sa. How-
e e , in ce ain cases, he pa h had inclined pa s due o he s a s o a igue om di e -
en planes by he p esence o po osi y, o in he inal s ages o he ac u e, due o de ia-
ions o he so ma e ial whe e g ea e de o ma ions we e p esen ed.
Figu e 4 p esen s he ailu e modes obse ed in each specimen o he di e en se ies.
Each se ies had a main ailu e mode ha p e ailed o e he o he s, and all se ies p e-
sen ed a leas wo main and wo addi ional ailu e modes. As can be seen, in S1 and S3
se ies he FM1 mode p e ailed, in S2 se ies he FM2 mode is mo e ele an , while in S5
se ies he FM3 mode is dominan . The abo e is s ongly ela ed o he co esponding
p esence o impe ec ions in each weld bead; see Table 5. Figu e 4 also illus a es, in he
ske ches on he c oss-sec ions o he weld beads, he s a s and pa hs ollowed by he ou
ailu e modes and ha all he ac u es in he specimens occu ed wi hin he FZ and
HAZ. Conside ing he s a s on unde ill and he s a s on excess weld and unde cu s, i
was obse ed ha he las domina ed in S1, S2, and S3 se ies while he i s domina ed in
S5 se ies. The FM4 mode, which co esponds o po osi y, caused ew s a s in all se ies,
Me als 2021,11, 1499 9 o 22
Table 5. Con .
Failu e Mode
(Se ies)
Fa igue S a
Si e-Impe ec ion
(Side)
De ails App oxima e Shape o
F ac u ed Su ace Rema ks
FM4
(S5, S1, S2, S3) cen e -po osi y (la e al
side) single po e o se e al on
o nea he su ace app oaching he middle o
a semi-ellip ical
in some cases
in luenced by unde ill
close o co ne
Me als 2021, 11, x FOR PEER REVIEW 9 o 22
FM4
(S5, S1, S2, S3)
cen e -po osi y
(la e al side)
single po e o se e al on o
nea he su ace
app oaching he middle o a
semi-ellip ical
in some cases
in luenced by unde ill
close o co ne
The FM1 ailu e mode was due o he unde cu s a weld oo o he S1 and S3 se ies;
he e was gene ally mo e han one unde cu ha gene a ed semi-ellip ical c acks. In he
FM2 ailu e mode, mul iple impe ec ions along he weld oo caused ailu es, especially
in he S2 se ies. In hese cases, he p esence o semi-ellip ical c acks was no e iden . The
FM3 ailu e mode was p esen in p ac ically all he welded se ies and he a igue s a s
we e loca ed in he unde ill and he ipples. The ipples co esponding o he S5 se ies
we e smalle ; see Table 5. The FM4 ailu e mode e e s o ailu e due o he p esence o
po es ha we e p esen in all se ies bu in g ea e numbe s in he S5 se ies. The po es
caused a igue ailu es a he la e al side o he specimens gene ally when hey we e lo-
ca ed nea o on he su ace. This ailu e can also be in luenced by he unde ill a he
bo de o he elemen , as illus a ed in Table 5.
I should be no ed ha in app oxima ely 44% o he ac u ed specimens, a leas wo
ailu e modes we e obse ed (as illus a ed in FM2 mode, S3 se ies in Table 5), howe e ,
in mos cases, only one mode was decisi e o a igue ailu e. The a igue pa h was gen-
e ally s aigh om he weld oo h ough hickness o he unde ill o ice e sa. How-
e e , in ce ain cases, he pa h had inclined pa s due o he s a s o a igue om di e -
en planes by he p esence o po osi y, o in he inal s ages o he ac u e, due o de ia-
ions o he so ma e ial whe e g ea e de o ma ions we e p esen ed.
Figu e 4 p esen s he ailu e modes obse ed in each specimen o he di e en se ies.
Each se ies had a main ailu e mode ha p e ailed o e he o he s, and all se ies p e-
sen ed a leas wo main and wo addi ional ailu e modes. As can be seen, in S1 and S3
se ies he FM1 mode p e ailed, in S2 se ies he FM2 mode is mo e ele an , while in S5
se ies he FM3 mode is dominan . The abo e is s ongly ela ed o he co esponding
p esence o impe ec ions in each weld bead; see Table 5. Figu e 4 also illus a es, in he
ske ches on he c oss-sec ions o he weld beads, he s a s and pa hs ollowed by he ou
ailu e modes and ha all he ac u es in he specimens occu ed wi hin he FZ and
HAZ. Conside ing he s a s on unde ill and he s a s on excess weld and unde cu s, i
was obse ed ha he las domina ed in S1, S2, and S3 se ies while he i s domina ed in
S5 se ies. The FM4 mode, which co esponds o po osi y, caused ew s a s in all se ies,
The FM1 ailu e mode was due o he unde cu s a weld oo o he S1 and S3 se ies;
he e was gene ally mo e han one unde cu ha gene a ed semi-ellip ical c acks. In he
FM2 ailu e mode, mul iple impe ec ions along he weld oo caused ailu es, especially in
he S2 se ies. In hese cases, he p esence o semi-ellip ical c acks was no e iden . The FM3
ailu e mode was p esen in p ac ically all he welded se ies and he a igue s a s we e
loca ed in he unde ill and he ipples. The ipples co esponding o he S5 se ies we e
smalle ; see Table 5. The FM4 ailu e mode e e s o ailu e due o he p esence o po es
ha we e p esen in all se ies bu in g ea e numbe s in he S5 se ies. The po es caused
a igue ailu es a he la e al side o he specimens gene ally when hey we e loca ed nea
o on he su ace. This ailu e can also be in luenced by he unde ill a he bo de o he
elemen , as illus a ed in Table 5.
I should be no ed ha in app oxima ely 44% o he ac u ed specimens, a leas wo
ailu e modes we e obse ed (as illus a ed in FM2 mode, S3 se ies in Table 5), howe e , in
mos cases, only one mode was decisi e o a igue ailu e. The a igue pa h was gene ally
s aigh om he weld oo h ough hickness o he unde ill o ice e sa. Howe e , in
ce ain cases, he pa h had inclined pa s due o he s a s o a igue om di e en planes
by he p esence o po osi y, o in he inal s ages o he ac u e, due o de ia ions o he
so ma e ial whe e g ea e de o ma ions we e p esen ed.
Figu e 4p esen s he ailu e modes obse ed in each specimen o he di e en se ies.
Each se ies had a main ailu e mode ha p e ailed o e he o he s, and all se ies p esen ed
a leas wo main and wo addi ional ailu e modes. As can be seen, in S1 and S3 se ies he
FM1 mode p e ailed, in S2 se ies he FM2 mode is mo e ele an , while in S5 se ies he
FM3 mode is dominan . The abo e is s ongly ela ed o he co esponding p esence o
impe ec ions in each weld bead; see Table 5. Figu e 4also illus a es, in he ske ches on he
c oss-sec ions o he weld beads, he s a s and pa hs ollowed by he ou ailu e modes
and ha all he ac u es in he specimens occu ed wi hin he FZ and HAZ. Conside ing
he s a s on unde ill and he s a s on excess weld and unde cu s, i was obse ed ha
he las domina ed in S1, S2, and S3 se ies while he i s domina ed in S5 se ies. The FM4
mode, which co esponds o po osi y, caused ew s a s in all se ies, howe e , in S5 se ies i
inc eased as a consequence o i s highes pe cen age o po osi y (3.5%) [28].
3.3. E ec o Weld Bead Geome y and Impe ec ions
In o de o e alua e he e ec exe ed by he weld p o ile and geome ical impe ec-
ions on he a igue beha io , he s ess concen a ion ac o (SCF), K
, co esponding o he
op and bo om sides o each welded se ies we e de e mined by he ini e elemen me hod
Me als 2021,11, 1499 16 o 22
Me als 2021, 11, x FOR PEER REVIEW 16 o 22
Figu e 11. Residual s esses p o iles in a igue specimens.
3.5.3. Fa igue Limi E alua ion
In p e ious sec ions, i was shown ha o low s ess le els, he app oach o educ-
ing a igue s eng h h ough s ess-concen a ing e ec can be used. To conside he e -
ec o he mean s ess in he analysis o he a igue s eng h a wo million cycles o he
welded se ies, due o i s simplici y, he modi ied Goodman line will be used acco ding o
he exp ession:
𝐾 𝜎
𝑆+𝐾 𝜎
𝑆 =1
𝑛
(2)
whe e
𝜎
and
𝜎
a e he nominal al e na ing and mean s esses applied and bo h a e
equal o ∆σ/2 (acco ding o s ess a io R = 0);
𝐾
, is he e ec i e s ess concen a ion
ac o calcula ed using he ela ionship o sensi i i y o no ch p oposed by Pe e son [37];
𝑆
and
𝑆
a e he ul ima e s eng h and he a igue limi o he ma e ials ha will be
es ima ed o each welded se ies and BM h ough he ha dness HV, as 3.0 × HV and 1.5 ×
HV, espec i ely, and
𝑛
is he ac o ha e alua es he p oximi y o he men ioned
ailu e c i e ia o he local s esses a impe ec ions o he specimens. When he esidual
s esses a e conside ed, hey will be added o he mean applied s ess
𝜎
.
Table 8 shows he da a used o he de e mina ion o he
𝑛
ac o s o bo h (wi h
esidual s esses and wi hou esidual s esses o he welded se ies) condi ions and im-
pe ec ions indica ed he e. Figu e 12 illus a es he posi ion o he a igue ailu e poin s
o he specimens acco ding o he mean and al e na ing local s esses, in ela ion o e-
spec i e modi ied Goodman lines. When examining he conco dance be ween he as-
sumed ailu e c i e ion and he cases conside ed, i was ound ha i is excellen in he
case o he BM, gene ally good o all cases o he welded se ies when esidual s esses
we e included and unde es ima ed when hey we e no included; see Table 8 and Figu e
12. The e is a good ag eemen wi h and wi hou esidual s ess when he
𝐾
alues a e
low o unde ill (cases 2 and 4), and in con as o he highes alues o
𝐾
(cases 1 and
5). Pa icula ly o he excess weld and he unde ill o he S2 and S5 se ies, espec i ely,
Figu e 11. Residual s esses p o iles in a igue specimens.
3.5.3. Fa igue Limi E alua ion
In p e ious sec ions, i was shown ha o low s ess le els, he app oach o educing
a igue s eng h h ough s ess-concen a ing e ec can be used. To conside he e ec o
he mean s ess in he analysis o he a igue s eng h a wo million cycles o he welded
se ies, due o i s simplici y, he modi ied Goodman line will be used acco ding o he
exp ession:
K σa
Se
+K σm
Su
=1
nG
(2)
whe e
σa
and
σm
a e he nominal al e na ing and mean s esses applied and bo h a e equal
o
∆σ
/2 (acco ding o s ess a io R = 0);
K
, is he e ec i e s ess concen a ion ac o
calcula ed using he ela ionship o sensi i i y o no ch p oposed by Pe e son [
37
];
Su
and
Se
a e he ul ima e s eng h and he a igue limi o he ma e ials ha will be es ima ed
o each welded se ies and BM h ough he ha dness HV, as 3.0
×
HV and 1.5
×
HV,
espec i ely, and
nG
is he ac o ha e alua es he p oximi y o he men ioned ailu e
c i e ia o he local s esses a impe ec ions o he specimens. When he esidual s esses
a e conside ed, hey will be added o he mean applied s ess σm.
Table 8shows he da a used o he de e mina ion o he
nG
ac o s o bo h (wi h
esidual s esses and wi hou esidual s esses o he welded se ies) condi ions and impe -
ec ions indica ed he e. Figu e 12 illus a es he posi ion o he a igue ailu e poin s o he
specimens acco ding o he mean and al e na ing local s esses, in ela ion o espec i e
modi ied Goodman lines. When examining he conco dance be ween he assumed ailu e
c i e ion and he cases conside ed, i was ound ha i is excellen in he case o he BM,
gene ally good o all cases o he welded se ies when esidual s esses we e included
and unde es ima ed when hey we e no included; see Table 8and Figu e 12. The e is a
good ag eemen wi h and wi hou esidual s ess when he
K
alues a e low o unde ill
(cases 2 and 4), and in con as o he highes alues o
K
(cases 1 and 5). Pa icula ly o
he excess weld and he unde ill o he S2 and S5 se ies, espec i ely, he e is he g ea es
disc epancy (close o 20%) be ween he expe imen al esul s and he assumed c i e ion
(cases 3 and 6) when he esidual s esses a e conside ed.

Me als 2021,11, 1499 17 o 22
Me als 2021, 11, x FOR PEER REVIEW 17 o 22
he e is he g ea es disc epancy (close o 20%) be ween he expe imen al esul s and he
assumed c i e ion (cases 3 and 6) when he esidual s esses a e conside ed.
Figu e 12. Fa igue ailu e poin s o specimens and modi ied Goodman lines.
Table 8. Da a o a igue s eng h assessmen based on he modi ied Goodman line.
Case Condi ion Se ies
Impe ec ion K
ρ
𝐾
Ha dness Residual
S ess
Fa igue Lim-
i s
𝑛
Fac o
(mm) (HV) (MPa) (MPa) RS
1
no RS
1 as-welded S1-unde cu 3.29 0.06 2.33 335 130 180 1.08 1.60
2 bo om side- emo ed S1-unde ill 1.75 0.53 1.60 335 130 380 0.90 1.10
3 as-welded S2-excess weld 2.25 0.06 1.74 345 90 270 1.20 1.47
4 bo om side- emo ed S2-unde ill 1.77 0.60 1.63 345 90 390 0.94 1.09
5 as-welded S3-unde cu 4.41 0.03 2.74 350 50 210 1.05 1.22
6 as-welded S5-unde ill 1.95 0.27 1.74 370 200 215 1.17 1.90
7 no-welded Base me al --- --- --- 295 --- 600 --- 0.98
1
RS: esidual s esses.
The e ec s o ha dness, esidual s esses, and s ess concen a ion on each welded
se ies in he as-welded condi ion can be desc ibed as ollows: he S1 se ies p esen ed he
lowes a igue s eng h due o he combina ion o a high SCF a he unde cu , a medium
alue o esidual s ess, and a ela i ely low ha dness. The S5 se ies, despi e ha ing he
highes ha dness and al hough he SCF was medium, due o he high alue o he esid-
ual s esses, i also p esen ed low a igue s eng h. The S3 se ies, wi h a low alue o e-
sidual s esses and a high ha dness, did no achie e a g ea e s eng h o a igue because
i had he highes SCF due o he sha p unde cu in he weld oo . The S2 se ies achie ed
he highes a igue s eng h o all se ies wi h medium SCF and ha dness alues and a
ela i ely low esidual s ess alue. I can be in e ed ha his se ies can achie e g ea e
a igue s eng h i he mul iple small impe ec ions p esen along he weld oo dec ease.
In o he wo ks, he ad e se e ec o many small impe ec ions in addi ion o he weld
bead p o ile on a igue s eng h has also been epo ed [38,39].
Figu e 12. Fa igue ailu e poin s o specimens and modi ied Goodman lines.
The e ec s o ha dness, esidual s esses, and s ess concen a ion on each welded
se ies in he as-welded condi ion can be desc ibed as ollows: he S1 se ies p esen ed he
lowes a igue s eng h due o he combina ion o a high SCF a he unde cu , a medium
alue o esidual s ess, and a ela i ely low ha dness. The S5 se ies, despi e ha ing he
highes ha dness and al hough he SCF was medium, due o he high alue o he esidual
s esses, i also p esen ed low a igue s eng h. The S3 se ies, wi h a low alue o esidual
s esses and a high ha dness, did no achie e a g ea e s eng h o a igue because i had
he highes SCF due o he sha p unde cu in he weld oo . The S2 se ies achie ed he
highes a igue s eng h o all se ies wi h medium SCF and ha dness alues and a ela i ely
low esidual s ess alue. I can be in e ed ha his se ies can achie e g ea e a igue
s eng h i he mul iple small impe ec ions p esen along he weld oo dec ease. In o he
wo ks, he ad e se e ec o many small impe ec ions in addi ion o he weld bead p o ile
on a igue s eng h has also been epo ed [38,39].
Rega ding he a igue limi s achie ed by S1 (380 MPa) and S2 se ies (390 MPa) in
he bo om side- emo ed condi ion, al hough he a igue limi o he S2 se ies is expec ed
o be highe because i s ha dness is g ea e and he esidual s esses a e lowe , he sligh
di e ence may be due, as al eady poin ed ou in a p e ious sec ion, o he g ea e dep h o
he unde ill and o he e ec combined wi h he weld ipples. In he case o he beha io
o he S5-F9 specimens, which showed conside ably g ea e a igue s eng h han he o he
specimens o he S5 se ies, he weld p o ile in he bo om side was examined wi h mo e
de ail. I was ound ha he unde ill alues we e below he a e age o he se ies and ha
he a ia ions along he weld axis we e small, as illus a ed in o he wo k [
28
]. The la e
implies ha he SCF o his se ies is lowe and he e o e i s a igue s eng h is highe .
The p e ious analysis showed ha he SCF is a good p edic o o a igue limi in
absence o mul iple small impe ec ions, such as hose o S2 se ies ha we e no easily
de ec ed o when he SCF is p ope ly calcula ed (which was no he case o he S5 se ies).
Con e sely, i shows a g ea e ec o he esidual s esses ha is magni ied by he SCF
and by he mean applied s ess. In summa y, al hough he esidual s esses ound can be
conside ed small, hey ad e sely a ec he a igue s eng h o he welded specimens, as
well as he high SCFs due o he weld bead geome y and he small associa ed impe ec ions.
Me als 2021,11, 1499 18 o 22
Meanwhile, he high ha dness in he FZ and CG-HAZ allows he imp o emen o he
s eng h o he welded se ies.
3.6. Fa igue Limi P edic ions
The es ima es a low s esses showed ha he a igue s eng h can be p edic ed i
he ha dness, esidual s esses, weld geome y, and impe ec ions o he welded join s
a e known. The e o e, using he exp ession (2) wi h
nG
= 1 and he da a in Table 8,
he a igue s eng h a wo million cycles in e ms o s ess ange was p edic ed and he
co esponding esul s o each welded se ies and condi ions a e shown in Table 9 oge he
wi h he expe imen al esul s and he ela ion ha compa es bo h esul s. Conside ing
all he esul s, he e is a good ag eemen be ween he expe imen al and p edic ed alues.
Howe e , a di e ence o g ea e han 15 pe cen was ound o he S2 and S5 se ies. Fo
he S2 se ies, his can be a ibu ed, as al eady no ed, o impe ec ions in he weld oo ha
he s ess concen a ion ac o does no conside . Fo he S5 se ies, he di e ence may be
he esul o a welding speed ange (1.75 o 2.00 m/min) and he e o e he alue o he SCF,
which can ac ually be highe han he one used (
K
, 1.95) since he la e was de e mined
based on he a e age dimensions o he weld beads and a small impe ec ions in he weld
ipples.
Table 9. Fa igue limi p edic ions.
Se ies-Impe ec ion Condi ion Fa igue Limi s
Expe imen al P edic ed Ra io
S1-unde cu As-welded 180 201 0.90
S1-unde ill Bo om side- emo ed 380 332 1.14
S2-excess weld As-welded 270 336 0.80
S2-unde ill Bo om side- emo ed 390 363 1.07
S3-unde cu As-welded 210 222 0.95
S5-unde ill As-welded 215 292 0.74
Addi ionally, ega ding he abo e p edic ions, and o explain he e ec o he impe -
ec ions p esen in he weld oo o he S2 se ies and due o he small size o he unde cu s
p esen in he S1 se ies, he Mu akami’s ela ions p oposed o p edic he a igue limi we e
applied o he men ioned se ies. The ela ions ha e he o m:
σw=1.43 (HV +120)
√A ea1/6 1−R
2∝
(3)
∝=0.226 +HV/10,000, (4)
whe e
σw
(in MPa) is he a igue limi ,
HV
is he Vicke s ha dness,
R
is he s ess a io
and
√A ea
(in
µ
m) is he size pa ame e o he impe ec ion. The da a shown in Table 10
co esponds in he case o he S1 se ies o he a e age size o unde cu s, while in he case
o he S2 se ies, i co esponds o he a e age dep h o 10 measu emen s on he long and
na ow impe ec ions, which a e p ac ically con inuous in he weld oo . In bo h cases, he
√A ea
pa ame e was calcula ed as
√A ea
=a
√10
, whe e ais he c ack dep h, acco ding
o Mu akami’s ecommenda ion o his ype o impe ec ion (shallow su ace c ack) [
12
].
In he s ess a io, he esidual s esses o Table 8we e conside ed and h ough an i e a i e
p ocess, in which a igue limi alues we e assumed un il equali y in exp ession (3) was
eached, he a igue limi s we e p edic ed, which a e shown in Table 10 as well as he
espec i e compa isons wi h he expe imen al esul s.
Me als 2021,11, 1499 19 o 22
Table 10. Da a and pa ame e s o p edic ion o a igue limi s.
Se ies
Impe ec ion
C ack Sizes
Leng h, Dep h √A ea Fa igue Limi s
(mm, µm) (µm) Expe imen al
(MPa)
P edic ed
(MPa) Ra io
S1-unde cu 1.11, 40 126 180 214 0.84
S2-shallow c ack >0.23, 22 70 270 254 1.06
The esul s o Table 10 show ha adequa e p edic ions can be achie ed h ough he
app oach p oposed by Mu akami. In he case o he S2 se ies, he p edic ion is be e
adjus ed o he expe imen al alue, while in he case o he S1 se ies, a simila esul was
ob ained. Howe e , in he p edic ions based on his las app oach, i is necessa y o know
he impe ec ion and i s size, which may no be e iden , as in he case o he S2 se ies,
whe e only a e he ac u e o he specimens, hey can be obse ed. Con e sely, he e
may be a ia ions in he sizes o he impe ec ions, which equi es measu emen s and he
applica ion o some c i e ion ha in he p esen case, was he a e age size. In he case
o unde cu s ( o se ies S1), a be e p edic ion can be achie ed conside ing ha 4 o 5
unde cu s can be p esen in each specimen; he e o e, i is mo e likely ha he size is g ea e
han he a e age size (40
µ
m). Conside ing ha he dep h o he unde cu s a ied om 15
o 105
µ
m [
28
], o example, an unde cu dep h o 90
µ
m, he a igue limi will be 180 MPa,
which is he same as he expe imen al esul .
4. Conclusions
Fo ou lase bu join s in a hin HSLA s eel pla e, he e ec s o he weld p o ile,
impe ec ions, ha dness and esidual s esses we e conside ed o explain he expe imen al
S-N cu es and o p edic ions a low s ess le els, applying app oaches based on bo h
s ess-concen a ing e ec and Mu akami’s ela ionship. The main conclusions d awn a e:
•
The a igue s eng h o he welded se ies exceeded he FAT100 e e ence cu e wi h
a igue limi s in he ange o 180 o 340 MPa, p esen ing mul iple impe ec ions as
shallow bu sha p, and conside ed as c ack-like impe ec ions and wi h B and D
quali y le els acco ding o he ISO13919-1 s anda d;
•
Al hough each se ies p esen ed se e al a igue ailu e modes due o he p esence o di -
e en impe ec ions in he weld bead, a dominan ailu e mode s ongly ela ed o he
impe ec ion wi h he highes SCF was obse ed o each se ies:
3.29—unde cu —S1,
2.25—excess weld—S2; 4.41—unde cu —S3; 1.95—unde ill—S5;
•
A low s ess le els, he local p ope ies o each welded se ies: ha dness, esidual
s ess, and weld bead geome y, de e mined he a igue limi s and hei ends we e
in good ag eemen wi h he expe imen al esul s. Bo h high SCF and ela i ely low
esidual ensile s esses (<200 MPa) a ec ed he a igue limi s; only when SCFs a e low
(<2.0) can he le el (<130 MPa) o esidual ensile s esses no be conside ed, while he
local ha dness inc eased he a igue limi s o he welded se ies al hough i s in luence
is lowe han ha o he o he wo ac o s;
•
The p edic ions o he a igue limi s we e accep able by he s ess-concen a ing e ec
when he e we e no small impe ec ions associa ed wi h excess weld, unde cu , o
unde ill, while when hese we e p esen o o small unde cu s, he ela ionship
p oposed by Mu akami was app op ia e.
Au ho Con ibu ions:
Concep ualiza ion, P.G.R. and J.F.; me hodology, P.G.R., A.C.B., C.C., and J.F.;
so wa e, P.G.R.; alida ion, P.G.R., F.A., and A.C.B.; o mal analysis, P.G.R.; in es iga ion, P.G.R.;
w i ing—o iginal d a p epa a ion, P.G.R.; w i ing— e iew and edi ing, F.A., A.C.B., and C.C.;
supe ision, J.F. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Me als 2021,11, 1499 20 o 22
Funding:
The au ho s acknowledge he suppo p o ided by he Uni e sidad de las Fue zas
A madas-ESPE o he schola ship and Má io da Cos a Ma ins and Fe nando Mei eles o he
O hopedia Medica Company o lase welding manu ac u ing. This esea ch is sponso ed by
FEDER unds h ough he p og am COMPETE–P og ama Ope acional Fac o es de Compe i i idade—
and by na ional unds h ough FCT–Fundação pa a a Ciência e a Tecnologia–, unde he p ojec
UIDB/00285/2020.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : No applicable.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Nomencla u e
aC ack dep h
√A ea Mu akami’s a ea pa ame e
Cpa ame e o he S-N cu e
HV Vicke s ha dness
mSlope o S-N cu e in log-log scales
NNumbe o cycles
K S ess concen a ion ac o
K E ec i e s ess concen a ion ac o
RS ess a io equal o minimum s ess di ided by maximum s ess
nGGoodman c i e ia ac o
Su Tensile ul ima e s eng h
SeFa igue limi
∆σNominal s ess ange
$Impe ec ion adius
σaNominal al e na ing s ess
σmNominal mean s ess
σwFa igue limi acco ding Mu akami’s exp ession
∝Mu akami’s ac o
Abb e ia ions
ASTM Ame ican Socie y o Tes ing and Ma e ials
BM Base me al
CG-HAZ Co se-g ain hea -a ec ed zone
FAT Fa igue class cu e
FEM Fini e elemen me hod
FG-HAZ Fine-g ain hea -a ec ed zone
FCG Fa igue c ack g ow h
FCGR Fa igue c ack g ow h a e
FM Failu e mode
FZ Fusion zone
HAZ Hea -a ec ed zone
HSLA High-s eng h low-alloy
HV Ha dness Vicke s
IIW In e na ional Ins i u e o Welding
ISO In e na ional O ganiza ion o S anda diza ion
NDT Nondes uc i e es ing
HI Hea inpu
SCF S ess concen a ion ac o
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