Au oma ic Segmen a ion o he Seconda y Aus eni e-phase Island
P ecipi a es in a Supe duplex S ainless S eel Weld Me al
Vic o H. C. Albuque que1& Rod igo Y. M. Nakamu a2& Jo˜
ao P. Papa2
Clei on C. Sil a3&Jo˜
ao Manuel R. S. Ta a es4
1Uni e sidade de Fo aleza, Cen o de Ciˆ
encias Tecnol´
ogicas, Fo aleza, B azil
2Depa amen o de Compu ac¸ ˜
ao, UNESP - Uni Es adual Paulis a, Bau u, B azil
3Depa amen o de Engenha ia Me al´
u gica e Ma e iais, Uni e sidade Fede al do Cea ´
a, Fo aleza, B azil
4Uni e sidade do Po o, Faculdade de Engenha ia, Po o, Po ugal
Duplex and supe duplex s ainless s eels a e class o ma e ials o a high impo ance o enginee ing pu poses,
since hey ha e good mechanical p ope ies combina ion and also a e e y esis an o co osion. I is known
as well ha he chemical composi ion o such s eels is e y impo an o main ain some desi ed p ope ies.
In he pas yea s, some wo ks ha e epo ed ha γ2p ecipi a ion imp o es he oughness o such s eels, and
i s quan i ica ion may e eals some impo an in o ma ion abou s eel quali y. Thus, we p opose in his wo k
he au oma ic segmen a ion o γ2p ecipi a ion using wo pa e n ecogni ion echniques: Op imum-Pa h Fo es
(OPF) and a Bayesian classi ie . To he bes o ou knowledge, his i he i s ime ha machine lea ning
echniques a e applied in o his a ea. The expe imen al esul s showed ha bo h echniques achie ed simila
and good ecogni ion a es.
1 INTRODUCTION
Duplex and supe duplex s ainless s eels a e a impo -
an class o ma e ials o enginee ing, which ha e an
excep ional co osion esis ance and good mechani-
cal p ope ies combina ion (Nilsson 1992). The suc-
cess o hese alloys is associa ed o he mic os uc-
u al balance o phases, in which e i e and aus eni e
ha e app oxima ely he same p opo ions. All hese
cha ac e is ics ha e mo i a ed he use o duplex and
supe -duplex s ainless s eels in a wide a ie y o in-
dus ial sec o s, such as chemical ones, pe ochemical
and oil & gas (Ta a es e al. 2010; Bas os e al. 2007).
The balance o phases is in luenced by he chemi-
cal composi ion o he alloys, and also by he cooling
a e expe imen ed du ing i s p oduc ion (Hemme and
G ong 1999; Hemme e al. 2000). Howe e , depend-
ing on he manu ac u ing p ocess, his p opo ion can
be changed and hen he p ope ies deg aded. One o
he mos impo an p ocesses used in he manu ac u -
ing and epai ing o pipes and equipmen s o indus-
ial applica ions is he welding, in which he s eel is
subjec ed o a high cooling a e. The high empe a u e
eached du ing he welding cycle causes he aus en-
i e dissolu ion, and consequen ly one may obse e an
inc easing in he e i e con en , ha ming he ough-
ness and duc ili y (Ko ecki and Hilkes 1994; He z-
man e al. 1997). In mul ipass welding, he ehea ed
zone by deposi ion o subsequen weld beads causes,
as main mic os uc u al changes, he dissolu ion o
ch omium ni ides and also he p ecipi a ion o sec-
onda y aus eni e (γ2) (Rami ez e al. 2004; Rami ez
e al. 2003).
Some wo ks ha e epo ed ha γ2p ecipi a ion im-
p o es he oughness o he duplex and supe -duplex
s ainless s eels (Lippold and Al-Rumaih 1997; Lee
e al. 1999). On he o he hand, he low ch omium,
molybdenium and ni ogencon en s o he γ2a e
ha m ul o co osion esis ance (Nilsson and Wilson
1993; Nilsson e al. 1995). Based on hese aspec s,
i is e y impo an o quan i y he amoun o γ2in
welded join s, especially in usion zone, in o de o
imp o e he weld quali y. Howe e , his quan i ica ion
is no s aigh o wa d, mainly because he seconda y
aus eni e o med is mo e e iden when he p ecipi-
a es a e loca ed inside he e i e g ain, wi h needles
shape and also wi h he p esence o γ2islands. Thus,
he quan i ica ion o such islands is usually ca ied ou
by manual ope a ions using all pu pose image analy-
sis so wa es, demanding a long ime and use expe i-
ence.
1
In his pape , we p opose he au oma ic segmen a-
ion o γ2islands using machine lea ning echniques,
ocusing on he Op imum-Pa h Fo es (OPF) (Papa,
Falc˜
ao, and Suzuki 2009) and a Bayesian classi-
ie (Duda, Ha , and S o k 2000). As a as we know,
his is he i s ime ha OPF is applied in o his do-
main, as well as any o he compu a ional echnique,
once ha hese p ecipi a es ha e ne e been au oma -
ically segmen ed up o da e.
The emainde o he pape is o ganized as ollows.
Sec ion 2 e isi s he classi ie s, and Sec ion 4 discuss
he expe imen al esul s. Finally, Sec ion 5 s a es he
conclusions.
2 MACHINE LEARNING BACKGROUND
This sec ion add esses a e iew abou he pa e n
ecogni ion echniques applied.
2.1 Op imum-pa h Fo es classi ie
The OPF classi ie wo ks by modeling he p oblem o
pa e n ecogni ion as a g aph pa i ion in a gi en ea-
u e space. The nodes a e ep esen ed by he ea u e
ec o s and he edges connec all pai s o hem, de in-
ing a ull connec edness g aph. This kind o ep esen-
a ion is s aigh o wa d, gi en ha he g aph does no
need o be explici ly ep esen ed, allowing us o sa e
memo y. The pa i ion o he g aph is ca ied ou by a
compe i ion p ocess be ween some key samples (p o-
o ypes), which o e op imum pa hs o he emaining
nodes o he g aph. Each p o o ype sample de ines i s
op imum-pa h ee (OPT), and he collec ion o all
OPTs de ines de op imum-pa h o es , which gi es
he name o he classi ie (Papa, Falc˜
ao, and Suzuki
2009).
The OPF can be seen as a gene aliza ion o he
well known Dijks a’s algo i hm o compu e op imum
pa hs om a sou ce node o he emaining ones (Dijk-
s a 1959). The main di e ence elies on he ac ha
OPF uses a se o sou ce nodes (p o o ypes) wi h any
pa h-cos unc ion. In case o Dijks a’s algo i hm, a
unc ion ha summed he a c-weigh s along a pa h
was applied. Fo OPF, we used a unc ion ha gi es
he maximum a c-weigh along a pa h, as explained
be o e.
Le Z=Z1∪Z2be a da ase labeled wi h a unc-
ion λ, in which Z1and Z2a e, espec i ely, a aining
and es se s such ha Z1is used o ain a gi en classi-
ie and Z2is used o assess i s accu acy. Le S⊆Z1a
se o p o o ype samples. Essen ially, he OPF classi-
ie c ea es a disc e e op imal pa i ion o he ea u e
space such ha any sample s∈Z2can be classi ied
acco ding o his pa i ion. This pa i ion is an op i-
mum pa h o es (OPF) compu ed in ℜnby he image
o es ing ans o m (IFT) algo i hm (Falc˜
ao, S ol i,
and Lo u o 2004).
The OPF algo i hm may be used wi h any smoo h
pa h-cos unc ion which can g oup samples wi h sim-
ila p ope ies (Falc˜
ao, S ol i, and Lo u o 2004). Pa -
icula ly, we used he pa h-cos unc ion max, which
is compu ed as ollows:
max(⟨s⟩) = {0i s∈S,
+∞o he wise
max(π· ⟨s, ⟩) = max{ max(π),d(s, )},(1)
in which d(s, )means he dis ance be ween samples
sand , and a pa h πis de ined as a sequence o ad-
jacen samples. As such, we ha e ha max(π)com-
pu es he maximum dis ance be ween adjacen sam-
ples in π, when πis no a i ial pa h.
The OPF algo i hm assigns one op imum pa h
P∗(s) om S o e e y sample s∈Z1, o ming an
op imum pa h o es P(a unc ion wi h no cycles
which assigns o each s∈Z1 Si s p edecesso P(s)
in P∗(s)o a ma ke nil when s∈S. Le R(s)∈S
be he oo o P∗(s)which can be eached om P(s).
The OPF algo i hm compu es o each s∈Z1, he cos
C(s)o P∗(s), he label L(s) = λ(R(s)), and he p e-
decesso P(s).
The OPF classi ie is composed o wo dis inc
phases: (i) aining and (ii) classi ica ion. The o me
s ep consis s, essen ially, in o inding he p o o ypes
and compu ing he op imum-pa h o es , which is he
union o all OPTs oo ed a each p o o ype. A e ha ,
we pick a sample om he es sample, connec i o all
samples o he op imum-pa h o es gene a ed in he
aining phase and we e alua e which node o e ed he
op imum pa h o i . No ice ha his es sample is no
pe manen ly added o he aining se , i.e., i is used
only once. The nex sec ions desc ibe in mo e de ail
his p ocedu e.
2.1.1 T aining
We say ha S∗is an op imum se o p o o ypes when
OPF algo i hm minimizes he classi ica ion e o s o
e e y s∈Z1.S∗can be ound by exploi ing he
heo e ical ela ion be ween minimum-spanning ee
(MST) and op imum-pa h ee o max (All`
ene, Au-
dibe , Coup ie, Cous y, and Ke i en 2007). The ain-
ing essen ially consis s in inding S∗and an OPF clas-
si ie oo ed a S∗.
By compu ing an MST in he comple e g aph
(Z1,A), we ob ain a connec ed acyclic g aph whose
nodes a e all samples o Z1and he a cs a e undi-
ec ed and weigh ed by he dis ances dbe ween ad-
jacen samples. The spanning ee is op imum in he
sense ha he sum o i s a c weigh s is minimum
as compa ed o any o he spanning ee in he com-
ple e g aph. In he MST, e e y pai o samples is con-
nec ed by a single pa h which is op imum acco ding
2
o max. Tha is, he minimum-spanning ee con ains
one op imum-pa h ee o any selec ed oo node.
The op imum p o o ypes a e he closes elemen s o
he MST wi h di e en labels in Z1(i.e., elemen s ha
all in he on ie o he classes). By emo ing he
a cs be ween di e en classes, hei adjacen samples
become p o o ypes in S∗and OPF can compu e an
op imum-pa h o es wi h minimum classi ica ion e -
o s in Z1. No e ha , a gi en class may be ep esen ed
by mul iple p o o ypes (i.e., op imum-pa h ees) and
he e mus exis a leas one p o o ype pe class.
2.1.2 Classi ica ion
Fo any sample ∈Z2, we conside all a cs connec -
ing wi h samples s∈Z1, as hough we e pa o he
aining g aph. Conside ing all possible pa hs om S∗
o , we ind he op imum pa h P∗( ) om S∗and la-
bel wi h he class λ(R( )) o i s mos s ongly con-
nec ed p o o ype R( )∈S∗. This pa h can be iden-
i ied inc emen ally by e alua ing he op imum cos
C( )as:
C( ) = min{max{C(s),d(s, )}},∀s∈Z1.(2)
Le he node s∗∈Z1be he one ha sa is ies Equa-
ion 2 (i.e., he p edecesso P( )in he op imum pa h
P∗( )). Gi en ha L(s∗) = λ(R( )), he classi ica ion
simply assigns L(s∗)as he class o . An e o occu s
when L(s∗)=λ( ).
2.2 Bayesian Classi ie
Le p(ωi|x)be he p obabili y o a gi en pa e n x∈
ℜn o belong o class ωi,i= 1,2,...,c, which can be
de ined by he Bayes Theo em (Jaynes 2003):
p(ωi|x) = p(x|ωi)P(ωi)
p(x),(3)
whe e p(x|ωi)is he p obabili y densi y unc ion o
he pa e ns ha compose he class ωi, and P(ωi)co -
esponds o he p obabili y o class he ωii sel .
A Bayesian classi ie decides whe he a pa e n x
belongs o he class ωiwhen:
p(ωi|x)> p(ωj|x), i,j = 1,2,... ,c, i =j, (4)
which can be ew i en as ollows by using Equa ion 3:
p(x|ωi)P(ωi)> p(x|ωj)P(ωj), i,j = 1,2, ...,x, i =j
(5)
As one can see, he Bayes classi ie ’s decision unc-
ion di(x) = p(x|ωi)P(ωj)o a gi en class ωis ongly
depends on he p e ious knowledge o p(x|ωi)and
P(ωi),∀i= 1,2,...,c. The p obabili y alues o
P(ωi)a e s aigh o wa d and can be ob ained by cal-
cula ing he his og am o he classes, o ins ance.
Howe e , he main p oblem is o ind he p obabil-
i y densi y unc ion p(x|ωi), gi en ha he only in-
o ma ion we ha e is a se o pa e ns and i s co e-
sponding labels. A common p ac ice is o assume ha
he p obabili y densi y unc ions a e Gaussian ones,
and hus one can es ima e hei pa ame e s using he
da ase samples (Duda, Ha , and S o k 2000). In he
n-dimensional case, a Gaussian densi y o he pa e ns
om class ωjcan be calcula ed by:
p(x|ωi) = γexp[−1
2(x−µj)TC−1
i(x−µj)],(6)
in which
γ=1
(2π)n/2|Ci|1/2,(7)
and µiand Cis and o , espec i ely, o he mean and
he co a iance ma ix o class ωi. These pa ame e s
can be ob ained by conside ing each pa e n x ha be-
longs o class ωiusing:
µi=1
Ni∑
x∈ωi
x(8)
and
Ci=1
Ni∑
x∈ωi
(xxT−µiµT
i),(9)
in which Nimeans he numbe o samples om class
ωi.
3 MATERIALS AND METHODS
In o de o e alua e he pe o mance o he ma-
chine lea ning algo i hms o au oma ic iden i ica-
ion o he seconda y aus eni e islands in mic os uc-
u e o supe duplex s ainless s eels, mul ipass welds
we e pe o med using gas me al a c welding p ocess
(GMAW). A es ing bench wi h an indus ial obo
and an elec onic welding powe supply was used o
p oduce he sample. The alloy used was he UNS
S32750 (SAF 2507) supe duplex s ainless s eel pipes
wi h 19 mm hickness as base me al and as ille me al
was AWS ER 2594.
Samples o me allog aphic e alua ion we e ex-
ac ed om welded join s and con en ionally p e-
pa ed h ough mechanical g inding and polishing us-
ing silicon ca bide sandpape and diamond pas , e-
spec i ely. An elec ochemical e ching o e eal he
mic os uc u e was ca ied ou using an aqueous solu-
ion wi h 40% ol. o ni ic acid (HNO3) and applying
a po en ial o 2.0 V du ing 40 seconds.
We used op ical mic oscopy images wi h 200×and
1000×o magni ica ions. These images we e p e i-
ously labeled by a echnician in o posi i e (γ2islands)
3
and nega i e (backg ound) samples. Figu e 1 displays
hese images.
(a) (b)
(c) (d)
Figu e 1: Mic oscopic images used in he expe i-
men s: o iginal images wi h magni ica ions o (a)
200×and (c) 1000×, and he espec i ely manual
segmen a ions in (b) and (d).
Now, imagine an in e ac i e classi ica ion ool in
which he use can selec same posi i e and nega-
i e samples in o de o classi y he emaining image.
A e ha , he use may wan o e ine he classi ica-
ion p ocess by ma king ano he se o samples, and
hen o execu e he p ocess again. In mos applica-
ions, one know ha he e ec i eness o classi ica ion
is s ongly ela ed wi h he aining se size, since we
ha e mo e in o ma ion o ain he classi ie . In his
wo k, we would like o simula e his use beha io
by andomly selec ing some samples o aining, and
hen o classi y he emaining image. The pe cen ages
used o aining we e: 30% and 50%.
In his wo k, each pixel o be classi ied was de-
sc ibed by a ex u e ke nel a ound i s neighbo hood
and also by i s g ay alue. In o de o ex ac ex u e
in o ma ion, we applied he Gabo il e (Feich inge
and S ohme 1997), which can be ma hema ically
o mula ed as ollows:
G(x,y,θ,γ,σ,λ,ψ) = ex′2+y′2σ2
2σ2cos(2πx′
λ+ψ),
(10)
whe e x′=xcos(θ) + ysin(θ)and y′=xsin(θ) +
ycos(θ). In he abo e equa ion, λmeans he sinu-
soidal ac o , θ ep esen s he o ien a ion angle, ψis
he phase o se , σis he Gaussian s anda d de ia ion
and γis he aspec spa ial a io.
The main idea o Gabo il e is o pe o m a con-
olu ion be ween he o iginal image Iand Gθ,γ,σ,λ,ψ
in o de o ob ain a Gabo - il e ed ep esen a ion as:
ˆ
Iθ,γ,σ,λ,ψ =I∗Gθ,γ,σ,λ,ψ,(11)
in which ˆ
Iθ,γ,σ,λ,ψ deno es he il e ed image. Thus,
one can ob ain a il e bank o Gabo il e ed images
by a ying i s pa ame e s. We used a con olu ion il e
o size 3×3wi h he ollowing Gabo pa ame e s ha
we e empi ically chosen and based on ou p e ious
expe ience:
•6di e en o ien a ions: θ= 0◦,45◦,90◦,135◦,
225◦and 315◦;
•3spa ial esolu ions: λ= 2.5,3and 3.5. No ice
ha , o each one o λ alues, we applied di -
e en alues o σ, say ha σ= 1.96,1.40 and
1.68;
•ψ= 0 and
•γ= 1.
Once we ge he Gabo - il e ed images (one can see
ha we ha e 6×3 = 18 images), we hen compu e
he ex u e ea u es a pixel pas he se o co espond-
ing g ay alues among hese images. Thus, each pixel
is desc ibed by 19 ea u es, being 18 o hem ela ed
wi h ex u e and he emaining one is he o iginal g ay
alue. A e classi ica ion p ocess, we applied a 3×3
mode il e in o de o pos -p ocessing he image.
In ega d o he pa e n ecogni ion echniques, o
OPF we used he LibOPF (Papa, Suzuki, and Falc˜
ao
2009), which is a ee ool o he design o classi ie s
based on o op imum-pa h o es . Fo Bayesian clas-
si ie (BC) we used ou own implemen a ion.
4 EXPERIMENTAL RESULTS
We desc ibe in his sec ion he esul s ob ained. Fig-
u es 2 and 3 display, espec i ely, he images classi-
ied wi h BC and OPF.
In o de o emphasize he impo ance o mode il e ,
Figu e 4 displays he image o Figu e 1a classi ied
by BC wi h and wi hou mode il e . No ice ha he
image in Figu e 4b is equal o he image o Figu e 2a.
One can see ha he esul s ob ained using 30% o
he whole image o aining a e be e when we used
he BC classi ie in case o Figu e 1a. Using 50% he
esul s appea o be simila . In ega d o Figu e 1c,
bo h classi ie s achie ed close esul s using 30% and
50% o aining. I is impo an o shed ligh o e
ha , o bo h echniques, he mode il e played an
impo an ole o il e he images a e classi ica ion.
Table 1 displays he ecogni ion a es o Figu es1a.
One can see ha BC ou pe o med OPF using 30%
o he whole image o aining, while OPF ou pe -
o med BC he second case, i.e., using 50% o he
samples o ain he classi ie s. Table 2 displays he
ecogni ion a es o Figu e1c.
4
(a) (b)
(c) (d)
Figu e 2: Classi ied images wi h BC using: (a) 30%
and (b) 50% o aining and (c) 30% and (d) 50% o
aining. The images (a)-(b) and (c)-(d) e e , espec-
i ely, o he o iginal images in Figu e 1a and Fig-
u e 1c.
(a) (b)
(c) (d)
Figu e 3: Classi ied images wi h OPF using: (a) 30%
and (b) 50% o aining and (c) 30% and (d) 50% o
aining. The images (a)-(b) and (c)-(d) e e , espec-
i ely, o he o iginal images in Figu e 1a and Fig-
u e 1c.
Classi ie T aining % Accu acy
OPF 30 68.51%
BC 30 69.14%
OPF 50 77.31%
BC 50 75.96%
Table 1: Recogni ion a es o he image in Figu e 1a.
The mos accu a e classi ie s a e bolded.
The OPF classi ie achie ed be e esul s han BC
(a) (b)
Figu e 4: Figu e 1a classi ied: (a) wi hou and (b) wi h
he mode il e .
Classi ie T aining % Accu acy
OPF 30 70.62%
BC 30 69.85%
OPF 50 79.13%
BC 50 82.41%
Table 2: Recogni ion a es o he image in Figu e 1c.
The mos accu a e classi ie s a e bolded.
using 30% o aining, while he la e ou pe o med
in case o 50%. Howe e , one can see ha he esul s
a e e y simila o bo h classi ie s using 30% and
50% o aining in he employed images.
5 CONCLUSIONS
This pape was conce ned on he p oblem o γ2island
segmen a ion, which can p o ide impo an in o ma-
ion abou s eel’s quali y and mechanical p ope ies.
In o de o do ha , we applied wo supe ised pa e n
ecogni ion echniques, Op imum-Pa h Fo es (OPF)
and a Bayesian classi ie (BC), on wo labeled images
wi h 200×and 1000×o magni ica ions, espec i ely.
Aiming o simula e an use beha io o selec posi-
i e and nega i e samples, we conduc ed expe imen s
wi h 30% and 50% o he whole images o ain-
ing, o u he classi y he emaining pixels. The ain-
ing samples we e andomly chosen, and desc ibed by
hei g ay alues and ex u e ea u es. In ega d o
ecogni ion a es, bo h classi ie s achie ed simila e-
sul s. A mode il e was applied o enhance he quali y
o images a e classi ica ion.
Thus, we may conclude ha he esul s we e e y
p omising, since his was he i s wo k ha add essed
he p oblem o au oma ic segmen a ion o γ2islands
in seconda y aus eni e-phase p ecipi a es.
Acknowledgmen s
The au ho s a e g a e ul o FAPESP g an
#2009/16206-1. The i s au ho hanks Na ional
Council o Resea ch and De elopmen (CNPq) and
Cea ense Founda ion o he Suppo o Scien i ic
and Technological De elopmen (FUNCAP) o
p o iding inancial suppo h ough a DCR g an o
UNIFOR .
5

REFERENCES
All`
ene, C., J. Y. Audibe , M. Coup ie, J. Cous y,
and R. Ke i en (2007). Some links be ween
min-cu s, op imal spanning o es s and wa e -
sheds. In Ma hema ical Mo phology and i s
Applica ions o Image and Signal P ocessing
(ISMM’07), pp. 253–264. MCT/INPE.
Bas os, I. N., S. S. M. Ta a es, F. Dalla d, and
R. P. Noguei a (2007). E ec o mic os uc u e
on co osion beha io o supe duplex s ainless
s eel en i omen condi ions. Sc ip a Ma e ialia
(Ox o d) 57, 913–916.
Dijks a, E. W. (1959). A no e on wo p oblems
in connexion wi h g aphs. Nume ische Ma he-
ma ik 1, 269271.
Duda, R. O., P. E. Ha , and D. G. S o k (2000).
Pa e n Classi ica ion. Wiley-In e science Pub-
lica ion.
Falc˜
ao, A. X., J. S ol i, and R. A. Lo u o (2004).
The image o es ing ans o m heo y, al-
go i hms, and applica ions. IEEE T ansac-
ions on Pa e n Analysis and Machine In el-
ligence 26(1), 19–29.
Feich inge , H. G. and T. S ohme (1997). Gabo
Analysis and Algo i hms: Theo y and Applica-
ions (1s ed.). Bi khause Bos on.
Hemme , H. and O. G ong (1999). A p ocess
model o he hea -a ec ed zone mic os uc-
u e e olu ion in duplex s ainless s eel weld-
men s: Pa i. he model. Me allu gical and
Ma e ials T ansac ions A 30(11), 2915–2929.
Hemme , H., O. G ong, and S. Klokkehaug (2000).
A p ocess model o he hea -a ec ed zone
mic os uc u e e olu ion in duplex s ainless
s eel weldmen s: Pa ii. applica ion o elec-
on beam welding. Me allu gical and Ma e i-
als T ansac ions A 31(13), 1035–1048.
He zman, S., B. B olund, and P. Fe ei a (1997).
An expe imen al and heo e ical s udy o hea -
a ec ed zone aus eni e e o ma ion in h ee du-
plex s ainless s eels. Me allu gical and Ma e i-
als T ansac ions A 28(2), 277–285.
Jaynes, E. T. (2003). P obabili y Theo y: The
Logic o Science. Camb idge Uni e si y P ess.
Ko ecki, D. J. and J. L. P. Hilkes (1994). Weld-
ing p ocesses o duplex s ainless s eels. In
P oceedings o he Fou h In e na ional Con-
e ence on Duplex S ainless S eels, Volume 2,
Glasgow, Sco land.
Lee, K. M., H. S. Cho, and D. C. Choi (1999).
E ec o iso he mal ea men o sa 2205 du-
plex s ainless s eel on mig a ion o δ/γ in e -
ace bounda y and g ow h o aus eni e. Jou nal
o Alloys and Compounds 285(1-2), 156–161.
Lippold, J. C. and A. M. Al-Rumaih (1997).
Toughness and pi ing co osion o duplex
s ainless s eel weld hea a ec ed zone mi-
c os uc u es con aining seconda y aus eni e.
In P oceedings o he Con e ence o Duplex
S ainless S eels, Maas ish , The Ne he lands,
pp. 1005–1010.
Nilsson, J. O. (1992). O e iew: Supe duplex
s ainless s eels. Ma e ials Science and Technol-
ogy 8, 685–695.
Nilsson, J. O., L. Ka lsson, and J. O. Ande sson
(1995). Seconda y aus eni e o ma ion and i s
ela ion o pi ing co osion in duplex s ainless
s eel weld me al. Ma e ials Science and Tech-
nology 11(3), 276–283.
Nilsson, J. O. and A. Wilson (1993). A. in luence
o iso he mal phase ans o ma ion on ough-
ness and pi ing co osion o supe duplex s ain-
less s eel sa 2507. Ma e ials Science and Tech-
nology 9(6), 545–554.
Papa, J. P., A. X. Falc˜
ao, and C. T. N. Suzuki
(2009). Supe ised pa e n classi ica ion based
on op imum-pa h o es . In e na ional Jou nal
o Imaging Sys em and Technology 19(2), 120–
131.
Papa, J. P., C. T. N. Suzuki, and A. X. Falc˜
ao
(2009). LibOPF: A lib a y o he design
o op imum-pa h o es classi ie s. So wa e
e sion 2.0 a ailable a : h p://www.ic.
unicamp.b /∼a alcao/LibOPF.
Rami ez, A. J., S. D. B andi, and J. C. Lippold
(2004). Seconda y aus eni e and ch omium ni-
ide p ecipi a ion in simula ed hea a ec ed
zones o duplex s ainless s eels. Science and
Technology o Welding and Joining 9(4), 301–
313.
Rami ez, A. J., J. C. Lippold, and S. D. B andi
(2003). The ela ionship be ween ch omium ni-
ide and seconda y aus eni e p ecipi a ion in
duplex s ainless s eels. Me allu gical and Ma-
e ials T ansac ions A 34A(8), 1575–1597.
Ta a es, S. S. M., C. Scandian, J. M. Pa dal, T. S.
Luz, and F. J. da Sil a (2010). Failu e analysis
o duplex s ainless s eel weld used in lexible
pipes in o sho e oil p oduc ion. Enginee ing
Failu e Analysis 17, p. 1500–1506.
6