Automatic segmentation of the secondary austenite-phase island precipitates in a superduplex stainless steel weld metal

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