Delta Ferrite

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Introduction

The residual δ-ferrite that remains atroom temperature once a stainless steelhas been welded, that is, after it has expe-rienced the process of melting followed bysolidification, will determine the mater-ial’s properties and behavior during itsservice lifetime. It is well known that pri-mary ferritic solidification avoids the hotcracking phenomenon in austenitic stain-less steels, but the determination of the so-lidification mode requires a metallo-graphic analysis, which is a destructivetest. Therefore, in practical terms, a mini-mum δ-ferrite content of 3–4 FN (FerriteNumber) is considered an acceptable in-dicator to ensure the absence of hot crack-

ing during solidification. However, forspecific applications or service conditions,it is necessary to impose a maximum δ-fer-rite content; for example, for high-temperature conditions or thermal cycles(350°–900°C) when δ-ferrite can sufferfrom spinodal decomposition or be trans-formed into (σ) sigma-phase, causing em-brittlement and a decrease in corrosion re-sistance. Chromium and molybdenumsegregation enriches σ (sigma)-phaseformed at the austenite/ferrite (γ/δ) grainboundaries, causing a depletion of theseelements in the matrix and raising the ma-terial’s vulnerability to corrosion. It is alsonecessary to establish a maximum δ-ferritecontent in the case of stainless steels usedunder cryogenic conditions, as it influ-ences the material’s ductility and the low-temperature toughness. Some authorssuch as Brouwer (Ref. 1), and especiallyLefebvre (Ref. 2), present detailed guidesof the appropriate δ-ferrite contents ac-cording to the application for which thestainless steel is intended. In practicalterms, the welding specifications includedin fabrication contracts demand a level ofδ-ferrite for welded assemblies. There-fore, the level of ferrite is a parameter tobe measured by the quality assurance staffand its value should be set according to therisk that the welded material could expe-rience a decrease in its properties.

The relationship between the δ-ferritecontent, and the mechanical and corro-

sion-resisting properties in stainless steels,has encouraged researchers to discoverpredictive tools and measurement meth-ods since the early part of the 20th century.Predictive methods are essential duringthe design stage of a project in order tohave a good approach to the δ-ferrite levelthat will be achieved, when a weld depositor pad is not available, or when differentoptions of welding consumables are beingconsidered.

When an experimental determinationof δ-ferrite content is carried out, the lit-erature (Refs. 1, 3–8) recognizes thatwithin the same weld pad, local variationsof δ-ferrite could be shown, due to com-positional microsegregation related tovariations in cooling conditions or alsodue to a loss of elements during the weld-ing process. It is also recognized that forthe same combination of base materialand consumable, differences in the exper-imental values can also be found related tothe specific welding procedure and pa-rameters used. Therefore, whatever FNvalue is allocated to a weld metal shouldbe derived from an average obtained fromseveral measurements taken, as stated inthe standard DIN 32514 (Ref. 5).

Presented below is a chronology of thedifferent methods that researchers haveproposed. It includes predictive and meas-urement methods. The advantages anddrawbacks of the currently used methodsare also considered.

Chronology of Predictive andMeasurement Methods

Historically, authors have contributedto the literature with revisions and collec-tions of the different methods used for theforecast and measurement of δ-ferrite instainless steels. Worthy of notice is the re-vision carried out in 1986 by Stalmasek(Ref. 7), showing 25 documented ways todetermine δ-ferrite, or the revisions writ-ten by Kotecki (Ref. 9) in 1997 and Lundin(Ref. 10) in 1999. In 1985, Olson (Ref. 11)presented a comprehensive review onmethodology, starting at 1920 with Strauss

Predictive and Measurement Methodsfor Delta Ferrite Determination

in Stainless Steels

A chronological review from the first predictive diagram in 1920 up to the latestmathematical model is presented

BY M. ASUNCIÓN VALIENTE BERMEJO

KEYWORDS

Stainless Steelsδ-ferriteSchaeffler DiagramDeLong DiagramWRC-1988 DiagramWRC-1992 DiagramArtificial Neural NetworkFNN-1999ORFN

M. ASUNCIÓN VALIENTE BERMEJO ([email protected]) is an independent re-searcher and consultant, Barcelona, Spain.

ABSTRACT

Controlling the δ-ferrite content instainless steels is of utmost impor-tance as its content will influence thematerial properties and its on-site be-havior in terms of weldability, corro-sion resistance, toughness, and ther-mal stability. The δ-ferrite content canbe determined by taking real meas-urements using magnetic or quantita-tive metallographic determination, oralternatively can be approached byusing well-recognized predictivemethods like the WRC-1992 diagramor the FNN-1999 artificial neural net-work, which are fed by the chemicalcomposition of the weld deposit. Thispaper presents a chronological reviewfrom the first predictive diagram in1920 up to the latest mathematicalmodel, including also an overview ofthe different measurement methodsavailable. The advantages, drawbacks,scope, and limitations of predictiveand measurement methods are alsooutlined.

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and Maurer who introduced a diagram Crvs. Ni to forecast the metallographicphases in rolled stainless steels. Figure 1shows the later modification that Maurermade to the initial diagram. From thatdate, World War II was the motivation forstudies on the development of Cr-Ni com-positions for dissimilar welds in militaryarmour, which led researchers to focus onexpressions to correlate the chemical com-position of alloys with suitable stability be-tween δ-ferrite and γ-austenite phases.According to that, in 1938 Newell andFleischman established a mathematicalequation (Equation 1) to describe theboundary between austenitic microstruc-ture and a (γ-austenite + δ-ferrite) mixedmicrostructure.

In 1943, Field, Bloom, and Linnert(Equation 2); Binder, Brown, and Franksin 1949; and Thomas, also in 1949 (Equa-tion 3), proposed similar equations to es-tablish the boundary between austenitestability and the formation of δ-ferrite, butgrouping in the same arm of the expres-sion all the alloying elements that pro-moted the same microstructural phase.

Ni + 0.5Mn + 30C= 1.1(Cr+Mo+1.5Si+0.5Nb) – 8.2 (3)

The next natural step was taken in 1946by Campbell and Thomas who proposed theconcept of chromium equivalent for the firsttime during the microstructual study ofwelded alloy 25Cr-20Ni while adding small

quantities ofmolybdenum andniobium. The con-cept of equivalentincluded the con-tribution of thosealloying elementsresponsible for thespecific phase for-mation, as depictedin Equation 4.

Creq = Cr +1.5Mo + 2Nb (4)

These initialresearches, basedon the linearizedcontribution of thealloying elementsto the microstruc-ture, were thebasis for the nextδ-ferrite predic-tive diagrams thatwere developedprior to 2000, when complex neural net-works based on nonlinear regressionsemerged.

In 1947, Schaeffler published his firstdiagram (Fig. 2A), which presented hisfirst expressions for chromium and nickelequivalents in the axes (Equation 5) andplotted the microstructual phases observed.

As shown in the diagram, the mi-crostructural boundary between γ-austen-ite and the two phases (δ-ferrite+ γ-austenite) is claimed to follow asecond-degree expression (Equation 6).

In 1948, Schaeffler published a reviseddiagram (Fig. 2B) with iso-ferrite lines ex-pressed as % ferrite (Ref. 12), which hadbeen determined by quantitative metal-lography, and eventually, in 1949, the cur-rently known Schaeffler diagram was pre-sented (Ref. 13) (Fig. 2C). The expressionfor the chromium equivalent calculation(Equation 7) was changed, decreasing therelative weight of molybdenum, silicon,and niobium compared with the equiva-lent initially proposed (Equation 5). How-ever, the microstructural phases observedand the %-vol ferrite were still shown.

NiCr Mo Mn C=

+( )+ ( )+

2 16

12 230 0.10 8 (1)

2-

- -

Ni Mn CCr Mo

+ + =+ −( )

+0.5 302 16

1214 (2)

2

Cr Cr Mo Si Nb

Ni Ni Mn Ceq

eq

= + + +

= + +

⎧

⎨⎪ 1.8 2.5 2

0.5 30⎩⎩⎪

⎫

⎬⎪

⎭⎪(5)

NiCr

eqeq= +

−( )12

12(6)

216

Fig. 1 — Maurer diagram,1939 version. Composition range: Cr (0–26%)and Ni (0–25%) (Ref. 11).

Fig. 2 — The various Schaeffler diagrams. A — 1947 version; B — 1948 ver-sion (Ref. 11); C — 1949 definitive version (Ref. 13).

A

C

B

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Creq = Cr + Mo + 1.5Si + 0.5Nb (7)

This diagram was claimed to give aglobal precision of ± 4%-vol ferrite, or ± 3 FN for 78% of cases, and it has beenextensively used for ferrite prediction inwelded stainless steels and for microstruc-ture prediction in dissimilar welds oncethe characteristic percentage dilution dueto the welding process is known.

In 1956, DeLong (Refs. 14–17) ex-panded the austenite-ferrite transitionarea of Schaeffler’s diagram and estab-lished the first version of his diagram —Fig. 3A. DeLong studied the influence ofthe nitrogen on the reduction of δ-ferritecontent observed in the weld metal due tothe entrance of this element into the weldpool because of turbulence in the gas flowin GMAW and GTAW or due to an exces-sive arc length in SMAW. He quantifiedthe austenitizing effect of the nitrogenwith a coefficient of 30 (like carbon) in theexpression of nickel equivalent, while heconsidered valid the last Schaeffler’s ex-

pression for chromium equivalent (Equa-tion 8). DeLong also modified the locationof the iso-ferrite lines of Schaeffler inorder to improve the diagram’s precisionfor new higher alloyed austenitic materials(AISI 309, 316, 317), and he used mag-netic determination instead of metallo-graphic determination in his first diagram.It was claimed that diagram presented aglobal precision of ± 3%-vol ferrite for92% of cases, improving the predictionsmade by Schaeffler’s diagram foraustenitic stainless steels. DeLong basedhis first diagram on the results obtainedfrom the preparation of around 600 as-welded samples prepared by SMAW.

In 1973, DeLong presented a revisionof his first diagram (Ref. 15) (Fig. 3B). Themain innovation was the presence of twoferrite scales, as it included the previous

%-vol iso-ferrite lines and also incorpo-rated the Ferrite Number (FN), which wasthe new scale the Welding ResearchCouncil (WRC) standardized. FerriteNumber will be explained in more detaillater. DeLong also complemented the di-agram with new experimental results fromGTAW and GMAW weld pads in order toreplace the ancient extrapolations he hadestablished for ferrite contents higherthan 8 FN; therefore, changes in the slopesof the iso-ferrite lines were carried out toimprove the ferrite prediction of higher al-loyed stainless. For 95% of cases, preci-sion was claimed to be ± 3 FN for GMAWand GTAW and ± 4 FN for SMAW.

Parallel to research on welding, otherauthors, in particular Potak (Ref. 18) in1972 and Schoefer (Ref. 19) in 1974, estab-lished their own Creq and Nieq coefficientsand developed diagrams for microstruc-tural prediction including δ-ferrite contentin the specific case of stainless steel castings.Figure 4 shows the Potak diagram, which in-cludes both Creq

M and CreqF equivalents

Cr Cr Mo Si Nb

Ni Ni Mn C Neq

eq

= + + +

= + + +

1.5 0.5

0.5 30 30

⎧⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪(8)

Fig. 3 — The DeLong diagrams. A — 1956 version (Ref. 11); B — 1973 definitive version (Ref. 15).

Fig. 4 — Potak diagram (Ref. 18). Compositional application range of thediagram: Cr, 10–22%; Ni, <10%; C and N, 0.03–0.20%.

Fig. 5 — Schoefer diagram (Ref. 20). Cr, 17–28%; Ni, 4–13%; Mo, 0–4%;Nb, 0–1%; and up to 0.20% C, 0.20% N, 2% Mn, and 2% Si.

A B


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representing the influence of alloying ele-ments in the formation of martensite andferrite, respectively. Figure 5 shows theSchoefer diagram for castings, wheredashed lines show the error interval. ASTMStandard A800-1991 (Ref. 20) recognizesthe method for δ–ferrite prediction in stain-less steel castings.

Until 1973, the main technique for theexperimental determination of δ-ferritecontent was based on metallography. Thesample was etched by a reagent to revealcontrast between δ-ferrite and γ-austenitephases and a grid was superimposed overthe image obtained by microscopy to de-termine by point-counting the percentageof δ-ferrite in the sample. The limitationsof this technique will be mentioned later.During the same period, magnetic meth-ods for the experimental determination ofδ-ferrite appeared, based on the ferro-magnetic response of the δ-ferrite over theparamagnetism of austenite.

Schaeffler in 1949 and Delong in 1956presented the δ-ferrite content in their di-agrams in terms of %-vol of δ-ferrite.However, at that time there was a seriousproblem in terms of the experimental re-producibility because every laboratorycould use its own metallographic reagentwith different phase-contrast capacity, oralternatively whatever magnetic equip-ment could be used. Consequently, whenthe δ-ferrite content was measured, a widevariability and dispersion of results was re-ported from different laboratories carry-ing out the test.

The WRC, the International Institute ofWelding (IIW), and other researchers suchas Björkroth (Ref. 21) stated the need to es-tablish a standard for the determination ofδ-ferrite content in stainless steels. In thisway, the WRC with the IIW established aprocedure in 1972 for the standardization ofδ-ferrite measurements. The arbitrary termFerrite Number was defined according tothe attractive force between a standard

magnet and a set of primary standards madeof mild steel substrate electroplated withdifferent thicknesses of nonmagnetic coat-ing. The procedure defined the relationshipbetween FN and the primary standards andit also established a series of secondary cal-ibration standards to be used when mag-netic measurement equipment cannot becalibrated with primary standards. Soon af-terward, in 1974, the American Welding So-ciety (AWS) published this procedure asthe standard AWS A4.2 (Ref. 22), and laterit was adopted also as ISO 8249 (Ref. 23).All the specific details related to the stan-dards and the procedure can be found in thebibliography (Refs. 7, 9).

From that historical moment, DeLongupdated his diagram in 1973 to the new FNscale, and since then researchers and in-dustry have tended to limit the use of the% ferrite scale because of the absence of areference standard and the lack of agree-ment in its quantification procedure.

Between 1973 and 1988, researcherssuch as Hull (Ref. 24) and Kotecki (Refs.25–27) studied the effect of certain alloyingelements on the level of δ-ferrite and pro-posed new coefficients for some elements inthe chromium and nickel equivalents.Specifically, Hull proposed new chromiumand nickel equivalents (Equation 9), addingthe contribution of some minor alloying el-ements on the Schaeffler diagram and pro-posing a second-degree contribution formanganese on the nickel equivalent.Kotecki studied the influence of molybde-num, manganese, and silicon and proposedcorrections for the DeLong coefficients(Equation 8), reducing the molybdenum co-efficient in the Creq from 1 to 0.7, and re-garding manganese a constant value of 0.35in the DeLong Nieq. This was suggested be-cause in those alloys with concentrationshigher than 2.5% Mn, DeLong seemed tounderestimate the FN value. Regarding sil-icon, Kotecki considered that the coeffi-cient of 1.5 proposed by Schaeffler and De-

Long overestimated the effect of this ele-ment, and he suggested a coefficient closeto 0.1. However, some years later in 1992,Kotecki did not include any coefficient forsilicon nor for manganese and he returnedto the unitary coefficient for molybdenumin his new diagram.

In 1982, Kotecki (Refs. 28, 29) solved anew practical problem that emerged fromthe arrival in the market of a new group ofstainless steels, the duplex types, with con-tents of approximately 50%-vol δ-ferrite.The previously established standard theWRC promoted and the AWS adopted in1974 only allowed measurements up to 28FN, due to the available equipment andthe established calibration standards.Using a counterweight with Magne-Gageequipment and a wider range of primarystandards, Kotecki managed to measureferrite contents up to 100 FN. The WRCand AWS accepted this methodology, andconsequently, the revised AWS A4.2-86and the first edition of ISO 8249-1985added the calibration standards to coverthe whole measurement range includingduplex stainless steels.

In 1988, Siewert, McCowan, and Olson(Ref. 30) developed a new diagram for theprediction of δ-ferrite content using a sys-tem of multivariable linear regressionswhere FN was the dependent variable andevery alloying element was an independ-ent variable. With the help of software,they optimized the linear regressions withan iterative process until the diagram wascomplete. The input data used to developthe linear regressions belonged to theWRC database (Ref. 31), which includes

Ni Ni Mn Mn N

C Coeq

= + − +

+ +

0.11 0.0086 18.4

24.5 0.41

2

++

= + + + +

+

0.441.21 0.48 2.27 0.72

2

CuCr Cr Mo Si V W

eq

..20 0.14 0.21 2.48Ti Nb Ta Al+ + +

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

⎫

⎬

⎪⎪⎪

⎭

⎪⎪⎪⎪

(9)

Fig. 6 — WRC-1988 diagram (Ref. 30). Better precision when the compositionrange is between the following: Creq: 17–30%, Nieq: 9–17%, and Mn <10%,Mo <3%, N <0.2%, Si<1%.

Fig. 7 — Comparative histograms: WRC-1988/DeLong/Schaeffler (Ref. 31).Note: “new diagram” refers to WRC-1988 and “revised Schaeffler” refers toDeLong’s.

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the chemical composition and the FNvalue of 923 stainless alloys. Unlike De-Long’s diagram, which was only based onAISI-300 austenitic stainless steels, thisnew diagram also included data for higheralloyed austenitics, duplex and other ex-perimental alloys, increasing the predic-tion range up to 100 FN. Other importantdifferences from former diagrams werethe representation of the solidificationmodes (A, AF, FA, F) instead of the met-allographic phases, and the fact that it in-cluded the lines or boundaries betweenthe different solidification modes. The di-agram was designated as WRC-1988 (Fig.6) and the chromium and nickel equiva-lents proposed by the authors are shown inEquation 10.

The predictions made with the WRC-1988 diagram were compared with thosemade with the Schaeffler and DeLong di-agrams for the samples collected in theWRC database (Ref. 31). In order to es-tablish a fair comparison with DeLong,only data with FN<18 were considered,

since DeLong’s diagram was not designedfor higher δ-ferrite content alloys. It wasclaimed that the WRC-1988 predicted84% of cases with an error better than ±2.5 FN, while DeLong predicted only 66%of cases with this same level of error. Es-tablishing the comparison with Schaef-fler’s diagram, for samples with FN>18, itwas claimed that only 35% of cases wouldhave an error better than ± 9 FN and forsamples with FN<18, 52% of cases wouldhave an error in the range of ± 2.5 FN. Itwas stated that DeLong’s diagram pre-sented an improvement compared withSchaeffler’s, but it was also clear that theWRC-1988 diagram improved DeLong’s.In order to illustrate these differences be-tween the diagrams’ accuracy, Fig. 7 showsthe corresponding histograms. Checkingthe WRC-1988 goodness-of-fit using com-positions and experimental FNs differentfrom the WRC database, it was claimedthat for data up to 35 FN, the diagramshowed an error of ± 4 FN for 95% ofsamples (confidence interval 2σ) and forsamples with FN > 35, the error couldreach up to ± 10 FN for 95% of samples.

In 1992, Kotecki and Siewert (Refs. 32,33) made a modification to the WRC-1988diagram, adding a coefficient for copper in

the nickel equivalent (Fig. 8 and Equation11) in order to improve the accuracy of theFN prediction in those duplex stainlesssteels containing around 2% Cu. The ex-tension of the axes — in Schaeffler’s style— was also considered, and the new dia-gram, known as the WRC-1992 diagram,was designed to be used for predictingchemical compositions and FN values forwelds or claddings on dissimilar materials,according to the percentage dilution oc-curring in the procedure.

In 1994, this WRC-1992 diagram re-placed DeLong’s diagram in the ASMEIII code, and it is still considered valid foraustenitic and duplex stainless steels.

Later, in 1999, Kotecki (Refs. 34, 35)increased the application of the WRC-1992 diagram for stainless steel claddingswith 1, 4, and 10% manganese, wherebythe influence of manganese on themartensite boundaries was included onthe same WRC-1992 diagram — Fig. 9.Since Schaeffler’s diagram, nobody hadpublished work on the limits of martensite

Ni Ni C N

Cr Cr Mo Nbeq

eq

= + +

= + +

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

35 20

0.7(100)

Ni Ni C N Cu

Cr Cr Mo Nbeq

eq

= + + +

= + +

⎧

⎨⎪

⎩⎪

35 20 0.25

0.7

⎫⎫

⎬⎪

⎭⎪(11)

Fig. 10 — FNN-1999 artificial neural network sketch (Ref. 42). Fig. 11 — Comparison among forecast methods: New model, WRC-1992diagram, and FNN-1999 neural network (Ref. 47).

Fig. 8 — WRC-1992 diagram (Ref. 32). Compositional limits: Creq , 17–31%;Nieq , 9–18%.

Fig. 9 — WRC-1992 diagram with martensite boundaries for 1, 4, and 10%Mn (Ref. 35).


formation until Kotecki did so.The last of these diagrams was devel-

oped in 2000 by Balmforth and Lippold(Ref. 36) in order to represent the mi-crostructures and the % ferrite in ferriticand martensitic stainless steels. In this case,as both martensite and ferrite have mag-netic response, it was necessary to carry outa metallographic analysis to distinguisheach phase and the iso-ferrite lines are ex-pressed as % ferrite.

From the end of the 1990s until today, in-novations related to the prediction of ferritecontent in stainless steels have accompa-nied development of powerful computersoftware. Examples include the Aström re-gression (Ref. 37) (Equation 12) or Kannanregression (Ref. 38) (Equation 13) for theprediction of FN in FCAW claddings of du-plex, based on welding parameter settings.Also worthy of mention is the research car-ried out in 2007 by Anderson et al. (Ref. 39)regarding the influence of molybdenum onthe ferrite content of stainless steel welds.

FN = –48.53 – 13.85 C + 12.73 Si + 1.16 Mn + 3.89Cr – 3.14 Ni + 4.60 Mo+ 10.10 Cu – 20.36 N (12)

However, in the 21st Century, a signif-icant advancement in the prediction of FNhas been the development of artificialneural networks, which have also beenused to establish relationships betweenthe chemical composition of the materialsand some physical properties. For exam-ple, Bhadeshia et al. (Ref. 40) proposedneural networks for the prediction of fa-tigue crack growth and creep rupture. Inthe case of FN prediction, Vasudevan et al.(Ref. 41) and Vitek et al. (Refs. 42–45)have developed neural networks based onthe chemical composition of austeniticand duplex stainless steels using the WRCdatabase (Ref. 31) as input data.

The artificial neural network is a mul-tivariable nonlinear regression methodthat can identify complex relationships be-tween variables that are difficult to recog-nize by linear regression. The method isbased on the interaction between threelayers, as shown in Fig. 10. The first layeris constituted of input nodes representingthe concentration of each alloying ele-ment; in the case of Vitek’s network, it is

formed by 13 elements. Secondly, there isa hidden layer with an adjustable numberof nodes that have to be optimized inorder to get the best forecast in the resultbut without overloading the system ofvariables. For Vitek’s network, this isachieved with six hidden nodes. The thirdlayer is the output layer containing onesingle node whose value is the predictedFN value.

Vitek recognized that the residual δ-ferrite content at room temperature de-pends on different variables that are in-terconnected, such as the chemicalcomposition, the solidification mode, andthe cooling rate, which in turn control thesolid-state transformation δ→γ. There-fore, Vitek stated that the chromium andnickel equivalent expressions, which con-sider the influence of every alloying ele-ment as a constant throughout all the com-position ranges and which do not considera possible interaction between the alloyingelements, are a very simplified way to dealwith the subject.

Vitek developed two neural networksbetween 2000 and 2003, the FNN-1999,which only considered the chemical com-positions as input data, and the ORFN,which added the weld cooling rate to thepreviously mentioned parameters.

To develop the ORFN neural network,Vitek used cooling rate data from differ-ent sources. He used the WRC database,which includes compositional data fromarc welding samples but not cooling rates,and he considered taking a constant valueof 10°C/s for all those samples. For thenew welds he prepared with the laserbeam welding process, due to the small di-mensions of the sample, in some cases hecould not use magnetic methods for the δ-ferrite determination and had to use quan-titative metallography, while in othercases, he used some mathematical expres-sions given in the bibliography. However,it was found to be difficult to consolidatethe cooling rate data originating from dif-ferent sources, so cooling rate data weregiven within an order of magnitude.

Vitek’s ORFN neural network applica-tion range is between the following:10–3.106 °C/s, 0–131 FN, 14.7–32% Cr,4.6–33.5% Ni, 0.008–0.2% C, 0.01–6.85%Mo, 0.35–12.7% Mn, 0.003–1.3% Si. Ac-cording to Vitek’s study, the FNN-1999neural network is claimed to make a moreaccurate prediction than the WRC-1992 di-agram and the ORFN neural network.However, in the case of laser or high-energyprocesses, which are related to high coolingrates, it is claimed the ORFN neural net-work makes the most accurate predictions.

In 2010, the author of this paper pre-sented a new method for forecasting FN inaustenitic stainless steels under arc elec-tric solidification conditions (Refs. 46, 47).That work led to the conclusion that FN

depends on two variables: the total allow-ing level (Creq+Nieq) and the ratioCreq/Nieq. By using Hammar and Svens-son’s equivalents (Ref. 48) (Equation 14),a general expression was proposed (Equa-tion 15).

In order to validate the new general ex-pression (Equation 15), the WRC database(Ref. 31), which contains 279 sampleswhose chemical compositions are within therange of the austenitics, was used. There-fore, the Creq and Nieq were calculatedfrom the chemical composition provided bythe database and then the (Creq +Nieq) and(Creq /Nieq) values were calculated for eachsample and introduced in Equation 15 inorder to obtain a predicted FN value. Thepredicted FN values were then comparedwith the experimental FN provided by thedatabase. Statistical processing confirmsthat the expected error is + 1.01 with a ±1.06 FN confidence interval for a probabil-ity of 68% and a ± 2.12 FN confidence in-terval for a probability of 95%. Therefore,the general expression provides FN estima-tion with an error of 1.01 FN ± 2.12 FN anda probability of 95%.

The level of error given by Equation 15could be compared with the DeLong andWRC-1988 histogram shown in Fig. 7. Asshown there, for the FN range between 0and 18, DeLong’s histogram is centered atan error of +2 FN with a ± 8 FN confi-dence interval, and for the same FN range,the WRC-1988 is centered at –1 FN with a± 4 FN for a confidence interval of 95%.These are higher errors than those ob-tained with the general expression inEquation 15.

As has been demonstrated, the mostaccurate methods for forecasting FN inarc welding were the WRC-1992 diagramand the FNN-1999 neural network. There-fore, to compare the accuracy and good fitbetween those methods and the newEquation 15, the chemical composition ofthe 87 samples prepared in the researchwere used as input data for the threemethods and the results are depicted inFig. 11. The dotted red line represents theideal 1:1 trend, where the experimental

FN I S N

T

= − − +

− +

31.596 3.750 4.333 1.000

1.750 0.771II S NIT ST

2 2 21.479 0.5211.375 2.000

I Weldin

− +

+ −

= gg currentWelding speedDis

( )

( / min)

AS cmN

=

= ttance from the tipofthe torchtothe surfaceTorchangle

( )

(degrees)

mmT =

⎧

⎨⎨

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎫

⎬

⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪

(13)

Cr Cr Mo

Ni Ni Mn C Neq

eq

= +

= + + +

⎧

⎨⎪

⎩⎪

1.37

0.31 22 14.2

⎫⎫

⎬⎪

⎭⎪(14)

FN Cr Ni

Cr

eq eq

eq

= − +( )+ +

54.22 126.26

–48.11 37.14 ++( )⎡⎣⎢

⎤⎦⎥

⎛

⎝

⎜⎜⎜

⎞

⎠

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and the calculated FN values match. Therose circles represent the correlation be-tween the experimental FN and the FNpredicted with the WRC-1992 diagram,while the orange triangles refer to theFNN-1999 neural network and the greensquares represent the correlation of thegeneral expression Equation 15. It isshown that the WRC-1992 underestimatesthe FN value throughout all the composi-tion ranges while the FNN-1999 makes anaccurate forecast for samples withFN<10. However, similar to WRC-1992,that method also underestimates the val-ues for samples with FN>15. It is clearthat the general expression provides bet-ter matches than do WRC-1992 and FNN-1999 for these 87 samples.

Current Methods forMeasurement and Prediction ofδ-Ferrite: Scope and Limitations

This section presents the scope andlimitations of the currently used measure-ment techniques and predictive methods.

Predictive Methods

Predictive methods have their scope andapplication in those cases where the projectis in a preliminary study stage where theweld pad is not yet available, or when dif-ferent alternatives of welding consumablesare under consideration and obtaining anestimate of the δ-ferrite content is of im-portance. Well-known construction codeslike ASME Section III have accepted theaccuracy of the predictive methods and,consequently, the use of such methods is de-manded in some nuclear procedures andfabrication contracts.

Currently, the WRC-1992 diagram isstill the most used method in the industry,but as has been shown in the previous sec-tion, the neural networks and the recentnew method (Equation 15) for austeniticshave demonstrated higher accuracy.

Prediction diagrams need the input ofthe chemical composition of the weld metalwhose δ-ferrite content is going to be pre-dicted. In general terms, the accuracy of thechemical composition entered determinesthe accuracy given by the diagrams. Low ac-curacy in the composition or the use of con-sumable composition instead of weld metalcomposition would imply more inaccuracyin the prediction. It should be noted thateach diagram has been obtained accordingto specific assumptions in terms of linearregressions, and that variations in thechemical composition could also be attrib-uted to the specific welding process and itssettings. For example, the chromium con-tent can change in SAW depending on thespecific flux used, or in SMAW, GTAW, orGMAW the atmospheric nitrogen could beabsorbed into the weld pool if the arc

length is too long. Moreover, diagrams alsohave another limitation, which is the factthat the influence of the cooling rate on theresidual δ-ferrite is not considered, andthey have been developed only to be usedunder electric arc conditions. Regardingthis point, some studies (Refs. 49–52) con-firm that the conventional diagrams pro-posed by Schaeffler, DeLong, and forWRC-1992, are not suitable for use underthe range of cooling rates associated withhigh-energy welding processes like laserbeam (LBW) or electron beam (EBW), andconsequently, the estimation of the δ-fer-rite content obtained from the diagramswould not be correct under those condi-tions. Some researchers (Refs. 50, 52, 53)have proposed modifications of the tradi-tional Schaeffler diagram in order to adaptit to higher cooling rate conditions, butthese modifications have their limitations.

Regarding the limitation of artificialneural networks, it comes from the accu-racy and the size of the database used fortraining the network, as well as from theinner architecture of the net that needs tobe optimized. The FNN-1999 neural net-work was generated from the same data-base as the WRC-1992 diagram; there-fore, it does not take into considerationthe effects of cooling rate, and it is onlyrecommended for FN prediction of arcwelds. Regarding the ORFN neural net-work, difficulties with the consolidation ofcooling rates have been described, but themethod can be used to forecast FN for arcwelding and laser beam welding.

Finally, the recently presented expres-sion (Equation 15) is only valid foraustenitic stainless steel arc welds.

Measurement Methods

There are several different techniquesfor the measurement and determinationof δ-ferrite; however, magnetic determi-nation is the most extensively used in theindustry because it is nondestructive andprovides an immediate result. This sectiondescribes the scope and limitation of thedifferent techniques currently used.

Magnetic Determination

The WRC recommends magnetic de-termination techniques based on attrac-tive force and magnetic permeability. Itsstandardization (AWS A4.2 and ISO8249) has greatly contributed to the re-duction of disagreements between labora-tories. Moreover, these techniques arequick, nondestructive, and can be used inlaboratories, on-site, or in fabricationlines for quality control. All the details re-lated to the standardization, calibration,and description of the primary and sec-ondary standards can be found in detail inRefs. 5, 7, 9, 17, 22, 23, and 54. Essentially,

the method is based on the magnetic re-sponse of the δ-ferrite phase as against thenonmagnetic γ-austenite phase.

The techniques employed by differentcommercial equipment differ in the specificmagnetic parameters used to correlate themagnetism with the level of δ-ferrite. Themain magnetic techniques currently in useare based on the attractive force (such asMagne-Gage magnetic balance) and on themagnetic permeability (Fischer Feritscopeequipment), while some earlier techniqueswere based on magnetic saturation and theMössbauer effect.

The technique based on magnetic sat-uration allowed the determination of %vol of δ-ferrite in the sample, but the in-tensity of magnetic saturation depends onthe chemical composition of the δ-ferrite,which is not easy to determine. Moreover,the technique was destructive and neededthe sample to be machined into a precisecylinder.

The attractive force technique is basedon the force required to separate the fer-romagnetic sample from a standardizedpermanent magnet in the equipment. Themeasurement of this force was correlatedto the FN scale using calibration stan-dards. The classic example of this equip-ment (Magne-Gage) is generally consid-ered the reference tool of its type.

The magnetic permeability technique isbased on placing a probe coil on the samplethat produces a low-frequency electric field,which interacts with the δ-ferrite to gener-ate a magnetic field. The voltage induced bythis magnetic field in a separate pickup coilon the probe is proportional to the magneticpermeability and therefore is a direct func-tion of the δ-ferrite content. This techniqueuses calibration standards. The approxi-mate volume the probe analyzes is around10 mm3, and some practical limitations needto be considered:• The technique requires minimum di-

mensions of the sample and a minimumdistance from the probe to the edge ofthe sample. These minimum dimen-sions depend on the specific equipmentused. Using the technique with under-sized samples or placing the probe nearthe edge of the sample causes a drop inthe measured FN values. The latter isknown as edge effect.

• When highly ferromagnetic materialsare close to the measurement point, forexample in cases of stainless steelcladdings on carbon steel plates, it isalso necessary to exceed a minimum dis-tance from the probe to the highly fer-romagnetic material. If not, overestima-tion of the Ferrite Number will occur.

• Measurements need to be done on flatsurfaces so that the probe contacts per-pendicularly on the sample. Regardingthe degree of roughness, results ob-tained from some WRC round-robins

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(Refs. 55, 56) showed surface finishing(as-welded, polished, and ground) is asignificant variable that influences theFN reading by around ± 10–12%, butit was not possible to establish a con-sistent trend.As the δ-ferrite distribution is not ho-

mogeneous in the weld metal, it is neces-sary to ensure a suitable number of read-ings throughout the sample in order to getan accurate and representative FN value.

Metallographic Determination

Metallographic determination consistsof doing a visual quantitative counting —manually or automatically — of the numberof subdivisions where the presence of δ-fer-rite is detected in a previously polished andmetallographically etched sample.

This method is based on the interna-tionally accepted assumption that the fer-rite volumetric proportion is analogous tothe proportion at the surface measured.The %-vol of δ-ferrite is an arbitrary valuethat depends on different factors or inher-ent error sources in the method, like thereagent selection, the operator’s ability todistinguish the δ-ferrite from other phasesor precipitates, such as carbides, sul-phides, σ-phase, the settings and adjust-ments in contrast if the measurement isdone automatically, the measurementprocedure (magnification), the countingrules and the statistical coverage to ensurea representative number and distance be-tween points. All these provoke wide dis-persion of results between laboratories.

As has been stated, the δ-ferrite distri-bution is not homogeneous in the weld de-posits; therefore, it is first necessary tocheck that the selected area is microstruc-turally representative of the whole sample.Other inconveniences are the difficulty indetermining with accuracy the countingwhen the ferrite morphology is too thin,such as in cases of eutectic or skeletal fer-rite morphologies.

Since 1976, the ASTM E562 (Ref. 57)standard, which was revised in 2008, hasdescribed the procedure for systematicmanual point counting and for the statisti-cal estimation of the volume (%) of a mi-crostructurally identified phase. Thispoint counting can be considered valid forthe δ-ferrite determination in castingswhere size and morphology of the ferritephase is coarser, but it is not recom-mended for weld metals due to the irreg-ular and thin morphology of the δ-ferrite.

A suitable field of application forquantitative metallography is the deter-mination of the δ-ferrite in the heat-affected zone (HAZ) of duplex welds, asthis is so narrow that magnetic measure-ments do not give accurate results due tothe influence of contiguous materials. Inthis sense, TWI (The Welding Institute)

established in 1993 (Ref. 58) some prac-tical recommendations for point count-ing of the duplex.

Other Minority Methods: X-Ray Diffraction,Electrochemistry, and VSM

This final section shows some minoritymethods that have been found in theliterature.

X-ray Diffraction. The technique isbased on exposure of the stainless steelsample to a monochromatic X-radiationand, depending on the crystallographicstructure of the phases present (BCC fer-rite, FCC austenite), there will be reflec-tion peaks for each phase whose intensitywill be related to the concentration of eachphase in the sample.

According to the literature (Refs. 7, 10,16, 19, 59), the quantitative determinationof δ-ferrite in stainless steel welds has notbeen satisfactory, possibly because thefine skeletal morphology of the δ-ferriteand the compositional segregations be-tween the dendrite core and the matrixmake the diffraction patterns diffuse. Theequipment is expensive and it has onlybeen used in laboratory studies.

Electrochemical Determination. Thistechnique was proposed by Gill et al. (Ref.60) in 1979. It is based on dissolving the γ-austenite phase and keeping the δ-ferritephase passivated by exposing it to an elec-trolyte and a predetermined voltage;therefore, the selective dissolution of theaustenite isolates the δ-ferrite, which canbe gravimetrically determined.

The limitations and inconveniences arerelated to the fact that this is a destructivetechnique, and that it is necessary first toestablish the austenite polarization dia-gram for each alloy where the technique isapplied, because the correct voltage is re-quired to ensure the total dissolution ofthe austenite. It is also an extremely slowmethod, as it is said to take 40 hours to dis-solve the austenite in a 1-mm-thick samplewith 3%-vol ferrite.

Magnetometer with Sample Vibration(VSM). This technique was used by Elmerand Eagar in 1990 (Ref. 61) to measurethe δ-ferrite content in very small weldsamples of mass 5 mg and less than 0.5 mmthickness from EBW and LBW stainlesssteels (cooled at around 104–105 °C/s). Thesmall dimensions of the samples would notallow a magnetic measurement or quanti-tative metallography; therefore, the au-thors used a magnetometer with samplevibration and a technique based on satu-ration magnetization of the ferrite.

Conclusions

Determination of δ-ferrite content instainless steel weld deposits is a topic thathas generated much interest and chal-

lenged researchers from the early days ofwelding until today, which is the reasonfor the development of such a variety ofpredictive and measurement methodssince 1920. Despite their practical limita-tions, wherever it is possible, experimen-tal measurements based on magnetic de-termination are better than predictivemethods, whose accuracy is mainly de-pendant on the reliability of chemicalcomposition. However, in those caseswhere the weld deposit is not availablesuch as in the early stage of projectswhere alternative welding consumablesare being considered, or simply when it isnecessary only to get an approximatevalue, then predictive methods such asWRC-1992, FNN-1999, and the recentlypresented model for austenitics (Equa-tion 15) have their scope.

Acknowledgments

The author gratefully acknowledges thesupport of Metrode Products Ltd. and is es-pecially indebted to Dr. Zhuyao Zhang andAdam W. Marshall. The current research ispart of the doctoral degree thesis titled“Modelization of δ-ferrite content (FN) inaustenitic stainless steels under electric arcconditions,” which was submitted for thedegree of Doctor in Chemistry by the au-thor at the University of Barcelona, June 29,2010. The supervision of Dr. Pere Moleraand Dr. Núria Llorca from the Departmentof Materials Science and Metallurgical En-gineering at the University of Barcelona isalso gratefully acknowledged.

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