Effects of Alloying Elements on the Ferrite Potential of

781 © 2015 ISIJ

ISIJ International, Vol. 55 (2015), No. 4, pp. 781–790

Effects of Alloying Elements on the Ferrite Potential of Peritectic and Ultra-Low Carbon Steels

Rahul SARKAR,1)* Arunava SENGUPTA,1) Vimal KUMAR2) and Shiv Kumar CHOUDHARY1)

1) Research and Development, Tata Steel, Jamshedpur, 831001 India.2) Metallurgical and Materials Engineering Department, NIT Trichy, Tiruchirappalli, Tamil Nadu, 620015 India.

(Received on August 11, 2014; accepted on January 5, 2015)

Solidification of steels involving the peritectic reaction are inherently prone to longitudinal facial crackingduring casting, owing primarily to the large volume shrinkage associated with delta-ferrite to austenitetransformation occurring at high temperatures. Therefore casting of those steels requires a lot of caution.Ferrite Potential (FP) is widely accepted as a measure of the tendency of steels to form delta-ferrite duringsolidification. However, the most commonly used definition of Ferrite Potential is strictly applicable onlyto plain carbon steels while commercial steels may contain several other alloying elements. Therefore, theexisting definition may not express their actual Ferrite Potential. In view of this, a new correlation hasbeen developed in the present work for evaluating the true Ferrite Potential for multi-component steels.Influences of several common alloying/solute elements have been considered while developing the pres-ent model. Present model development involved rigorous thermodynamic calculations aimed at determin-ing the interactions among various solute elements and their overall influence on the peritecticcompositions and the peritectic transformation temperature. In addition, assumed quadratic dependenceof peritectic compositions and temperature on the concentrations of alloying elements has beenemployed besides the application of non-linear multi-variate regression analysis. Finally, present correla-tions have been extensively validated against literature data as well as actual plant observations. In com-parison to other models, reasonably better agreement between the current model predictions and plantdata has been obtained. The present model has helped the plant operators in selecting the right parame-ters for casting operations.

KEY WORDS: steel; peritectic transformation; Ferrite Potential; longitudinal crack; continuous casting;alloying elements.

1. Introduction

Continuous casting of steel slabs having compositionclose to the peritectic point is often difficult as compared toother grades. These steels undergo the peritectic (L + δ →γ) transformation during solidification,1) which is accompa-nied by large volume shrinkage since the molar volume ofγ (austenite) is considerably less than that of both liquid (L)and delta-ferrite (δ) phases. The temperature range in whichthis shrinkage occurs corresponds to the so-called zero-ductility-temperature range where the ductility of steels isvery low and hence peritectic grades of steel are extremelyprone to cracking. Thus, casting of such steels requires spe-cial precautionary measures like casting at a speed some20% lower than that of ordinary carbon grades and usingspecial type of mould fluxes.2)

As the propensity of cracking depends upon the extent ofperitectic transformation, the tendency of steels to form del-ta-ferrite (δ) during solidification is an important parameterin continuous casting operations. This tendency is often

measured in terms of its Ferrite Potential (FP) which isdefined as:3)

....................... (1)

where [%C] is the mass percent of carbon in steel and theconstant terms (2.5, 0.5) are determined in such a way thatFP satisfies the following criteria:

where CA = 0.1, CB = 0.18 and CC = 0.5 for simple Fe–Csystems (Fig. 1).

Based on this definition of FP, plain carbon steels havebeen classified into two major categories:3)

•　Depression Grades: 0.8 < FP < 1.0•　Sticker Grades: FP < 0 or FP > 1.0

It is the casting of depression grades that is more prob-lematic, since they are more prone to longitudinal cracks ascompared to the sticker grades. Therefore, in order to ensuresmooth casting operation it is important to correctly classifyperitectic steels into depression and sticker grades based ontheir chemical compositions.

* Corresponding author: E-mail: [email protected]: http://dx.doi.org/10.2355/isijinternational.55.781

FP = −[ ]( )2 5 0 5. * . %C

FP

when

when

when

====

1

0

0 8

[% ]

[% ]

. [% ]

C C

C C

C C

A

C

B

© 2015 ISIJ 782

ISIJ International, Vol. 55 (2015), No. 4

The above expression of Ferrite Potential (Eq. (1)) isstrictly valid only for plain carbon steels. Commonly, com-mercial steels are multi-component alloys of iron containingvarious alloying elements other than carbon. These elementsmay alter the peritectic transformation behaviour of steelsby shifting the peritectic compositions (CA, CB and CC)either to the left or to the right and thereby affect their actualFerrite Potential. Earlier efforts to determine the effects ofalloying elements on Ferrite Potential consisted of simplyreplacing the [%C] in the definition of Ferrite Potential withcarbon equivalent [%C]e where [%C]e may be obtained fromone of the available correlations.3) But strictly speaking, inpresence of other elements all the relevant peritectic com-positions get shifted from their original values and replacingonly [%C] with [%C]e would not suffice. Rather, the defini-tion of Ferrite Potential itself needs modification and a gen-eral expression based on composition dependent values ofCA, CB and CC needs to be developed.

Preliminary attempts in determining the effects of alloy-ing elements on the peritectic compositions and tempera-tures based on thermodynamics were made by Kagawa etal.4) More recently, efforts have been made to determine theeffects of alloying elements on CA and CB through develop-ment of peritectic predictor equations using computationalthermodynamic approaches.5,6) However, in none of theexisting models/correlations effects of all types of alloyingelements on the peritectic transformation have been consid-ered. Also while such correlations seem to give goodpredictions in their respective composition ranges, the uni-versality of these correlations is questionable since they aremostly regression based models. Insufficient information isavailable in literature on the effects of various alloying ele-ments on the composition CC (Fig. 2). In view of the above,present work was undertaken for developing precise corre-lations/model for the prediction of true peritectic behaviourof multicomponent steels, particularly those commerciallyproduced at Tata Steel, India. In the new peritectic predictormodel, equations for all the three relevant compositionsmarked in Fig. 2 (i.e. CA, CB and CC) as well as the peritectictransformation temperature TP (which also plays an impor-

tant role in casting operations) have been developed. Final-ly, the predicted results were validated against plant data forchecking their reliability.

2. Formulation

In general, the Ferrite Potential (FP) of an alloy-steel canbe expressed by the following equation:

.......................... (2)

And the classification based on FP should be done as:

•　Depression Grades: for < FP < 1

•　Sticker Grades: for 0 < FP < or FP > 1

The compositions CA, CB and CC can be calculated fromactual steel compositions.

2.1. Expressions for Composition Dependence of Peri-tectic Compositions and Temperature

In the present work, actual peritectic carbon compositionsfor multi-component steels (i.e. CA, CB and CC) have beenassumed to have a quadratic dependence on the concentra-tions of the alloying elements and can be expressed by thefollowing correlation:

... (3)

Where, C = actual peritectic carbon composition for multi-component steels

C0 = peritectic carbon composition for pure Fe–Cbinary system

[%i] = concentration of element i in weight per centai = coefficient of the first order concentration term

for the alloying element ibij = coefficient of the second-order concentration

term containing the product of the concentra-tion of alloying element i with that of j

Fig. 1. Pure Fe–C phase diagram showing the classification of per-itectic steels based on Ferrite Potential. (Online version incolor.)

Fig. 2. Schematic representation of the effect of alloying elementson the peritectic compositions and temperature of steel.(Online version in color.)

FP =−[ ]( )−( )

C C

C C

C

C A

%

( )

( )

C C

C CC B

C A

−−

( )

( )

C C

C CC B

C A

−−

C C a i b i j c ii ij ii= + [ ]+ [ ] [ ]+ [ ]∑ ∑∑ ∑02

* % * % * %


783 © 2015 ISIJ

cii = coefficient of the second order concentrationterm containing the square of the concentra-tion of alloying element i.

Besides composition, alloying elements also affectthe peritectic transformation temperature (TP). In fact, in thepresence of certain alloys in higher proportion the peritectictransformation occurs over a range of temperatures ratherthan at a fixed temperature.7) Consequently, a three-phaseL + δ + γ appears in the phase diagram which is schemati-cally shown in Fig. 2. The effects of alloying elements onthe peritectic start temperature (TP,s) have also been investi-gated in the present work. Following the same approach, TP,s

is expressed as a quadratic function of the concentration ofelements:

.......................................... (4)

Where TP = equilibrium peritectic transformation tempera-ture for pure Fe–C system

di = coefficient of first order concentration term foran alloying element i

dij = coefficient of second-order concentration termcontaining the product of concentrations ofalloying elements i with that of j

eii = coefficient of second order concentration termcontaining the square of the concentration ofelement i.

Equations (3) and (4) constitute the theoretical expressionsfor the actual peritectic predictor equations considered inthe present work for steels containing various solute ele-ments besides carbon.

3. Results and Discussion

3.1. Selection of Alloying Elements and their Composi-tion Ranges

In the present calculations, the effects of 12 elements rel-evant to grades manufactured in Tata Steel, India have beeninvestigated using ThermoCalc Version S (TCCS®) andTCFE7 database. The combined effects of these elementshave been evaluated through several thermodynamic andregression based calculations. The composition ranges ofsolute elements are shown Table 1. Also, an index numberhas been assigned to each element in order to facilitate itsreference later in the text, as shown in Table 1.

Out of these 12 elements, elements 1–7 are commonlypresent in almost all steels in varying quantities (Table 1).These elements are expected to affect the peritectic compo-sitions and temperature not only because of their individualeffects but also due to the interactions amongst them. Werefer to these elements as primary alloying elements. Ele-ments 8–12 on the other hand, are present only in some ofthe grades. Commonly, they are present in relatively muchsmaller proportions as compared to the primary alloyingelements. Thus, although each one of them may have someeffect on the peritectic compositions and temperature, theinteraction amongst them as well as with the primary alloyingelements can be neglected due to their small concentrationsin steel. Those elements have been referred to as secondaryalloying elements in the present case.

3.2. Effect of Individual Elements on Peritectic Compo-sitions and Temperature

In order to determine the influence of each element on theperitectic compositions and temperature, a large number ofpseudo binary Fe-C-i phase diagrams were generated usingThermoCalc Version S (TCCS®) and TCFE7 database foreach element (i.e. i) for their respective composition rangesas shown in Table 1. The corresponding relative deviationwith respect to pure Fe–C binary was determined for eachcase.

3.2.1. Effect of Mn, Si, Cr and NiThe effects of these four elements on peritectic composi-

tions and temperature are shown in Figs. 3(a)–3(d). Mn andNi being austenite stabilizers, shift all the three relevant per-itectic compositions (i.e. CA, CB and CC ) to the left. Si beinga ferrite stabilizer, its effect is just opposite to that of Mn andNi. Thus it shifts all the above three compositions towardsthe right in the pseudo-binary phase diagrams. The effect ofCr on the peritectic compositions is somewhat incongruous.Cr, being ferrite-stabilizer shifts CB to the right as expected.However, Cr shifts both CA and CC to the left, as can be seenin Figs. 3(a)–3(c).

It is evident from Fig. 3(d) that Si has the most significanteffect on TP,s. It considerably decreases the TP,s temperaturewhich is congruent with its tendency to stabilize ferrite. Nibeing an austenite stabilizer increases TP,s but its effect onTP,s was found to be less pronounced. In the compositionranges presently considered, Cr hardly had an impact on TP,s.Manganese being an austenite stabilizer is expected toincrease TP,s. However, in the chosen composition range Mnwas found to slightly decrease the peritectic transformationtemperature (TP,s).

3.2.2. Effect of Al, S and PFigures 4(a), 4(b) and 4(c) show the effects of Al, S and

P on the peritectic compositions. Al being a ferrite-stabilizershifts all the three compositions to the right. The individualeffect of P on the peritectic compositions was found to rel-atively insignificant. However as will be discussed later, inpresence of other elements especially Mn, P was found to

T T d i e i j f iP s P i ij ii, * % * % * * %= + [ ]+ [ ] [ ]+ [ ]∑ ∑∑ ∑ 2

Table 1. Range of alloying elements chosen for calculations.

Index Element Min. Comp.(wt.%)

Max. Comp.(wt.%)

Avg. Comp.(wt.%)

1 Mn 0.13 1.4 0.765

2 Si 0.001 0.4 0.2005

3 Cr 0.001 0.46 0.2305

4 Ni 0.001 0.25 0.1255

5 Al 0.01 0.09 0.05

6 S 0.002 0.025 0.0135

7 P 0.01 0.09 0.05

8 Mo 0.001 0.01 0.0055

9 N 0.004 0.01 0.007

10 V 0.001 0.06 0.0305

11 Ti 0.001 0.02 0.0105

12 Nb 0.001 0.05 0.0255

© 2015 ISIJ 784


have a noticeable effect on the peritectic compositions andtemperature. Sulfur seemed to have quite a significant effecton the peritectic compositions. Presence of S even in con-centrations low (<0.025%) was found to influence the peri-tectic compositions CA and CB significantly by shifting themtowards the left in the phase diagram. The effect of S on CC,was found to be relatively less pronounced but nonetheless

it also shifts CC to the left.In the composition range considered, Al did not seem to

have an effect on TP,s. The effect of S on TP,s is not signifi-cant but the presence of S, even in very small quantities pro-motes the formation of L + δ + γ region. Congruent with itstendency to stabilise ferrite, P was found to decrease TP,s asshown in Fig. 4(d).

Fig. 3. Effect of Mn, Si, Cr and Ni on: (a) CA; (b) CB; (c) CC and (d) TP,s. (Online version in color.)

Fig. 4. Effect of Al, S and P on: (a) CA; (b) CB; (c) CC and (d) TP,s. (Online version in color.)


785 © 2015 ISIJ

3.2.3. Effect of Mo, N, V, Ti and NbAs evident from Table 2, Mo was found to have practi-

cally no effect on CA, CB CC or TP,s. Influence of elementsN, V, Ti and Nb on CA, CB , CC and TP,s are shown in Figs.5(a)–5(d). Nitrogen being a strong austenite stabiliser shiftsCA, CB and CC towards the left. On the other hand, V, Ti, andNb are all carbide formers and hence tend to stabilize theferrite phase. But in the small composition ranges consid-ered here, these elements could combine with only a verysmall amount of carbon and most of the carbon stillremained in the solid solution. Thus, their ability to stabilizeferrite was found to be limited. V shifted CA, CB and CC tothe right and its effect on CC was more significant as com-pared to those on CA and CB. Ti was observed to have verylittle effect on CA, CB and CC. Nb shifted both CA and CB

towards left while its effect on CC was found to be less sig-nificant and can be neglected for all practical purposes. Theeffects of V, Ti and Nb on TP,s were comparable and all ofthem tend to decrease TP,s.

3.3. Evaluation of Constants of Peritectic PredictorEquations

The effects of individual elements on the peritectic compo-sitions and temperature have been discussed in Section 3.2.To determine the combined effects of these elements, a totalof 298 pseudo-binary phase diagrams containing all the 12

pertinent elements have been constructed using ThermoCalcVersion S (TCCS®) and TCFE7 database. Subsequently,coefficients of peritectic predictor equations were calculatedusing multi-variate non-linear regression analyses.

3.3.1. Rationale Behind Selecting Terms in Peritectic Pre-dictor Equations

From Eq. (3):

Differentiating Eq. (3) with respect to[%i], for a particular iwe get:

........... (5)

If [%j]=0, Eq. (5) reduces to:

...................... (6)

From Eqs. (5) and (6) the following can be easily deduced:– First, if [%i] − C curves at constant [%j] are straight

lines, then cii s are all zeros.– Secondly, if the slopes of [%i] − C curves at constant

[%j] and at [%j] = 0 are equal then bij are all zeroes.In order to select the appropriate second order terms for

peritectic predictor equations a large number of Fe-C-i (atconstant [%i]) and Fe-C-i-j (at constant [%i] and [%j])phase diagrams were constructed (where i and j representdifferent alloying elements considered in this study). All thedifferent combinations of i and j have been considered.From different plots of [%i] − CA, [%i] − CB, [%i] − CC and[%i] − TP,s and using the information from Eqs. (5) and (6),the necessary second-order concentration terms have beenselected. It has been found that among all the different sec-

Table 2. Effects of molybdenum on peritectic compositions andtemperature.

Mo (wt. %) CA CB CC TP,s (°C)

0.001 0.09274 0.17162 0.52729 1494.773

0.01 0.09279 0.17178 0.52785 1 494.6933

Percent Shift 0.05885 0.09257 0.10691 0.00533

C C a i b i j c ii ij ii= + [ ]+ [ ] [ ]+ [ ]∑ ∑∑ ∑02

* % * % * % * %

∂∂[ ]

= + [ ]+ [ ]∑C

ia b j c ii ij ii

% * % * * %2

∂∂[ ]

= + [ ]C

ia c ii ii

% * * %2

Fig. 5. Effect of N, V, Ti and Nb on: (a) CA; (b) CB; (c) CC and (d) TP,s. (Online version in color.)

© 2015 ISIJ 786


ond-order concentration terms, only four of them have sig-nificant effects on CA, CB and CC. Three out of these fourterms involve the products of the concentration of Mn withSi, S and P while the fourth one is the square of the concen-tration of Mn. Thus only these four second order terms areretained in the equations for CA, CB and CC and other termsare neglected. Similarly for TP,s, it has been observed thatonly the second-order term involving the products of theconcentration of Mn and P has a significant effect on TP,s.As before, this term has been retained while the other sec-ond-order terms have been neglected in the equation for TP,s.The final predictor equations thus developed may be repre-sented as follows:

.......................................... (7)

....... (8)

3.3.2. Final Predictor EquationsTotal of 298 pseudo-binary Fe–C phase diagrams were

generated using ThermoCalc Version S and TCFE7 database.Constant terms for the predictor equations have been esti-mated using non-linear multi-variate regression and the finalperitectic predictor equations have been obtained as follows(Eqs. (9)–(12)). The ranges of application are shown inTable 1. High values of R2 (Figs. 6(a)–6(d)) for all the co-relations indicate excellent agreement between the calculat-ed and the predicted values.

.......................................... (9)

........................................ (10)

.........................................(11)

........................................ (12)

3.4. Validation of Regression ModelsCorrelations developed in the present work have been

validated against the literature data as well as plant data.

C C a i b Mn Si b Mn

S b Mn

i= + [ ]+ [ ] [ ]+ [ ][ ]+ [ ]

∑0 12 16

17

* % * % * % * % *

% * % * %PP c Mn[ ]+ [ ]112

* %

T T d i e Mn PP s P i, * % * % * % = + [ ]+ [ ] [ ]∑ 17

C MnA = + − −−

0 0927 0 0471 0 0859 0 0237

0 5429

. . *[% ] . *[% ] . *

[% ] . *[%

Si

Ni SS N

Ti Nb V

] . *[% ] . *

[% ] . *[% ] . *[% ] .

− −− + +

0 3553 0 0361

0 0136 0 0106 0 10997

5 6239 0 0165

0 9962 2

*

[% ]*[% ] . *[% ]*[% ] . *

[% ] ( . )

Mn Si Mn S

Mn R

− −

=

C Mn Si

Cr

B = − − −−

0 1716 0 0589 0 1776 0 0053

0 0410

. . *[% ] . *[% ] . *

[% ] . *[%NNi] . *[% ] . *

[% ] . *[% ] . *[% ] .

+ −− − −

0 0473 0 9453

0 0160 0 6884 0 02

Al

S P N 883

0 0147 0 0285 0 2342

02

*

[% ] . *[% ] . *[% ] . *

[% ]*[% ] (

Ti Nb V

Mn Si

− + +

=R .. )992

C Mn Si

Cr

c = − − −−

0 5274 0 0124 0 1424 0 0154

0 0981

. . *[% ] . *[% ] . *

[% ] . *[%NNi Al

S P N

] . *[% ] . *

[% ] . *[% ] . *[% ] .

+ −− − +

0 0934 0 3871

0 0553 2 0916 0 12226

0 2363 0 0729

0 05 2

*

[% ] . *[% ]*[% ] . *[% ]*

[% ] . *[% ] (

V Mn Si Mn

P Mn

+ +

− RR2 0 993= . )

T Si Cr

S

P s, . . *[% ] . *[% ] . *

[% ] . *

= − − −−

1 494 643 18 846 1 295 71 433

55 847 [[% ] . *[% ] . *

[% ] . *[% ] . *[% ]

P N

Ti Nb V

+ −− − +

87 915 12 138

12 175 11 283 79.. *

[% ]*[% ] ( . )

916

0 9962Mn P R =

Fig. 6. Comparison between the calculated and predicted values of: (a) CA; (b) CB; (c) CC and (d) TP,s.


787 © 2015 ISIJ

One-year data on longitudinal cracks observed in variousslabs were collected and critically examined and used forthe validation of the present work.

3.4.1. Validation with Literature DataThe predictor equation for CB has been compared with

other existing correlations between CB and compositiondeveloped by Xu et al.5) and Blazek et al.6) Figures 7(a)–7(c) show the co-relation between the calculated values ofCB and those predicted by the different models.5,6) The pres-ent model represents a greater value of R2 and a smaller val-ue of RMSD (Root Mean Square Deviation). It can thus beconcluded that in the composition ranges considered here,the present correlation fits the calculated data much betterthan any of the pre-existing models.

The reliability of the present predictor equations was alsotested by comparing the calculated and predicted values ofFerrite Potential (FP). A steel sample having each alloyingelement in the average composition (Table 1) has beenselected. The calculated values of FP as a function of [%C]are then plotted against the values predicted by three of theexisting models and the current model. These three pre-existing models include the one based on the equation forplain carbon steels (Eq. (1)), one based on carbon equivalentformulation by Wolf 3) and another based on Blazek’s et al.’scorrelation.6) It is once again evident from Fig. 8 that thecurrent model fits the calculated values of FP much betterthan other models.3,6) Also, it is interesting to note that forthe steel sample considered here, the presence of alloyingelements has shifted the carbon range for depression gradesfrom an initial value of 0.1–0.18% to 0.055–0.11% (as dem-onstrated in Fig. 8) thereby elucidating the need for the clas-sification of peritectic steels based on actual compositionsrather than based solely on carbon percentage.

Direct validation of the regression model for TP,s was notpossible since there is no literature available on the effectsof alloying elements on TP,s. However, Wang et al.8) pro-posed an equation for calculating the liquidus temperatureTliq from the concentration of its alloying elements. Notingthat for [%C] = CC, Tliq = TP,s the predicted values of Tliq (for[%C] = CC) are plotted with calculated values of TP,s in Fig.9.

From Fig. 9, it is evident that the calculated values cor-relate very well with those predicted by Wang et al.8) (themaximum deviation is <10°C). This difference might be dueto two reasons. First of all, Wang et al.’s8) correlation doesnot take into account the effects of N while the alloys select-ed for calculations contained N in the range 40–100 ppm(Table 1). Nitrogen is expected to decrease Tliq still furtherbut its effect cannot be quantified since there is no literatureavailable on the effects of N on Tliq. Secondly, the equationby Wang et al.8) have been derived by considering simpleFe-i binary systems while the present calculations have beendone for actual pseudo binary systems containing all thealloying elements. Thus, the equation predicted by Wang etal.8) neglects the effects of interaction between different ele-

Fig. 7. Comparison of the calculated values of CB with the valuespredicted by various models: (a) Xu et al.;5) (b) Blazek etal.6) and (c) Present model.

Fig. 8. Comparison of present calculation of Ferrite Potential withthose predicted from different models.3,6) (Online versionin color.)

© 2015 ISIJ 788


ments. A correction factor has later been introduced into theproposed equation to account for the interactions but the useof a constant term seems unreasonable because the interac-

tion terms are expected to be strong functions of composi-tions. Hence the equation overestimates the values of Tliq

thereby accounting for the small difference between the cal-culated and the predicted values.

Further, to test the accuracy of the calculated phase dia-grams, some of the measured values of liquidus temperature(Tliq) from Wang et al.8) and austenite formation temperature(Tγ) from Xu et al.5) have been compared with the calculatedvalues for the same steel compositions (Tables 3 and 4) andplotted in Fig. 10.

As evident from Tables 3 and 4, there is reasonably goodagreement between the measured and the calculated values(the deviation in all the cases being <10°C) which indicatesthat the present calculations done using TCCS® are correct.Also, the present set of calculated values for Tγ correlatesexcellently with those calculated by Xu et al.5) using Fact-sage and both of these values are slightly higher than themeasured values. This is because the calculated values arefor equilibrium conditions while the measured data are foractual industrial (non-equilibrium) conditions. Under coolingrates relevant to industrial processes, L + δ → γ transforma-tion takes place at temperatures lower than the equilibrium

Fig. 9. Comparison between the calculated values of TP,s with thevalues predicted using Wang et al.8) (Online version incolor.)

Table 3. Measured and calculated values of liquidus temperatures for some steels.8)

Steel Components, % MeasuredTemp. (°C)

Calculatedby Wang (°C)

PresentCalculation (°C)C Si Mn P S Ni Cu Mo Cr

0.19 0.2 0.15 0.021 0.03 0.12 0 0 0 1 508 1 510 1 516.72

0.38 0.24 0.65 0.014 0.028 0.07 0 0 0 1 490 1 494 1 499.88

0.42 0.25 0.63 0.015 0.025 0.09 0 0 0 1 486 1 490 1 496.41

0.43 0.32 0.58 0.027 0.031 0.1 0 0 0 1 488 1 489 1 494.35

0.47 0.31 0.69 0.017 0.021 0.06 0 0 0 1 485 1 486 1 491.21

0.54 0.26 0.92 0.017 0.025 0.12 0 0 0 1 479 1 477 1 485.28

0.59 0.23 0.16 0.014 0.02 0.1 0 0 0 1 480 1 477 1 485.66

0.19 0.29 0.93 0.017 0.026 0.06 0 0 1.2 1 502 1 506 1 511.60

0.16 0.27 0.45 0.035 0.03 4.2 0 0 1.36 1 487 1 488 1 500.21

0.35 0.25 0.69 0.018 0.009 0 0.005 0.026 0.0019 1 492 1 496 1 502.87

0.66 0.23 1 0.011 0.003 0 0.005 0.023 0.0026 1 464 1 466 1 474.49

0.194 0.273 0.53 0.02 0.006 0 0.0001 0.0003 0.0002 1 512 1 510 1 516.54

0.452 0.219 0.67 0.013 0.0048 0.0024 0.0001 0.0002 0.0002 1 490 1 488 1 494.93

0.143 0.207 1.18 0.014 0.005 0 0.0001 0.0003 0.003 1 514 1 511 1 518.11

0.297 0.183 0.48 0.015 0.003 0.0017 0.0003 0.002 0.002 1 504 1 503 1 509.52

Table 4. Measured and calculated values of austenite formation temperature for some steels.5)

Steel composition (Mass %) MeasuredTemp. (°C)

Calculatedby Xu (°C)

PresentCalculation (°C)C Si Mn P S Al Cr Ni Mo

0.11 0.12 1.25 0.04 0.018 0.038 0.06 0.03 0.07 1 475 1 482 1 483.1013

0.12 0.27 1.53 0.01 0.005 0.029 0.02 0.03 0.03 1 477 1 485 1 485.7217

0.18 0.44 1.26 0.016 0.025 0.004 0.01 0.02 0.06 1 473 1 481 1 481.8587

0.19 0.4 1.42 0.012 0.007 0.006 0.07 0.13 0.02 1 480 1 484 1 485.2973

0.36 0.27 0.58 0.015 0.012 0.004 0.08 0.05 0.02 1 483 1 488 1 488.3469

0.2 0.25 0.9 0.014 0.039 0.036 0.081 1.05 0.06 1 474 1 490 1 489.9664

0.27 0.02 0.32 0.006 0.008 0.044 1.66 3.5 0.42 1 490 1 498 1 497.1786

0.29 0.21 0.62 0.012 0.006 0.011 1.11 0.15 0.21 1 475 1 488 1 487.0218

0.35 0.24 0.67 0.01 0.02 0.004 0.92 0.05 0.19 1 480 1 486 1 486.544


789 © 2015 ISIJ

transformation temperature (Fig. 11). For the same reason,the calculated values of Tliq are also slightly higher than themeasured values as evident from Table 4.

3.4.2. Validation with Plant DataThe regression models developed to predict peritectic

behaviour is also validated using industrial data for slabs castin LD2&SC, Tata Steel Jamshedpur Works over the past oneyear. Typical dimension of slabs cast is 11 m * 1 250 mm *215 mm. The casting speed varies in the range of 1.2–1.7 m/min and the average casting speed is 1.5 m/min.Figure 12(a) shows a typical longitudinal crack observed inone of the low carbon steel slabs. Slabs in which longitudi-nal cracks were observed all contained carbon in the range0.035–0.185%. This range was divided into 10 classes inintervals of 0.015% and in Fig. 12(b) the relative frequencyof longitudinal cracks (η) is plotted against the carbon rangefor each class. This quantity η is defined as:

It is evident from Fig. 12(b) that η is maximum in therange 0.095–0.11% and it decreases both to the left and alsoto the right of this range. Thus it can be concluded that in

the composition ranges of different elements presentlyconsidered (Table 1), the tendency of slabs to develop lon-gitudinal cracks is maximum when carbon is in the range0.095–0.11%.

To correlate the industrial data on cracks with the peritec-tic behaviour, η is plotted against the deviation from peri-tectic composition ([%C] − CB) for different carbon rangesin Fig. 13 where CB is calculated using Eq. (10). Also tocompare the efficacy of the present model vis-à-vis otherexisting models, η is plotted against the values of this devi-ation ([%C] − CB) predicted by other available correlationsin the same Fig. 13. Under non-equilibrium conditions theFe–C phase diagram shifts down and CB shifts to the left byΔCB which has been shown schematically in Fig. 11. Hu etal.9) estimated the value of ΔCB for cooling rates relevant tothin slab casting. But in thick slab casting, the cooling rateof the solidifying shell is relatively lower and hence the ΔCB

is smaller than that for thin slab casting. However, in theabsence of any data on this shift ΔCB for thick slab casting,we start with the value of ΔCB reported by Hu et al.9) andthen simulate it in our model to best-fit the industrial datafor thick-slab casting. Presently, ΔCB = 0.02.

It is evident from Fig. 13 that if CB is calculated using the

Fig. 10. Comparison between the measured values of Tliq and Tγ

with those calculated using different models.5,8)

η =Number of slabswith longitudinal cracks in thespecified carbon raange

Total number of slabswith longitudinal cracks%∗100

Fig. 11. Schematic representation of the effects of non-equilibriumcooling on the equilibrium Fe–C phase diagram. (Onlineversion in color.)

Fig. 12. (a) A typical longitudinal crack observed in one of the low carbon steel slabs; (b) Relative frequency of longitu-dinal cracks (η) in cast slabs for different carbon content/ranges. (Online version in color.)

© 2015 ISIJ 790


proposed correlation (Eq. (10)), η is maximum when thedeviation from peritectic composition ([%C] − CB) is zero.This is consistent with the industrial results because the ten-dency to develop longitudinal cracks is expected to be thegreatest at the peritectic composition, that is when [%C]=CB.10) Xu et al.5) also reported that the propensity of longi-tudinal cracks is maximum when the value of this deviation([%C] − CB) is zero. However if CB is calculated using anyof the other existing correlations,5,6) η does not show a peakat [%C] = CB which is not consistent with the industrialresults. This happens because for the composition rangesconsidered here each of these correlations over-estimates CB

(Figs. 7(a), 7(b)) and hence the peak is obtained at somenegative value of this deviation ([%C] − CB). Thus, it isproved once again that the regression model developed inthe present work is most appropriate for the chosen compo-sition ranges and can thus be reliably used in the design andoptimization of steel compositions for different applications.Furthermore, the results can be used as a reference forselecting the process parameters for continuous casting oflow carbon as well as peritectic steels.

4. Conclusions

Salient features of the present work are as follows:(1) New correlation for evaluating the Ferrite Potential

(FP) has been proposed taking into account the effects ofvarious alloying elements on the peritectic transformation ofmulti-component steels.

(2) Influence of various elements on the peritectic com-positions (CA, CB and CC) and the peritectic start temperature(TP,s) has been investigated based on rigorous thermodynam-ic calculations.

(3) While developing the current predictor equations(for CA, CB, CC and TP,s), interactions amongst various alloy-ing elements were also taken into account. Developed cor-relations exhibited reasonably good degrees of goodness offit as indicated by the high values of R2 (>0.99) and low val-ues of RMSD. In addition, the proposed models were foundto provide relatively better description of peritectic transfor-mation in comparison to other existing ones.

(4) Adequacy of model prediction was rigorously eval-uated against the literature as well as extensive plant data oflongitudinal cracks. Good agreement between the predictedand the calculated values of liquidus and solidus tempera-tures indirectly proved that the thermodynamic calculationsdone in the present work were correct. Model predictionswere also found to be consistent with the industrial data onlongitudinal cracks thus further validating the calculations.

(5) Finally, present model has been found to be usefulfor selecting the casting parameters for various grades ofsteel in the plant.

REFERENCES

1) H. Fredriksson: Met. Sci., 10 (1976), 77.2) T. Emi and H. Fredriksson: Mater. Sci. Eng. A, 413–414 (2005), 2.3) M. M. Wolf: Continuous Casting, Vol. 9, Iron & Steel Society,

Warrendale, PA, (1997), 63.4) A. Kagawa and T. Okamoto: Mater. Sci. Technol., 2 (1986), 997.5) J. Xu, S. He, T. Wu, X. Long and Q. Wang: ISIJ Int., 52 (2012), 1856.6) K. E. Blazek, O. Laze, III, P. L. Guano and D. L. Kellogg: Iron Steel

Technol., 5 (2008), 80.7) P. Presoly, R. Pierer and C. Bernhard: Metall. Mater. Trans. A, 44

(2013), 5377.8) X. Wang, X. Wang, B. Wang, B. Wang and Q. Liu: Steel Res. Int.,

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Fig. 13. Relationship between the relative frequency of longitudi-nal cracks (η) and the deviation of actual carbon contentfrom the peritectic composition ([%C] − CB) calculatedusing different models.5,6) (Online version in color.)

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