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METALLURGICAL AND MATERIALS TRANSACTIONS 50TH ANNIVERSARY COLLECTION

Review of Peritectic Solidification Mechanismsand Effects in Steel Casting

GHAVAM AZIZI, BRIAN G. THOMAS, and MOHSEN ASLE ZAEEM

Surface quality and castability of steels are controlled greatly by initial solidification. Peritecticsteels suffer more from surface quality problems, including deep oscillation marks anddepressions, crack formation, and breakouts than other steels. This paper reviews currentunderstanding of the fundamental mechanisms of initial solidification of peritectic steels thatlead to these problems. First, different empirical relations to identify peritectic steel grades fromtheir alloy compositions are summarized. Peritectic steels have equivalent carbon content thattakes their solidification and cooling path between the point of maximum solubility in d-ferriteand the triple point at the peritectic temperature. Surface defects are related more to thesolid-state peritectic transformation (d-ferrite fi c-austenite) which occurs after the peritecticreaction (L + d fi c) during initial solidification. Some researchers believe that the peritecticreaction is controlled by diffusion of solute atoms from c phase, through the liquid, to the dphase while others believe that c growth along the L/d interface involves microscale heat transferand solute mixing due to local re-melting of d-ferrite. There is also disagreement regarding theperitectic transformation. Some believe that peritectic transformation is diffusion controlledwhile others believe that massive transformation is responsible for this phenomenon. Alloyingelements and cooling rate greatly affect these mechanisms.

https://doi.org/10.1007/s11663-020-01942-5� The Minerals, Metals & Materials Society and ASM International 2020

I. INTRODUCTION

THE castability of high-quality steel depends onavoiding breakouts, cracks, and surface quality prob-lems. The surface quality of steel products is mainlydetermined by the early stages of solidification in themeniscus region of the mold.[1–8] Steels which undergothe peritectic transition are the most difficult tocast.[2,9–14] This is attributed to the volume contraction(shrinkage) associated with the peritectic phase trans-formation.[15–17] This shrinkage leads to the formationof an air gap between the steel shell and the mold duringthe CC process and decreases the heat flux. This leads tolocally thinner and hotter regions of the solidified shell,

which causes uneven shell growth that leads to surfacedepressions, deep oscillation marks, cracks, andbreakouts.[18–24]

Steels within the peritectic composition range includehigh-strength low-alloy (HSLA) Steels, and recentlyadvanced high-strength steels (AHSS), which are allused extensively in different products due to theirexcellent mechanical properties, which include highstrength and toughness.[25–28] The automotive industryis increasingly utilizing steels with peritectic compositionrange (AHSS, HSLA, etc.), to reduce vehicle weight.Peritectic steels are widely applied in pipelines, navyvessels, and nuclear power plant components.[28,29]

Therefore, there is a great need to produce these steelswithout defects.[25]

Peritectic steel solidification occurs in two distinctstages involving liquid (L), delta-ferrite (d), and austen-ite (c): the peritectic reaction (L + d fi c) followed bythe peritectic transformation (d fi c).[30–33] The peritecticreaction occurs just below the peritectic temperature,when liquid and delta-ferrite are in contact and react toform austenite. This corresponds to the L + d + cthree-phase point in the binary phase diagram,[34] or tothe 3-phase region on sections through a multicompo-nent phase diagram, such as shown in Figure 1(a).During the peritectic reaction, an austenite layer grows

GHAVAM AZIZI, BRIAN G. THOMAS, and MOHSEN ASLEZAEEM are with the Department of Mechanical Engineering,Colorado School of Mines, 1610 Illinois Street, Golden, CO, 80401.Contact e-mail: [email protected]

Manuscript submitted April 14, 2020.Article published online August 27, 2020.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 51B, OCTOBER 2020—1875

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along the L +d interface, as pictured in the upper rightframe of Figure 1(b). After the liquid locally runs out,then the remaining d-ferrite transforms to austenite bysolid-state transformation. The peritectic transforma-tion starts by thickening of the austenite layer immedi-ately behind the tip of this advancing c platelet, asshown in Figure 1(b),[35] where it proceeds on twofronts, growing into both the liquid on one side of theplatelet and the d interior on the other. Later, towardthe center of the dendrite, the interior d–c interface hasmoved far away from the liquid, so further austenitegrowth into the d ferrite involves only a single movinginterface. Note that spatially, these different steps ofperitectic solidification occur at different places, andproceed in different directions relative to the thermalgradient, which is oriented downwards in Figure 1(b).

In this paper, the proposed mechanisms of peritecticsolidification are reviewed in detail and then the effectsof peritectic solidification on surface quality, austenitegrain size, hot ductility, segregation, and crack forma-tion of cast product are discussed. But first, the differentcalculations used to identify peritectic steel grades fromtheir compositions are summarized.

II. IDENTIFICATION OF PERITECTIC STEELS

As casting of peritectic steels is difficult, it is impor-tant to identify a peritectic steel from its composition. Ifa new grade of steel is predicted to be a peritectic, thenappropriate actions can be taken at the caster, such asapplying appropriate mold powders with high solidifi-cation temperature to lower the surface coolingrate,[36–38] and/or casting at a lower speed.[10] Low-alloycommercial steels can be characterized by their carboncontent, with corrections according to the other alloyingelements. Predicting the occurrence of the problematicperitectic transformation in high-alloy steels is moredifficult, and involves the relative amounts of more thanone other elements (such as carbon, nickel, andchromium in stainless steels,[39] or in AHSS[40,41]).

In the Fe-C phase diagram for low-alloy steels,shown in Figure 1, four different solidification behav-iors can be categorized according to their effectivecarbon content. These include range I, for effectivecarbon content less than point CA, range II for carbonbetween CA and CB, range III for carbon between CBand CC, and range IV, for carbon above CC. Steels inrange II are known as peritectic steels and are the mostdifficult to cast because they experience transformationfrom d to c that coincides with the final stage ofsolidification. While in range I, d to c transformationstarts and ends in the solid state. In range III, thetransformation occurs in the presence of liquid and inrange IV, the steel solidifies as austenite so the d to ctransformation does not take place at all and there isno contraction.The position of points CA, CB, and CC in the

pseudo-binary phase diagram of Fe and effectivecarbon content have been defined in different ways inprevious research. When carbon is the only significantalloying element, Point CA is given between 0.088 wtpct C* and 0.1 pct C,[42–44] point CB ranges from 0.16to 0.18 pct C,[41,43,44] and CC is about 0.53 pct C.

[43]

The position and temperature of points CA, CB, andCC change significantly according to the alloy content,however. Alloying elements change the effective car-bon content, and are classified as either ferrite formers,which tend to shift the points to the right (highercarbon) or austenite formers, which have the oppositeeffect. Increasing alloy content also extends the ternary(L + d + c) phase region in Figure 1. Differentexperiments[41,45–49] have been conducted to determineif a steel exhibits peritectic behavior, and differentempirical equations[50–55] have been proposed to pre-dict this, as discussed in the next sections.*

Fig. 1—(a) Iron-carbon phase diagram showing peritectic steels (shaded) and their phase transformations and (b) schematics of the peritecticreaction and subsequent peritectic transformation.

*All alloy compositions in this paper are given in weight pct.

1876—VOLUME 51B, OCTOBER 2020 METALLURGICAL AND MATERIALS TRANSACTIONS B

A. Experimental Measurements

Differential scanning calorimeter (DSC) measure-ments can identify the temperatures of phase transfor-mations in steels,[56–61] based on detecting theaccompanying small changes in enthalpy. This includesthe ability to identify peritectic steel grades from thedistinctive second peak in their enthalpy rate–tempera-ture profile during cooling.[46,48,49,62] Confocal micro-scopy, discussed in Section III can augment the DSCmeasurements by visualizing these phase transforma-tions.[62] The ultimate test is behavior in the commercialcaster, where peritectic steels experience more variationsand defects than other steels, as discussed in Section IV.

All alloys show a large peak in the DSC curves at hightemperature during the phase transformation betweenthe molten steel and either d-ferrite or austenite.[46] Theperitectic reaction, when present, generates a significantsecond peak, at the lower ‘‘peritectic temperature’’[46,62]

because it involves austenite forming at the expense ofliquid, in addition to d ferrite. This second peak may notappear in DSC cooling curves, however, if the coolingrate is too high, for reasons discussed later.[46,62] Thesolid-state transformation from d ferrite to austenite hasa small third peak,[46,62] which is often difficult to detect.

As an example, Figure 2 shows typical DSC resultsfor four steels,[41] which are supported by high-temper-ature confocal laser scanning microscopy (HT-CLSM)observations. Figure 2 shows one heating curve for atypical non-peritectic steel (top left frame with 0.08 pctC), so there is no significant enthalpy peak beforemelting. The other three frames in Figure 2 all show asecond large, sharp peak due to the peritectic reaction,indicating that these are all peritectic steels. Thisincludes a new advanced high-strength steel (lower rightframe with 2 pct Al), which is not correctly identified asbeing peritectic by current models, which are discussedin the next section.

B. Calculation Methods

Several different methodologies have been proposedto predict if a steel is a peritectic, based on its exhibitingadverse solidification behavior, such as susceptibility todepressions and cracks. These methods include empir-ical equations based on an equivalent carbon contentrange, alloy-dependent critical points, ferrite potential,and CALculation of PHAse Diagrams (CALPHAD)methods. These are discussed in turn below.

Fig. 2—The DSC measurement of different steel grades. Reprinted with permission from Ref. [41].


1. Carbon equivalent range methodsSeveral different models have been proposed to

predict if a steel exhibits peritectic behavior based oncalculating the carbon equivalent (CP) of the steelalloy. If the calculated carbon equivalent is between acritical range, such as falling between CA = 0.09 pct Cand CB = 0.17 pct C (peritectic region in Figure 1)then the steel is considered to be peritectic and itssensitivity to depressions and cracks is high. Wolf[52]

proposed the following equation for carbonequivalent.

CP ¼ C½ � þ 0:02 Mn½ �þ 0:04 Ni½ � �0:1 Si½ � �0:04 Cr½ � �0:1 Mo½ �; ½1�

where brackets contain weight percent of alloying ele-ments. Howe[63] proposed the following alternative.

CP ¼ C½ � þ 0:04 Mn½ � þ 0:1 Ni½ �þ 0:7 N½ � �0:14 Si½ � �0:04 Cr½ ��0:1 Mo½ � �0:24 Ti½ �:

½2�Xia et al.[50] suggests the following equation for

calculation of carbon equivalent.

CP ¼ C½ � þ 0:02 Mn½ � �0:037 Si½ �þ 0:023 Ni½ � �0:0189 Mo½ � �0:7 S½ � þ 0:0414 P½ �þ 0:003 Cu½ � �0:0254 Cr½ � �0:0267 Ti½ � þ 0:7 N½ �:

½3�Normanton and other researchers at Trico Steel and

British Steel[64] proposed two more equations for thecalculation of carbon equivalent,[64]

CP ¼ C½ � þ 0:01 Mn½ � þ 0:009 Si½ � þ 0:02 Ni½ �þ 0:003 Cr½ � �0:007 Mo½ � þ 0:009 V½ � þ 0:008 P½ �þ 0:147 S½ � þ 0:5 N½ � þ 0:007 Cu½ � þ 0:007 Ti½ �þ 0:05 Al½ � þ 0:04 Nb½ �;

½4�

CP ¼ C½ � þ 0:043 Mn½ � �0:14 Si½ �þ 0:1 Ni½ � �0:083 Cr½ � �0:063 Mo½ � �0:13 V½ �þ 0:029 P½ � þ 0:11 S½ � þ 1:06 N½ �þ 0:037 Cu½ � �0:024 Ti½ �: ½5�

As can be seen in Eqs. [1] through [5], the equivalentweight concentrations of austenite-forming elements(Mn, Ni, Cu, and N) are added to the C content andthe ferrite-forming element Mo is subtracted, asexpected. The elements P, Al, and Nb are ferrite-form-ing elements,[65] yet their terms are added to the Ccontent in several equations. The effects of Si, Cr, Ti, V,and S are not consistent between equations.

2. Alloy-dependent critical points methodsBlazek et al.[66] proposed a different method, defining

a steel as peritectic when its carbon content is betweenCA and CB, which change with alloy composition asfollows:

CA ¼ 0:0896 þ ð0:0458AlÞ�ð0:0205MnÞ�ð0:0077SiÞþ ð0:0223Al2Þ�ð0:0239NiÞ þ ð0:0106MoÞþ ð0:0134VÞ�ð0:0032CrÞ þ ð0:00059Cr2Þþ ð0:0197WÞ;

½6�

CB ¼ 0:1967þ ð0:0036AlÞ � ð0:0316MnÞ � ð0:0103SiÞþ ð0:1411 Alð Þ2Þ þ ð0:05ðAlSiÞÞ�ð0:0401NiÞþ ð0:03255MoÞ þ ð0:0603VÞ þ ð0:0024CrÞþ ð0:00142 Cr2

� ��ð0:00059ðCrNiÞÞ þ 0:0266W:

½7�This relation, which was based on thermodynamic

calculations with ThermoCalc[67] is reported to beaccurate for many steel grades,[66] and has successfullybeen implemented into several steel plants to enableappropriate choice of mold powder and casting prac-tice.[66] However, this relation may be inaccurate forsteels with high Si content. The sign of the Si term in theeffective carbon equations is negative (shift CA to theleft), which may be opposite to expectations, so thisterm is controversial. Other studies[53] have confirmedthat increasing Mn shifts the peritectic range to the leftand agrees with Blazek[66] that Al shifts the peritecticrange to the right. Those studies also found that S shiftsthe peritectic range to the left and P shifts it to theright.[53] Clearly, there is still some disagreement regard-ing the effects of several elements on peritecticformation.

3. Ferrite potentialWolf introduced the term, ‘‘ferrite potential,’’ as a

measure of the extent of peritectic behavior experiencedwith a given steel alloy.[52] ‘‘Ferrite potential’’ is alsodefined as the solid fraction of primary ferrite duringsolidification. Using the ferrite potential concept, steelscan be categorized into depression-sensitive andsticker-sensitive grades. Peritectic steels are depressionsensitive, owing to their greater shrinkage, and tend tosuffer from deep oscillation marks and uneven shellgrowth, leading to surface cracks and other defects, asdiscussed in Section IV. Non-peritectic steels are moresticker-sensitive, tending to stick to the mold walls,which leads to a higher risk of sticker breakouts.[68–70]

Although the ferrite potential is affected most by thecarbon content, it is also affected by other alloyingelements.[52] Some elements stabilize the austenite (Ni,Mn, Co, N, and Cu) while others are believed tostabilize the ferrite (Cr, W, Mo, Al, and Si).[65] Forlow-alloy steels, the ferrite potential (FP) can becalculated as follows[52]:

FP ¼ 1:25�2:5 CP½ �; ½8�

where CP is carbon equivalent and is calculated usingEq. [1], where 0

the tendency for depressions, crack formation, anduneven shell growth is high. Steels in this range aredepression-sensitive grades (steel type A) and steelsoutside this range (FP < 0.85 or FP > 1.05) aresticker-sensitive grades (steel type B).[52] The effect offerrite potential on the tendency of depression forma-tion is shown in Figure 3.

Sarkar et al.[55] generalized the Wolf ferrite potentialfor peritectic solidification by including the effects ofalloying elements on the CA, CB, and CC points, asfollows:

CA ¼ 0:0927þ ð0:0471MnÞ�ð0:0859SiÞ�ð0:0237NiÞ�ð0:5429SÞ�ð0:3553NÞ�ð0:0361TiÞ�ð0:0136NbÞþ ð0:0106VÞ þ ð0:1097Mn SiÞ�ð5:6239MnSÞ�ð0:0165Mn2Þ;

½9�

CB ¼ 0:1716�ð0:0589MnÞ�ð0:1776SiÞ�ð0:0053CrÞ�ð0:0410NiÞ þ ð0:0473AlÞ�ð0:9453SÞ�ð0:0160PÞ�ð0:6884NÞ þ ð0:0283TiÞ�ð0:0147NbÞþ ð0:0285VÞ þ ð0:2342MnSiÞ;

½10�

CC ¼ 0:5274�ð0:0124MnÞ�ð0:1424SiÞ�ð0:0154CrÞ�ð0:0981NiÞ þ ð0:0934AlÞ�ð0:3871SÞ�ð0:0533PÞ�ð2:0916NÞ þ ð0:1226VÞþ ð0:2363MnSiÞ þ ð0:0729MnPÞ�ð0:0729Mn2Þ:

½11�Using the same form as Wolf,[52] they[55] redefined

ferrite potential as follows:

FP ¼ CC � C½ �CC � CA

; ½12�

where [C] is the carbon weight percentage. WhenCC�CBCC�CA

A. Experimental Methods for Studying PeritecticSolidification

Four experimental methods have been widely used tostudy peritectic solidification, including the solid/liquiddiffusion couple experiment, high-temperature confocallaser scanning microscopy (HT-CLSM), X-ray imaging,and directional solidification.

In the solid/liquid diffusion couple experi-ment,[75,90–94] a steel alloy is melted in a crucible andthen is slowly cooled down to a specific temperature (forexample 1696 K) to crystallize a small amount of theaustenite, leaving residual liquid with an equilibriumcarbon content at peritectic point. Then, a sample of adifferent steel alloy (d-ferrite) from a lower temperaturefurnace is positioned just above the alloy already in thecrucible. The two alloys are then brought into contactwith each other for a preset length of time, forming adiffusion couple, before rapidly dropping into ice water.A longitudinal cross section is etched to reveal thesolidification microstructure, and the thickness of theaustenite formed between the regions formerly contain-ing d-ferrite and liquid, as well as measuring the carbondistribution. Although it is a powerful technique toinvestigate solidification under isothermal condi-tions,[95,96] other methods are needed for realistic highcooling rates.

HT-CLSM,[41,56] is a powerful improvement to theconventional optical microscope that focusses a laserbeam into a small area on the surface of a high-tem-perature sample of molten steel.[33,62,80,97–99] Whilecarefully cooling at a desired rate, solidification on theliquid surface can be observed by building up imagespixel-by-pixel from photons emitted from the fluo-rophores. The different solid and liquid phases can bedistinguished due to their emissivity differences.HT-CLSM can operate at high temperatures (over1800 �C), has controllable depth of field[100,101] and highresolution (0.15 lm).[102] It can record high-frequencyimages in real time for realistic cooling rates (e.g., 3000�C/min)[102] and sample sizes (e.g., 8 mm).[102] Eventhough only the surface can be seen, the ability ofHT-CLSM to visualize peritectic solidification in situand in real time is revolutionizing our understanding ofthe phenomenon.

Time-resolved X-ray imaging has recently beenapplied to investigate solidification of steels.[82,103–105]

In a synchrotron radiation facility, hard X-rays withphoton energy ranging from 10 to 100 keV can penetratethrough the bulk metallic material to obtain X-rayimages. These systems feature high-contrast, high-reso-lution images due to monochromatic light, high coher-ency, and high brightness. X-ray imaging has the bigadvantage over HT-CLSM of being able to observe thereal three-dimensional microstructure evolution insidethe bulk volume of the sample.[104]

Finally, directional solidification is a laboratoryprocess in which molten metal is drawn downward ata controlled withdrawal speed, V, through a controlledtemperature gradient, G.[106–108] Heating block temper-atures beside the sample path are controlled to maintainsteady-state conditions in the moving sample in theframe of reference of the laboratory, with a stationarysolidification front located between the hot zone towardthe top of the apparatus and the cold zone below. Thiscontinuous process enables controlled conditions forexperimental measurements of solidification, whichinclude the concentration and microstructure profiles.Although the thermal field tends to stabilize the process,the concentration field may produce fluid flow andmorphological instabilities near the solidification front,depending on how the liquid density varies with soluteconcentration.[109] These opposing effects may causeinstabilities that equilibrate in amplitude, making thissystem an excellent vehicle for the careful study of phasetransformation dynamics.[110] Due to its ability tocontrol the local casting conditions, which may enablehigh thermal gradients[111] and deep supercool-ing,[112–114] this technique is good for fundamental studyof solidification behavior, especially when combinedwith X-ray imaging to observe the in situ microstructureevolution.[115,116]

B. Diffusion Control Mechanism for the PeritecticReaction

Many modeling and experimental investigations ofthe peritectic reaction in steel have concluded that it iscontrolled by the diffusion of solute atoms, especiallycarbon.[75,80,86,90,98,117] According to the equilibriumFe-C phase diagram (Figure 1), at the peritectic tem-perature, d-ferrite at only 0.1 pct C is in equilibrium withaustenite at 0.18 pct C and liquid at 0.52 pct C. Growthof the austenite plate thus requires the rejection of solute(carbon) into the liquid, which is proposed by many tobe limited by the rate of solute diffusion through theliquid away from the region, specifically carbon in thiscase. As this peritectic solidification phenomenon occursat high temperatures (1495 �C in Fe-C binary alloys),early experimental investigations were rare. Thus, earlystudies of peritectic solidification applied analyticalmodels based on diffusion laws to study the peritecticreaction of steel.[32,72–74]

Many models of the peritectic reaction have beendeveloped to predict the growth rate of the austenitelayer along the d-ferrite/liquid interface during theperitectic reaction, which are based on solving Fick’ssecond law for the diffusion of solute atoms through theaustenite phase and mass balances on solute transportacross the interfaces.[72,73] One analytical solution forthe c-platelet growth rate, Vc

[74] in a hypothetical binaryFe-m system, includes the effects of tip radius on theinterfacial diffusion:


Vc ¼9

8p

� �DLmq

� �x2; ½13�

x ¼ X1� 2Xp � X

2

2p

;½14�

X ¼ ðCL=cm � CL=dm Þ

ðCL=cm � Cc=Lm Þ; ½15�

where DLm is the diffusion coefficient in the melt of thesolute, m such as carbon[33] or nickel,[117] through theliquid steel, q is the tip radius of the edge of the grow-ing austenite plate along the d/L interface (Fig-ure 1(b)); X is relative dimensionless supersaturationof solute atoms in the liquid above equilibrium at the

two interfaces; CL=cm and C

L=dm are the solute atom con-

centrations in the liquid in equilibrium with the c and

d phases, respectively; and Cc=Lm is carbon concentra-tion in the c in equilibrium with the liquid. These dif-fusion models typically assume no barrier to c-phasenucleation upon reaching the peritectic temperature.[73]

This model was extended to better consider surfacetension and the capillarity (Gibbs–Thompson) effectbetween c austenite and d ferrite[74]

Vc ¼27DLRT k

c=Lfe � k

c=Lm

� �C

L=cm � CL=dm

� �

128prd=cVLm

Xx

� �3; ½16�

where R is the gas constant; kc=Lfe and k

c=Lm are the par-

tition coefficients of iron and solute, respectively, at

the L/c interface; rd=c is the surface tension between dand c and is equal to the interface elastic strain energyper unit area at the interface between d and c; and VLmis the molar volume of the liquid steel. Lateral growthrate is strongly dependent on X, which determines bythe shape of the phase diagram just below the peritec-tic temperature. The above calculations were con-ducted for an Fe-Ni binary system for different Xvalues and the calculated growth rates agree reason-ably well with measured growth rates.[80]

The peritectic reaction has been studied at differenttemperatures[75] using the method proposed by Ueshimaet al.[86] The results showed that decreasing temperatureincreases the peritectic reaction rate.[75] This is suggestedto be due to the significant increase in carbon concen-tration gradient in the interfaces of austenite with liquidand d ferrite caused by decreasing temperature. Theaccompanying decrease in the diffusion coefficient is toosmall to offset the increase in concentration gradient.[75]

Images in Figure 4 from a HT-CLSM study of ahyper-peritectic alloy with 5.1 pct Ni[80] show thataustenite appears at the triple point formed by theboundaries of two planar d grains with the liquid. Thisaustenite platelet grows very fast with lateral movementalong the L/d interface, and thickens as it

simultaneously grows slowly into both the liquid andthe d ferrite. The measured lateral growth rate (peritecticreaction) increases from 30 to 145 lm/s with increasingcooling rate.[80] This sequence of peritectic reaction stepshas been reported for hyper-peritectic carbon steel(Fe-0.42 pct C)[33] and for Fe-Ni systems.[117] Lateralgrowth (peritectic reaction) was much faster (2970 lm/s)in the Fe-C alloy than in the Fe-Ni alloy. This wasattributed to the higher diffusion rate of carbon in Fe-Cliquid than Ni in Fe-Ni liquid.[33]

In another experimental study on Fe-4.7 pct Ni[98]

observing the growth rate of austenite platelets duringthe peritectic reaction, it was concluded that the nickeldiffusion field controlled the growing austenite plates,which is greatly influenced by the tip radius at the edgeof the plate. Three regimes were observed for austenitegrowth along the d-ferrite/liquid interface: (1) constanttip shape and velocity of two austenite platelets growingtoward each other, while their diffusion fields areindependent, (2) flattening tip shape and decreasingvelocity, when the plates approach each other, and theirdiffusion fields likely begin to interact; and (3) suddendistortion of the platelet tips, and increasing velocity,when the adjacent growing austenite tips interfere,indicating that their diffusion fields have drasticallychanged.[98]

C. d-Ferrite Re-melting Mechanism for the PeritecticReaction

Based on experimental observations, several research-ers have concluded that the peritectic reaction velocity isvery fast and thus cannot be controlled only by diffusionof carbon through the c phase.[31,76,80] The re-melting offerrite ahead of advancing c phase during the peritecticreaction has been proposed by Hillert[118] as an impor-tant mechanism that controls the peritectic reaction.This phenomenon has been confirmed by experimentalobservations[31,76] and phase-field simulations whichinclude both diffusion and microscale heat transfer[85,119]

and are discussed in the following paragraphs.Hillert[118] proposed that re-melting of the d-ferrite

interface occurs near the d/c/L triple point near the edgeof the growing austenite platelet tip. Furthermore, thisre-melting was proposed as evidence for a new

Fig. 4—Lateral growth of c at L/d interface in the early stages of theperitectic reaction of Fe-4.86 pct Ni alloy. Reprinted with permissionfrom Ref. [80].


mechanism for control of the peritectic reaction rate.During cooling from above the peritectic reactiontemperature, the formation of austenite with composi-tion of CLc causes the rejection of carbon into the liquid

ahead of austenite plate which is growing along the L/dinterface. In this situation, the carbon concentration atthe L/c interface (CcL) is higher than the carbonconcentration at the L/d interface (CdL), as shown inFigure 5. The d ferrite is in contact with liquid which isenriched with carbon (above the equilibrium concentra-tion) so it leads to some re-melting of ferrite.

Recent experiments[76] by in situ HT-CLSM observa-tion (Figure 6) obtained visual evidence of this proposedmechanism for the peritectic reaction, in which a thinaustenite plate grows along the interface and re-meltingof ferrite takes place at the edge of the growing austeniteplatelet. This landmark experimental observationrevealed that the tip velocity at the edge of the growingaustenite layer is in the range of 1.4 9 103 to 12.5 9 103

lm/s. These researchers argued that this rate is higherthan that can be explained by diffusion of carbon alone,and that the rate-limiting step in the peritectic reaction isdissipation of the latent heat of transformation, ratherthan carbon diffusion.[120] Although these experimentalobservations are very clear, other mechanisms cannot bedismissed, because surface phenomena might affect thebehavior being visualized on the surface in thesemicroscope images, relative to that in the bulk volumeinterior of the sample and the real process.

The analytical model in Eqs. [13] through [15] wasused to calculate the growing velocity of an austeniteplate[76] due to carbon diffusion, and even for a very lowtip radius of 0.15 lm, the predicted tip velocity wasmuch lower than the experimentally observed rate in anFe-C system[76] of 400 to 12,500 lm/s at high under-cooling. Thus, it was concluded that the peritecticreaction is not controlled by carbon diffusion alone.[76]

Considering the latent heat of transformation, there-melting of d-ferrite was proposed to improve theprediction of the reaction rate. Growth rates werecalculated using the following equation for directionalsolidification[121]:

Vmax ¼KsGsqL

; ½17�

where Ks is the thermal conductivity, taken for d fer-rite, Gs is the thermal gradient in the solid (K/m), q isdensity, and L is the latent heat of fusion, taken to be62.8 kJ/kg for peritectic transformation in this 0.18 pctC alloy, The calculated growth rates of the austeniteplatelet with and without considering re-melting arecompared in Figure 7. Without considering re-melting,the tip velocities are 19 to 855 lm/s for thermal gradi-ents of 1 to 45 K/mm, which are considerably lowerthan the measured velocities. Including 50 kJ/kg oflatent heat released by austenite formation to remeltsome of the d-ferrite, the calculated reaction velocityincreased to 315 to 12,500 lm/s, which is in the rangeof the measurements.Based on these findings, an alternative mechanism for

the peritectic reaction was proposed. Some of the latentheat released by the austenite formation could remeltsome nearby ferrite. Then, instead of requiring diffusionto transport carbon away from the solidifying austenitetip, the re-melted d ferrite (0.1 pct C) mixing with theenriched liquid (0.52 pct C) ahead of the austenite tip(0.18 pct C) could produce liquid at roughly the requiredcomposition for the solid austenite. The austenite tip

Fig. 5—Linearized Fe-C phase diagram showing phase compositionsat different interfaces (solid black lines show equilibrium; dashedblack lines show metastable extensions, and thick dashed red linesshow undercooled conditions where peritectic reaction actuallyoccurs). Reprinted with permission from Ref. [76] (Colorfigure online).

Fig. 6—HT-CLSM images of the peritectic reaction in Fe-0.18 pctC, (a) start of peritectic reaction, (b) initiation of austenite layer atliquid/d-ferrite interface, (c) growth of austenite layer along thatinterface, (d) close-up of austenite layer showing re-melting ofd-ferrite ahead of its growing edge, and (e) schematic of previousframe. Reprinted with permission from Ref. [76].


therefore can grow into liquid at about the samecomposition, without the need for much carbon diffu-sion. This would enable the high austenite growth ratesobserved.

The re-melting phenomenon has also been observedby other HT-CLSM experiments.[31] A sequence ofevents during intermittent austenite growth in a Fe-0.43pct C alloy near equilibrium is shown in Figure 8, with aschematic illustrating the expected temperature evolu-tion provided below. To explain the discontinuousgrowth in this figure, these authors argue that there-melting of d-phase occurs first and causes the suddenc plate growth. When temperature is relatively constant,all three phases are proposed to be in equilibrium andno diffusion takes place (Figure 8 top frames 1, 3, 5, and7). Decreasing temperature creates a driving force fordiffusion. In both Fe-C and Fe-Ni systems, this drivingforce is much higher for the solute atoms than for the

iron atoms. Thus, the partitioning of solute atomsoccurs first and causes re-melting of some d-ferrite phase(Figure 8 top frames 2, 4, 6 with dashed lines andtemperature drops). After a certain amount (length dL)of d has re-melted, the c phase grows into the re-meltedregion. This mechanism agrees with Hillert[118] butcontrasts with Phelan et al.[76] who believe that there-melting of d ferrite takes place due to the dissipationof latent heat released during the growth of the c. There-melting phenomenon has been also reported inperitectic solidification of Fe-Ni alloys.[80]

The d-ferrite re-melting phenomenon has been con-firmed by several phase-field modeling studies.[84,122–124]

For example, Figure 9 shows how the d/c/L triple pointand associated interfaces move during c growth atdifferent undercoolings.[85] In addition to a sharper tipradius, increasing undercooling causes the d/L interfacenear this junction to move toward the d phase, whichindicates some re-melting of the d region.In another phase-field modeling study[119] of the

peritectic reaction focusing on the L/d/c triple point,the liquid region expands toward the d ferrite, as shownin Figure 10, again indicating melting of the d-phase infront of the growing c platelet. This melting reduces thelocal supersaturation, which enhances growth of the cplatelet. Thus, it appears that the peritectic reaction iscontrolled by a complex mechanism that involvesmicroscale heat transfer that causes some re-melting ofd ferrite near the tip of the advancing c platelet, andmixing of solute in the liquid phase, in addition to solutediffusion.

D. Diffusion Control Mechanism for PeritecticTransformation

Many researchers have proposed that the peritectictransformation in steel is controlled by diffu-sion.[31,32,74,75,125,126] The austenite layer initially growslaterally along the L/d solidification front, and locallyreplaces the L/d interface with a thin layer of austenite,

Fig. 7—Calculated growth rates of an austenite platelet along theliquid/d-ferrite interface with and without consideration of d-ferritere-melting. Reprinted with permission from Ref. [76].

Fig. 8—Sequence of events during incremental growth of c in a Fe-0.43 pct C alloy, showing temperature and microstructure at different times.Reprinted with permission from Ref. [31].


which is the peritectic reaction discussed in the previoussections. After the L/d/c triple-point junction has movedpast, the remaining c layer thickens by growing intoboth the solid d and into the liquid. This transformationof the d ferrite and liquid to austenite, which takes placeby solid-state phase transformation on one side of thislayer (dfi c), and the direct solidification of austenite onthe other side (L fi c), is referred to as the peritectictransformation. In the mechanism discussed in thissection, the growth of both sides of the austenite layer iscontrolled by diffusion.

Fredriksson and Nylén[32] proposed that the peritectictransformation is controlled by diffusion of solute fromthe melt to the d ferrite through the c austenite layer.They derived a theoretical model for the thickening rateof c during the peritectic transformation (F-N model)assuming that (1) the peritectic transformation is con-trolled by diffusion and proceeds at a low undercooling;

(2) the interface concentrations are in equilibrium; (3)the concentration gradients are linear in all three-phaseregions:

@dd=c

@t¼ Dc

dc

Cc=Lm � CL=cm

Cc=dm � Cd=cm

!

; ½18�

@dL=c

@t¼ Dc

dc

Cc=Lm � Cc=dm

CL=cm � Cc=Lm

!

; ½19�

where@dd=c@t and

@dL=c@t are the growth rates of c toward d

and toward the melt, respectively; dc is the instanta-neous c layer thickness; Dc is the diffusion coefficient

in c; Cc=Lm and CL=cm are the equilibrium concentrations

of solute m in c and in the melt at the L/c interface,

respectively, and Cc=dm and C

d=cm are the corresponding

equilibrium concentrations in c and in the d ferrite atthe d/c interface. Other researchers[125,127–130] proposedsimilar analytical diffusion-based models for describingperitectic transformation in different alloys.The F-N model was used[126] to calculate c platelet

growth due to carbon diffusion during the peritectictransformation in Fe-C systems. At an undercooling of5 �C below the peritectic temperature, and a cooling rateof 1 �C/min, the calculated growth rate with this modelagreed well with experimentally observed growth ratesfor Fe-0.42 pct C, as shown in Figure 11.[126] Althoughthe F-N model agrees reasonably well with measure-ments at low undercoolings for Fe-C alloys,[31] at highundercooling the F-N model predicts considerablyslower growth rates than measured.[75,90]

In the F-N model it is assumed that there is completemixing of solute in both the primary liquid and in the dphase. This assumption may be reasonable for isother-mal conditions or low cooling rates. However, when the

Fig. 9—Shape of interfaces calculated near the triple-point junction during the peritectic reaction at different undercoolings. Reprinted withpermission from Ref. [85].

Fig. 10—Phase-field simulation of tip region of the growing cplatelet, where L represents the original liquid region, and L¢represents the liquid region formed by melting some d phase.Reprinted with permission from Ref. [119].


cooling rate is fast, there is a substantial solute buildupin the liquid ahead of the c/L interface, creating a solutegradient in the liquid. A diffusion-controlled analyticalmodel of isothermal peritectic transformation wasdeveloped that considers solute diffusion in all threephases including this liquid solute gradient and reportedgood agreement with measurements.[131]

Experiments using the solid/liquid diffusion couplemethod measured[75] austenite plate thickness growth,based on etching to resolve the prior L/c and c/dinterfaces. The measured growth of the austenite plateswith time, while holding at 1696 K is shown inFigure 12.

The increase in measured thickness, x, fits roughlywith the theoretical exponent of 0.5 for diffusionalgrowth:

xc=L ¼ 5:4t0:57; ½20�

xc=d ¼ 80t0:5; ½21�

xt ¼ 85:7t0:5; ½22�

where t is time (s), xc=L and xc=d are the thickness (lm)of the c-phase solidified from the liquid phase andtransformed from the d-phase, respectively, and xt isthe total thickness of the c platelet. The measuredgrowth rates in this experiment match the calculatedgrowth rates, based on the diffusion-controlmechanism.[74]

These curve-fits of measured results show that duringperitectic transformation, the c/d interface does notmove until carbon concentration at this interfaceincreases, according to the solid-state partitioningobserved between the solvus lines in the phase diagram(Figure 1). This solute buildup requires carbon atoms todiffuse from the liquid phase through the c-phase to thisc/d interface. As shown in Figure 13, when carbonconcentration in the ferrite is less than 0.09 pct C, theinterface moves very slowly until carbon concentrationreaches saturation (equilibrium) at the interface. Thegrowth rate then follows the classic parabolic growth(0.5 exponent function) expected for diffusion-con-trolled systems.Other investigations of this peritectic transformation

have confirmed this growth relationship with the squareroot of time using measurements based on HT-CLSMobservations.[31,33] The rate constant, 85.7 lm/�s inEq. [22], actually depends on the diffusion coefficient ofcarbon in austenite, and the difference of carbonconcentration at the d/c and c/L interfaces.

Fig. 11—Calculated and observed migration of the c layer toward dand toward the melt during the peritectic transformation of Fe-0.42pct C alloy. Reprinted with permission from Ref. [126].

Fig. 12—Growth process of austenite phase at 1696 K. Reprintedwith permission from Ref. [75].

Fig. 13—Measured movement of the c/d interface during theperitectic transformation at 1763 K for various initial carboncontents in the d-phase. Reprinted with permission from Ref. [75].


HT-CLSM has also been used to measure isothermalperitectic reaction rates in Fe-Ni systems and comparedwith model predictions.[117] Observations showed thatincreasing undercooling caused increasing reactionrates. With low undercooling, the diffusion coefficientis high, so the driving force due to undercooling controlsthe reaction rate.[117] At high undercooling, however, thereaction rate decreases due to decreasing diffusioncoefficient, which comprises a diffusion-controlledregime. These trends were confirmed by calculationswith another diffusion model[72] but that model consid-erably underpredicted the measurements. This wasattributed to inaccurate diffusion coefficients in themolten metal and the neglect of diffusion in the solid.

Diffusion couple experiments showed that[132,133]

increasing cooling rate increased the migration rate ofboth d/c and L/c interfaces. For all cooling rates, the d/cinterface moved much faster than the L/c interface.[75]

This has been attributed to the smaller difference incarbon concentration at the d/c interface. Figure 14shows that at higher cooling rates, the total austenitethickness growth rates exceed the square root of coolingtime relationship expected from simple diffusion.

It has been experimentally shown that the peritectictransformation in steel can be very fast and thus difficultto explain by diffusion alone.[33,77] This implies that theperitectic transformation might be controlled by othermechanisms. Many researchers have used phase-fieldmodeling to investigate these possibilities.

Phase-field models have become an efficient methodto simulate phase boundary evolution during phasetransformations.[134–138] Phase-field models are based onminimizing total free energy everywhere in a highlyrefined computational grid of a representative solidify-ing domain, including bulk free energy, interfacialenergy, and elastic strain energy. Its advantages overother methods include its ability to calculate the

microstructure morphology, without needing to trackthe location of assumed interfaces, and to include thediffusion of multiple solute elements.[134]

Earlier works[75] found that the d/c interface movesfaster than the L/c interface, as already mentioned. Butphase-field simulations predict that increasing coolingrate from 10 to 100 K/min should cause this trend toreverse,[87,120] so at 100 K/min the L/c interface movesfaster. This is due to changes in the solute profile in theliquid, as shown in Figure 15. A flatter solute profile ispredicted at 10 K/min than at 100 K/min. According tothe diffusion mechanism, the carbon flux from austeniteto the liquid depends on the carbon diffusion coefficientand the concentration gradient in the liquid, as perFick’s Law. Early researchers ignored this change ofcarbon concentration in the liquid so do not predict thisreversal in the growth rate trend.Peritectic solidification was simulated[83] using

another phase-field model which showed that growthrates of the c phase follow parabolic growth kinetics byfocusing on the dependencies of the peritectic transfor-mation on the values of the partition coefficient andsolid diffusivities.[139] The distance travelled by each

interface is governed by a parabolic law xij ¼ aijt1=2 inwhich aij is a ‘‘parabolic’’ rate constant. The dependenceof this parabolic rate constant on the partition coeffi-cient (kdc) is shown in Figure 16. aLc is almost indepen-dent of partition coefficient, but adc decreasesconsiderably as the partition coefficient increases. Thisis because the concentration difference at the c/dinterface increases with increasing of kdc; while thevalue of kLc has no effect on the concentration differenceat c/d interface. By raising concentration difference atthe c/d interface, the amount of solute that must diffusefor d/c transformation increases, and consequently themigration distance of the c/d interface decreases.The relationship between parabolic rate constant and

diffusion coefficient is shown in Figure 17. The rateconstant at the c/L interface is independent of soliddiffusivity but the constant rate at the c/d interfacedecreases with decreasing solid diffusivity. Migration ofthe c/d interface was more sensitive to Dd than to Dc;due to the larger concentration gradient in the c phasethan in the d phase. When the solid diffusivities are toosmall, the peritectic transformation rate is determinedonly by c solidification. These authors conclude that theperitectic transformation is initially controlled bysolid–solid transformation, and when the solid–solidinterface velocity decreases, austenite plate thickens bydirect solidification.Additionally, isothermal peritectic transformation has

been simulated for dilute Fe-C alloys, by focusing on asingle c-platelet growing into the L- and d-phases.[119,131]

The interfaces were assumed to be in quasi-equilibriumand peritectic transformation governed by diffusion.The results matched expectations that by increasingundercooling, the tip growth velocity of plateletincreases considerably, as seen in Figure 18. At thesame time, the platelet thickness decreases. Experimen-tal data for a Fe-0.43 pct C alloy[77] are also included in

Fig. 14—Effect of cooling rate on the relationship between totalaustenite platelet thickness and square root of cooling time.Reprinted with permission from Ref. [132].


this figure. Phase-field simulation of peritectic reactionand transformation in an Fe-Mn system[140] againindicated that diffusion was rate controlling.

E. Massive Transformation Mechanism for the PeritecticTransformation

Massive transformation has been proposed as anotherexplanation of the high velocities observed for theperitectic transformation.[33,80–82,88,141] Massive trans-formation involves a change in crystal structure on anatomic scale without compositional partitioning orsolute diffusion, and typically occur during rapid cool-ing.[142,143] Massive transformations are observed whenthe competing equilibrium transformations involvingsolute diffusion are prevented (constrained), such as theaustenite to a-ferrite transformation in steel at highcooling rates.[144,145] Massive transformations are ther-mally activated, meaning that they proceed when aparticular temperature is reached, more according towhen the volume free energy of the new product phase islower than the parent phase, more than when a certaindiffusion-controlled compositional requirement isachieved. They require nucleation of the new phaseand growth, due to the random migration of individualatoms across the interphase boundary[146,147] and theyinvolve length scales that are so short range thatdiffusion effects are very small.[147] Once nucleationtakes place, the new phase grows at high velocities (up to1 to 2 cm/s) with approximately the same rate in alldirections. The rate of massive transformation is

Fig. 15—Comparison of simulated solute profiles at cooling rates of 10 K/min (left) and 100 K/min (right), in an Fe-0.18 pct C alloy, under atemperature gradient of 200 K/cm, at the initiation of the peritectic transformation. Reprinted with permission from Ref. [120].

Fig. 16—Dependence of parabolic rate constant, aij, on partitioncoefficient, kcd: Reprinted with permission from Ref. [139].

Fig. 17—Dependence of parabolic rate constant on the diffusioncoefficient. The diffusion coefficients, Dd and Dc, were defined as Dd= qd Dd

i and Dc = qc Dci , respectively, with Dd

i = 4 9 10�9 and Dci

= 6.0 9 10�10. Reprinted with permission from Ref. [139].

Fig. 18—Tip velocity of platelet as a function of undercooling.Reprinted with permission from Ref. [119].


between diffusional transformation rates (nm/s) and thediffusionless martensitic transformation, which occursat a velocity near to the speed of sound (~ 103 m/s).[65]

As discussed in earlier sections, the rate of peritecticsolidification of steel in undercooled conditions is veryhigh, and is claimed by some researchers not to beexplained by the diffusion models discussed previ-ously.[33,80–82,88,141] The observed high transformationrates have been attributed to massive phase transfor-mation from d to c or to direct solidification of c fromliquid. In fact, non-equilibrium conditions were pro-posed to constrain the nucleation of c phase untilconsiderable undercooling below the peritectic temper-ature and then upon nucleation, growth proceedsextremely fast. Different nucleation constraints andtransformation mechanisms have been proposed andare discussed in the next sections.

Peritectic solidification in Fe-0.14 pct C alloys wasmeasured[33] to be very fast (3.64 to 5.45 mm/s) for theperitectic transformation (thickening of c austenite toferrite and liquid). The thickening rate of austenite isbetween 3.64 and 5.54 mm/s. Also the migration rate ofthe c/d interface was measured to be faster than themigration rate of the L/c interface during the peritectictransformation. In Fe-0.14 pct C, the peritectic trans-formation was believed to be too fast to be controlled bydiffusion,[33] which was instead attributed to massivetransformation. On the other hand, in Fe-0.42 pct C, theperitectic transformation was believed to be controlledby diffusion.[33] No explanation was provided to explainthe difference between these two alloys.

Others researchers[80] used HT-CLSM to study peri-tectic solidification in an Fe-5.1 pct Ni system. Again,high peritectic transformation rates were observed andattributed to massive transformation. This was attrib-uted to the primary d-ferrite being a metastable phasewhich transformed massively to c.

Peritectic solidification in a medium-alloy steel[81] hasbeen studied using directional solidification and thermalanalysis. Segregation of chromium which was measuredby EPMA appeared to cause direct solidification ofaustenite from liquid without a peritectic reaction.[148]

Based on the alloy segregation pattern and presence oflattice defects and thermal analysis, these authors arguethat the peritectic transformation where austenite pre-cipitates directly from d ferrite is a diffusionless trans-formation, which started at 5 K undercooling.[81] Thistransformation caused an observed sudden rise intemperature, followed by diffusion-controlledtransformation.

Yasuda et al.[82] investigated peritectic solidification ina Fe-0.45 pct C-0.6 pct Mn-0.3 pct Si using a syn-chrotron radiation X-ray system. Two different mech-anisms were proposed for solidification of this alloyaccording to the cooling rate. At 10 K/min, the first ddendrite grows and later transforms to c austenite,proceeding from the root to the tip of the dendrites, asillustrated in Figures 19(a) and (b). This transformationoccurs in the mushy region and is essentially conven-tional, diffusion-controlled peritectic solidification.

At a higher cooling rate of 50 K/min, however, thespecimen initially solidified without c phase formationand later after complete solidification, the d grains alltransform into c phase in the solid state suddenly, within1 second. This transformation occurred 100 K below theliquidus temperature. Because the d/c phase transfor-mation occurred in the single c phase region, theseresearchers argued that solute redistribution was notrequired. The relatively large undercooling suggestedthat c nucleation was difficult, so the eventual peritectictransformation from d to c was governed by a massivetransformation. Furthermore, the volume shrinkage ofthis transformation was suggested to induce melt flow toexplain the white grooves in the specimen inFigure 19(d).

F. Nucleation Constrained Peritectic SolidificationMechanism

As discussed above, massive transformation mayoccur when diffusional transformations are constrained,which may occur with high cooling rates and under-coolings. In this situation, the delay of nucleation of theperitectic reaction step is proposed to combine it withthe peritectic transformation step into a single massivetransformation mechanism for peritectic solidifica-tion.[80–82,148] Two different mechanisms have beenproposed to constrain c nucleation, to enable massived/c transformation, which are discussed in the followingsubsections.

1. Nucleation constraint due to high d/c interfaceenergySeveral researchers have recently proposed that mas-

sive transformation is the mechanism for peritecticsolidification, due to the delay of c nucleation in d ferritesufficiently to prevent the peritectic reaction, owing tohigh d/c interfacial energy.[82,141] In situ observations ofperitectic solidification using synchrotron radiationX-ray imaging in Fe-0.45 pct C-0.6 pct Mn-0.3 pct Sialloy were used to explain absence of a conventionalperitectic reaction. Instead, at cooling rates above 0.3 K/s, very fast solid-state d/c transformation wasobserved.[82] The d/c massive transformation needsmuch higher undercooling than the peritectic reaction,which suggests that difficulty with c nucleation wasresponsible for this undercooling. This nucleation diffi-culty was attributed to poor lattice matching betweenBCC d ferrite and FCC austenite.[149] Due to the highnucleation energy of 0.41 J/m2 needed to create the d/cinterface,[141] the peritectic reaction to form c wasprevented until high undercooling.[82] Then, once thefirst austenite nucleus formed, the next nuclei ofaustenite grains form simultaneously.To investigate the d–c massive phase transformation

mechanism, the nucleation of c phase on variousinterfaces was investigated using phase-field model-ing.[141] The simulation results showed that after thefirst austenite nucleus forms on the d/c interface, thedriving force (energy barrier) needed to form each


additional nucleus drops by half. This suggests theeventual possibility of athermal nucleation, where thereis no need for thermal activation. Heterogeneous nucle-ation onto existing c phase is much easier than formingnew nuclei. This is termed concurrent c phase nucle-ation, as sketched in Figure 20.[141] Following initialnucleation at d/d grain boundaries, subsequent nucleiform onto the initial nuclei, where the energy barrier islower, and later at triple junctions. These predictionsagree with in situ observations of d/c massive transfor-mation which measured average d/c interface velocitiesof 200 mm/s.[89] This accelerated nucleation mechanismdeserves further study, including investigation of therole of solute redistribution, in order to clarify thismassive transformation mechanism to explain peritecticsolidification.

2. Nucleation constraint due to solute diffusionMany experimental studies have reported consider-

able undercooling for nucleation of austenite in peritec-tic solidification, and propose that d to austenitetransformation takes place by massive transformation,due to atomic diffusion through the solute field at the L/d interface.[77,85,150]

At non-equilibrium solidification conditions, there isa large solute gradient between liquid and d ferrite. Priorto nucleation, clusters of atoms with an FCC crystalstructure (austenite) are proposed to form within thesolute diffusion field from liquid to d ferrite and assolute atoms pass through these clusters, the rates ofattachment and dissolution of atoms to the clustersdiffer. This flux of solute atoms through the cluster isproposed to increase its Gibbs free energy for cnucleation, which increases the undercooling requiredfor nucleation.[88]

This mechanism to explain the high undercooling forc nucleation was investigated using a HT-CLSM cou-pled with a concentric solidification technique.[88] Fe-Cand Fe-Ni alloys were examined for the same conditionsand cooling rates (7 �C/s) and it was observed that eventhough the concentration gradient of nickel was ~ 10times higher than that of carbon, the higher diffusivityof carbon (DdC ¼ 5� 10�9 m

2/s) led to a much higher

flux JdC = 0.15 lm/s of carbon atoms compared to theflux JdNi = 0.007 lm/s of nickel atoms (D

dNi = 2.1 9

10�11 m2/s). Measurements have shown that the neces-sary undercooling for d/c phase transformation in Fe-Calloy is 8 K, whereas in the Fe-Ni alloy this

Fig. 19—X-ray images of Fe-0.45 pct C alloy solidification suggesting diffusion-controlled peritectic reaction at 10 K/min (a) early time and (b)later time; and massive d/c transformation at 50 K/min (c) early time and (d) later time. Reprinted with permission from Ref. [82].


undercooling is only 1 K, so peritectic solidificationtakes place by massive transformation and diffusion ofsolute atoms, respectively.[88]

The solidification of steels with 0.1, 0.18, and 0.43 pctC was investigated using HT-CLSM,[77] which noted thedecrease in primary d fraction with increasing Ccontent, leading to different solute gradients at the d/cinterface and different undercoolings observed for cnucleation. As shown in Figure 21, three differentmorphologies of peritectic transition were observedfor the three steels, which were classified into threedifferent solidification modes. In 0.43 pct C steel, theperitectic reaction takes place near equilibrium condi-tions at 63 lm/s, with a planar morphology, so isproposed to be diffusion controlled. For 0.18 pct C, theperitectic transformation proceeded with 3 K under-cooling at 6000 lm/s followed by cellular/dendriticgrowth. Finally, in 0.1 pct C steel, massive transforma-tion of d into c occurred within a fraction of a secondwith 22K undercooling below the equilibrium peritectictemperature. These results were confirmed by otherresearchers.[150]

IV. EFFECTS OF PERITECTICSOLIDIFICATION

Understanding peritectic solidification in steels is ofgreat practical importance, because peritectic solidifica-tion causes many different problems during commercialcasting processes such as continuous casting. Theseproblems include the formation of deep oscillationmarks, surface depressions, and interfacial gaps in themold that lead to lower heat flux, thinner, and non-uni-form (rippled) solidified shell thickness and accompa-nying catastrophic breakouts, increased susceptibility tosurface crack formation and accompanying oxide sliv-ers, larger austenite grain size leading to lower hotductility, and consequently more defects in the finalproduct, including internal cracks and accompanyingmacrosegregation. The following sections explore cur-rent understanding of these effects of peritecticsolidification.

A. Mold Heat Transfer and Shell Growth

During casting of steel, heat flux from the solidifyingsteel to the mold is a strong function of carboncontent,[9,22] as seen in Figure 22, where the lowest heattransfer rate is measured for the peritectic 0.10 pct Csteel. This landmark observation was first published bySingh and Blazek,[9] based on continuous casting of 839 83 mm square billets on a laboratory caster at 21 mm/s. The corresponding shell thickness profiles were alsomeasured for different steel grades, by inducing break-outs during operation. The measured shell growthprofiles roughly follow the parabolic relation,[151]

s ¼ kt0:5; ½23�

where s is solidified shell thickness, t is solidificationtime below the meniscus in the mold, and k is thesolidification constant. The shell of the peritectic steelis thinner, as seen in the measurements in Figure 23,so the solidification constant in Eq. [23] is only 22mm/�min for the peritectic (0.1 pct C) steel, comparedwith over 25 mm/�min for low-carbon (0.05 pct C)and high-carbon (> 0.2 pct C) steels. Although the dif-ference is small, it is very consistent and very signifi-cant to steel quality, as explained later. This slowershell growth of peritectic steels is caused by the gener-ally lower mold heat transfer, shown in Figure 22, andwas suggested to be caused by shrinkage differencesrelated to the solid-state transformation from d-ferriteto c, which is discussed in Section IV–C.[9]

More important than the thinner shell, however, is thejagged nature of the shell thickness profile for theperitectic steel, which indicates the much larger vari-ability in shell growth of this steel grade. Figure 24compares the appearance of the surface and interior ofperitectic and non-peritectic steels.[9] While non-peritec-tic (0.4 pct C) steels solidify with a relatively smoothinterior, the peritectic steel (0.1 pct C) experiences severeripples on the inside of the shell. In commercial casters,these ripples, which represent local thin, hot, and weak

Fig. 20—Concurrent c-phase nucleation as a possible mechanism ofd to c massive phase transformation in carbon steel showingaustenite nuclei at different times. Reprinted with permission fromRef. [141].


regions in the solidifying shell, are extremely detrimentalbecause they often lead to dangerous and costly break-outs, which are more common in peritectic steels.[152]

These ripples and thin spots in peritectic steel shellsare caused by corresponding deep depressions on theshell surface. Figure 24 also clearly shows the roughsurface of the peritectic steel billet which contains manydepressions.[9] In contrast, the high-carbon (0.4 pct C)steel which has a smooth shell thickness profile also hasa very smooth surface. A close-up of a breakout shell inFigure 25 shows that each oscillation mark or depres-sion on the shell surface causes a thin region in the shell,in proportion to its severity.[153] The cause of the surface

depressions is not due to variations in oscillation of themold, because the mold in this study was notoscillated.[9]

B. Surface Depressions and Air Gap Formation

Depressions and oscillation marks in the as-cast shellsurface can be characterized by the surface roughness,which during initial solidification corresponds to deeperinterfacial gaps between the shell and the mold. Mea-surements of commercial-cast steel show that peritecticsteels and ultra-low-carbon (ULC) steels experiencemuch more surface roughness problems than other steel

Fig. 21—Three different modes of the peritectic phase transition observed during concentric solidification in a HT-CLSM: (a) planar(diffusion-controlled), (b) coarse cellular/dendritic (diffusion-controlled), and (c) fine cellular/dendritic (massive transformation). Reprinted withpermission from Ref. [77].

Fig. 22—Effect of carbon content on mold heat-transfer rate duringcontinuous casting. Reprinted with permission from Ref. [9].

Fig. 23—Steel shell growth profiles during continuous casting,comparing peritectic (0.10 pct C) and non-peritectic (0.7 pct C) steelgrades. Reprinted with permission from Ref. [9].


grades, as shown for example in Figure 26.[17] Thisfigure is clearly the inverse of Figure 22 (with theaddition of data points for ULC steel), which indicatesthat the rougher surface increases the thermal resistanceof the interface between the mold and shell, which

directly causes lower heat transfer. Many other studieshave confirmed that peritectic steels experience deeperair gaps and rougher as-cast surfaces.[19,21,154–156]

Fundamental experimental investigation of thisbehavior can be obtained from the study of freedeformation of a solidifying droplet, which was mea-sured for different steels by Dong.[157] Steel dropletssolidified onto a chill plate exhibit a curved bottomshape, with a curvature that varies strongly with carboncontent. The greatest curvature, indicating lift-off fromthe plate, was observed with near to pure iron (or‘‘ultra-low’’ carbon steel) and with near to 0.1 pct C(peritectic steel). Both plain low-carbon hypo-peritecticsteel (e.g., 0.05 pct C) and higher-carbon hyper-peritec-tic steel (e.g., 0.2 pct C) show much less curvature(flatter surface) and consequently less gap formationand depression-related problems.

C. Steel Shrinkage Behavior

A direct measurement of the effect of carbon contenton solidification shrinkage with time in a steel ingotcasting is shown in Figure 27.[16] A peak in shrinkage isobserved for the peritectic steel (0.1 pct C). Note thatthis peak arises very early during solidification. Theincrease in shrinkage relative to other grades is about 0.3mm, which remains constant during subsequentsolidification.[16]

Measurements of thermal contraction in binaryalloys[158] naturally show a peak for peritectic steels(0.1 pct C), as shown in Figure 28. Shrinkage contrac-tion during the solidification of steels with 0.05 to 0.2 pctC has been measured.[159,160] Peritectic steels (0.1 and0.13 pct C) achieved their maximum contraction withina few seconds of solidification, perhaps explaining theirpropensity for surface depressions. In low-carbon steels,the maximum contraction arises after solidification iscomplete.[159,160]

The root cause of the shrinkage peak in peritecticsteels is the d fi c transformation from body-cen-tered-cubic d to face-centered-cubic c, which decreasesthe molar volume by 2.5 to 3.0 pct.[161] Shrinkagecalculations of a solidifying steel shell, such as given inFigure 29, show that linear shrinkage increases withtime for all steel grades.[17] For peritectic steel (0.126 pct

Fig. 24—Surface and cross section views of solidified shells ofcontinuous-cast steel billets, comparing (a) peritectic steel and (b)non-peritectic steel. Reprinted with permission from Ref. [9].

Fig. 25—Close-up of steel breakout shell showing local thin regionscaused by corresponding deep surface depressions. Reprinted withpermission from Ref. [153].

Fig. 26—Effect of carbon content on the surface roughness of thesolidified shell. Reprinted with permission from Ref. [17].


C), the shrinkage is considerably larger, especially nearthe start of solidification. With low-carbon steels, the dto c transformation occurs somewhat later, after thesolidified shell is thick enough to withstand the shrink-age, so perhaps is the reason for less bending deforma-tion due to shrinkage in these grades.[17]

Another study of shrinkage behavior with steelgrade[15] noted that in low-carbon (0.05 to 0.09 pct C)steel, the temperature range of the d/c transformation is12 to 40 K, while for ultra-low-carbon (0.003 pct C) andperitectic steel (0.18 pct C) this transformation theoret-ically occurs at a unique temperature. Thus, theyconcluded that ULC and peritectic steels should expe-rience more severe shrinkage problems, owing to thenarrow temperature range and accompanying high rateof d/c transformation. In contrast, the d/c transforma-tion is much slower in low-carbon steels, so theshrinkage is presumably less.[15] In a hyper-peritecticsteel containing 0.45 pct C or more, all of the d ferritetransforms to c while liquid is still present, leaving c tosolidify directly from the residual molten steel after theperitectic reaction is completed. Thus, the volumeshrinkage accompanying the d/c transformation can beaccommodated by liquid infiltration and does not leadto shrinkage problems, which require relative shrinkagebetween two solid (or nearly solid) phases. The rate of d/c transformation is suggested to play an important roleon the formation of shrinkage depressions and theirconsequences of air gap formation and cracks.[15]

Other researchers[19] explored the reason for moreuneven shell growth in ULC and peritectic steels(relative to low-carbon and hyper-peritectic steels),building on that the idea that the rate of the d/ctransformation is faster in ULC and peritectic steels. A‘‘stress index’’ was proposed by simply calculating theproduct of the shrinkage volume occurring for solidfraction from 0.7 to 1.0, and the estimated d/c transfor-mation rate. This index is shown in Figure 30 as afunction of carbon content.[19] The agreement of thisindex with measured trends suggests that uneven shellgrowth may worsen with increased cooling rate.[15]

Another index of solidification shrinkage was alsoproposed as a criterion for crack susceptibility, Rv, asfollows,[20]

Fig. 27—Influence of carbon content on shrinkage of steel ingots atvarious times. Reprinted with permission from Ref. [16].

Fig. 28—Influence of carbon content on thermal contraction ofiron-carbon alloys at different temperature intervals below solidustemperature. Reprinted with permission from Ref. [158].

Fig. 29—Calculated shrinkage of solidifying shell vs. time from thestart of casting. Reprinted with permission from Ref. [17].


Rv ¼ DVð1� LÞ; ½24�

where L is the mass fraction of liquid remaining afterperitectic solidification estimated from the lever ruleon the Fe-C phase diagram, and DV is the volumeshrinkage of peritectic solidification, calculated from

DV ¼1q1� 1q21q1

; ½25�

where q1 is the density of (L + d), and q2 is the den-sity of c, (L + c) or (d + c), using measured steel den-sity at different temperatures and phase fractions.[20]

This Rv index is shown in Figure 31 to reach a peakfor peritectic steels as expected, and again suggeststhat solidification shrinkage due to the d/c volumechange is the main reason for depression problems inthese grades. This figure also suggests that the peakmoves to higher carbon contents with segregation andnon-equilibrium cooling conditions.

To explain how d/c shrinkage leads to depressions, itis important to note that bending to form a depression ismore complex than simple linear shrinkage. Tempera-ture gradients leading to shrinkage gradients is onemechanism to explain this behavior. Wolf and othershave proposed another mechanism, that microstructurenon-uniformities during the peritectic transformationmay also contribute: Figure 32 suggests two differentpossible scenarios.[162] At high cooling rates, or withperitectic steels which may have insufficient carbondiffusion to the interior of the dendrites, Figure 32(a)illustrates how austenite might nucleate first on thedendrite exterior, with mainly transverse movement ofthe c/d interface inwards, leaving d ferrite along thecenter of each dendrite. When that d ferrite eventuallytransforms to c, the shrinkage would be mainly trans-verse (perpendicular to the solidification direction),leading directly to bending strain (and depressions) orto interdendritic hot-tear cracks, if the bending wereconstrained. At low cooling rates, or with higher carboncontent, Figure 32(b) depicts how the d/c interfacemight propagate from the dendrite tip to its root,following the isotherms under equilibrium conditions.This would lead to axial shrinkage of the dendrite lengthin the solidification direction, which would not tend tocause any bending or tensile stress across the interden-dritic region. Such microstructural effects should beexplored as a potential mechanism for the increasedbending and cracks observed in peritectic steels.

Fig. 30—Effect of carbon content on stress index (product ofsolidification volume and d/c transformation rate). Reprinted withpermission from Ref. [19].

Fig. 31—Rv shrinkage index variation with carbon content fordifferent cooling conditions. Reprinted with permission from Ref.[20].

Fig. 32—Schematic of different directions of the peritectictransformation, (a) transverse shrinkage at high cooling rates orcarbon starved (peritectic), which leads to depressions and cracksand (b) axial shrinkage at low cooling rates or high carbon, C> 0.2pct which leads to no problems.[162]


In addition to the importance of increased shrinkageon the behavior of peritectic steels, many researchershave noted that austenite is much stronger than d-ferriteat a given temperature.[12,163,164] Advanced thermal-me-chanical computational models have been applied toinvestigate the effect of steel alloy (carbon content) onthermal distortion of the bottom of solidifying steeldroplets,[165] and on deflection of the tip of the solidi-fying steel shell during a level drop in a continuouscasting machine near the meniscus.[12,163] These modelsinclude the temperature, phase fraction, and composi-tion dependency of both the steel density (and corre-sponding shrinkage) and the strength, using anelastic–viscoplastic constitutive relation. The predictionsof these models match the observed trends of increasedbending deformation in ULC and peritectic steels.Sample results, shown in Figure 33, reveal that thesesteels experience deeper depressions, which becomemuch more severe with level fluctuations.[12,163]

D. High-Temperature Ductility and Hot Tearing

Cracks form during commercial casting processes dueto a combination of metallurgical embrittlement andtensile stress. Most longitudinal surface cracks andinternal cracks are caused by a hot-tearing mechanism

during initial solidification that involves severe embrit-tlement and failure strains of only about 1 pct. Steelcomposition plays a critical role, in part, because itcontrols the high-temperature ductility. Many studieshave been conducted on steel ductility, as reviewedelsewhere,[166–168] so only a few points relevant toperitectic steels are emphasized here.Metallurgical properties during solidification are

shown schematically in Figure 34. Above the zerostrength temperature (ZST), the steel behaves like liquid,and any applied tensile strain will simply pull apart thedendrites, and draw liquid in to fill the space. Below theliquid impenetrable temperature (LIT), the feeding ofbulk liquid is prevented by the dendrite network. Belowthe zero ductility temperature (ZDT) or non-equilibriumsolidus temperature, solidification is sufficiently com-plete that the solid can withstand significant load andductility is high. Between LIT and ZDT is a brittletemperature range that is susceptible to hot tearing.Others suggest a brittle temperature range between theZST and ZDT.[169] In these critical temperature ranges,strength is low due to the liquid matrix, so any appliedtensile strain will open up a crack, which is filled bydrawing in surrounding segregated liquid. Strain sourcesinclude mechanical deformation, thermal contraction,and the d/c phase transformation. The typical solid

Fig. 33—Simulated shell tip distortion for three steel grades with and without level fluctuations, showing increased depressions in ULC andperitectic steels. Reprinted with permission from Ref. [12].


fraction between LIT and ZDT is 0.9 to 0.99, whichextends with increasing cooling rate, to below theequilibrium solidus temperature.[13,170]

Many researchers have investigated the importanteffect of alloying elements on high-temperature steelductility.[171–178] Residual impurity elements, such as S,P, Cu, Sn, Sb, and Zn, are well known to be detrimentalbecause they segregate into the interdendritic liquid,lowering the ZDT and thereby decreasing the failurestrain.[168,171] Many of these elements have low partitioncoefficients, leading them to concentrate in the austenitephase.[2] Phosphorus, for example, segregates duringsolidification to austenite over 10 times more than whensolidifying to ferrite.[2] Alloys which undergo the

peritectic reaction, change their solidification modefrom ferritic to austenitic, leading to more segregation,lower ZDT, and lower high-temperature ductility.Alloys with higher segregation have lower non-equi-

librium solidus temperature (Ts) and consequently havethinner effective shell thickness, that is completely solidwith mechanical strength. Figure 35 shows that theperitectic steels (0.1 pct C) have the highest effective shellthickness, while high-carbon steels suffer the mostembrittlement and are thus more prone to hot-tearcracks.[2] However, the thicker effective shell of theperitectic steels experiences more bending and beingstronger, can support a higher ferrostatic pressure, thusleading to deeper surface depressions. Consequently,increased interfacial gap resistance, leading to lowerheat flux in the mold decreases the shell growth locallyand creates hot spots, so it increases the risk of surfacecrack formation and breakouts.[3,11,13,18–20]

E. Internal Cracks

Internal cracks are one the most important problemsaffecting commercial steel casting processes, such ascontinuous casting. These cracks form due to hottearing as a result of tensile stresses which are inducedby mechanical deformation, thermal contraction, andphase transformation, combined with the loss of hotductility near the solidus temperature discussed in theprevious section. They are generally not actually cracks,because interdendritic liquid is drawn in between theseparating dendrites to prevent an actual void. However,this results in a region of macrosegregation in the shapeof the crack. This macrosegregation is a worse productdefect than a void, because it cannot be closed orotherwise removed by rolling or other subsequentoperations. It is important to note that during initialsolidification, the mushy zone is at the surface of thesteel strand, so surface cracks, especially longitudinalsurface cracks, can initiate at the meniscus due to thesame high-temperature embrittlement and hot-tearingmechanism as internal cracks.Many investigations on cracks due to hot tearing

during casting of steel alloys have been conducted andare discussed in this section. Different criteria forhot-tear crack formation have been proposed, includingcritical strain[169,171,179–183] and critical fracturestress.[184,185] Critical strain for internal crack formationhas been reported to range from 0.5 to 3.8pct,[169,181,182,186] or from 1.6 to 2 pct,[187,188] dependingon the steel composition. One critical strain criterion forperitectic steel (0.14 pct C) suggests a critical tempera-ture range of Ta �30

where ec is the critical strain which when exceededlocally causes a hot tear; _e is the local strain rate; andDTB is the critical temperature range for the alloy, cor-responding to the solid fraction range of 0.9 to 0.99pct solid, which equals LIT - ZDT. Because strain andstrain rate are tensors with different components whichaccumulate with time, attention should be paid to theirdirections, which could differ.[190] It should be notedthat this criterion predicts that high-carbon andhigh-alloy steels with high solidification temperatureranges (and large DTB) experience smaller criticalstrains, so are easier to crack. In contrast, peritecticsteels experience smaller solidification temperatureranges, and so have higher critical strains, whichagrees with the high-temperature hot ductility findingsdiscussed in the previous section.[171] Higher strain ratealso decreases the critical strain and makes cracksmore likely, but is difficult to quantify.

Other researchers have suggested critical fracturestress in the mushy zone as a criterion for crackformation.[23,191–194] The fracture stress of solidifyingshell has been measured using submerged split chilltension testing method.[184,195] According to this crite-rion, hot-tear cracks form in the mushy zone when themaximum principal stress exceeds the local tensilestrength of the steel at that temperature.[196] Otherresearchers[197] using tensile testing at elevated temper-ature found that steels which undergo the peritecticreaction are more susceptible to crack formation,especially when the solidification experiences massivetransformation, owing to the fast shrinkage contraction.

Another crack criterion is based on the difference ofdeformation energy in the brittle temperature range andis shown in Figure 36 as function of carbon content,along with an experimentally measured crack index.[171]

Peritectic steels (0.12 pct C) are predicted to experiencethe largest tendency for cracking. This was attributed tothe large d/c transformation strain during solidificationleading to higher strain rates. High strain rates alsodecrease the critical strain for crack formation. Theseresults have been confirmed by Bernhard et al.[198]

These predictions agree with other research thatsuggests that steels with carbon content of 0.1 to 0.14pct C are more susceptible to internal cracking.[14,199,200]

However, they appear to disagree with some of thecritical strain predictions discussed earlier. This dis-agreement between different cracking criteria suggeststhat simple empirical relations are not easy to apply andthat phenomena such as local shell thinning and strainconcentration must be considered when predicting crackformation, as discussed in the next section.

F. Longitudinal Surface Cracks

Many studies[9,22,201,202] have found carbon content tobe the most critical factor which affects the formation oflongitudinal surface cracks. Because they usually initiateduring initial solidification near the meniscus, longitu-dinal surface cracks are governed by the same high-tem-perature ductility properties that govern internal cracks.In addition, they are greatly influenced by surfacedepressions, where strain can concentrate in the thinshell beneath them. Longitudinal surface cracks areformed most in the range of 0.09 to 0.18 pct C(hypo-peritectic range), as shown in Figure 37.[203] Thiswas attributed to the higher rate of shrinkage accom-panying the d/c transformation, which can be repre-sented by the corresponding density increase.[203]

Despite having high shrinkage, longitudinal cracks donot formed as much above 0.18 pct C. This wassuggested to be due to more liquid feeding available tocompensate the shrinkage in these hyper-peritecticsteels.Other researchers[24] have investigated critical strain

for crack formation in different steel grades using tensileand bending tests, and found that critical strain inperitectic steel is almost two times that of non-peritecticsteels (Figure 38). Thus, the longitudinal surface crackswhich form during the continuous casting of peritecticsteels are not caused by higher intrinsic crack sensitivityof these steels, but rather by the hot spots at the base ofdepressions caused by the d to c phase transformation inthe early stages of solidification.

Fig. 36—Effect of carbon content on experimentally measured crackindex and on difference of deformation energy in the brittletemperature range. Reprinted with permission from Ref. [171].

Fig. 37—Effect of carbon content on longitudinal surface crackindex. Reprinted with permission from Ref. [203].


G. Intermediate-Temperature Ductility Drop, AusteniteGrain size, and Transverse Cracks

Many surface cracks, especially transverse cracks,arise due to tensile stress and embrittlement of theaustenite grain boundaries at intermediate temperatures.A significant drop of ductility of steel at intermediatetemperatures, from ~ 700 �C to above 900 �C, has beenthe subject of many studies, reviewed elsewhere.[173] Thisductility drop or ‘‘trough’’ is due to the formation ofprecipitates, including sulfides and nitrides, whichweaken the austenite grain boundaries, especially whensoft and weak primary ferrite nucleates on the bound-aries to form ferrite films or networks. Embrittlement ismuch more severe when the austenite (c) grains are verylarge, because any applied tensile strain concentrateswithin a small number of grain boundaries.[178,204–208]

Intermediate-temperature ductility loss is important totransverse surface cracks, because they tend to form dueto axial and unbending strain low in a continuous

casting machine, when surface temperatures often fallwithin the critical temperature range for the intermedi-ate-temperature ductility trough.It has been widely reported that transverse cracks

form only in the presence of abnormally large austenitegrains, where a film of ferrite or precipitate form alongthe boundaries.[209–211] These abnormally large grainsare sometimes referred to as ‘‘blown grains.’’ Peritecticsteels are reported to experience larger austenite grainsize than steels with either lower or higher carboncontent.[212] Austenite grain size increases rapidly withincreasing temperature, due to grain growth, as shownin Figure 39.[211] This figure also shows that near-peri-tectic steel (0.16 pct C) experiences grain growth earlierand eventually attains a larger size.Other researchers have confirmed that near-peritectic

steels, such as 0.17 pct C, have larger austenite grain sizethan other steels, as shown in Figure 40.[205,213] It issuggested that[214] because liquid and d ferrite hinder thegrowth of c grains,[215] austenite grains start to growimmediately after transformation into the single phase cregion.[215,216] Adding phosphorus to 0.1 pct C steel hasbeen shown to decrease the primary austenite grainsize.[217,218] This was attributed to delaying the d/ctransformation to a lower temperature range.Austenite grain size can be predicted by[219]

�D ¼ 9:1� Tc � 3152 e_T

1þ e _T

" #

� 9044; ½27�

where �D is the final austenite grain size in lm; Tc isthe highest temperature of the totally austenitic region

for the steel composition (�C), and _T is the local cool-ing cooling rate (�C/s). Predictions at 3 different cool-ing rates for steels with different carbon contents and0.3 pct Si and 1.5 pct Mn all match closely with mea-surements for similar grades, as shown in Fig-ure 41.[219] These results confirm that austenite grainsize is larger in peritectic steels, with huge grainsexceeding 1 mm diameter in many cases.Transverse cracks are more severe with deep surface

depressions and oscillation marks.[213,219–221] This isexpected because the greater interfacial resistancebetween the shell and the mold leads to lower heat flux,

Fig. 38—Effect of carbon content on the critical strain for crackformation. Reprinted with permission from Ref. [24].

Fig. 39—Austenite grain growth with temperature and carboncontent (in situ melted and cooled from 1580 �C to test temperatureat 16.8 �C/min). Reprinted with permission from Ref. [211].

Fig. 40—The c grain size change by carbon content in terms of csingle-phase temperature in Fe-C phase diagram. Reprinted withpermission from Ref. [205].

1898—VOLUME

review of peritectic solidification mechanisms and effects in ......2020/04/14 · as casting of...

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