Cast Iron Solidification

Materials Science and Engineering A 413–414 (2005) 322–333

Solidification and modeling of cast iron—A shorthistory of the defining moments

Doru M. StefanescuThe Ohio State University, Columbus, Ohio, USA

Received in revised form 2 August 2005

Abstract

Human civilization has evolved from the Stone Age, through the Bronze Age to reach the Iron Age around 1500 B.C. There are many to contendthat today we are living in the age of engineered materials, yet the importance of iron castings continues to support the thesis that we are still in theIron Age. Cast iron, the first man-made composite, is at least 2500 years old. It remains the most important casting material, with over 70% of thetotal world tonnage. The main reasons for cast iron longevity are its wide range of mechanical and physical properties coupled with its competitiveprice.

This paper is a review of the fundamentals of solidification of iron-base materials and of the mathematical models that describe them, startingw chanicalp e discus.H performancer vered.©

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ith the seminal paper by Oldfield, the first to attempt modeling of microstructure evolution during solidification, to the prediction of meroperties. The latest analytical models for irregular eutectics such as cast iron as well as numerical models with microstructure output arsedowever, since the space does not permit an extensive description of the multitude of models available today, the emphasis is on model

ather than the mathematics of model formulation. Also, because of space constrains, white iron and defect occurrence will not be co2005 Elsevier B.V. All rights reserved.

eywords: Cast iron; Microstructure; Mechanical properties; Solidification; Analytical and computational modelling of solidification

. Introduction

While the primeval potter was the first to modify the state ofatter, he left little if any trace in the mythological and archeo-

ogical record. Thus, according to Eliade[1], the starting pointn understanding the behavior of primitive societies in relationo matter must be the relationship of primitive man to mineralubstances, in particular that of the iron-worker.

Primitive people worked with meteoric iron long beforeearning to extract iron from iron ore. The Sumerian wordN.BAR, the oldest word designating iron, is made up of theictogram ‘sky’ and ‘fire’. Similar terminology is found in Egypt

metal from heaven’ and with the Hittites ‘black iron from sky’.et metallurgy did not establish itself until the secret of smelt-

ng magnetite or hematite was discovered, followed by the art ofardening the metal through quenching. The beginning of thisetallurgy on an industrial scale can be situated at 1200–1000.C. in the mountains of Armenia[1]. In the European tradition

t was St. Peran, the patron saint of mines, who invented smeltingf metals.

Metal workers were so important in early history that sotimes they raised to the level of royalty. According to cersources, Genghis Khan was a simple smith before accedpower. In ancient Java, the genealogy of metallurgists, likeof princes, goes back to god. And, in most ancient culturesmetallurgist was believed to have a direct link to the divinnot of divine origin himself.

Thus, it is with a certain reverence that I approached theof reviewing the long history of the first man-made compite, cast iron, from its archeologically documented beginsome 2500 years ago, to the age of virtual cast iron, wits structure and properties are the outcome of computaexercises.

2. A short history of an old material

The earliest dated iron casting is a lion produced in Chin502 B.C. Introduction of cast iron in Europe did not occur uabout 1200–1450 A.D. Remarkable European cast iron artinclude the sewer pipes in Versailles (1681) and the iron bnear Coalbrookdale in England (1779). Before the inventio

E-mail address: [email protected]. microscope in 1860, only two types of iron were known, based

921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2005.08.180

D.M. Stefanescu / Materials Science and Engineering A 413–414 (2005) 322–333 323

Fig. 1. Correlation between the Mg residual and graphite shape[3].

on the appearance of their fracture: white and gray. Our knowl-edge of cast iron was extremely limited for a long time. In 1896,the first paper on cast iron to be published in the newly createdJournal of the American Foundrymen’s Association[2] statedthe following: “The physical properties of cast iron are shrink-age, strength, deflection, set, chill, grain and hardness. Tensitest should not be used for cast iron, but should be confinedto steel and other ductile materials. Compression test shoulbe made, but is generally neglected, from the common erroneous impression that the resistance of a small cube or cylindewhich is enormous, is always in excess of loads which can beapplied”. It took another 50 years for ductile iron to be discov-ered (1938–1940 independently by Adey, Millis and Morrogh).The major discoveries of cast iron ended in the 1970s with therecognition of compacted graphite (CG) iron as a grade in itsown merit. With that, the dependency of graphite shape on magnesium or cerium content was fully understood (see for exampleFig. 1 [3]).

Today, cast iron remains the most important casting materialaccounting for about 70% of the total world casting tonnage.The main reasons for cast iron longevity are the wide range ofmechanical and physical properties associated with its compet-itive price.

3. Critical discoveries in understanding thesolidification of cast iron

Before society accepts to continue sinking resources in thestudy of solidification rather than of global warming it isimportant to understand why solidification is important. Someof the quick answers include: solidification processing allowsmicrostructure engineering; solidification determines castingsoundness; heat treatment is scarcely used for cast iron; mostsolidification defects cannot be corrected through heat treat-ment. In summary, solidification is the main driver of castingproperties.

A good resource for the early discoveries that propelled castiron in its present position is Piwowarsky’s famous monographpublished in 1942[4]. According to this source, by 1892 Ledeburrecognized the role of silicon on the solidification structure ofcast iron, proposing the first equation correlating the carbon andsilicon content: (C + Si)/1.5 = 4.2–4.4.

Then, in 1924, Maurer designed his famous structural dia-gram that established direct correlation between the C and Sic firsta wasa ys-t des(

3

glya andA ont olingo rate,t if

ositio
Fig. 2. Roll’s schematic representation of p
le

d-r,

-

ontent of the iron and its as-cast microstructure. Thettempt to understand the solidification microstructurepparently that of Roll, who in 1934 outlined the “primary cr

als” using Baumann etching to show the position of Mn sulfiFig. 2).

.1. Nucleation and undercooling

Solidification starts with nucleation, which is stronffected by undercooling. Extensive work by Pattersonmmann[5] demonstrated that the effect of undercooling

he eutectic cell count depends on the way the undercoccurs. If undercooling is the result of increased cooling

hen the number of cells increases (Fig. 3). The opposite is true

n of MnS around grains and dendrites (after[4]).

324 D.M. Stefanescu / Materials Science and Engineering A 413–414 (2005) 322–333

Fig. 3. The effect of undercooling on the eutectic cell count[5].

undercooling is a consequence of the depletion of nuclei throughsuperheating.

While the analysis of solidification events was based formany years on indirect observations, it was not until 1961 whenthrough quenching from semisolid state, Oldfield[6] was ableto quantify the nucleation and growth of eutectic grains. Theseexperiments are the beginning of the effort of building the exten-sive database required for solidification modeling of cast iron.

Understanding nucleation was and continues to be the subject of extensive studies. Attempting to explain the efficiencyof metals such as Ca, Ba and Sr in the inoculation of lamel-lar graphite (LG) iron, Lux[7] suggested in 1968 that, whenintroduced in molten iron, these metals form saltlike carbidesthat develop epitaxial planes with the graphite, and thus constitute nuclei for graphite (Fig. 4). Later, Weis[8] assumed thatnucleation of LG occurs on SiO2 oxides formed by heteroge-

neous catalysis of CaO, Al2O3, and oxides of other alkalinemetals.

A similar theory of double-layered nucleation was proposedat the same time for spheroidal graphite (SG). Using the resultsof SEM analysis, Jacobs et al.[9] contended that SG nucleateson duplex sulfide-oxide inclusions (1�m dia.); the core is madeof Ca Mg or Ca Mg Sr sulfides, while the outer shell is madeof complex Mg Al Si Ti oxides. This idea was further devel-oped by Skaland et al.[10]. They argued that SG nuclei aresulfides (MgS, CaS) covered by Mg silicates (e.g., MgO·SiO2)or oxides that have low potency (large disregistry). After inocu-lation with FeSi that contains another metal (Me) such as Al, Ca,Sr or Ba, hexagonal silicates (MeO·SiO2 or MeO·Al2O3·2SiO2)form at the surface of the oxides, with coherent/semicoherentlow energy interfaces between substrate and graphite(Fig. 5).

Since graphite is in most cases an eutectic phase, a clearpossibility of its nucleation on the primary austenite exist. Rejec-tion of C and Si by the solidifying austenite imposes a highsolutal undercooling in the proximity of theγ phase, favor-able to graphite nucleation. Yet, little is known on this subject,mostly because of the difficulties to outline the primary austenitethrough metallographic techniques.

3.2. Crystallization of graphite from the liquid

hites -l ccursb 0fp h oftA hed r-e mostc

e epi
Fig. 4. Growth of graphite on th
-

-

The debate on the preferred growth direction of grapeems to have been initiated by Herfurth[11] who in 1965 postu

ated that the change from lamellar to spheroidal graphite oecause of the change in the ratio between growth on the [11 0]

ace (A direction) and growth on the [0 0 0 1] face of thegraphiterism (C direction). Experimental evidence for growth on bot

hese directions was provided by Lux et al.[12] in 1974 (Fig. 6).ssuming that the preferred growth direction for the SG is tAirection, Sadocha and Gruzleski[13] postulated the circumfential growth of graphite spheroids, which seems to be theommon.

taxial planes of saltlike carbides[7].


Fig. 5. Low potency (left) and high potency (right) nuclei for SG iron[10].

Today it is generally accepted that the spheroidal shape is thenatural growth habit of graphite in liquid iron. LG is a modi-fied shape, the modifiers being sulfur and oxygen. They affectgraphite growth through some surface adsorption mechanism[14].

3.3. Solidification of the iron–graphite eutectic

While considerable effort was deployed to understandthe solidification of the stable (Fe–graphite) and metastable(Fe Fe3C) eutectics, because of space restrictions only the for-mer will be discussed in some detail.

One of the most important concepts in understanding the vari-ety of microstructures that can occur during the solidificationof cast iron is that of the asymmetric coupled phase diagram,which describes non-equilibrium solidification. Such diagramsexplain for example the presence of primary austenite dendritesin the microstructure of hypereutectic irons. The theoretical

construction of these types of diagrams for cast iron was firstdemonstrated by Lux et al.[15] in 1975, and then documentedexperimentally by Jones and Kurz[16] in 1980. They succeededin constructing such diagrams for pure FeC alloys solidifyingwhite or with flake graphite. For a more detailed discussion onthis subject the reader could use reference[14].

In 1949, which is very early after the discovery of SG iron,Patterson and Scheil used experimental findings to state that SGforms in the melt and is later encapsulated in aγ shell. Thiswas later confirmed by Schobel [17] through quenching andcentrifuging experiments. In 1953, Scheil and Hutter[18] mea-sured the radii of the graphite and theγ shell and concluded thatthey develop such as to conserve a constant ratio (rγ /rGr = 2.3)throughout the microstructure. This ratio was confirmed theo-retically by Wetterfall et al.[19] who preformed calculations forthe steady-state diffusion-controlled growth of graphite.

Many other theories that did not gain wide acceptance in thescience community were advanced over the years. An exam-

FA

ig. 6. Experimental evidence of graphite growth along theA or C direction and schdirection and (b) growth of graphite along theC direction[12].

ematic representation of possible mechanisms. (a) Growth of graphite along the


Fig. 7. Influence of composition and solidification velocity on the morphology of the S/L interface. (a) Schematic representation[23,26] and (b) DS experiments[27].

ple is the gas bubble theory postulated by Karsay[20], whichinfers that a precipitating gas phase provides the phase boundaryrequired for graphite crystallization. Austenite precipitates thenat the graphite–gas interface.

Directional solidification (DS) experiments generated signifi-cant information on the mechanism of microstructure formation.Lakeland and Hogan[21] produced the first composition versusthermal gradient/solidification velocity ratio (C–G/V) diagramfor FG iron in 1968. The compositional variable was sulfur.It took another 18 years before the diagram was expanded toinclude SG and compacted graphite (CG) iron (%Mg–V) [22]and then extended to incorporate white iron (%Ce–G/V) [23].

Measurements of the average eutectic lamellar spacing inLG iron [21,24] demonstrated that it does not behave like aregular eutectic, since the average spacing was about an orderof magnitude higher than predicted by Jackson–Hunt for regulareutectics.

Using the knowledge accumulated from DS experiments per-formed by others as well as by themselves, and some ideasfrom the earlier work of Rickert and Engler[25], Stefanescu andcollaborators[23,26] summarized the influence of the amountof solute on the morphology of the solid–liquid (S/L) inter-face of graphitic iron as shown inFig. 7a. This concept waspartially validated through DS experiments by Li et al.[27](Fig. 7b).

Some interesting analogies were made by comparing imagesow teni llyi ,r sea dendi lears s-

tent with the results of phase-filed modeling[29] shown inFig. 8b and d.

Alternatively, to understand the interaction between austenitedendrites and graphite nodules in the early stages of solidifica-tion, the concepts developed for particle engulfment and pushingmay be used. For a description of this approach Refs.[14] and[28] are suggested.

Oldfield’s name surfaces again when attempting to under-stand the influence of a third element on the stable (Tst)and metastable (Tmet) temperatures. Indeed, using coolingcurve analysis, Oldfield[6] demonstrated that Si increases theTst− Tmet interval, while chromium decreases it. This informa-tion was used to correlate microstructure to the beginning andend of the eutectic solidification. It became a truism[30] thatif both the beginning and end of solidification occur above themetastable temperature, the solidification microstructure is gray.If both temperatures are underTmet, the iron is white, while ifonly one temperature is lower thanTmet the iron is mottled.

3.4. The gray-to-white structural transition (GWT)

The first rationalization of the GWT was based on the influ-ence of cooling rate on the stable and metastable eutectic tem-peratures. As shown inFig. 9, as the cooling rate increases, bothtemperatures decrease. However, since the slope ofTst is steeperthan that ofT , the two intersect at a cooling rate which is thec ss erc

ings andc h thes r thew itionw

btained from SEM analysis of microshrinkage in SG iron[28]ith results of phase-filed modeling of dendrites. The aus

te growing into the liquid will tend to grow anisotropican its preferred crystallographic orientation (Fig. 8a). Howeverestrictions imposed by isotropic diffusion growth will impon increased isotropy on the system. Consequently, theritic shape of the austenite will be altered and theγ-liquid

nterface will exhibit only small protuberances instead of cecondary arms (Fig. 8c) [14]. This interpretation is consi

-

-

metritical cooling rate (dT/dt)cr, for the GWT. At cooling ratemaller than (dT/dt)cr the iron solidifies gray, while at highooling rates it solidifies white.

Magnin and Kurz[31] further developed this concept by usolidification velocity rather than cooling rate as a variable,onsidering the influence of nucleation undercooling for bottable and metastable eutectics. Thus, a critical velocity fohite-to-gray transition and one for the gray-to-white transere defined.


Fig. 8. SEM images of dendrites and SG iron in microshrinkage regions (left) and phase-filed calculated images of dendrites (right). (a) Primary austenite dendrite[28], (b) simulated high anisotropy[29], (c) eutectic austenite dendrite and SG aggregate[28] and (d) simulated no anisotropy[29].

Fig. 9. Critical cooling rate for the GTW transition.

3.5. Dimensional variation during solidification

Soon after the discovery of SG iron researchers noted thatits dimensional variation during solidification is quite differentthan that of LG iron. In 1954 Gittus[32] measured the expansionof SG iron over the eutectic interval and showed that it wasfive times higher than that of LG iron. Hillert[33] explainedthis surprising finding by noting that most graphite forms whensurrounded by austenite. Graphite expansion occurring durinsolidification imposes considerable plastic deformation on theaustenite. Yet, specific volume calculations suggest that graphitexpansion should be the same for FG and SG irons.

Some 20 years later, using a different experimental device thaincluded a riser feeding the test casting, Margerie[34] found that

LG iron expands about 0.2–0.5% during eutectic solidification,while no significant expansion occurs in SG iron because of massexpulsion into the riser. This expulsion occurs because SG ironundergoes mushy solidification while LG iron solidifies with askin (Fig. 10).

3.6. Melt control

The progress in the understanding of the correlation betweenthe solidification microstructure and temperature undercoolinggenerated interest in the possibility of using cooling curves(CC) to predict not only the chemical composition but even themicrostructure. After initial work by Loper et al.[35], Naro andWallace[36] showed that eutectic undercooling continuouslydecreases as the cerium addition to the iron increases, and thatthis is directly related to the change in microstructure from LG,to SG, to white. Then, it was found that compacted graphite(CG) iron solidifies with larger recalescence than either LG orSG iron[37,38]. This proved to be a significant discovery sinceit is currently used for process control in at least two patentedtechnologies for the manufacturing of CG iron.

In 1972 Rabus and Polten[39] used the first derivative of theCC, which is the cooling rate, to attempt to precisely identifythe points of interest on the CC such as beginning and start ofsolidification. Other researchers followed[40] and attempted tou tailss on[ s toi ra

riesf hite

g

e

t

se the CC and its derivative to predict microstructure deuch as 80% nodularity[41] and then the latent heat of fusi42]. This proved to be an elusive goal, in spite attemptmprove the standard Newtonian analysis[43] or to use Fourienalysis[44].

Today CC analysis is a standard control tool in iron foundor evaluating the chemical composition as well as grap


Fig. 10. Schematic illustration of solidification mechanisms of continuously cooled lamellar and spheroidal graphite cast iron[14].

shape, inoculation efficiency, shrinkage propensity and others.The ATAS equipment developed by NovaCast has the added fea-ture that it can store information developed in a specific foundryand incorporate it into an expert system. It outputs 20 of the mostimportant thermal parameters of the CC.

As both the CC and the dimensional variation are strongindicators of the phase transformation occurring in the solidi-fying alloy, Stefanescu et al.[45] combined the two methods byadding quartz rods to a standard sand cup for CC, and using adisplacement transducer to simultaneously measure temperatureand dimensional variation (Fig. 11). The method proved to bevery efficient in the characterization of graphite shape and waspatented as part of a technology for CG iron production within-process operative control. A similar approach was promotedlater by Yang and Aalhainen[46] that even used the derivativeof the dimensional variation curve to predict the amount of car-bides.

F sionv

4. Critical innovations in the development ofmathematical models for cast iron

In this section we will present a summary of the main ana-lytical and computational models developed for cast iron.

4.1. Analytical modeling of cast iron

Two years after the development of the Jackson–Hunt modelfor regular eutectics, Tiller[47] attempted to avoid one of thelimitations of the JH model, which is that it could only beused for directional solidification. He developed a model forthe cooperative growth of a eutectic spherical grain of LG andaustenite. The model predicted that the correlation betweensolidification velocity and lamellar spacing obeys the relation-ship λV1/2 = 4× 10−6. This theoretical result was confirmedexperimentally by Lakeland in 1968.

The first analytical model to describe growth of the eutec-tic in SG iron was proposed in 1972 by Wetterfall et al.[48].The model assumed diffusion controlled steady-state growthof graphite through theγ shell. This model has survived thetest of time and is used today in most computational mod-els for microstructure evolution. Under the assumption that theratio between the radii ofγ and graphite remains constant dur-ing solidification, the equation derived for the growth velocityod

du -l ermali sei d, andt cetedp r thei d thatt y thee xist,λ st f thef ust bep del.

ig. 11. Results of measurement of temperature, cooling rate, and dimenariation for a CG iron.

al

f graphite was simplified by Svensson and Wessen[49] torGr/dt = 2.87× 10−11�T/rGr.

The irregular nature of the LG-γ eutectic was not confrontentil 1987, when Magnin and Kurz[50] proposed their irregu

ar faceted/non-faceted eutectic model assuming non-isothnterface. They further assumed that theγ phase that has a diffunterface grows faster than the graphite phase that is facetehat branching occurs when a depression forms on the fahase. To impose a non-isothermal coupling condition ove

nterface, they ascribed a cubic function. They demonstratehe smallest spacing of the lamellar eutectic is dictated bxtremum condition, but that a larger spacing will also ebr, dictated by a branching condition.λbr can be calculated ahe product between a function of the physical constants oaceted phase and a material constant. This constant mostulated (guessed) which limits the generality of the mo


Recently, Catalina et al.[51,52] proposed a modifiedJackson–Hunt model for eutectic growth applicable to both reg-ular and irregular eutectics. The model relaxes the assumptionof isothermal interface and accounts for the density differencebetween the liquid and the two solid phases. Four character-istic spacings for which the undercooling exhibits a minimumwere identified:λ�, λ�, λSL (for the average undercooling ofthe S/L interface), andλiso =λex (spacing at which the inter-face is isothermal equal to the one derived from the extremumcriterion). It is remarkable thatλiso =λex was derived withoutinvoking the extremum criterion. However, isothermal growth isnot possible in all eutectic system. Fe–C alloys do not grow withan isothermal interface. The minimum spacing is determined byλSL, while the average spacing byλGr. Spacing adjustment ofirregular eutectics occurs through the branching of the facetedphase.

4.2. Computational modeling of cast iron—analytical heattransport + transformation kinetics

The era of computational modeling of cast iron was started bythe brilliancy of a scientist whose name has already been quotedseveral times in this paper. It is that of Oldfield[53], who, in1966 developed a computer model that could calculate the cool-ing curves of LG iron (Fig. 12). His seminal paper includedm allyd utec-t thera crossa eri-m theb g ofm

avor.Y thisp eld’sw imes u andT lingc d in1 he

Fig. 12. Experimental and calculated cooling curves, quenched iron sample andequations for nucleation and growth proposed by Oldfield[53].

influence of nucleation and growth rate constants on the widthof the mushy zone in LG and SG iron.

The next significant development in the field belongs toFredriksson and Svensson[57,58]who combined an analyticalmodel for heat transfer with parabolic growth law for LG andwhite iron, carbon diffusion throughγ shell for SG iron, anda model for cylindrical shape CG. They were also the first tointroduce the Johnson–Mehl approximation for spherical grainimpingement.

At the same time and using similar procedures, Stefanescuand Kanetkar[59] included in the model primary and eutecticsolidification, as well as the eutectoid transformation, calcu-lating for the first time the room temperature microstructure(Fig. 13).

Incremental improvements were contributed by variousresearchers. Lacaze et al.[60] modified the mass balance equa-tion in the carbon diffusion model for SG iron to include calcula-tion of the off-eutectic austenite. Fras et al.[61] further improvedthe carbon diffusion model by solving for non-stationary diffu-

F cylin

any innovations including parabolic laws with experimenterived constants for nucleation and growth of spherical e

ic grains, correction for grain impingement against one anond against the wall, and a computer model for heat flow acylinder similar to FDM. Validation against published expents was also included. Oldfield’s model is indisputablyasis of the current advances in computational modelinicrostructural evolution during solidification.Nobody ever remembers number 2 in any human ende

et, the author of this paper will have to take credit forosition, since in 1973 he was the first one to continue Oldfiork [54]. Using an analytical model for heat transport and ttepping procedure to generate cooling curves, Stefanescrufinescu[55] studied the effects of inoculants on the coourves and the nucleation constants. A third paper followe978 when Aizawa[56] used Oldfield’s model to examine t

ig. 13. Calculated cooling curves (left) and fraction of phases (right).M is the
drical bar modulus. Full lines are for pearlite, dotted lines are for ferrite[59].


sion, including diffusion in liquid, and considering the ternaryFe C Si system.

The next challenge of significant industrial interest was theprediction of the GWT. Fredriksson et al.[62] and Stefanescuand Kanetkar[63] approached it in 1986. By including both thestable and metastable phases in the calculation of the fractionsolid, it was possible to output the solid fractions of gray andwhite eutectics. The basic equation was:

fS = 1 − exp

[−4π

3

(NGrr

3Gr + NFe3Cr3

Fe3C

)]

whereN is the number of grains andr is their radius.

4.3. Computational modeling of cast iron—numericaltransport + transformation kinetics

The first coupled FDM energy transport–solidification kinet-ics model for SG iron was proposed in 1985 by Su et al.[64].They used Oldfield’s nucleation model, carbon diffusion con-trolled growth through theγ shell, and performed some valida-tion against experiment. It was not until 1991 that a FDM energytransport–solidification kinetics model for SG iron was extendedto room temperature by Chang et al.[65]. They modeled theγ ⇒ α transformation as a continuous cooling transformationand attempted some validation against experimental work.

The first attempt to use a numerical model to predict theG1 portm ticso odelp

c asi andg ed form ena asta nt ofS

s,c atedt d-u andt wasi

4m

cro-s wass plicat turee theCu wtht tion

Fig. 14. The influence of Si and initial cooling rate on structural transition in a3.6% C, 0.5% Mn, 0.05% P, 0.025% S cast iron[67].

Two selected computer generated pictures at some intermedi-ate fS and atfS = 1 are presented inFig. 16. The reader willnotice that each nodule is surrounded by an austenite grain.Yet experimental evidence suggests that more than one graphitespheroid is found in the eutectic austenite grains (see for exam-ple microshrinkage SEM images in Ref.[28] or color etchingmicrostructures in Refs.[28,70]).

Beltran-Sanchez and Stefanescu[71] improved on the previ-ous model by including solidification of primary austenite grainsand by initiating graphite growth once graphite nuclei came incontact with the austenite grains. After contact, graphite wasallowed to grow through the diffusion-controlled growth mech-anism.

F icalc

WT appears to belong to Stefanescu and Kanetkar[66] who in987 developed an axisymmetric implicit FDM heat transodel coupled with the description of the solidification kinef the stable and metastable eutectics. They validated mredictions against cast pin tests.

A few years later, Nastac and Stefanescu[67] produced aomplete FDM model for the prediction of the GWT, which wncorporated in ProCast. The model included the nucleationrowth of the stable and metastable phases and accounticrosegregation. The model demonstrated such phenom

he influence of Si segregation on theTst− Tmet interval for graynd white irons, and the influence of cooling rate and amoui on the gray-to-white and white-to-gray transitions (Fig. 14).Mampey[68] included fluid flow in the transport calculation

ompared filling simulation with experiment, and demonstrhe influence of mold filling on the final distribution of nole count. He also illustrated the shifting of thermal center

he reduction of radial temperature differences when flowncluded (Fig. 15).

.4. Computational modeling of cast iron—visualization oficrostructure

The transformation of the computer into a dynamic micope that transformed cast iron into a virtual materialpearheaded by Rappaz and his collaborators with their apion of the cellular automaton (CA) technique to microstrucvolution modeling. Not surprisingly, the first application ofA technique to cast iron is due to Charbon and Rappaz[69] whosed the classic model for diffusion-controlled graphite gro

hrough the austenite shell to describe SG iron solidifica

-

.ig. 15. Calculated effect of fluid flow on the thermal profile of a cylindrasting[68].


Fig. 16. Virtual solidification microstructures of SG cast iron.

Fig. 17. Comparison between experimental and simulated LG iron grain struc-ture in cylindrical rods of various diameters[72].

Leube et al.[72] derived a branching criterion from theMagnin–Kurz model for irregular eutectics to calculate the max-imum spacing in FG iron. They calculated the minimum spacingas per Jackson–Hunt. Their model allows calculation of the aver-age length of lamellae for all grains in one volume element and ofthe average of the longest graphite lamella. An interesting inno-vation was the simulation of the eutectic grain structure (Fig. 17)based on Johnson–Mehl-tesselation (Monte-Carlo simulation).

4.5. Computational modeling of cast iron—mapping ofmechanical properties

Mapping of microstructure evolution through computationalmodeling made possible mapping of mechanical properties, ina clear departure of the older approaches in predicting mechanical properties from statistical models relying on compositionand cooling rate, or from numerical models using criteria func-tions. Svensson et al.[73] used a control volume FDM modelfor heat transfer coupled to transformation kinetics models topredict room microstructure. Then, hardness was calculated aa function of microstructure and experimentally derived coeffi-cients.

A complete model for prediction of static mechanical prop-erties of LG and SG irons was proposed by Catalina et al[74,75]. First a spherical symmetry model for growth of theeutectic grain of LG was developed, assuming carbon diffusionc wthm ted.P te ot odef elong trainc to

calculate the strength of LG iron. After systematic validation ofthe various subroutines, they were implemented in Caterpillar’scomprehensive simulation tool–CAPS. Extensive validation byCaterpillar’s scientists proved that the model could be used as areliable tool for quality control and design.

Finally, we must mention a model by Leube and Arnberg[76] that claims prediction of tensile strength from fraction ofaustenite and average of maximum graphite flake length.

5. Concluding remarks

We believe that this review demonstrates that our knowledgeof cast iron solidification has advanced to the point that few areasare still in need of research. Areas of interest remain nucleation,metal-mold interface interactions, and semi-solid processing.

Simulation of microstructure and properties has also madegigantic strides. Computer software companies offer completepackages. For example, in a recent paper, Weber et al.[77] statedthat Magmasoft offers integrated simulation of the entire process(mold filling, solidification, and cooling) using a micromodel-ing approach to investigate final structures and properties of ironcasting. The model accounts for inoculation and growth condi-tion of specific alloys. It predicts graphite morphology (lamellar,nodular), carbide formation, and microstructure length scale(eutectic grain size, type, and average size of lamellae or num-ber of nodules). It calculates the eutectoid transformation andt hard-n sup-p waso

od-e thatc cifict l ares orlyk fur-t

R

ress,

ceed-982,

ontrolled growth. Then a carbon diffusion-controlled groodel for ferrite growth and graphite thickening was perfecearlite growth was simulated based on minimum growth ra

he Fe C X component systems. The earlier developed mor SG iron was also used. The hardness, strength, andation of SG iron was computed on the basis of the isosondition, while a modified Grifith model was implemented

-

s

.

-

fl-

hus final structure. The model predicts properties such asess, yield and tensile strength and fracture elongation. Toort these contentions validation against industrial castingsffered.

So, are we at the end of the road? Not so fast! While mls can do a lot they are not yet transportable, meaningonsiderable calibration is required for the conditions speo the particular foundry. This is because nucleation modetill highly empirical, and many physical properties are ponown. Thus, we believe that the field has still potential forher development.

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