ISIJ International, Vol. 50 (2010), No. 6, pp. 847–853

1. Introduction

Ductile iron characterize high sensitivity on cooling ratewhat in consequence leads to structural gradients.1,2) As aresult there are continuous changes of structural features ofcast iron with changes of its properties accordingly.

It has been proved3,4) that it is possible to produce thinwall ductile iron (TWDI) with wall thickness even below3 mm (without chills, cold laps and misruns). TWDI can belighter than their substitute made of aluminum alloys5–7)

and characterized similar or better mechanical properties,definitely better dumping capacity. From an economicspoint of view costs involved in producing ductile iron ismuch lower than the ones corresponding to Al alloys.5,6) Allthe technological aspects involved in the production of thinwall ductile iron castings, should have been worked out be-fore considering the development aluminum alloys castingsas cast iron substitutes.

Numerous studies have been published on thin wall duc-tile iron, particularly on the solidification morphologies,8)

microstructure characterization,3,9,10) mechanical prop-erties,11,12) carbide formation factors,1,13,14) production,15,16)

mould filling17,18) and thermal analysis.19) Moreover, variousexperimental relationships have been developed betweenthe chemical composition,10,14,16) pouring temperature,14)

spheroidization and inoculation practice,14,15) casting geom-etry,20) plate thickness,2,10,14) and mould materials.21) Yet,most of these works are limited to simple plate shaped cast-ings.

Casting with the shape of Archimedes spiral can be usedto analyze technological features of ductile iron as well asthe kinetics of solidification. In TWDI castings the firststage of metal cooling is of great importance. This stageembraces metal cooling from pouring temperature to the

onset of the solidification process. Pouring temperature (inmould represented by initial temperature of liquid metal)and also its further drop as a result of intensive heat transfermould-flooding metal are responsible for gradient structure,exhibited by variations in graphite nodule count, ferrite andcementite fractions in a cross section of a casting. Simula-tion of solidification of ductile iron can be helpful for un-derstanding the mechanism of gradient structure formationin TWDI. The aim of this work is to perform numericalsimulation of TWDI with hypereutectic composition and itsexperimental verification.

2. Experimental

A modeling lay-out was designed for thin wall castings.Modeling lay-out, which is shown in Fig. 1(a), consist ofgating system and Archimedes spirals with 1.5 m lengthand 0.001�0.015 m, 0.002�0.015 m and 0.003�0.015 msections, respectively. Common gating system enabled si-multaneously filling spiral cavities with different wall thick-ness. Ductile iron employed in the present work was pro-duced in a medium-frequency induction furnace of 15 kgcapacity. The raw materials were Sorelmetal, commerciallypure silicon, and steel scrap. The metal was preheated at1 450°C and then poured into the mould. Mould was madeof chemically bounded silica sand. Spheroidization and in-oculation processes were made in the mould, which wasequipped with a reaction chamber containing a mixture of0.85% spheroidizer (44–48% Si, 5–6% Mg, 0.25–0.4%La, 0.8–1.2% Al, 0.4–0.6% Ca) and 0.5% of inoculant(73–78% Si, 0.75–1.25% Ca, 0.75–1.25% Ba, 0.75–1.25%Al) connected to a mixing basin. In addition, post-inocula-tion occur in the mixing basin by introducing 0.1% of inoc-ulant. The role of the mixing basin is to ensure that com-

Solidification of Thin Wall Ductile Iron Castings with Hypereutectic Composition

Marcin GÓRNY

AGH University of Science and Technology Chair of Cast Alloys and Composites Engineering, 30-059, Reymonta 23, Krakow,Poland. E-mail: mgorny@agh.edu.pl

(Received on November 24, 2009; accepted on March 30, 2010 )

Numerical calculations are presented describing the solidification of a thin wall ductile iron castings with ahypereutectic composition. Numerical model was implemented in Matlab–Simulink environment. The modeltakes into account the presence of off-eutectic austenite as well as primary graphite. Experimental verifica-tion was made using casting with the shape of Archimedes spiral. Thermal analysis showed that there ishigh temperature drop of liquid metal due to intensive heat transfer between the flowing metal stream—themould material. Thermal analysis along with microstructure observations were made and show reasonableagreement of numerical calculations with experimental measurements.

KEY WORDS: ductile iron; thin wall castings; thermal analysis; numerical simulation.

847 © 2010 ISIJ

plete mixing of the liquid iron occurs after dissolution ofthe magnesium and inoculant alloys. Just after filling themixing basin, a graphite plug is removed to enable metalflow into the mould cavity reproducing Archimedes spiralswith 1.5 m length and different wall thickness (Fig. 1(a)).The chemical composition of the produced ductile ironswas 3.60% C; 3.10% Si; 0.03% Mn; 0.025% P; 0.01% S;and 0.039% Mg.

Temperature of metal in mould cavity was estimatedusing unsheathed thermoelements wires in regular 0.1 mdistances. Flooding metal stream in mold cavity closes cir-cuit of unsheathed thermoelements wires (K type) withthickness of 0.2 mm connected to the digital data acquisi-tion system (AGILENT 34970 A). In Fig. 1(b) it is showncastings of Archimedes spirals with wall thickness of0.001, 0.002 and 0.003 m. Castability of tested cast iron forwall thickness 3 mm was 0.86 m.

3. Microstructure

Characterization of graphite morphology and matrix mi-crostructure was performed on cross sections at differentdistance from the beginning of the spiral. The graphite mor-phology was characterized using image analysis softwareLeica QWin (v 3.5.0). The two dimensional spatial size dis-tribution of nodules was converted to a three dimensionalsize distribution using Wiencek22) equation. In Fig. 2 there

are presented microphotographs of structure as a functionof spiral length.

Results of metallographic experiments along with resultsfrom thermal analysis are summarized in Table 1.

From analysis of the graphite distribution (an example oftypical histogram is shown in Fig. 3) result that bimodalhistogram represents graphite morphology. From metallo-graphic analysis estimation of average radii of eutectic (Re)and primary (large) graphite (Rg) were made (see Table 1).The presence of large nodules indicates that they have nu-cleated before the eutectic part of the solidification and bythat had longer time to grow. As the growth is controlled bydiffusion, a higher cooling rate will require a higher num-ber of primary graphite nodules. This means that primarygraphite nodule count increases as distance from the inletincreases (higher cooling rate). As a result of turbulent fluidflow of liquid metal larger nodules can be dragged by metalstream and in consequence number of primary graphitenodules can increase more pronounced with increasing dis-tance from the inlet to the mould cavity.

The main group of the nodules has nucleated during theeutectic part of the solidification. As the distance from theinlet increases initial temperature of metal decreases (seeTable 1). As a consequence cooling rate (near eutectic equi-librium temperature) and maximum undercooling at theonset of eutectic solidification increases, cause increase ingraphite nodule count (Ng and Ne). Summing up fluid flow

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Fig. 1. a) Casting lay-out (spiral dimensions in “mm”), b) photographs of Archimedes spirals with different wall thick-ness.

Fig. 2. Microstructure of ductile iron in spiral with wall thickness of 3 mm at different distance from the beginning ofspiral: a) 0.01 m, b) 0.1 m, c) 0.2 m, d) 0.3 m, e) 0.4 m, f) 0.5 m, g) 0.6 m.

can affect nodule count distribution (Fig. 3) especially byincreasing second group of nodules that is primarygraphite. Microstructure is of pearlitc–ferritic matrix, freefrom chills. Near inlet there is almost ferritic matrix as a re-sult of thermal heating from down-gate. As distance frominlet increases ferrite fraction ( ff) decreases (see Table 1).From microstructure observations there are seen ovalshaped spaces surrounded by graphite nodules. They arebelieved to be remaining from austenite dendrites.

4. Numerical Simulation

Numerical simulation uses well known heat balanceequation it the form of:

....(1)

where: T, temperature; To, initial temperature of the mould;t, time; v, volume of the casting; A, surface area of the cast-ing; r , density of the metal; c, specific heat of metal; DHf,latent heat; dfs/dt, evolution of solid fraction; km, thermalconductivity of the mould material; rm, density of themould material; cm, specific heat of the mould material.

The process of ductile iron solidification with the hyper-eutectic composition is divided into the following stages:Stage I: The solidification of primary graphite. Stage II:Eutectic solidification. Stage III: The solidification ofaustenite in the form of dendrites.

Stage I

Solidification in ductile iron with hypereutectic composi-tion (carbon equivalent �4.26) start with nucleation andgrowth of graphite spheres in the liquid after undercooling

below liquidus equilibrium temperature of graphite. Thistemperature is given by Eq. (2) in the form23):

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

The model describing the growth of graphite in liquid isgiven in work.23) This model is based on the assumptionthat the diffusion area is a space limited by two concentricspheres. The inner sphere coincides with the surface of asphere of radius Rg(t) and the outer radius amounts Rl.

Growth rate equation of graphite spheres in a liquid hasthe form of:

..................(3)

Where: D, diffusion coefficient of carbon in liquid; and rg,density of graphite.

After integration of Eq. (3) radius of the graphite is givenby:

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

Using the relationship between the degree of undercooling(DT) and the concentration difference (DC�Co�Ce) in theform (Fig. 4) DC�DT/mg

we have:

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

and:

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

In a model, it is assumed instantaneous nucleation.27) Evo-lution of graphite fraction can be expressed by Eq. (7):

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

where: Ng, is the nodule count (of primary graphite).Evolution of graphite fraction covers the period from un-

dercooling below equilibrium temperature for graphite liq-uidus until the temperature of eutectic transformation. InStage I the concentration of carbon in the liquid varies fromthe value of Co (initial carbon content) up to Ce (carbon

df

dtN R

dR

dtg

g g2 g

� 4π

dR

dt

D T

m

t

g g g�

2

2

ρΔ

RD T

mtg

g g

�2

ρΔ

RD

C C tgg

o e� �2

ρ( )

dR

dt t

DC Cg

go e� �

1

2

2

ρ( )

TC

g

0.31Si 0.33P

2.5710�

� � ��

1 33

.

k c

tT T A c

dT

dtH

df

dtm m m

o fsρ

πρ ρ( )� � �v v Δ

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Table 1. Results from metallographic examinations and thermal analysis.

Fig. 3. Histogram of graphite nodule count.

content in graphite eutectic).

Stage II

This stage involves nucleation and growth in terms ofundercooling below eutectic equilibrium temperature(Te)

24):

.................(8)

Stage II will be divided into two periods.

Period 1

After reaching the eutectic composition, just below theeutectic equilibrium temperature there is nucleation ofaustenite envelope on a primary graphite nodules and startthe growth of globular eutectic on primary graphite.Growth of austenite envelope is given by the equation25):

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

Where: C2, C3: carbon content in austenite, at austenite/graphite and austenite/liquid interface respectively, C4, Cgr:carbon content in bulk liquid and graphite, Rg, Re: radii ofaustenite envelope and eutectic graphite, respectively.

From the mass balance in the volume of (4/3)pRg3 the ra-

dius of graphite can be calculated from25):

.....(10)

Concentrations C2, C3, and C4 can be expressed as a func-tion of undercooling. Assuming that the JE�, E�S� and BC�lines for the Fe–C system are straight, the compositions inEq. (10) can be given by

....(11)

where: Cg, Ce, they are respectively the concentration ofcarbon in the points E� and C� of Fe–C–Si system; m2, m3,m4, coefficients of directional lines, respectively E�S�, JE�and BC� in the Fe–C–Si system.

Evolution of austenite fraction can be given by Eq. (12):

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

where: Ne, is the nodule count (eutectic graphite nodules).Equation (12) includes (1�fs) term to account for grain

impingement. This is called the correction factor due toslowdown in the growth impact of growing grain.26)

Period 2

Period 2 in Stage II involves nucleation and growth ofgraphite eutectic nodules and nucleation and growth ofaustenite envelopes. Nucleus of eutectic graphite growthfreely in liquid up to the dimension of the Ro. In this periodtheir growth is calculated using a similar procedure as forthe primary graphite nodules taking into account under-cooling below the extrapolated liquidus for graphite. Oncethe graphite is the radius amounted ro there is diffusioncontrolled growth of graphite though austenite shell usingEqs. (9) and (10). Austenite envelope growth is calculatedusing an Eq. (12).

Stage III

Stage III involves nucleation and growth of austenitedendrites. This phase occurs after undercooling below ex-trapolated liquidus for austenite (Tg). It is assumed instanta-neous nucleation of austenite. Austenite liquidus is givenby24):

...........(13)

In this paper, the growth of equiaxed austenite dendriteswill be described by the relationship27):

.............................(14)

where

......................(15)

Rd, radius of austenite dendrite; DL, diffusion of carbon inaustenite; G , Gibbs–Thompson parameter; m, liquidus slopelines for austenite in Fe–C system; CL, carbon concentra-tion in liquid.

Evolution of austenite dendrite fraction can be given byEq. (16):

...............(16)

Where: Nd, number of austenite dendrites; dRd/dt, growthrate of austenite dendrites. Equation (16) includes (1�fs) toaccount for grain impingement. Spheres28) are not com-pletely filled by the network-type dendrites. It is assumedthat internal fraction of solid amounts gd�0.2–0.4.

Matlab-SymulinkTM (version R2009a) was used for nu-merical calculations of the solidification of a spiral-shapedTWDI casting with a wall thickness of 3 mm. With accessto high-performance computing algorithms and mecha-nisms for analysis of Matlab-Simulink enable quickly andefficiently carry out complex calculations. Here are themethod of numerical solving of differential equations andlinear integration, differentiation, interpolation and approx-imation of functions and many others.

Numerical calculations were performed on the basis ondata taken from experiments that are the initial tempera-tures of metal in mould and the results from metallographic

df

dtg N R

dR

dtfd

d d d2 d

s� �4 1π ( )

μπ

��

D

m k CL

L2 2 1Γ ( )

dR

dtTd � μ γΔ 2

T Cγ � � � �1636 113( 0.25Si 0.5P)

df

dtN R

dR

dtfγ

γγπ� �4 12

e s( )

C CT

mC C

T

mC C

T

m22

33

44

� � � � � �γ γΔ Δ Δ

, , e

R C C R C C R C Cγ3

4 3 4 2( ) ( ) ( )� � � � �g3

gr e3

gr

( )( )

( )C C

dR

dt

R C C

R R RD4 3

3 2� ��

�

γ

γ γ

e

e

Te 5.25Si 14.88P� � �1153 97.

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Fig. 4. Fragment of the Fe–C equilibrium system.

studies (such as the number of spheres of graphite). Experi-mental studies made it possible to obtain the actual coolingcurves of ductile iron. Physical properties used in numeri-cal modeling are summarized in Table 2.

5. Experimental Results and Discussion

In Fig. 5 there are shown cooling curves resulting fromnumerical modelling compared with experimental curvesobtained at different distances from the beginning of thespiral.

Results of computer simulation show fairly good compli-ance with the experimental results. Both numerical calcu-lated and experimental curves show recalescence, that is,the temperature difference between the highest and lowesttemperatures. However, the predicted recalescence is some-what higher than determined by thermal analysis.

Flowing metal stream through the mould cavity heats itup. In consequence conditions of heat exchange along theflowing path are changing. Increasing distance from theinlet is accompanied by a shorter contact time of liquidmetal with a mould, which increases the cooling rate. Cool-ing rate (see Table 1) in turn affects and increase the maxi-mum undercooling at the onset of graphite eutectic. Maxi-mum undercooling estimated from thermal analysis andfrom simulation are graphically shown in Fig. 6. The pre-heating during filling can has an influence on the tempera-ture measurement so as to reduce DTm.

Maximum undercooling obtained from simulation showsrather good conformity with experimental measurements.This is especially important because undercooling is thedriving force measure for the nucleation stage during solid-ification. Not all substrates in the undercooled melt play anactive role in the nucleation process. The minimum sub-strate sizes, which become active nucleation sites, decreasecontinually at increasing degrees of undercooling. In conse-quence nodule count increases. An influence of undercool-ing on eutectic nodule count estimated by metalographicexaminations is show in Fig. 7.

Undercooling started from 48°C (at x�0.01 m) and ifdistance from inlet increases it goes up to the value of

65°C. When maximum degree of undercooling increases,below the cementite eutectic formation temperature, chillscan be formed in the structure. Below in Fig. 8 there areshown results of simulation both primary and eutecticgraphite radii along with their austenite envelopes.

Calculated graphite radii can be compared with experi-mental. An average eutectic radius for x�0.10 m amountsRe�3.42 mm (see Table 1). Simulation gives radius at theend of solidification amounted Re�2.75 mm. In case of pri-mary graphite results are as follows: Rg (exp.)�9.03 mmand Rg (sim.)�6.12 mm. Simulation show a little lower radiiin comparison to experimental results. The differences areconnected with the effect of fluid flow, temperature dropand heating of the mould by flowing metal stream. Thelonger time of flowing metal stream the lower temperaturedrop and the lower cooling rate as a result of change inthermal parameters of a mould with temperature. In thisconnection fluid flow has an effect to the temperature distri-bution. Mainly it can be manifested by different slope oftemperature–time curve before maximum undercooling(see Fig. 5). During fluid flow temperature can decreasesbelow liquidus temperature for graphite. From this timeflowing metal stream can have already nucleated primarygraphite nodules, which growth in this period is not takeninto account in numerical calculations. Moreover graphitekeep growing even after the end of solidification, which isalso not included in simulation. From these reasons simu-lated radii are understated.

It is worth to note that thin wall castings, which solidifywith high cooling rate cause the melt undercooled belowextrapolated liquidus line for austenite. As a result nucle-ation and growth of austenite dendrites takes place. Figure9 presents undercooling below the extrapolated lines foraustenite, which is the driving force measure for the solidi-fication of austenite dendrites.

Influence of the solidification of austenite dendrite oncooling curve is pronounced and it is shown in Fig. 10.

From Fig. 10 follows that nucleation and growth ofaustenite dendrites have an important thermal effect. It isvisible by change in the slope on the cooling curve and alsodecreases in both undercooling and recalescence. In model-

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Table 2. Selected values used in simulation.

ling of the solidification of ductile iron austenite dendritesshould be taken into account. Especially in thin wall cast-ings, because reducing wall thickness fraction of austenite

dendrites increases.19) Such solidification behavior mani-fested by presence both primary graphite and austenite den-drites can be taken into account by numerical simulation

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Fig. 5. Comparison of the cooling curves predicted by the model and the experimentally measured cooling curves for thedifferent thermocouple position (x). Solid lines-simulation, dotted lines-experimental.

Fig. 6. Maximum undercooling as a function of spiral length. Fig. 7. Eutectic nodule count versus maximum undercooling.

given in this work. Moreover the database of experimentaldata in the form of thermal analysis and the metallographicinvestigation for different initial temperatures makes mod-eling of TWDI reliable.

Casting with the shape of Archimedes spiral is designedto the measure of fluidity. Aside from technological aspectin production TWDI (how is the fluidity of ductile iron fora given wall thickness) it represents different cooling condi-tions as the result of the fact that the metal flowing in themould channel cavity heated it, and thus changing condi-tions for the exchange of heat flowing stream—the mouldmaterial. It has a pronounce effect on structure and in con-sequence on casting properties. Inhomogeneous of structure

parameters can be observed. It usually applies to nodulescount and to a smaller extent to the matrix. From work1) re-sults that risers or multiply inlets can significantly reducestructure inhomogeneity.

6. Conclusions

(1) It has been adopted the model describing the solidi-fication of ductile cast iron with hypereutectic compositionin Matlab-Simulink environment. The model takes into ac-count the presence of off-eutectic austenite as well as pri-mary graphite. Both phases are typical for thin wall ductileiron castings.

(2) Experimental verification using casting with theshape of Archimedes spiral was done. Thermal analysisalong with microstructure observations showed that coolingcurves predicted with the presented model gives reasonableagreement with experimental measurements.

(3) Thermal analysis showed that there is high tempera-ture drop of liquid metal due to intensive heat transfer be-tween flowing metal stream—the mould material. Tempera-ture drop can have a pronounce effect on structure and inconsequence casting properties.

REFERENCES

1) E. Fras, M. Górny and H. F. Lopez: AFS Trans., 116 (2008), 577.2) M. Górny: Arch. of Foudry Eng., 7 (2007), 73.3) E. Fras, M. Gorny and H. F. Lopez: AFS Trans., 116 (2008), 601.4) M. Lessiter: Eng. Cast. Solid., 2 (2000), 37.5) E. Fras, M. Górny and W. Stachurski: Fou. Rev., 56 (2006), 230.6) S Katz: Fou. Manag. Tech., (1997), 34.7) M. Górny: Arch. Foudry Eng., 9 (2009), 143.8) C. Yeung, H. Zhao and W. B. Lee: Mater. Charact., 40 (1998), 201.9) O. Dogan, K. Schrems and J. Hawk: AFS Trans., 111 (2003), 949.

10) R. E. Ruxanda, D. M. Stefanescu and T. S. Piwonka: AFS Trans.,110 (2002) 1131.

11) F. R. Juretzko, L. P. Dix, R. E. Ruxanda and D. M. Stefanescu: AFSTrans., 112 (2004), 773.

12) J. W. Torrance and D. M. Stefanescu: AFS Trans., 112 (2004), 757.13) A. Javaid, J. Thompson, M. Sahoo and K. G. Davis: AFS Trans., 107

(1999), 441.14) A. Javaid, J. Thompson and K. G. Davis: AFS Trans., 110 (2002),

889.15) C. Labrecque and M. Gagne: Int. J. Cast Met. Res., 16 (2003), 313.16) J. F. Cuttino, J. R. Andrews and T. S. Piwonka: AFS Trans., 107

(1999), 363.17) F. Mampaey and Z. A. Xu: AFS Trans., 105 (1997), 95.18) M. Górny: Arch. Foudry Eng., 9 (2009), 137.19) K. M. Pedersen and N. Tiedje: Mater. Sci. Forum, 508 (2006), 63.20) D. M. Stefanescu, R. E. Ruxanda and L. P. Dix: Int. J. Cast Met.

Res., 16 (2003), 319.21) R. E. Showman, R. C. Aufderheide and N. Yeomas: Mod. Cast.,

(2006), 29.22) K. Wiencek and J. Rys: J. Mater. Eng., 3 (1998), 396.23) E. Fras: Solidification of Cast Iron, AGH, Cracow, (1981), 163.24) E. Fras: Theoretical Basis for Crystallization, AGH, Cracow, (1986),

424.25) E. Fras: Solidification of Metal and Alloys, PWN, Warsaw, (1992),

188.26) A.N. Kolgomorov: Bulletin de l’Academie des Sciences de l’URSS, 3

(1937), 355.27) D. M. Stefanescu: Science and Engineering of Casting Solidification,

2nd ed., Springer, NY, (2009), 168.28) I. Dustin and W. Kurz: Z. Metallkd., 77 (1986), 265.

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Fig. 8. Radii of eutectic (Re) and primary (Rg) graphite, respec-tively, radii of austenite envelopes for eutectic (Rg) andprimary (Rgg) graphite, respectively and solid fraction de-noted by fs (results for x�0.10 m).

Fig. 9. Simulated undercooling below the extrapolated lines foraustenite (x�0.10 m).

Fig. 10. Modelling with including and excluding the possibilityof austenite dendrites nucleation (x�0.10 m).