Diffusion Modeling and Experimental Verification of Pearlite/Ferrite Formation in Ductile Iron

S. N. Lekakh and V. L. Richards

Missouri University of Science and Technology, Rolla, MO

Copyright 2010 American Foundry Society

ABSTRACT The eutectoid reaction in industrially produced ferritic and pearlitic/ferritic (Cu-alloyed) ductile irons was modeled and studied experimentally. Thermal analysis and quantitative SEM/metallography were used. A non-steady state diffusion model with a moving reaction boundary was applied for a three-dimensional spherical cell representing a graphite nodule surrounded by a ferrous alloy matrix. The experimentally verified rate of eutectoid reaction was in agreement with that calculated for ferritic ductile iron. Transformation in Cu-alloyed ductile iron occurred at larger undercooling due to alloying element segregation. For the experimental study of this phenomenon, additional homogenization was applied by heat treatment and hot plastic deformation. The ferrite/pearlite ratio and calculated final segregation of alloying elements having different diffusion mobility were compared. In the first stage of homogenization, decreasing Cu and Mn segregation increased ferrite content while homogenization at longer times also eliminated Si-segregation and increased pearlite content and hardness of the matrix. These results could be used in future work for quantitative prediction of the complex interaction effects of inoculation, cooling rate and alloy composition on ductile iron properties. INTRODUCTION The metal matrix plays an important role in mechanical properties of irons with spherical graphite (ductile iron). Commonly used ductile iron with ferrite, ferrite-pearlite and fully pearlite matrix could be produced from the same base melt by variations in silicon content and alloying by Cu, Mn or Sn additions. Graphite nodule size and number as well as cooling rate are also important parameters which control the pearlite/ferrite ratio. Lalich and Loper1 applied a geometrical model constituting a spheroidal graphite particle in a surrounding metal matrix. To this model they applied experimental data to forecast the structure in casting. The parameters considered in their model were graphite nodule count per unit area (NS, 1/mm2), graphite volume percent (VG, %) and cooling rate (T’, °C/min). The rate of austenite-to-ferrite transformation during continuous cooling of ductile iron is controlled by, so -

called long-range carbon diffusion from austenite saturated by carbon to graphite nodules with diffusion distances measured in tens of microns. The metastable austenite-to-pearlite transformation has a significantly different reaction mechanism when compared to stable austenite-ferrite decomposition. The austenite-to-pearlite transformation occurs with two orders of magnitude less carbon diffusion distance between cementite and ferrite plates than the carbon diffusion distance during ferrite formation in ductile iron. Lacaze and Gerval2 reviewed the previously published models and developed a diffusion model of austenite decomposition in spherical cell which contained a graphite nodule surrounded by a metal matrix. Alloying elements such as Cu and Mn retard the rate of austenite-to-ferrite eutectoid reaction and promote undercooling which eventually encourages the meta-stable austenite-pearlite transformation3,4. The role of these alloying elements could be in decreasing the rate of carbon diffusion due to high concentration near the graphite region (inverse Cu-segregation) or decreasing carbon activity in the intercellular region (normal Mn-segregation)5. It was shown6 that segregation of Cu during solidification of iron with 3.95%C and 0.44%Cu was approximately 1.5 times higher than segregation of Cu in medium carbon steel (0.44%C) with the same average Cu content. Electron probe analysis (EPM) showed5 that Mn, Cu and Mo segregation ratio (maximum/minimum concentrations of elements) in ductile iron increased with an increase in diameter of the casting bars. Regarding the segregating tendency among different studied alloying elements, normal segregating elements such as Mn and Mo showed more segregation ratio than the inverse segregating elements such Cu and Ni. In addition, segregation of Mo was more significant than Mn, and that for Cu was greater than Ni. Silicon also has the large inverse segregation forming a halo of high concentration around graphite nodules increasing local carbon activity and promoting formation of ferrite rings. The segregation forms during eutectic growth of graphite/austenite shell from the melt. Such substitutional type alloying elements as Si, Mn and Cu have low diffusion mobility in austenite7 and are practically immobile during continuous cooling of the solid casting. The degree of segregation of alloying

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elements increases with increasing in the diameter of casting (i.e. segregation becomes more significant as the solidification time of casting increases). In this work, the effect of alloying element segregation on eutectoid reaction and the consequent structure of the metal matrix was modeled and experimentally studied using thermal analysis of as-cast, heat treated and hot plastically deformed ductile iron. PROCEDURES MODELING The rate of eutectoid reaction in ductile iron during continuous cooling casting is generally controlled by long-range interstitial carbon diffusion from carbon saturated austenite through the growing ferrite shell to graphite nodules. Non-steady-state diffusion modeling was applied to the meshed individual three dimensional spherical cell containing a graphite nodule surrounded by a series of concentric metal matrix shells (Fig. 1a). Geometrical representation of the real ductile iron structure was done with using correlations between three-dimensional (index “v”) and two-dimensional (index “s”) structure parameters known1,2 from quantitative stereology. An example of these parameters for the spherical cell containing 20 μm diameter graphite (DV) and different number of outside shells (n) and outside diameter D is given in Table 1. By varying the diameter of graphite (DV and DS) and number of shells (n) one can design structures with different graphite nodule counts per unit of volume (NV), or unit of area (NS) and graphite volume fraction (VG, %) in ductile iron. Table 1. 2-d and 3-d ductile iron structure representation in spherical cell

DV,

μm

DS,

μm

n D, μm NV,

1/mm3

NS,

1/mm2

VG %

3 32

39643

435-

508

16.6

4 36

27842

348-

401

11.6

5 40

20297

286-

325

8.5

20 13-

15

6 44

15249

239-

268

6.4

The metal matrix was modeled as consisting of concentric shells. This model was used in two computational approaches. In the first approach, this model was applied for prediction of the position of a moving boundary between austenite and a growing ferrite layer around graphite nodule. The special algorithm was applied for

changing the value of carbon diffusivity in Fe-FCC to Fe-BCC iron when the reaction in one particular shell was completed. This was necessary and appropriate because carbon diffusion mobility in ferrite is orders of magnitude larger than in austenite. In the second approach, this model was used for computing austenite homogenization with respect to substitutional elements during heat treatment. In this case, inside (for Si and Cu) or outside (for Mn) shell regions were inserted with higher concentration of these elements as an initial condition and permeable interior boundary conditions were applied (Fig. 1b). These initial conditions represent elemental segregation which originates during solidification. The typical values of Si, Cu and Mn segregation in the metal matrix near a graphite nodule and near a cell boundary were taken from literature5,6. The “Transport and Reaction” module of Fluent CFD software was used, applying the state solver. For a first approximation, a multi component dilute model, in which diffusion mobility of element i does not depend on concentration of element j was used. The experimental values of diffusivity and activation energy of C, Si, Mn and Cu in Fe-FCC and Fe-BCC were taken from literature7,8. The examples of calculated isothermal austenite transformation (724°C/1335F) controlled only by carbon diffusion in ferritic ductile iron with different nodules number (NS) and graphite volume (V) for graphite nodule diameter DV =20 μm are shown in Fig. 2. Continuous cooling transformation was modeled also for comparison with experimentally verified kinetics.

a)

b)

Fig. 1. Spherical cell with graphite nodule surrounded by numerous of concentric metal matrix shells (a) and modeling of segregation by inserting internal shell region with higher Cu content (b).

Paper 10-083.pdf, Page 2 of 8AFS Proceedings 2010 © American Foundry Society, Schaumburg, IL USA

0

0.2

0.4

0.6

0.8

1

0 50 100 150

Tran

sfo

rmat

ion

Time (sec)

230 1/mm2

420 1/mm2

1100 1/mm2

a)

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800

Tran

sfor

mat

ion

Time (sec)

8.5% graphite

11% graphite

16% graphite

b)

Fig. 2. An example of isothermal (724°C) transformation in ductile iron with different graphite nodule count (a) and graphite volume (b). EXPERIMENTAL The samples (12 mm height) were taken from industrially cast tensile bars (20 mm diameter). Two heats used were as-cast 65-45-12 mostly ferritic (referred as ductile iron 1) and as-cast 80-55-06 having pearlite/ferrite structure, produced by alloying with low level Cu (noted as ductile iron 2) (Table 2). Table 2. Chemical compositions (weight %) of ductile irons

C Si Mn Cu Cr Mg S

DI1 3.82 2.41 0.36 0.2 0.03 0.037 0.01

DI2 3.82 2.36 0.37 0.5 0.03 0.039 0.002

Quantitative phase analysis (DS, VG, NS, orientation of graphite particles, shape factor S=Dmin/Dmax and ferrite area) was done with using optical metallographic images (ImageJ® software) and automated SEM/EDX ASPEX system (Table 3).

Table 3. Quantitative phase analysis in ductile irons

DS,

μm

NS,

mm-2

VG %

S Ferrite, %

DI1 (as-cast) 11.3 640 9.9 1.3 77.7 DI2 (as-cast) 10.9 610 9.8 1.4 33.8 DI2 (deformed) 12.9 434 9.8 2.4 -

The rate of eutectoid reaction can be significantly affected by segregation of interacting alloying elements occurring during solidification. To study this effect, the eutectoid reaction was evaluated in as-cast samples as well as after partial and full thermal homogenization. In addition to homogenization heat treatment at high temperature (935°C/1715F - 975°C/1787F, up to 36 hours, Ar protection), some of samples were hot rolled with 44% reduction prior to heat treatment. Hot plastic deformation was used as a tool for alloy homogenization. It was assumed that such intensive plastic deformation of a heterogeneous structure would produce significant mixing of micro-volumes with different alloying element concentrations. The as-cast samples and those given the various homogenization treatments and hot rolled were heated additionally at 920°C/1688F for 60 minutes and cooled in the furnace at the same cooling rate (0.25 °C/sec). Ductile iron microstructures in the as-cast condition and after hot rolling are given in Fig. 3. National Instrument DAQ was used for monitoring temperature. Newtonian thermal analysis was applied for the calculation of the rate of eutectoid reaction9. The rate of reaction heat liberation (dQ/dτ, J/g*sec) was calculated from the experimental value of the first derivative (dT/dτ, °C/sec) and the calculated value of the zero line (Z,°C/sec):

⎟⎠⎞⎜

⎝⎛ −

τ=

τZ

d

dTC

d

dQp Equation 1

a) b)

c) d)

Fig. 3. Structure of as-cast (a) and deformed (b) ductile iron 1, as-cast (c) and deformed (d) ductile iron 2.

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In this work, the Newtonian method was used for the qualitative analysis of the eutectoid reaction rate with improvements in zero line calculation based on experimentally measured temperature before (coefficients A1, °C and A2, sec-1) and after transformation (coefficients A3, °C/sec3 se and A4, °C/sec4):

4start4

3start321 AAAAT )()()exp( τ−τ+τ−τ+τ=

Equation 2 An example of the rate of transformation calculated from an experimental cooling curve of ductile iron is given in Fig. 4. The reaction rate curve indicated the existence of two regions of ferrite and pearlite formation. Typically, pearlite formation occurred at higher reaction rate and at lower temperature than ferrite formation.

0

0.2

0.4

0.6

0.8

1

700

720

740

760

780

800

200 300 400 500 600 700 800

Tran

sfo

rmat

ion

, rat

e, m

in-1

Tem

pe

ratu

re, 0

C

Time, sec

Temperature

Transformation

Rate

Ferrite Pearlite

Fig. 4. An example of eutectoid transformation in ductile iron based on the thermal analysis during continuous cooling.

EUTECTOID REACTION IN DUCTILE IRONS Cooling and austenite transformation curves were computationally modeled in a hypothetical cell constituting a graphite nodule surrounded by austenite. The model results shown in Fig. 5 are based on the specific geometric parameters of ductile iron 1 (Table 3). The model assumed that the rate of transformation was controlled by carbon diffusion through the growing ferrite shell. Fig. 5 also has the experimental cooling and transformation kinetics curves for ductile iron 1. The continuous cooling process had the same cooling rate in both model and experiment. It could be seen that computed and experimental processes are generally in good agreement with respect to the total transformation times. This indicates that austenite/ferrite transformation is indeed principally controlled by long-range interstitial carbon diffusion.

One specific detail of the calculated and experimental curves were significantly different. The model predicted higher initial reaction rate when ductile iron under-cooled below austenite/ferrite decomposition temperature than was observed experimentally. At that point in the process, there would be a large ratio of reaction surface to volume of ferrite formed and a low average distance for carbon diffusion. For comparison, the experimentally measured transformation had some incubation period which may be related to nucleation of the initial active carbon layer on the graphite nodule surfaces and Cu segregates near the nodule surface. Also, the model which was used did not calculate the austenite/pearlite transformation because this reaction has a different mechanism and much shorter diffusion distance for carbon. In spite of the latter limitations, the final ferrite/pearlite ratio could be predicted from this model by using an equilibrium transformation temperature known from thermodynamics. The volume of austenite transformed into ferrite was calculated up to reaching that temperature. The diffusion model result, when combined with the thermodynamic estimate was similar to the measured experimental result (Fig. 5).

0

0.2

0.4

0.6

0.8

1

600

650

700

750

800

0 100 200 300 400 500 600

Tra

ns

form

ati

on

Te

mp

era

ture

, 0C

Time, sec

Tcal

Texp

Sexp

Scal

Ferrite

Pearlite

Fig. 5. Comparison of calculated (cal) and experimental (exp) cooling (T) and transformation (S) curves for ductile iron 1. The comparison of the experimental cooling curve and the rate of eutectoid transformation versus time in the two ductile iron compositions which were studied is given in Fig. 6a. The transformation rate versus temperature for the same ductile irons is presented in Fig. 6b. Ductile iron 1 has mostly ferritic structure and a small amount of pearlite that was formed at a lower temperature indicated by a visible second peak on the rate curve versus time. The transformation in this iron occurred without undercooling. In ductile iron 2, with Cu alloy addition, eutectoid transformation moved to a lower temperature region, the pearlite forming reaction occurred with undercooling and had higher rate (shorter reaction time). It should be noted that approximately the same cooling conditions were applied in both cases. When the

Paper 10-083.pdf, Page 4 of 8AFS Proceedings 2010 © American Foundry Society, Schaumburg, IL USA

transformation rate of ductile iron 2 was plotted versus temperature, the rate curve had a typical loop because two reaction rates corresponded to the same temperature (before and after undercooling). Analysis of reaction rate versus temperature allows excluding the possible effect of variations in experimental cooling rate and was used in this study.

0

0.1

0.2

0.3

700

720

740

760

780

800

200 400 600 800

Rat

e, m

in-1

Tem

per

atu

re, 0

C

Time , sec

T (ductile iron 1)

T (ductile iron 2)

Rate (ductile iron 1)

Rate (ductile Iron 2)

a)

0

0.1

0.2

0.3

700 720 740 760 780

Ra

te, m

in-1

Temperature, 0C

Ductile iron 1

Ductile iron 2

b)

Fig. 6 Comparison of cooling and reaction rate curves versus time (a) and reaction rate versus temperature (b) for ductile iron 1 and ductile iron 2. EFFECT OF SEGREGATION OF ALLOYING ELEMENTS AND DISCUSSION Substitutional solute elements that are known to affect carbon activity and diffusivity are Mn, Si and Cu. Segregation patterns of these elements develop during solidification of ductile iron since the spheroidal graphite grows while enveloped in an austenite shell. Since these three elements are substitutional solutes they have diffusivities that are orders of magnitude lower than carbon. These substitutional elements are not readily redistributed during an eutectoid reaction. These results showed that the austenite-to-ferrite eutectoid reaction was mainly controlled by long-range carbon diffusion. Three main factors which could have an effect on ductile iron structure are:

-three-dimensional parameters of geometrical structure (graphite nodule diameter, number, volume) that define an average carbon diffusion distance -cooling rate defines reaction temperature and time -carbon diffusivity which could be affected by substitutional solute elements in the iron-carbon base system. The effects of segregation and redistribution of manganese, silicon and copper solutes on production of ferrite and pearlite matrices in ductile iron were both computationally modeled and experimentally studied using high temperature homogenization and hot plastic deformation techniques. A computational model constituting of a series of concentric austenite shells around a graphite nodule was used for the initial condition to represent segregation of substitutional elements originating in the solidification process. A previous study5,6 showed that copper and silicon have higher concentrations in the layer adjacent to the graphite nodule and manganese is concentrated in inter-cellular region (Fig. 7a). Smoothing the segregation of these elements during 950°C/1742F homogenization is shown in Fig. 7b. The characteristic parameter of homogenization which was calculated is shown on the abscissa as the ratio of concentrations in internal and external shells.

0

0.5

1

1.5

2

2.5

3

3.5

4

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Si,

we

igh

t %

Cu

an

d M

n, w

eig

ht %

Distance from graphite, μm

As-cast

Cu

Mn

Si

a)

0

0.5

1

1.5

2

0 100 200 300 400 500 600 700 800 900

Seg

reg

atio

n

Time, min

C

Cu

Mn

Si

b)

Fig. 7. Initial segregation (a) and calculated diffusion homogenization in ductile iron at 950°C (b).

DI 2

DI 2

DI 1

DI 1

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The calculated segregation was used to design experiments with different holding times which would allow decreasing the segregation of copper, manganese or silicon. The effect of preliminary hot deformation before homogenization heat treatment was also evaluated. The rate of austenite transformation versus temperature during continuous cooling two types of studied ductile iron with spherical graphite and hot deformed graphitic cast iron with elongated graphite is shown in Fig. 8. Hot plastic deformation accelerated the incubation period of ferrite formation in both ductile iron alloys, increasing ferrite area (Fig. 3). This effect could be associated with increasing the reaction surface and decreasing diffusion distance in ductile iron with elongated graphite.

0

0.05

0.1

0.15

0.2

0.25

0

0.2

0.4

0.6

0.8

1

700 720 740 760 780

Rat

e , m

in-1

Tran

sfor

mat

ion

Temperature, 0C

Transformation (not deformed)

Transformation (deformed)

Rate (not deformed)

Rate (deformed)

a)

0

0.05

0.1

0.15

0.2

0.25

0

0.2

0.4

0.6

0.8

1

700 720 740 760 780

Rat

e , m

in-1

Tran

sfor

mat

ion

Temperature, 0C

Transformation (not deformed)

Trandformation (deformed)

Rate (not deformed)

Rate (deformed)

b)

Fig. 8 Effect of hot plastic deformation on austenite transformation in ductile iron 1 (a) and ductile iron 2 (b). Two homogenization temperatures at 975°C/1787F and 930°C/1706F for time intervals from 4 to 30 hours were studied with using ductile iron 2. After applying homogenization, the cooled samples were additionally re-heated at 920°C/1706F for austenite saturation by carbon and cooled at the same cooling rate (0.25 °C/sec) as was used in the above-described previous experiments. Short term heat treatment at high temperature decreased

hardness and increased ferrite content in ductile iron 2 (Fig. 9). According to the modeling result, a significant decrease of copper segregation was expected. Dissolution of copper in the austenite matrix could relieve its effect of impeding carbon diffusion. Decreasing manganese segregation also could have an effect on ferrite formation through increasing carbon thermodynamic activity in the intercellular regions. The true driving force of diffusion is the gradient of chemical activity and not the concentration gradient which serves as a reasonable approximation only in cases of constant activity coefficient. Increasing homogenization time had a reverse effect on austenite decomposition kinetics. Fifteen and twenty four hour treatments increased hardness and decreased ferrite area (Fig. 9). In many cases, the typical ferrite halo around graphite nodules did not form (Fig. 10d). This could be a result of decreasing silicon segregation around graphite nodules and related decrease of carbon activity and consequent decrease of diffusional transport.

0

0.1

0.2

0.3

0.4

710 720 730 740 750 760

Rat

e, m

in-1

Temperature, 0C

1 h

4 h

8 h

23 h

a)

0

20

40

60

160

170

180

190

200

0 5 10 15 20 25

Ferr

ite,

%

Har

dnes

s, H

B

Time, hour

HB

Ferrite

b)

Fig. 9. Effect of homogenization time at 975°C on transformation rate (a), hardness and ferrite area (b) in pearlite/ferrite ductile iron.

Not deformed

Deformed

Not deformed

Deformed

1 h

4 h

8 h

23 h

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a) b)

c) d)

Fig. 10. Microstructure of pearlite/ferrite ductile iron after 1 h (a), 8 h(b) and 16 h (c and d) homogenization at 975°C. Fig. 11 presents effect of homogenization temperature and additional hot deformation on hardness of ductile iron 2. All curves had the minimal hardness values, position of which depended on homogenization temperature while hot plastic deformation accelerated process by reducing segregation. Hot plastic deformation also promotes ferrite formation by decreasing diffusion distances as a result of changing graphite shape factor (Table 2). It is interesting to note that in all cases some increasing hardness and decreasing ferrite area were observed during long time treatment. The position of these critical points well related to the predicted time for decreasing segregation of the elements studied.

140

160

180

200

220

0 5 10 15 20 25 30 35

Har

dn

ess

, HB

Time, hour

930C,not deformed

930C, deformed

975C, not deformed

Fig. 11. Effect of homogenization temperature and time on hardness pealite/ferrite DI.

CONCLUSIONS Experiments and computational modeling were applied to study the kinetics of austenite decomposition in two types of industrial ductile irons. The experimentally measured rate of stable austenite-to-ferrite eutectoid transformation was fitted to an applied carbon diffusion model. In alloyed ductile iron, segregation of substitutional elements (silicon, manganese and copper), that originated during solidification, could control carbon diffusion and ferrite/pearlite ratio. Computational modeling trials to test redistribution of these substitutional solutes in ductile iron showed a significant effect on the eutectoid reaction. It was shown, that homogenization by heat treatment or/and hot deformation could decrease or increase hardness and ferrite/pearlite ratio depending on the diffusivity and thermodynamic properties of the alloying elements. The results could be used in the future for quantitative prediction of the complex effect of inoculation, cooling rate and alloy composition on ductile iron properties. ACKNOWLEDGEMENTS The authors would like to thank metallurgist Craig Sederholm at Rochester Metal Products for supplying ductile iron. REFERENCES 1. Lalich M. and Loper C., “Describing the Eutectoid Transformation in Hyper-Eutectic Ductile Irons”, AFS Trans., vol. 80, pp 238-244 (1973)

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2. Lacaze J. and Gerval V., “Modeling of the Eutectoid Reaction in Spheroidal Graphite Fe-C-Si alloys”, ISIJ International, vol. 38, 7, pp. 714-722 (1998) 3. Lacaze J., Boudot A., Gerval V., Oquab D. and Santos H., “The Role of Manganese and Copper in the Eutectoid Transformation of Spheroidal Graphite cast Iron”, Metallurgical and Material Transactions A, 28A, 10, pp. 2015-2025 (1997) 4. Sertacha J., Larranaga P., Lacaze J., and Insausti M., “Experimental Investigations on the Effect of Copper upon the Eutectoid Transformation of As-cast and Austenitized Spherical Graphite Cast Iron, Proceeding of The Carl Loper Cast Iron Symposium, AFS, WI (2009) 5. Lin B., Chen E. and Lei T., “The Effect of Segregation on the Austemper Transformation and Toughness of Ductile Irons”, Journal of Materials Engineering and Performance, vol. 7(3), 06, pp. 407-419 (1998) 6. Yuam, Y.,Sassa K., Iwai K., Wang, Q., He J., and Asai S., “Copper Distribution in Fe-Cu and Fe-C-Cu Alloys Under Imposition of an Intensive Magnetic Field”, ISIJ International, vol. 48 (7), pp. 901-905 (2008) 7. Fridberg J., Torndahl L. and Hillert M., “Diffusion in Iron”, Jern-kontorets annaler.,153, 6, pp. 263-276 (1969) 8. Franke P. and Inden G., Am Assessment of the Si Mobility and Application to Phase Transformation inSilicon Steels, Z. Metallkd. 88 10, p. 795 (1997) 9. Barlow J.O. and Stefanescu D.M., "Computer-aided Cooling Curve Analysis Revisited", AFS Trans., vol. 105, pp. 349-354 (1997)

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