Study of the Austempering Transformation Kinetics in Compacted Graphite Cast Irons

In this work, the phases involved in the transformation austenite ferrite (cid:1) high-carbon austenite in cast irons were assessed by means of Mössbauer spectroscopy and hardness measurements for samples austempered at five different temperatures between 573 and 673 K with two Mn contents. The C content in the high-carbon austenite was found to have a dependence of t 0.40 (cid:2) 0.05 on the austempering time t , which evidences that diffusion of carbon has taken place. The kinetic parameter k determined using the Johnson–Mehl–Avrami equation has a maximum of 3.9 (cid:3) 10 (cid:4) 3 (s (cid:4) 1 ) at (cid:1) 623 K and corrobo-rates that Mn slows the transformation rate.


I. INTRODUCTION
CAST irons are part of a large family of multicomponent ferrous alloys, which solidify in the irregular eutectic system. [1]These alloys can transform according to either the stable iron-graphite system or the so-called "metastable" iron-Fe 3 C system.Although both forms of cast irons have technological significance, the most important one is the stable iron-graphite system because the different graphite morphologies influence the mechanical and physical properties.In the case of the compacted graphite cast iron, the thermal fatigue resistance is the most relevant property. [2]n addition, the austempering treatment can help improve the mechanical properties of the material.The heat treatment starts with an annealing at an austenitizing temperature (T ␥ ), follows with a quenching in a salt bath held at temperatures between 573 and 673 K-this is the austempering step, which can be divided in three stages, and ends with a quenching down to room temperature.
Along the initial stage of austempering (stage I), the parent austenite, ␥ p , transforms into acicular ferrite, ␣, and highcarbon austenite, ␥ hc , (␥ p ␣ ϩ ␥ hc ), attaining a microstructure called ausferrite.The transformation is promoted by the nucleation and growth of ferrite needles that reject carbon atoms into the surrounding austenite.The nucleation is governed by the variation of the volume free energy, which is proportional to the undercooling generated by the difference between the austenitizing and the austempering temperatures. [3]][7][8][9][10][11] Afterward, the transformation stops temporarily and a steadystate period begins (stage II), in which the amounts of acicular ferrite and high-carbon austenite remain approximately constant.Along stage II, also called processing window, the material acquires its optimum mechanical properties.When the metastable high-carbon austenite eventually decomposes → into the more thermodynamically stable ferrite and carbides, stage III starts and the mechanical properties decline, particularly ductility and toughness.
According to the literature on cast irons, [12,13] the growth process during stage I is controlled by the diffusion of carbon atoms through austenite.The process is driven by the difference in the chemical potentials between austenite and ferrite.Consequently, a pileup of carbon atoms results at the ␥ hc /␣ interface.Once the local equilibrium is reached, the mechanism becomes controlled by the diffusion of carbon atoms from the interface into the austenite matrix and the driving force becomes proportional to the carbon concentration gradient. [13]However, it has been suggested that in steels, the growth mechanism of ferrite needles during the bainitic transformation is displacive. [14]In this case, there is a fast redistribution of carbon in austenite before the formation of the needles by a martensitic mechanism. [15]Regardless of which the driving mechanism is, the increase of the carbon content contributes to render the austenite more stable at room temperature and shifts the martensite starting point below room temperature.The fraction of austenite that has not become rich enough in carbon transforms into martensite during the cooling to room temperature.
In this work, we have studied the stage I kinetics of a low-Mn compacted graphite (CG) cast iron austempered at temperatures between 573 and 673 K and compared the results with those obtained for high-Mn cast irons. [16,17]To determine the austempering kinetics, Mössbauer spectroscopy was used to monitor the evolution of the relative fraction of high-carbon austenite.The kinetics was analyzed in the frame of the Johnson-Mehl-Avrami equation determining the thermal dependence of the kinetics parameters k (constant rate of the transformation) and n (time exponent). [18,19]he carbon enrichment of austenite was determined from the Mössbauer spectra using the Fe 8 C 1Ϫy model. [20]Diffusional models [21] were applied to determine the carbon austenite contents enrichment mechanism.Hardness tests and micrographic studies were also performed to assess the advance of the transformation.

II. EXPERIMENTAL
The samples were prepared according to the ASTM A-395 norms as quoted in References 16 and 17.Their composition  is listed in Table I.The samples were austenitized at 1173 K and austemperized for various times at temperatures between 573 and 673 K.The microstructure evolution was followed by Mössbauer spectroscopy, micrography, X-ray diffraction, and microhardness tests.Details of the sample preparation and the measurement conditions have been described in previous works. [16,17]The way in which the volume fractions are obtained from the Mössbauer results is included in the Appendix.

A. Austenitizing Step
Previously to proceed with the austemperization, the samples were subjected to an austenitization step to homogenize the solutes in the austenite phase.Figure 1 shows a typical metallography of the samples after the treatment at 1173 K for 60 minutes.The samples can be seen to have uniformly distributed vermicular graphite precipitates.Also, after the Nital 2 pct attack, no segregation of any phase is noticeable.
Although it is known that different segregation elements, such as Si and Mn, could cause the C composition of the matrix to be inhomogeneous and so influence the carbon solubility in the matrix, the two elements segregate in different ways; while Si segregates inversely to the size of the eutectic cell and reduces the C solubility, Mn segregates into intercellular regions, thus increasing the carbon solubility and delaying the austempering transformation in these regions.These differences can be seen in Figure 2, which illustrates the microprobe analysis results for Mn and Si concentrations in the bulk of the eutectic cell.Consequently, since the austempering times in the current study are relatively short (1 to 30 minutes), the approximation that the austempering transformation takes place in the bulk of the eutectic cells is a good one.

B. The Austempering Kinetics
The austempering kinetics from 573 to 673 K was analyzed through the austempering time evolution of the relative spectral area fraction (f ␥ ) of the Mössbauer austenite signal along stage I.
Figure 3 shows the evolution with austempering time of the Mössbauer spectra of samples with different Mn content, austempered at 623 K for three different times.The six broad lines comprising the sextets of the ferromagnetic phases, i.e., ferrite and martensite, [22] are observed in the spectra together with paramagnetic signals associated to austenite.As the austempering treatment proceeds, the contribution of austenite increases, portraying the progress of the transformation.The ferromagnetic signal is more   The ferrite/martensite subspectra were reproduced using three hyperfine interactions, I 1 , I 2 , and I 3 , whose average parameters were, correspondingly, The first interaction is common to iron probes both in ferrite and martensite without near neighbor C atoms. [22]The remainder magnetic interactions are associated to Fe atoms with C atoms placed at first and second neighbor sites. [22]ue to the lack of resolution in the present velocity range, the austenite subspectra were simulated with only two interactions (a single line and a quadrupole doublet) instead of the three interactions usually associated to the different Fe-C configurations in austenite. [20]This approximation does not affect the areas associated to austenite and ferrite/martensite phases.The normalized relative fraction of each magnetic interaction was found to remain constant during the austempering.However, the microstructure of these phases seems to be different in alloy A than in alloy B, since contribution of I 1 is more important in alloy B (Figure 4), suggesting a higher ferrite percentage.
The evolution of the austenite relative fraction is displayed in Figure 5 for both alloys.The inset in the figure displays the entire austempering kinetics where the three transformation stages can be clearly seen.The setting up of the plateau (stage II) allows attaining the maximum of retained austenite.In the studied temperature range, a sigmoidal behavior of f ␥ is observed along stage I of transformation.The austempering kinetics was also followed by measuring the decrease in hardness, which occurs as a consequence of the reduction of the martensite content with the austempering time.The hardness measurements of Figure 6 are found to accompany the f ␥ evolution.

C. The C Concentration Evolution
To follow the carbon concentration evolution (C ␥ ) with temperature and austempering time in the austenite phase, a series of Mössbauer spectra were taken in the velocity range Ϫ2 to ϩ2 mm/s, where the austenite pattern spreads out in detail.Typical spectra are shown in Figure 7 for the  indicated times austempered at 623 K. Genin's model [20] assuming a Fe 8 C 1Ϫy (0 Ͻ y Ͻ 1) solid solution and a repulsive interaction between carbon atoms-was used to describe the different Fe-C configurations in the austenite lattice.The austenite subspectra were reproduced with three hyperfine interactions associated to (a) iron atoms without near neighbor or next near neighbor C atoms (⌫ 00 ), (b) iron atoms with only one near neighbor C atom (⌫ 10 ), and (c) iron atoms without near neighbor C atoms but with n second neighbor C atoms (with n between 1 and 4) (⌫ 0n ).The results of the fitting procedure are shown in Table II, where the normalized relative fractions f ij are also reported (i, j ϭ number of C atoms first and second neighbors, respectively).
Because the intensity of the ⌫ 00 singlet decreases, the evolution of f ij indicates that the C concentration increases with austempering time.Assuming that the Mössbauer-Lamb factors are the same for all the Fe sites in austenite, the average atomic carbon concentration of this phase can be determined using the occupation probabilities of Reference 20 from the f ij normalized relative fraction.The validity of the results was checked through x-ray diffraction patterns taken on alloy B samples austempered at 623 K.The x-ray patterns, displayed in Figure 8, were analyzed by the Rietveld method. [23]The actual C concentration in the samples was determined combining the lattice parameters (a) extracted from the diffraction patterns with the known a vs composition relation for fcc Fe-C alloys. [22]The resulting latticeparameter and the inferred concentration values for the various alloys are listed in Table III.Within the experimental errors, the carbon concentrations determined by both methods agree.
Once the validity of Genin's model [20,24] was checked by the coincidence of the results of both techniques, the evolution of C ␥ with austempering time and temperature was analyzed.The results are shown in Figure 9, where an increase of the C concentration with austempering time is observed.The average C content is slightly smaller in alloy A, indicating that Mn slows the enrichment of austenite with C.

IV. DISCUSSION
During stage I, the progress of the austenite relative fraction, over the temperature range studied, follows a sigmoidal behavior, as shown in Figure 5, typical of transformations governed by nucleation and growth processes. [18,19]Generally, the development of the microstructure in cast irons and steels is described using the classical Johnson-Mehl-Avrami theory. [18]Consequently, the kinetics of transformation were analyzed with the following equation: [1]   where k is the constant rate of the transformation (which involves both nucleation and growth), while the time exponent n determines the type of process that governs the transformation. [18]The term X(t) is the transformed fraction defined as ␦ is the isomer shift, ⌬ is the quadrupole splitting, ⌫ is the line width, f ij are the normalized fractions of the austenite phase for different configurations of Fe, and f␥ is the total fraction of austenite.Errors are quoted as subindexes.
*Parameter held fixed while fitting.
where f ␥ (0) is the value of austenite at the beginning of austempering; f ␥ (t) and f ␥ (f) are the relative fractions of austenite at time t and after the completion of the transformation, respectively.The kinetics parameters k and n were determined from the linear form of the Johnson-Mehl-Avrami equation and reported in Table IV for the cast iron samples studied.For all temperatures and Mn concentrations, the resulting n values are closer to 1.6 indicating a localized nucleation with decreasing rate and diffusion-controlled growth. [18]In agreement with previous results on cast irons, [12,13] the growth process seems to be controlled by diffusion.The n parameters obtained in CG cast iron can be compared with those reported for austempered ductile irons (ADI) of nodular morphology [12] with several Mn concentrations.The values of the time exponent n obtained in ADI were comprised between 1.07 and 2.09, indicating that the process could be associated with a localized nucleation and a transformation controlled by diffusion.
The variation of the parameter k with the temperature is illustrated in Figure 10, which displays an Arrhenius plot of k as a function of the inverse temperature.The observed maximum in k at 623 K indicates a non-Arrhenius-type dependence and resembles closely the characteristic "C" curve of the time-temperature-transformation (TTT) diagram. [25]he kinetics was also analyzed by using hardness test, determining for each temperature the time needed to reach a hardness 100 units higher than the plateau value from the evolution of hardness with the austempering time (displayed in Figure 6) and the results shown in Figure 11.It is considered that this time indicates that 60 to 80 pct of the transformation has been completed. [26]The shortest time for both alloys is achieved at Ϸ623 K in coincidence with the maximum value of the constant rate k, suggesting a faster kinetics at this temperature.Nevertheless, the low-Mn CG cast iron displayed the tendency to another peak at Ϸ673 K.At the same time, Figure 11 also shows that the times estimated to complete 60 to 80 pct of the transformation are higher for the high-Mn CG cast iron, likely as a consequence of the slowing of the austempering kinetics due to the Mn presence.
The thermal dependence of the constant rate k can be interpreted as a balance between the nucleation and growth processes.The temperature dependence of the nucleation process suggests that as the undercooling ⌬T increases, the volume free energy change increase, promoting a higher nucleation rate. [3]Concurrently, according to references 7 through 9, the growth rate is proportional to the C concentration gradient at the interface ferrite/austenite interface.Hence, at high transformation temperatures, the growth rate is high and the nucleation rate is slow, indicating that this is the temperature that primarily controls the transformation rate.The opposite situation occurs at low temperatures; the reaction becomes mainly dependent on the growth rate, which is determined by diffusion. [9]he constant rate k displays larger values in austempered CG cast irons than in ADI, indicating that the austempering kinetics is nearly one order of magnitude faster in CG. [12] This result suggests that the variation in the constant rate might be ascribed to the morphological differences of the graphite phase because the graphite/matrix interface area is from 2 to 3 times higher in compacted graphite than in nodular graphite.The larger interface area in CG cast iron provides more nucleation sites for ferrite and consequently the nucleation is favored.In addition, ADI exhibits a linear dependence of k with the inverse of the temperature in the narrower range of 623 to 693 K.
The Mn effect on the austempering kinetics is chiefly portrayed by the constant rate k.The results reveal that the constant rate is larger in alloy B than in alloy A. The Mn affects  *The C content was determined using the empirical relation of Ref. 22 for x-ray diffraction and the Fe g C (1Ϫy) model for Mössbauer spectra. [20] both the phase equilibria and the rate at which the transformation occurs. [13]The ability of Mn to slow the carbon diffusion into austenite is well known. [11,27] f this were the only process controlling the current austempering kinetics, it would have to be able to reproduce the variation of the diffusion coefficient with Mn concentration considering the change in carbon-carbon interaction energy of Reference 28.However, for a concentration of Mn 5 times larger in A samples than B samples, only a 3 pct difference would be observed according to the model of reference. [11]This is also contrary to the findings of the k behavior in ADI systems. [12]It could be suggested that the results cannot only be described by the assumptions of the model of Reference 11.In addition, it is known that the driving force is also affected by the Mn content due to the change of the carbon content C o ␥ in the austenite matrix during austenitization and Fig. 11-Austempering temperature vs the time needed to complete 60 to 80 pct of the transformation. [26]Squares and circles correspond to alloys A and B, respectively.the C content (C ␥ ) variation of the high-carbon austenite. [13]his is particularly evident in Figure 12.
The determination of the carbon content (Figure 9) allows analyzing the driving force of the austempering transformation, which has been established [4,5,13] to be proportional to the difference (C ␥ -C o ␥ ), where C ␥ is the maximum carbon contents in the austenite stabilized during austempering and C o ␥ is the austenite carbon contents in the austenite after austenization.The value of C o ␥ can be calculated using the following empirical relationship: [29] The values obtained for C o ␥ were 0.92 and 0.94 wt pct for the alloy A and B, respectively, while the maximum C ␥ can be obtained from the experimental data displayed in Figure 9.The (C ␥ -C o ␥ ) values are higher for alloy B than for alloy A throughout the austempering temperature range studied, as shown in Figure 12.These results suggest that the driving force for alloy B is higher with respect to the high-Mn alloy, in agreement with preceding reported k values.
In a rough approximation, if the carbon enrichment of the austenite phase is controlled by diffusion, the C amount (f ␥ C ␥ ) [4,5,6] incorporated into austenite should be directly related to the diffusion length [21] and consequently proportional to t 0.5 .In the temperature range studied, an average dependence on t 0.40Ϯ0.05was found.The exponent, almost equal to the ideal one, would be an indication that the process is governed by the C diffusion.The slight difference might be explained taking into account the dependence of the diffusion coefficient on the carbon concentration, [3,9] which was considered constant in the present analysis.

V. SUMMARY AND CONCLUSIONS
The kinetics of the austempering transformation in CG with two different Mn concentrations (0.11 and 0.58 wt pct) in the temperature range 573 through 673 K were compared.The kinetics parameters n and k were determined analyzing the results with the Johnson-Mehl-Avrami equation.
The current results of the rate constant k, the hardness tests, and the estimations of the driving force confirm that Mn slows the transformation rate.
The evolution of k with the temperature for highconcentration Mn alloy displays a maximum at Ϸ623 K, suggesting that at low temperatures, the growth process controls the transformation, while at higher temperatures, nucleation becomes the controlling process.This evolution is in close relation with the characteristic "C" curve of the TTT diagrams.
The effect of graphite morphology on austempering kinetics has been evaluated as a function of the constant rate k.The values obtained in austempered CG cast irons are higher with respect to ADI, corroborating the faster kinetics in CG cast iron.
The C content (f ␥ C ␥ ) depends on the Mn concentration but does not depend strongly on the austempering temperature.The results suggest that this process is controlled by the diffusion of C atoms from the ferrite/austenite interface into austenite, as shown by the t 0.40 Ϯ 0.05 dependence of the C content.

Fig. 2 -
Fig. 2-Microprobe analysis results of the Si and Mn concentrations vs the distance along the bulk of the eutectic cell: -alloy A, and ᭹-alloy B.

Fig. 3 -Fig. 4 -
Fig. 3-Mössbauer spectra belonging to alloys A and B austempered at 623 K at the austempering times indicated in the figures.

1 Fig. 5 -
Fig. 5-Evolution of the retained austenite relative fraction, f ␥ , with the austempering time for alloys A and B: ᭹-673 K, and -573 K.The lines are guides for the eye.The inset shows the complete transformation kinetics at 623 K, in which the three stages of austempering transformation are observed.

Fig. 7 -
Fig. 7-Mössbauer austenite pattern obtained using a low-velocity range for alloys A and B austempered at 623 K at the austempering times shown.

Fig. 8 -
Fig. 8-X-ray diffractograms of alloy B austempered at 623 K for the time shown.The bottom bar diagrams indicate from, top to bottom, ferrite, austenite, and martensite phases.

Fig. 9 -
Fig. 9-Austenite carbon concentration as a function of the austempering time and temperature calculated according to the model of Ref. 20: ᭹-673 K, and -573 K.

Fig. 10 -
Fig. 10-Variation of the parameter k with the inverse of the austempering temperature.Squares and circles correspond to alloys A and B, respectively.

Fig. 12 -
Fig. 12-Driving force of the austempering transformation vs temperature.Squares and circles correspond to alloys A and B, respectively.