Modelling Upper and Lower Bainite Trasformation in Steels

ISIJ International, Vol. 45 (2005), No. 2, pp. 221–228

M. AZUMA, N. FUJITA, M. TAKAHASHI, T. SENUMA, D. QUIDORT1) and T. LUNG1)

Steel Products Lab.-1, Steel Research Laboratories, Nippon Steel Corporation, 20-1 Shintomi, Futtsu Chiba, Japan. E-mail: [email protected], [email protected], [email protected] 1) Physical Metallurgy Department, ARCELOR R&D, IRSID, Voie Romaine, BP30320; F-57283 Maizierés-les-Metz Cedex, France. E-mail: [email protected], [email protected] (Received on February 19, 2004; accepted in ﬁnal form on December 13, 2004 )

Bainite is of considerable importance in the design of high strength steels. There are two types of mor- phologies, upper and lower bainite. In upper bainite, cementite forms between adjacent bainitic ferrite plates. In certain steels, however, the cementite reaction is suppressed so that carbon-enriched austenite remains untransformed between bainitic ferrite plates. In lower bainite, cementite also has the opportunity to precipitate within bainitic ferrite plates. In order to model the development of these microstructures, it is necessary to treat the simultaneous formation of both the ferritic and carbide components of the microstructure. A theory has been developed to do exactly this, enabling the estimation of the phase fractions, the cementite particle size and the transition from upper to lower bainite. The results have been compared against experimental data. KEY WORDS: simultaneous reaction; upper/lower bainite; bainitic ferrite; cementite; austenite.

up to 1 000°C and cooled at 50°C/s with helium gas to the 1. Introduction temperatures between 300 and 450°C for isothermal trans- High strength steels are used widely as structural materi- formation to bainite. The austenite grain size was 60 mm als. Their microstructures frequently contain bainite. A after reaustenitisation at 1 000°C. Specimens were etched number of models for the evolution of bainitic microstruc- using 2 vol% nital (nitric acid in methanol) and the mi- tures have been developed1–5) but they either neglect the crostructures were observed using optical, scanning and precipitation of cementite, or treat the whole event as a sin- transmission electron microscopy. Precipitates were charac- gle reaction. It is in principle necessary to permit the simul- terized in a transmission electron microscope (TEM) using taneous formation of cementite and bainitic ferrite, albeit at X-ray energy-dispersive analysis and electron diffraction. different rates, in order to properly deal with upper and Cementite particle sizes were measured directly from TEM lower bainitic microstructures. The latter is distinguished micrographs of the carbon replicas. At least 100 particles from the former by the fact that some cementite is found were analyzed in each case. The carbide shape was found to within the bainitic ferrite plates, whereas in upper bainite be in the form of discs whose thickness and diameters were the carbides only precipitate between the plates. measured. The purpose of the present work was to develop a full ki- netic theory for the bainite reaction and to compare the pre- 3. Modelling dicted phase fractions, particle sizes and the nature of the bainite against experimental data. Figure 1 illustrates the essence of the model, which consists of four processes: 1) Diffusionless transformation of austenite into supersat- 2. Experimental Procedure urated bainite. Table 1 shows the chemical composition of steel, which 2) The escape of carbon evacuation from bainitic ferrite with its high carbon concentration should be amenable to into austenite. the upper to lower bainite transition. The steel was melted 3) Cementite precipitation in bainitic ferrite. using vacuum induction heating followed by casting. The 4) Cementite precipitation in carbon-enriched residual ingot was re-heated to 1 200°C and hot-rolled. The sheets austenite. were homogenized at 1 250°C for 3 d and cooled rapidly These reactions can be handled simultaneously using the with air, resulting in a martensitic microstructure which framework developed by Bhadeshia et al.6–8) Extended vol- proved difﬁcult to machine. The samples were therefore austenitised at 850°C, cooled to 600°C and held for 3 000 s Table 1. The chemical composition (mass%). in order to generate softer pearlite which could easily be machined into cylindrical specimens of 10 mm length and 3 mm diameter. These samples were heated in a dilatometer

austenite grain boundary sub-unit

lower bainite upper bainite microstructure microstructure

cementite carbon evacuation carbon evacuation

cementite

Fig. 1. Schematic illustration of upper and lower bainite microstructure development. Fig. 2. Schematic illustration of the carbon concentration profile at austenite (g)/bainitic ferrite (aB) interface. ume corrections9) were made for the major phases (austenite and bainitic ferrite) but were neglected for the cementite which has a small overall fraction.8) The resulting numeri- tion of temperature.12) cal scheme allowed the matrix composition to be modified The transformation exhibits an incomplete reaction in at each stage using the mean-field approximation.7,8) which growth is arrested well before the austenite achieves its para-equilibrium composition, consistent with diffusion- 3.1. Bainitic Ferrite less growth.10) It is therefore reasonable to assume that once The first stage in the transformation is the nucleation and nucleated, the growth rapidly to a finite volume.1,2) The sub- growth of laths or plates of ferrite in the form of arrays of unit size is as a function of temperature, austenite strength sub-units.10) Consistent with experimental evidence,10) it is and driving force for bainitic ferrite formation under para- 13) assumed that nucleation occurs with the diffusion of car- equilibrium. The width of sub-unit WaB, of which unit is bon, and that each plate of bainite also generates other nu- m m, is given by13): clei by autocatalysis. The nucleation rate IaB is then given → 1) g a 4 by : WaB f(T, Sg, DG ) 0.478 1.20 10 T → 1.2510 4TDG g a2.2010 3Sg...... (6) IaB (1 bVaB)Io ...... (1) where VaB is volume fraction of bainitic ferrite and b is au- where Sg is the strength of austenite in MPa, which has also tocatalysis constant, indicating that the nucleation sites in- been obtained empirically.13) However, the original equation crease in compliance with sub-unit formation. The initial doesn’t include Si effect on the strength, so it was added:14) nucleation rate Io is by classical nucleation theory11): Sg(10.26102 (T298) RT  Qγ   ∆Gγα→ B*  Io N exp C  exp  ...... (2) 0.47105 (T298)20.326108(T298)3 0 h  RT   RT  15.4 (3.6 23Wc 1.3WSi 0.65WMn) ...... (7) where N0 is the initial site density, R and h are gas and g Planck constants respectively and T is temperature in K. QC where Wi is mass% of i-th alloying element. It is assumed is the activation energy for carbon diffusion in austenite be- that the aspect ratio of sub-unit is constant in the tempera- cause the nucleation process has been reported to involve tures between 300 and 500°C. The value is obtained experi- 10) g→aB the diffusion of carbon. DG * is the driving force for mentally to be six so that the length of sub-unit LaB is given bainitic ferrite formation. It is given by12): by:

g → aB g → a DG *DG *GN ...... (3) LaB 6WaB ...... (8) 16 σ 3 ∆Gγα→ * π ...... (4) 3.2. Carbon Evacuation From Bainitic Ferrite to ∆ γα→ 3 Gv Austenite GN3.637(T273.18)2 540...... (5) Since the initial growth event is diffusionless, the excess carbon in the ferrite is expected to partition into the resid- where DG g → a* is the driving force for ferrite nucleation. ual austenite or precipitate as cementite. Since carbon diffu- g → a DG v is the chemical free energy change per unit volume sion in austenite is slower than in ferrite, the former is as- for ferrite nucleation under para-equilibrium.10) s is the in- sumed to control the partitioning. Figre 2 illustrates the terfacial energy per unit area. GN is the critical energy carbon concentration proﬁle at the interface between change to form bainitic ferrite nucleus, which is as a func- austenite (g) and bainitic ferrite (aB). The carbon concen-

g 15) tration in gX C is given by : servations. The diameter Lq in aB is, then, given by: L 5W ...... (14)  Z  q in aB q in aB γγ γαγ   ...... (9) XXCC() X C X Cerfc γ It is reported that cementite within bainitic ferrite has  2()Dt05.  C orientation relationship with bainitic ferrite.19,20) This is g ga ¯ g where X C , X C and XC are carbon concentrations normal caused by decreasing the interfacial energy, which is dealt to g/a B interface in austenite, at the interface under para- as one of fitting parameters in this model. equilibrium and average concentration in austenite respec- g 3.4. Cementite Precipitation in Austenite tively. DC is the diffusion coefficient of carbon in austenite. Z is the distance normal to austenite/bainitic ferrite inter- In upper bainite, cementite grows by a para-equilibrium face. Based on this profile, carbon flux in austenite is de- mechanism from the carbon-enriched residual austen- g 16,17) fined by carbon gradient at g/a B interface. X C increases as ite. Cementite precipitation is modelled by the same carbon evacuation into austenite from bainitic ferrite pro- way as from supersaturated bainitic ferrite as in the previ- ceeds. The carbon evacuation will stop when carbon con- ous section. centration in bainitic ferrite reaches para-equilibrium concentration. Assuming carbon flux balance in both austenite 4. Experimental Results and bainitic ferrite, carbon profile in bainitic ferrite can be given by: The micrographs of the specimens heat-treated at 300°C and 450°C for 1 000 s are presented in Fig. 3. At 450°C, the D g → (∂X g/∂z g D a (∂X aB/∂z) ...... (10) C C C) C C microstructure consists of bainite and retained austenite    Wα  (gR) and cementite precipitates between adjacent two XXααB B () XαγB XαB erfc B  ....(11) C C C C α 05. bainitic ferrite plates, which is a typical upper bainite mi-  4()Dt  C crostructure. At 300°C, the microstructure also consists of aB aBg ¯ aB where X C X C and XC are carbon concentrations nor- bainite and retained austenite but cementite precipitates mal to aB/g interface in bainitic ferrite, at the interface and within bainitic ferrite plates which is lower bainite mi- g average concentration in bainitic ferrite respectively, DC is crostructure. diffusion coefficient of carbon in ferrite. Figure 4 shows TEM micrographs of cementite particle analyzed (a), diffraction pattern from the particle (b) and 3.3. Cementite Precipitation in Bainitic Ferrite EDX analysis for the particle (c) for the carbon replica This model simultaneously deals with several reactions specimens held at 450°C for 1 000 s respectively. As indi- such as cementite precipitation both within bainitic ferrite cated in Fig. 4(c), cementite particle contains Si and Mn. and in austenite, of which nucleation sites depend on the From EDX analysis, Si/Fe and Mn/Fe ratio in cementite are chemical composition and heat treatment conditions. In calculated by the integration of energy dispersion for each lower bainite, cementite precipitates within bainitic ferrite. element and listed in Table 2. Si/Fe and Mn/Fe ratios in ce- Lower bainite tends to be found at low temperatures mentite are essentially equal to those in austenite. This re- where substitutional elements do not diffuse.16,17) It is as- mains the case for the 450°C heat-treatment, justifying the sumed that cementite precipitates under para-equilibrium. assumption of para-equilibrium precipitation. Nucleation is treated by classical nucleation theory.10,11) The nucleation rate I is, then, given by: q in aB 5. Comparison with Experiments 5.1. Parameters for Calculations RT  Qααθ  ∆G → *  C Thermodynamic parameters, such as driving forces for INoθαin B θα in B exp  exp  h  RT   RT  each nucleation, have been obtained using Thermo-Calc.21) The values of diffusion coefficients and activation energies ...... (12) for carbon in both ferrite and austenite listed in Table 322) were used for the calculations. a where Q C is the activation energy for carbon diffusion in There remain two unknown parameters, the initial nucle- a → q ferrite. DG * is the driving force for cementite nucleation site density N0 and the interfacial energy s for each ation under para-equilibrium condition. phase. N0 may be deeply related with grain size and dislo- As indicated in Fig. 3, the shape of cementite particles is cation density, which may work as nucleation site. s should experimentally found to be disc-like. The thickening rate depend on coherency. However, there may be difficulties to can be assumed to be parabolic, so the thickness Wq in aB is obtain physically reliable values of these parameters. For given by18): simplicity, they were treated as fitting parameters with constant values during whole event in this model. Figure 5 ααθαB 2 ()XXDC CC shows calculated changes in volume fractions of bainitic Wθα t ...... (13) in B θα αB θα αθ ferrite (aB) and cementite (q ) with site density of bainitic ()()XXXXCCCC aB ferrite N0 and interfacial energy between aB and austenite ¯ aB aB/g where XC is carbon concentration in bainitic ferrite. (g)s for kinetics at 450°C, where upper bainite is ex- X aq and X qa are the para-equilibrium carbon concentra- aB aB/g C C pected (Fig. 3). As N0 decreases or s increases, the tions at the bainitic ferrite/cementite interface. The aspect overall rate of reaction is reduced. Figures 6 and 7 show ratio is assumed to be constant value of five from TEM ob- calculated changes in volume fractions of aB and q and in

Fig. 3. Microstructures of the specimen heat-treated at 450°C and 300°C for 1 000 s. (a) Optical micrograph at 450°C for 1 000 s, (b) TEM micrograph at 450°C for 1 000 s, (c) Optical micrograph at 300°C for 1 000 s, (d) TEM micrograph at 300°C for 1 000 s.

Table 2. Mole fraction ratios of Si and Mn to Fe in cementite of the specimen heat-treated at 450°C for 1 000 s and steel compositions.

Table 3. Diffusion coefﬁcients and activation energies for carbon used in this model.22)

qaB q/aB netics changes with N0 and s at 300°C are similar to those at 450°C while cementite mainly forms in aB.

A set of N0 and s listed in Table 4 has been chosen and calculations were carried out, comparing with experiments.

5.2. Volume Fraction Changes and Transition Between Fig. 4. TEM micrograph (a), electron diffraction analysis (b) and Upper and Lower Bainite EDX analysis (c) for cementite particles in the specimen Volume fraction changes for each phase during isother- heat-treated at 450°C for 1 000 s. mal heat treatment at 450, 400 and 300°C are presented in Figs. 10, 11 and 12 respectively. cementite particle sizes in g with site density of cementite At 450 and 400°C (Figs. 10 and 11), cementite doesn’t qg q/g N0 and interfacial energy between q and gs for kinet- precipitate in bainitic ferrite, but mainly in austenite, which qg ics at 450°C respectively. Smaller values of N0 or bigger is typical of upper bainite. This is consistent with the TEM values of s q/g retard the formations of aB and q , especially observation shown in Fig. 3(b). Calculated volume fraction after the stasis, and lead to bigger mean sizes of cementite changes of bainitic ferrite, indicated by solid line, are in in g. Figures 8 and 9 show calculated changes in volume good agreement with experiments using dilatometry. fractions of aB and q and in cementite particle sizes with Because cementite forms slower at 400°C than 450°C, qaB site density of cementite N0 and interfacial energy be- transformation stasis, which is typical phenomena of bai- tween q and aB s q/aB for kinetics at 300°C, where lower nite transformation,10) is observed more clearly at 400°C bainite is expected (Fig. 3), respectively. The trends of ki- than 450°C.

aB Fig. 5. Effects of initial nucleation site density of bainitic ferrite N0 (a) and interfacial energy between bainitic ferrite (aB) and austenite (g) s aB/g (b) on volume fraction changes of aB and cementite (q ) in austenite as a function of holding time at 450°C.

qg Fig. 6. Effects of initial nucleation site density of cementite N0 (a) and interfacial energy between cemetite (q ) and austenite (g) s q/g (b) on volume fraction changes of aB and q in austenite as a function of holding time at 450°C.

As shown in Fig. 12, it takes longer for cementite to precipitate during transformation at 300°C, which results in a 5.3. Cementite Particle Size lower bainite microstructure, consistent with Fig. 3(d). Figure 13 shows the change of mean cementite particle Calculated volume fraction change of bainitic ferrite is also diameter in austenite with holding time at 450°C. The cal- in good agreement with experiments. culated result is in reasonable agreement with experiments The model seems to give the correct trends for the simul- in the early stage of isothermal holding. However, in longer taneous reactions, including transition between upper and holding time, the calculated size is greater than observed, lower bainite. implying perhaps that the mean ﬁeld assumption may not be adequate at the late stages of cementite particles precipi-

qg Fig. 7. Effects of initial nucleation site density of cementite N0 (a) and interfacial energy between cemetite (q ) and austenite (g) s q/g (b) on cementite particle size in g as a function of holding time at 450°C.

qaB Fig. 8. Effects of initial nucleation site density of cementite N0 (a) and interfacial energy between cemetite (q ) and austenite (aB) s q/aB (b) on volume fraction changes of aB and q in aB as a function of holding time at 300°C. tation. ment with experiments. Figure 14 shows the diameter change of cementite particle in bainitic ferrite with holding time at 300°C. In the 6. Conclusions early stage of isothermal holding, both volume fraction of bainitic ferrite and number of cementite particles are so A complete bainite kinetics theory which is consistent small that it may be difﬁcult to detect certain number of ce- with the mechanism of transformation has been established. mentite particles experimentally. There are therefore only The model can deal simultaneously with several reactions experiments during prolonged holding stage, where the cal- listed below. culated size of cementite in ferrite is in reasonable agree- 1) Bainitic ferrite formation in austenite.

Fig. 11. Volume fraction changes of each phase during isothermal holding at 400°C.

Fig. 12. Volume fraction changes of each phase during isother- Fig. 9. Effects of initial nucleation site density of cementite qaB mal holding at 300°C. N0 (a) and interfacial energy between cemetite (q ) and austenite (aB) s q/aB (b) on cementite particle size in aB as a function of holding time at 300°C.

Table 4. The parameters used in this model.

Fig. 13. Diameter changes of cementite in austenite during isothermal holding at 450°C.

Fig. 10. Volume fraction changes of each phase during isothermal holding at 450°C.

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