3. Microstructure and Transformation
Kinetics in Bainitic Steels
Proefschrift
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. dr.ir. J.T. Fokkema,
voorzitter van het College voor Promoties,
in het openbaar te verdedigen op dinsdag 2 december 2008 om 10.00 uur
door
Natalia Vadimovna LUZGINOVA
Master of Science (Physics)
Tomsk State University, Russia
Geboren te Bisjkek, USSR
5. Contents
1 General Introduction ...............................................................................1
1.1 Hyper-eutectoid steel...........................................................................2
1.2 Thermal treatment of hyper-eutectoid steel.....................................3
1.3 Outline of this thesis.............................................................................6
1.4 References ..............................................................................................9
2 Experimental...........................................................................................11
2.1 Materials...............................................................................................12
2.2 Dilatometry and Heat Treatment.....................................................16
2.3 Optical Metallography and Microhardness Measurements ........18
2.4 Electron Microscopy...........................................................................20
2.5 X-Ray Diffraction................................................................................21
2.6 Vibrating Sample Magnetometry.....................................................23
2.7 DICTRA simulations..........................................................................24
2.8 References ............................................................................................26
3 Experimental Characterization of Fe-C-Cr Steel...............................27
3.1 Introduction.........................................................................................28
3.2 Transformation kinetics and morphology of lower bainite.........29
3.3 Retained austenite ..............................................................................35
3.4 Thermal stability of retained austenite............................................37
3.5 Conclusions .........................................................................................44
3.6 References ............................................................................................45
4 Modeling of Lower Bainite Formation in Fe–C–Cr Steel.................47
4.1 Introduction.........................................................................................48
4.2 Reconstructive model.........................................................................50
4.2.1 Growth rate...................................................................................51
v
6. 4.2.2 Nucleation Rate............................................................................53
4.2.3 Overall kinetics for bainitic ferrite formation..........................57
4.3 Displacive model ................................................................................59
4.3.1 Nucleation rate.............................................................................60
4.3.2 Overall kinetics for bainite formation ......................................61
4.4 Discussion............................................................................................63
4.4.1 K1, K2, and t0 parameters in Quidort and Brechet’s
reconstructive model.................................................................................64
4.4.2 λ and κ parameters in Van Bohemen and Sietsma’s
displacive model........................................................................................67
4.5 Conclusions .........................................................................................74
4.6 References ............................................................................................76
5 Effect of Alloying Elements on the Spheroidization Process in
Hyper-eutectoid Steels.....................................................................................79
5.1 Introduction.........................................................................................80
5.2 Design of the spheroidization heat treatment................................82
5.3 Microstructural observations and hardness measurement..........83
5.4 Quantitative analysis of spheroidized microstructures................89
5.5 Discussion............................................................................................91
5.6 Conclusions .........................................................................................95
5.7 References ............................................................................................98
6 Effect of Alloying Elements on Cementite Dissolution in
Hyper-eutectoid Steels.....................................................................................99
6.1 Introduction.......................................................................................100
6.2 DICTRA simulations........................................................................101
6.3 Experimental observations..............................................................111
6.4 Conclusions .......................................................................................119
6.5 References ..........................................................................................120
7 Effect of Alloying Elements on Lower Bainite Formation in Hyper-
eutectoid Steels ...............................................................................................121
vi
9. 1 General Introduction
In this chapter, the description of hyper-eutectoid steel in general and SAE 52100
steel in particular is given in Section 1.1. In Section 1.2 the thermal treatments are
discussed in order to obtain the desired microstructure and properties of hyper-
eutectoid steels. The scope of the thesis is presented in Section 1.3.
10. General Introduction
1.1 Hyper-eutectoid steel
Hyper-eutectoid steel is a steel with a carbon concentration greater than the
eutectoid content (Figure 1.1), which will strongly depend on the concentrations of
other alloying elements. It should be noted that Figure 1.1 shows a quasi-binary Fe–C
phase diagram calculated for steel with 1.5 wt.% Cr, the A1–temperature line splits
up, depending on the other alloying elements. Upon cooling of hyper-eutectoid steel
from the fully austenitic region into the austenite and cementite (γ+Fe3C) region, first
cementite will start to nucleate and grow along the austenite grain boundaries. This
cementite is called pro-eutectoid cementite, as it forms before the eutectoid reaction
takes place. Upon further cooling more cementite will be formed and the
composition of the austenite will reach the eutectoid composition, and as the
temperature is lowered through the eutectoid temperature, all remaining austenite of
eutectoid composition will be transformed into pearlite. Pearlite with pro-eutectoid
cementite along the prior austenite grain boundaries is usually the initial
microstructure in hyper-eutectoid steels after casting and forming.
800
900
1000
1100
1200
1300
0.0 0.5 1.0 1.5 2.0
Carbon content, wt.%
Temperature,K
γ
γ
γ
γ
γ
γ + α
γ
γ
γ
γ
Fe3C
Pearlite
α + Fe3C
Proeutectoid Fe3C
Eutectoid Fe3C
Eutectoid composition
A 1
Figure 1.1. Schematic representation of the microstructures for a quasi-binary iron–carbon
alloy of hyper-eutectoid composition (Fe – 1.0 wt.% C – 1.5 wt.% Cr), as it is cooled from
the fully austenitic region to below the eutectoid temperature [1].
2
11. Chapter 1
The popular bearing steel SAE 52100 (1.01 wt.% C - 1.36 wt.% Cr - 0.32 wt.% Mn
- 0.25 wt.% Si) is one example of hyper-eutectoid steel. SAE 52100 steel possesses
many characteristics favorable to the production of tools, dies, precision components,
through-hardened bearings [2, 3], and it is relatively low in cost. For these
applications, SAE 52100 steel has excellent fatigue properties [4-6], high
compressive/tensile strength, high hardenability and hardness as well as a low level
of both solid and gas inclusions. Such excellent properties cannot be achieved with
the pearlitic microstructure obtained directly after casting and forming. In order to
develop the desired properties in this steel a special heat treatment is required. In the
next section the description of the entire heat treatment process for hyper-eutectoid
steel is presented.
1.2 Thermal treatment of hyper-eutectoid steel
As discussed in Section 1.1 the initial microstructure of hyper-eutectoid steel
consists of pearlite and pro-eutectoid cementite along the prior austenite grain
boundary (Figure 1.1). Such a pearlitic microstructure has a poor machinability,
which is considered to be a disadvantage for industrial applications. In order to
overcome this problem and to reduce the hardness of the material before machining
and further hardening treatment, a spheroidization treatment of cementite particles,
i.e. soft annealing should be performed (Figure 1.2, I). Two types of spheroidization
treatment are often used:
(i) Subcritical spheroidization below the A1–temperature (Figure 1.1), which is
mainly applied for hypo-eutectoid steels. During subcritical annealing of steels with
an initial pearlite structure, the cementite lamellae in pearlite break up into spheroids
driven by the reduction in surface energy [7, 8].
(ii) Intercritical spheroidization above the A1–temperature (Figure 1.1), which is
mainly applied for hyper-eutectoid steels in order to spheroidize and to partially
dissolve the grain boundary cementite [9-12]. During intercritical spheroidization an
3
12. General Introduction
incomplete dissolution of cementite occurs at the austenitisation annealing
temperature and upon slow cooling austenite with fine cementite particles
transforms into a mixture of ferrite and spheroidized cementite by the Divorced
Eutectoid Transformation (DET) reaction.
In the present work the main focus is on the intercritical spheroidization
treatment. The spheroidization annealing of hyper-eutectoid steels is of significant
interest not only for industrial application but also for the new insight that can be
gained on the spheroidization mechanism. Although various studies address the
principles of the intercritical spheroidization and successful empirical recipes have
been developed for certain alloys, many aspects regarding the mechanism of
intercritical spheroidization, the controlling parameters and the effect of alloying
elements remain uncertain.
Figure 1.2. Schematic representation of the heat treatment processes for hyper-eutectoid
steels.
The final desired properties of hyper-eutectoid steels are obtained after
intercritical austenitisation (Figure 1.2, II), when not all of the spheroidized cementite
4
13. Chapter 1
is dissolved, followed either by an isothermal formation of lower bainite (Figure 1.2,
III) or by quenching to room temperature to form martensite. The initial
microstructure before austenitisation consists of ferrite and spheroidized cementite
obtained by the intercritical spheroidization process discussed earlier. The presence
of incompletely dissolved cementite after austenitisation has a beneficial effect on the
rolling contact fatigue life of bearing steels [13]. By properly controlling the amount
of dissolved cementite the required composition of austenite can be obtained in order
to achieve a high hardness and yield strength of the product. Furthermore, the
dissolution process can significantly influence the subsequent bainite hardening [14].
For instance, the presence of a cementite volume fraction of 0.03–0.05 can prevent an
excessive austenite grain growth during austenitisation. It should be noted that
cementite dissolution in austenite has been extensively studied in the literature,
especially for the bearing SAE 52100 steel with 1.5 wt.% Cr [13-20]. However, the
influence of different alloying elements like cobalt and aluminum, as well as the
effect of different chromium contents on the austenitisation parameters, has not been
given much attention.
Many applications of SAE 52100 bearing steel require that the steel is heat-
treated to obtain a lower-bainitic microstructure as the final product (Figure 1.2, III).
By creating the lower bainite microstructure in this steel the advantageous
mechanical properties, such as excellent fatigue life, high strength and hardness, as
well as greater toughness than in fully martensitic steels can be achieved. It should be
noted that in hyper-eutectoid steels the lower-bainitic microstructure can only be
produced isothermally, since during continuous cooling of hyper-eutectoid steels
other transformation products can be formed like upper bainite and pearlite, the
presence of which will be a disadvantage for the mechanical properties of the
hardened components of bearings. Thus, the main disadvantage associated with the
production of steels with a lower bainite microstructure is that it is a time-consuming
process. In order to reduce the production time without loss of the desired
5
14. General Introduction
mechanical properties, a better understanding of bainite formation and a suitable
model of its kinetics are required.
The additions of alloying elements might significantly affect the bainite
formation kinetics in steels. For instance, Cr, the main substitutional alloying element
in SAE 52100 steel is a strong carbide-forming element, which can therefore be
expected to have a strong influence on the lower bainite formation. It is shown in the
literature [21] that even a small amount of chromium retards the reaction of austenite
decomposition into bainite compared with chromium-free steels. Beside this negative
retardation effect Cr has many positive effects in terms of hardenability,
spheroidization [9], and the resistance to decarburization [2]. The additions of other
alloying elements might be beneficial in order to accelerate the bainite formation in
Cr-containing steels by the increase of the free energy change accompanying the
austenite to ferrite transformation [22, 23].
1.3 Outline of this thesis
In this work the attention has been focused on the microstructure evolution and
the phase transformation kinetics in hyper-eutectoid steels, in a commercial SAE
52100 bearing steel and 7 model alloys with different concentrations of chromium,
cobalt and aluminum, but with the carbon content of model alloys being the same as
of a commercial SAE 52100 steel (1 wt.% C).
Chapter 2 describes the experimental equipment and the simulation software
extensively used throughout this thesis to study microstructure and transformation
kinetics in hyper-eutectoid steels. An overview of the material compositions studied
in this thesis is presented and a brief introduction of the experimental techniques is
given. In the present work dilatometry, optical metallography and X-ray diffraction
analysis were used to follow the phase transformation during different heat
treatments. A thermo-magnetic technique was used to study the evolution and the
thermal stability of retained austenite, and electron microscopy to reveal the details
6
15. Chapter 1
of the microstructural morphologies. The application of the DICTRA software [24] to
simulate the cementite dissolution kinetics during the austenitisation and
spheroidization process is discussed.
Chapter 3 focuses on the experimental characterization of the lower bainitic
microstructure of hyper-eutectoid SAE 52100 steel (1.01 wt.% C - 1.36 wt.% Cr - 0.32
wt.% Mn - 0.25 wt.% Si). The microstructure and the kinetics of isothermal formation
of lower bainite, and the evolution and thermal stability of retained austenite in SAE
52100 steel, is investigated using dilatometry, optical microscopy, electron
microscopy, X-ray diffraction and a thermo-magnetic technique.
Chapter 4 presents two different physical approaches to model the formation of
lower bainite in high carbon and chromium SAE 52100 steel. In the first model, a
reconstructive approach is used. Nucleation of bainitic laths is considered in the
general framework of the classical nucleation theory and a diffusion-controlled
growth model is used. In the second model, displacive growth of bainitic ferrite is
assumed, where the change in the bainite volume fraction is governed by the
nucleation rate. Model calculations are compared to the experimentally obtained
lower bainite fractions for SAE 52100 steel. The advantages and disadvantages of the
proposed models are discussed, and the appropriate model is chosen for the
description of the overall isothermal lower bainite formation in high-carbon steels.
In Chapter 5 the effect of alloying elements on the cementite spheroidization
process in hyper-eutectoid steels is investigated experimentally and theoretically. A
spheroidized structure in high carbon steel is obtained using an intercritical
spheroidization process, after which during the slow cooling of austenite with fine
cementite particles a divorced eutectoid transformation (DET) reaction occurs. A
criterion for the occurrence of the DET reaction, as opposed to pearlite formation, is
defined for the Cr-containing steels, and a reasonable agreement is found between
the criterion and the experimental results. This DET criterion is further extended for
steels with other alloying elements, like Co, Al and Mn.
7
16. General Introduction
Chapter 6 shows the effect of Cr, Co and Al as alloying elements on the
cementite dissolution during austenitisation in hyper-eutectoid steels with 1 wt.% C.
The dissolution of cementite is investigated with dilatometry, optical microscopy and
scanning electron microscopy. The austenitisation process parameters are chosen
from the results of DICTRA simulations, where the experimentally observed initial
size of cementite particles is taken into account. A comparison between results
calculated with DICTRA and experimental results for the kinetics of cementite
dissolution in hyper-eutectoid steels is discussed.
Finally, in Chapter 7 an investigation of the effect of alloying elements on lower
bainite formation in hyper-eutectoid steels is performed using dilatometry, scanning
electron microscopy and X-ray diffraction measurements. The displacive model is
successfully applied to describe the kinetics of lower bainite formation, including the
effects of both isothermal transformation temperatures and alloying elements.
8
17. Chapter 1
1.4 References
1. W.D. Callister: Materials Science and Engineering: An Introduction, 7th edition,
Wiley, New York, 2006, p. 298.
2. J.M. Beswick: Met. Trans. A, 1987, vol. 18A, pp. 1897–1906.
3. Y.B. Gou, C.R. Liu: J. Manuf. Sci. Eng., 2002, vol. 124, pp. 1–9.
4. G.E. Hollox, R.A. Hobbs, J.M. Hampshire: Wear, 1981, vol. 68, pp. 229–240.
5. F.C. Akbasoglu, D.V. Edmonds, Met. Trans. A, 1990, vol. 21A, pp. 889–893.
6. J.M. Hampshire, J.V. Nash, G.E. Hollox, in: J.J.C. Hoo (Ed.), Rolling Contact Fatigue
Testing of Bearing Steels, ASTM (American Society for Testing Materials),
Philadelphia, 1982, pp. 47–66.
7. S. Chattopadhyay, C.M. Sellars: Metallography, 1977, vol. 10, pp. 89–105.
8. D. Hernandez–Silva, R.D. Morales, J.G. Cabanas–Moreno: ISIJ Int., 1992, vol. 32,
pp. 1297–1305.
9. J.D. Verhoeven: Met. Mater. Trans. A, 2000, vol. 31A, pp. 2431–2438.
10. G.M. Michal, M.D. Novak: Austenite Formation and Decomposition, eds. E.B. Damm,
M.J. Merwin, Minerals, Metals and Materials Society, Warrendale, PA, 2003, pp.
397–413.
11. W. Hewitt: Heat Treatment of Metals, 1982, vol. 3, pp. 56–62.
12. T. Oyama, O.D. Sherby, J. Wadsworth, B. Walser: Scripta Met., 1984, vol. 18, pp.
799–804.
13. C.A. Stickels: Met. Trans. A, 1974, vol. 5, pp. 865–874.
14. L. Zhao, F.J. Vermolen, A. Wauthier, J. Sietsma: Met. Mat. Trans. A, 2006, vol. 37,
pp. 1841–1850.
15. J.M. Beswick: Met.Trans. A, 1978, vol. 18A, pp. 1897–1901.
16. J.M. Beswick: Met.Trans. A, 1984, vol. 15A, pp. 299–306.
17. K. Nilsson: Trans. ISIJ, 1971, vol. 11, pp. 149–156.
18. J. Epp, H. Surm, O. Kessler, T. Hirsch: Acta Mater., 2007, vol. 55, pp. 5959–5967.
19. E.L. Brown, G. Krauss: Met. Trans. A, 1986, vol. 17A, pp. 31–36.
9
18. General Introduction
10
20. C.A. Stickels, A.M. Janotik: Met. Trans. A, 1980, vol. 11A, pp. 467–473.
21. E.S. Davenport, E.S. Bain, N.J. Kearny: Trans. Met. Soc. AIME, 1930, vol. 90, pp.
117–154.
22. C. Garcia-Mateo, F.G. Caballero, H.K.D.H. Bhadeshia: ISIJ Int., 2002, vol. 43, pp.
1821–1825.
23. M. De Meyer, D. Vanderschueren, B.C. De Cooman: ISIJ Int., 1999, vol. 39, pp.
813–822.
24. ThermoCalc & DICTRA software: http://www.thermocalc.com.
19. 2 Experimental
Chapter 2 gives a description of the experimental equipment and the simulation
software extensively used throughout this thesis to study microstructure and
transformation kinetics in hypereutectoid steels. An overview of the materials
studied in this thesis is presented in Section 2.1. In Sections 2.2 through 2.6 a brief
introduction is given to the experimental techniques. Dilatometry (Section 2.2),
Optical Metallography (Section 2.3) and X-ray Diffraction analysis (Section 2.5) were
used to follow the phase transformation progress during different heat treatments.
Electron Microscopy (Section 2.4) was used to investigate the microstructure
morphologies, and Vibrating Sample Magnetometry (Section 2.6) to study the
evolution and the thermo-stability of retained austenite. The background on the
DICTRA calculations used to simulate cementite dissolution during the
austenitisation process is discussed in section 2.7.
20. Experimental
2.1 Materials
Materials studied in the present work were a commercial SAE 52100 steel (as a
base material) and 7 model high-carbon alloys. The composition of SAE (AISI) 52100
steel, in the literature also known as 100Cr6 (Germany), GCr15 (China), SUJ-2
(Japan), EN-31 (UK), ШХ15 (Russia), is listed in Table 2.1. The as-received SAE 52100
steel had a microstructure consisting of a ferrite volume fraction of 0.85 and a
spheroidized-cementite volume fraction of 0.15. The above mentioned spheroidized
microstructure was obtained (after casting and cold forming) by a soft-annealing
treatment, which was austenitisation at 1093 K for one hour, slow cooling to 963 K at
a rate of 10 K/hour, and air cooling to room temperature (Figure 2.1 (a)).
Table 2.1. Alloy composition of SAE 52100 steel in wt.%.
Fe C Si Mn Cr Ni Cu Mo Al S P
bal. 1.01 0.25 0.32 1.36 0.16 0.12 0.04 0.03 <0.02 <0.01
Besides SAE 52100 steel 7 model high-carbon alloys were studied in the
present thesis. The model steel compositions are listed in Table 2.2, where 1.5Cr steel
has a similar composition as the commercial SAE 52100 steel (Table 2.1). All alloys
were manufactured at the Corrosion and Metals Research Institute, Sweden by chill
casting under inert conditions using high–purity alloying metals, resulting in ingot
dimensions of 40×40×160 mm3. After casting, a chemical analysis of each ingot was
made and the ingots were further treated as shown in Figure 2.1 (b). Hot isostatic
pressing (HIP) was performed at a temperature of 1420 K and under a hydrostatic
pressure of 100 MPa for 4 hours, followed by furnace cooling to 1070 K at an average
rate of 12 K/min and cooling to room temperature at an average rate of 35 K/min, to
obtain a pore-free and homogenized structure. The microstructure of all model alloys
after HIPing consisted of pearlite and pro-eutectoid cementite at the prior austenite
grain boundaries.
12
21. Chapter 2
300
600
900
1200
0 2 4 6 8 10 12 14
Time, hours
Temperature,K
10 K/hour
Austenitization
for 1 hour
(a)
300
600
900
1200
1500
0 1 2 3 4
Time, hours
Temperature,K
5
12 K/min
Austenitization and HIP
for 4 hours
35 K/min
1420 K
1070 K
(b)
Figure 2.1. (a) – a soft-annealing treatment (cementite spheroidization) of SAE 52100 steel.
(b) – the HIP treatment of the model high-carbon alloys after casting.
All thermodynamic calculations for the investigated alloys were performed
using the ThermoCalc software (TCCR version, TCFE2 database) [1]. Figure 2.2
presents the quasi-binary Fe-C phase diagrams for steels with different Cr (Figure 2.2
(a)), Co (Figure 2.2 (b)) and Al (Figure 2.2 (c)) contents. Three-phase regions (ferrite,
austenite and cementite), which split A1 into two lines, are observed in the phase
diagrams for all steels. In this work lower and upper A1–temperatures are presented
as A1 and A′1, respectively.
13
23. Chapter 2
Characteristic temperatures and eutectoid compositions from the phase diagram are
listed in Table 2.3 and it can be seen that the addition of alloying elements changes
the phase equilibria for these steels significantly. The effect of alloying elements on
the phase equilibria will be discussed in detail in the Chapters 5 and 6.
Table 2.2. Alloy composition of model high carbon steels in wt.%.
Steel name Fe C Si Mn Cr Co Al
0.5Cr bal. 1.04 0.25 0.30 0.53 -- --
1.5Cr bal. 1.05 0.25 0.34 1.44 -- --
2.5Cr bal. 1.04 0.27 0.31 2.39 -- --
3.5Cr bal. 1.02 0.27 0.30 3.38 -- --
1Co-1.5Cr bal. 1.05 0.26 0.32 1.36 1.02 --
2Co-1.5Cr bal. 1.04 0.25 0.31 1.36 2.05 --
1Al-1Co-1.5Cr bal. 1.06 0.25 0.31 1.38 0.98 1.04
Table 2.3. Characteristic temperatures and eutectoid compositions.
Steel name A1, K A’1, K Acm, K c
eutw , wt.%
0.5Cr 1005 1010 1135 0.68
1.5Cr 1010 1015 1170 0.57
2.5Cr 1015 1025 1200 0.46
3.5Cr 1020 1030 1220 0.37
1Co-1.5Cr 1015 1025 1160 0.58
2Co-1.5Cr 1020 1030 1170 0.59
1Al-1Co-1.5Cr 1055 1160 1280 0.68
15
24. Experimental
2.2 Dilatometry and Heat Treatment
A Bähr 805 dilatometer was used to study the length change (dilatation) of the
specimen during a heat treatment. The monitoring of the dilatation is a commonly
used method to study phase transformations in steels. The cylindrical massive
specimens for dilatometry experiments were prepared with a size of 10 mm in length
and 5 mm in diameter. A specimen is placed in the dilatometer between two quartz
rods with a thermocouple spot-welded in the middle of specimen in order to control
the temperature. In the dilatometer the specimen is heated by induction. Sufficiently
high cooling rates (up to 85 Ks-1) are obtained by helium gas quenching. A
description of the phase transformations investigated in the present work is
presented in Chapter 1.
In the experiments to study the spheroidization process specimens were heated
to the austenitisation temperature Taus = 1040–1110 K at a rate of 120 K/min (Figure
2.3 (a)). After holding for 2 hours at the austenitisation temperature the specimens
were cooled at a cooling rate of 15 K/hour to 10 K above the A′1 temperature,
followed by cooling at 5 K/hour to 955 K, and further air cooling to room
temperature. The use of the dilatometer enables the recording of the change in length
and thus the progress of the phase transformations during heating, cooling and
isothermal holding can be followed (Figure 2.3 (b)). In order to perform the
spheroidization heat treatment of a large number of specimens a box furnace was
used. To prevent oxidation and decarburization of the material the specimens were
placed in quartz tubes filled with helium and sealed.
In the experiments to study the kinetics of cementite dissolution during
austenitisation, specimens were heated to the higher austenitisation temperature
Taus = 1090–1170 K at a rate of 120 K/min and austenitized for different times
(0-30 min), followed by quenching to room temperature (Figure 2.4, I).
16
25. Chapter 2
950
1000
1050
0 5 10 15
Time, hours
Temperature,K
A' 1
T aus =1040 - 1110 K
15 K/hour
5 K/hour
2 K/s
(a)
60
70
80
90
100
110
120
0 5 10
Time, hours
ChangeinLength,μm
15
80
90
100
110
120
0.05 0.10 0.15
Ferrite transformation
Austenitization
(b)
Figure 2.3. (a) – an example of a spheroidization heat treatment and (b) – the
corresponding change in length.
In the experiments to study the microstructural evolution and the kinetics of
lower bainite formation (Figure 2.4, II) specimens after austenitisation at Taus = 1090–
1170 K for 30 min were quenched to the bainite holding temperatures TLB = 480–
570 K, and annealed for different times (0–120 min), followed by quenching to room
temperature. The dilatation was recorded both during austenitisation and during the
lower bainite formation heat treatments (Figure 2.4 (b)).
All specimens for the further analysis described in Sections 2.3–2.6 were cut
from the dilatometry specimens.
17
26. Experimental
300
500
700
900
1100
1300
0 20 40 60 80 100 120 140 160
Time, min
Temperature,K
T LB = 483 - 573 K
T aus = 1093 - 1173 K
(I) (II)
(a)
-20
20
60
100
140
0 20 40 60 80 100 120 140 160
Time, min
ChangeinLength,μm
(I)
(II)
(b)
Figure 2.4. (a) – an example of (I) the austenitisation heat treatment followed by (II) the
formation of lower bainite. Dashed lines show the interrupt quenching after partial
transformation. (b) – the corresponding change in length.
2.3 Optical Metallography and Microhardness Measurements
A metallographic examination of each specimen was made with optical
microscopy. The microstructures were quantitatively analyzed using AnalySIS Image
Processing Software. To obtain a good contrast for the optical analysis of the
spheroidized microstructure and the microstructure after partial cementite
dissolution during the austenitisation process, the specimens were pre-etched in 5%
18
27. Chapter 2
Nital followed by Klemm’s tint etching (50 ml of saturated aqueous sodium
thiosulfate solution and 1 g of sodium disulfide). After etching cementite appears in
white, and ferrite and martensite appear in black or dark brown, enabling a reliable
setting for the threshold value for further quantitative analysis of the size and the
volume fraction of cementite (Figure 2.5).
(a)
0.E+00
5.E+04
1.E+05
2.E+05
0 30 60 90 120 150 180 210 240
Grey value
Numberofpixels
Black White
CementiteFerrite
Threshold
(b)
Figure 2.5. (a) – an example of a spheroidized microstructure after Klemm’s etching, (b) –
grey value distribution of the microphotograph of a spheroidized microstructure.
The prior austenite grain size was determined after etching in a saturated
picric acid solution with additions of HCl and the “Teepol” wetting agent [2]. The
analysis of the austenite grain size was based on the concept of the equivalent
diameter, where the equivalent diameter of an austenite grain is the diameter of the
circle that contains the same area as the austenite grain.
To observe the lower bainite microstructures, specimens were etched with 2%
Nital for 10 s; after the etching retained austenite and martensite were unaffected
(light), whereas lower bainite appeared black.
The Vickers hardness of all specimens was measured using the Buehler
automatic microhardness testing system OmniMent MHT 7.0 Rev.1 with a load of
19
28. Experimental
1 kg. Every hardness value presented in this work is the average of at least five
measurements.
2.4 Electron Microscopy
Scanning Electron Microscopy (SEM) measurements of SAE 52100 steel were
performed at TU Delft with a JSM-6500F Field Emission Scanning Electron
Microscope to characterize the overall morphology. Energy Dispersive X-ray
Spectroscopy (EDS) was used for chemical analysis of cementite particles. All
micrographs were obtained using a beam of 15 keV electrons. The microstructures
were examined after etching for 10 s in 2% Nital solution.
Scanning Electron Microscopy (SEM) measurements of the 7 model
hypereutectoid steels (Table 2.2) were performed at Corus with a Zeiss Ultra 55 Field
Emission Gun Scanning Electron Microscope to characterize the overall morphology.
The microscope was equipped with an in-lens electron optic system, which allows an
optimal recovery of secondary electrons and results in enhanced resolution.
Specimens were hot mounted in Polyfast resin, which is electrically conductive with
low emission in the vacuum chamber during examination. All micrographs were
obtained using a beam of 15 keV electrons. The microstructure details were examined
after etching for 5 s in 1% Nital solution.
Transmission Electron Microscopy (TEM) measurements were performed at TU
Delft using Philips CM30T microscope operating at 300KV. The bright field (BF) and
the selected area electron diffraction (SAED) techniques were used in order to
characterize the microstructure of lower bainite in SAE 52100 steel. Thin foils were
prepared for TEM study as follows: (1) specimen was cut by a diamante saw in slices
of approximately 1 mm thickness, (2) cut foils were ground and polished to 0.1 mm
thickness, (3) circular pieces of the foils were cut and placed on the TEM copper ring
and the final thinning was performed by conventional Ion Milling technique using
Gatan 691 Precision Ion Polishing System (PIPS).
20
29. Chapter 2
2.5 X-Ray Diffraction
X-ray diffraction measurements were carried out at room temperature on a
Bruker D8-Advance diffractometer equipped with a Vantec Position Sensitive
Detector (PSD). CoKα radiation was used and 2θ scans were performed with step
time of 0.6 s and step size of 0.025º. 2θ values were ranged from 40° to 130°,
containing four ferrite, four austenite and a set of cementite peaks. Typical XRD
scans are shown in Figure 2.6.
The EVA software suite (DIFFRACplus Evaluation Package, version 2.2) was
used to analyze the diffraction peaks. The volume fraction of retained austenite was
determined from the integrated intensities of austenite and ferrite peaks using the
method described in [3] with:
( )
( )∑ ∑
∑
++
=
α γ
γ
θγγ
γ
αα
α
γγ
γ
γ
n n hklhklhklhkl
n hklhkl
fRI
n
RI
n
RI
n
f R
1 1
1
11
1
(2.1)
where θf is the volume fraction of all carbides in the material, γ
hkl
I and are the
integrated intensities of austenite and ferrite peaks, respectively; nγ and nα are the
numbers of {hkl} lines for which the integrated intensities have been measured;
and are theoretical intensities [
α
hkl
I
γ
hkl
R
α
hkl
R 3] presented in Table 2.4.
Table 2.4. Theoretical line intensities (R-values) for the ferrite and austenite phases in
steel for Co radiation (λCo=1.79021Å) [3].
{hkl}phase {111}γ {200}γ {220}γ {311}γ {110}α {200}α {211}α {220}α
R 85.2 37.0 20.4 30.1 115.3 14.8 32.4 15.4
21
30. Experimental
0
50
100
40 60 80 100 120
2θ (degrees)
Intensity(CPS)
{110}α
{200}α
{211}α
{220}α
θθ
(a)
0
50
100
40 60 80 100 120
2θ (degrees)
Intensity(CPS)
{111}γ
{110}α
{200}γ
{200}α
{311}γ
{220}γ
{211}α
{220}α
θ
θ
(b)
Figure 2.6. Typical diffraction spectra of SAE 52100 steel. (a) – a soft-annealed specimen
(only diffraction peaks of ferrite (α) and cementite (θ) are observed), (b) – a specimen
annealed for 45 minutes at 503 K and quenched to room temperature (diffraction peaks of
ferrite (α), cementite (θ) and austenite (γ) are present). The intensity is shown in counts per
second (CPS).
The austenite lattice parameters (aγ) were calculated from the {311}γ austenite
diffraction peak [4]. The carbon content of austenite ( γ
cw ) in wt.% was calculated
from the austenite lattice parameter using the relationship:
22
31. Chapter 2
γ
γ 3.555 0.44 ca = + w (Å), (2.2)
which is considered to most reliably describe the variation of the retained austenite
parameter with carbon content [5]. The room temperature lattice parameter of
3.555 Å is given for pure Fe (austenite).
2.6 Vibrating Sample Magnetometry
Cylindrical specimens for the magnetization measurements with a size of 2 mm
in length and 2 mm in diameter were machined from dilatometry specimens using
an electro-discharging machine (EDM). All magnetic measurements were performed
in a LakeShore 7307 Vibrating Sample Magnetometer (VSM). Before experiments the
VSM was calibrated with a standard NIST nickel specimen. A typical magnetization
curve at room temperature for as-received SAE 52100 steel is presented in Figure 2.7.
To obtain the saturation magnetization values, Ms, the high-field part of the
magnetization curve was fitted to the equation described in [6]:
2
1s
a b
M M
H H
⎛ ⎞= − −⎜
⎝ ⎠
⎟ , (2.3)
where M is the magnetization at the applied magnetic field H, Ms the saturation
magnetization, a and b the fitting parameters.
To study the thermal stability of retained austenite the thermal cycles from 300 K
to 1173 K (high temperature magnetic experiment) and from 300 K to 10 K (low
temperature magnetic experiment) under a constant magnetic field of 0.79×106 A/m
(1 Tesla) were performed. Stepwise heating and cooling were carried out and the
magnetization was measured one minute after the set temperature was reached. The
high temperature magnetic experiments were performed in a High Temperature
23
32. Experimental
Oven (Model 73034) at a heating rate of 5 K/min and a cooling rate of 10 K/min. The
low temperature magnetic experiments were performed in a Closed Cycle
Refrigerator (Model 73018) at cooling and heating rates of 10 K/min.
-1.5
-0.5
0.5
1.5
-1.5 -0.5 0.5 1.5
Field, A/m x 10
-6
Magnetization,A/mx10
-6
Figure 2.7. Magnetization curve for as-received SAE 52100 steel.
2.7 DICTRA simulations
During the austenitisation processes described in Section 2.2 of this chapter
cementite dissolution in austenite occurs. In order to simulate the cementite
dissolution the DICTRA [1, 7] software package was used. In the DICTRA
simulations the cementite particle was spherical and the initial compositions of
cementite and austenite were inherited from the spheroidized cementite and ferrite.
It was assumed that during heating ferrite rapidly transforms into austenite without
any cementite being dissolved. This assumption is approximative, but it has been
applied before in the literature [8] and is considered to be realistic in case of high
carbon steels and sufficiently high austenitisation temperatures. It can be envisaged
that the initial stage of the dissolution process does actually partly occur during the
heating step. In DICTRA local equilibrium is assumed at the moving
24
33. Chapter 2
austenite/cementite interface. It should be noted that in DICTRA the dissolution of
only one spherical particle in a spherical volume element (austenite) is actually
simulated (Figure 2.8), which has been shown to be a good assumption [9] to
describe the change in volume fraction of cementite during the austenitisation
process.
Figure 2.8. Schematical representation of the system used in the DICTRA simulations. θ is
cementite, γ is austenite, Rtotal is a total radius of the system, Rθ is the cementite particle
radius, Rγ is the austenite radius.
The initial particle size was set to the average particle size observed
experimentally after the spheroidization heat treatment. The volume fractions of the
phases were determined by assuming that only the substitutional elements
contributed to the system volume and the initial state (the austenite size and the
initial compositions of phases) was obtained from ThermoCalc at a temperature of
A1 – 10 K. The effect of the surface tension was neglected, because the particle
diameter remained larger than 0.15 μm in all simulations.
25
34. Experimental
26
2.8 References
1. ThermoCalc & DICTRA software: http://www.thermocalc.com.
2. J. van der Sanden: SKF Report, 1978, № NL77M524.
3. C.F. Jatczak, J.A. Larson, S.W. Shin: Retained Austenite and Its Measurements by X-
Ray Diffraction, SAE Inc., Warrendale, 1980, p. 12.
4. B.D. Cullity: Elements of X-Ray Diffraction, Addison–Wesley Inc., Reading, 1978, p.
359.
5. N. Ridley, H. Stuart, L. Zwell: Trans. Met. Soc. AIME, 1969, vol. 245, pp. 1834–
1836.
6. J.W. Cahn, P. Haasen: Physical Metallurgy, Elsevier, Amsterdam, 1983, p. 2558.
7. A. Borgenstam, A. Engstöm, L. Höglund, J. Ägren: J. Phase Equilibria, 2000, vol. 21,
pp. 269–280.
8. M. Hillert, K. Nilsson, L-E. Törndahl: J. Iron and Steel Inst., 1971, vol. 209, pp. 49–
66.
9. Z-K. Liu, L. Höglund, B. Jönsson, J. Ägren: Met. Trans. A, 1991, vol. 22A, pp. 1745–
1752.
35. 3 Experimental Characterization of
Fe-C-Cr Steel
In this chapter, the kinetics of isothermal formation of lower bainite and the
evolution and thermal stability of retained austenite in SAE 52100 steel, 1.01C-1.36Cr-
0.32Mn-0.25Si (wt.%), is investigated with dilatometry, optical microscopy, electron
microscopy, X-ray diffraction and thermo-magnetic measurements. It is
demonstrated that an increase in carbon content of austenite with bainitic holding
time occurs, as a result of which the retention of a significant amount of austenite at
room temperature takes place in SAE 52100 steel. The thermal stability of retained
austenite is investigated. The temperature at which retained austenite starts to
decompose to ferrite and carbides upon heating varies with bainitic holding time.
The transformation of austenite to martensite during cooling to 10 K is found to be
not complete, and a large amount of austenite remains untransformed.
36. Experimental Characterization of Fe-C-Cr Steel
3.1 Introduction
High-carbon and chromium steels, for instance SAE 52100 steel, are widely used
in the bearing industry due to a combination of excellent fatigue life and high
strength. Most of the applications of SAE 52100 bearing steel require that the steel is
heat-treated to obtain either a martensitic or a lower-bainitic microstructure as the
final product. The important advantage of the production of lower bainite over
martensite is to gain greater toughness at the same hardness level. A hard martensitic
or lower bainitic microstructure leads to a reasonable bearings lifetime due to high
strength and high resistance to fatigue [1, 2]. When bearings are used in water-
containing environments, however, the martensitic microstructure is sensitive to
hydrogen-induced cracking, since twin boundaries in high carbon martensite are
susceptible to hydrogen adsorption and crack nucleation. As an alternative, lower-
bainite microstructures are produced, which give a similar fatigue life as a
martensitic one under good lubricant conditions, whereas in water-containing
environments fully lower-bainitic bearings show an increased fatigue life [2, 3].
When the service conditions of bearings are in the presence of water the lower
bainitic microstructure is therefore often desired despite the fact that the
manufacture of the steel with lower-bainitic microstructure is more expensive due to
an extra time-consuming isothermal holding.
Bainitic or martensitic microstructures are often obtained together with retained
austenite (γR). The amount and the morphology of γR in bearings is an important
issue. Austenite can often be retained in two forms: blocky and film types [4, 5]. The
former is relatively unstable, which significantly influences the dimensional stability
of the material [6]. The film austenite, located between bainitic ferrite plates, is very
fine and stable due to the small dimensions and the carbon enrichment. Such a fine
microstructure consisting of bainitic ferrite and film austenite gives an excellent
combination of strength and toughness in high Si steels [5] and, moreover, the
retained austenite islands can act as additional obstacles for crack propagation [7].
28
37. Chapter 3
The austenite decomposition into lower bainite results in the formation of a
microstructure consisting of ferritic plates and carbides within ferrite. To create a
lower-bainitic microstructure the heat treatment of SAE 52100 steel consists of a
partial austenitisation at temperatures of 1123–1143 K followed by the isothermal
holding at lower-bainitic temperatures (483–573 K). It should be noted that in this
steel the lower-bainitic microstructure cannot be produced by continuous cooling
without the formation of other transformation products like upper bainite and
pearlite, the presence of which will be a disadvantage for the mechanical properties
of the hardened components of bearings. The mechanical properties of SAE 52100
steel after lower-bainitic treatment, including fatigue life, are well studied in the
literature [1-3]. However, the details of the kinetics of lower bainite formation in
hyper-eutectoid steel and the role of retained austenite, which is of essential
importance for the use and application of the material, have not been reported in
much detail. To obtain a better understanding of the lower bainite formation a
dilatometry study together with metallographic observations, electron microscopy
and X-ray diffraction analysis has been performed (Section 3.2). The evolution of
retained austenite (Section 3.3) with bainitic holding time and its thermal stability
(Section 3.4) upon heating and cooling has been studied using X-ray diffraction and
thermo-magnetic measurements.
3.2 Transformation kinetics and morphology of lower bainite
In order to study the morphology and the evolution of the microstructure in
SAE 52100 steel during lower bainite hardening, partial transformation was
performed in the temperature range 480–570 K for different times, followed by
quenching to room temperature. The experimental transformation–temperature–time
diagram for the lower bainite formation in SAE 52100 steel is shown in Figure 3.1.
29
38. Experimental Characterization of Fe-C-Cr Steel
450
500
550
600
0.1 1 10 100 1000
Time, min
Temperature,K
Mstart=470 K
austenite +
5% cementite
lower bainite +
5% cementite
2% 90%50%
Figure 3.1. TTT diagram for lower bainite formation in SAE 52100 steel after
austenitisation at 1133 K for 30 min.
It should be noted that the initial microstructure of SAE 52100 steel after
austenitisation and before bainitic hardening consists of austenite and 5%
spheroidized cementite [8]. The bainite fractions are calculated from dilatometry
results using the lever rule and confirmed by optical microscopy. The martensite
starting temperature is obtained from dilatometry results and equals 470 K, which is
very close to the estimated value Mstart = 460 K using Andrew’s empirical equation
[9]. The reaction rate of lower bainite formation is strongly dependent on the
isothermal holding temperature, at higher transformation temperatures the
formation of lower bainite is faster than at lower temperatures.
A general view of a lower bainitic microstructure in hypereutectoid steel after
partial transformation for 10 and 20 min at 533 K is shown in Figure 3.2, where black
needles are lower bainite (LB), white particles are spheroidized cementite (θ) and the
rest is a mixture of martensite (α’) and retained austenite (γR). Although the optical
microscopy can be successfully used to estimate the volume fraction of lower bainite,
it is not able to reveal the individual plates of lower bainite, for which the high-
30
39. Chapter 3
resolution scanning and transmission electron microscopy have been used in the
present study.
(a) (b)
Figure 3.2. Optical metallography of the lower bainitic microstructure. (a) – 533 K for 10
min (total fraction of lower bainite is 0.15), (b) – 533 K for 20 min (total fraction of lower
bainite is 0.75). Black needles are lower bainite (LB), small white particles correspond to
the primary spheroidized cementite (θ), the grey matrix is formed by martensite (α’) and
retained austenite (γR).
Lower bainite formation is a decomposition of austenite into non-lamellar
aggregates of ferrite and cementite. Due to the low transformation temperatures at
which lower bainite is formed carbon cannot easily diffuse away into the austenite
from the firstly formed supersaturated ferritic plate. Therefore, the only way to
reduce the carbon content of bainitic ferrite is carbide precipitation. Usually the
precipitation of either cementite (θ) or ε– and η–carbides within ferrite is expected in
lower bainitic microstructures [10], which will depend on the composition of the steel
and the transformation time and temperature. Figure 3.3 shows a typical complex
microstructure of lower bainite in hardened SAE 52100 steel after partial
transformation at different temperatures. Spherical particles in all micrographs are
31
40. Experimental Characterization of Fe-C-Cr Steel
spheroidized cementite particles, which are undissolved during intercritical
austenitisation.
(a) (b)
(c) (b)
Figure 3.3. Lower bainitic microstructure revealed by scanning electron microscopy. (a) –
533 K for 5 min (lower bainite fraction is 0.02), (b) – 553 K for 10 min (lower bainite
fraction is 0.50), (c) – 573 K for 10 min (lower bainite fraction is 0.80), (b) – 553 K for 20 min
(lower bainite fraction is 0.90). θ corresponds to the primary spheroidized cementite, θLB to
carbide in lower bainite, α’ to martensite and γR to retained austenite. Black arrows show
prior austenite grain boundaries.
32
41. Chapter 3
It can be seen that lower bainite first nucleates at the prior austenite grain boundary
(Figure 3.3, black arrows) as a thin ferritic plate followed by the precipitation of
carbides within ferrite. As transformation progresses (Figure 3.3 (b–d)) additional
plates nucleate both at the sides of the original plates and intragranularly. It is shown
that the isothermal transformation temperature in the investigated temperature
range has no effect on the microstructural morphology. At all temperatures the
formation of lower bainite is observed.
During quenching to room temperature after partial transformation to lower
bainite not all of the residual austenite is transformed to martensite. The retained
austenite is very difficult to be distinguished from martensite by means of SEM, but
it can be seen that retained austenite films tend to be trapped between lower bainitic
plates (Figure 3.3 (d)) at high transformed fractions, when no martensite is formed
upon quenching. In the next sections the detailed analysis of the evolution and
thermal stability of retained austenite in SAE 52100 steel will be presented in more
detail.
In Figure 3.4 bright-field transmission electron microscopy shows the
morphology of lower bainite at high magnification. It can be seen that ferritic plates
with the thickness of 0.2–0.3 μm contain elongated rod–like carbide particles. In order
to identify the structure of the carbides observed here, selected area diffraction was
used and the measured spacings dhkl are compared with the theoretical values. The
analysis reveals that carbides in the ferritic plates have the orthorhombic structure of
cementite, and precipitate in a single variant within a given ferritic plate. Cementite
particles are inclined at about 60o to the longest side of the ferritic plate. The
precipitation of neither ε– nor η– carbides has been detected in SAE 52100 steel in the
present study.
33
42. Experimental Characterization of Fe-C-Cr Steel
(b)
(a)
(c)
Fe3C
Figure 3.4. (a) – Bright field transmission electron microscopy, specimen transformed at
503 K for 45 min (lower bainite fraction is 0.70). (b) and (c) – Diffraction pattern taken
along the [001]α zone axis reveals the orthorhombic Fe3C structure.
34
43. Chapter 3
3.3 Retained austenite
The volume fraction of retained austenite in SAE 52100 steel after different
bainite holding times/temperatures and quenching to room temperature is
determined by XRD, and shown in Figure 3.5. It can be seen that the fraction of
austenite retained at room temperature in SAE 52100 steel increases with the partial
decomposition of residual austenite into lower bainite up to a lower bainite fraction
of about 0.75. During the lower bainitic heat treatment the fraction of austenite
gradually decreases, but it becomes more stable with respect to martensite formation
during quenching to room temperature, which explains the maximum of retained
austenite observed at a high volume fraction of lower bainite (Figure 3.5).
0.00
0.03
0.06
0.09
0.12
0.15
0.18
0.0 0.2 0.4 0.6 0.8 1.0
Volume fraction of lower bainite
Volumefractionofretained
austenite
483 K
503 K
533 K
553 K
573 K
Figure 3.5. Retained austenite volume fraction vs. volume fraction of lower bainite. The
calculated error is due to counting statistics.
Usually the amount of retained austenite in the material will strongly depend on the
reaction temperature and alloy composition. For instance, in high silicon steels (or
steels with high concentrations of other alloying elements that retard the
precipitation of cementite from austenite and ferrite) after upper bainite formation
significantly more austenite is retained at ambient temperature than in low Si steels.
35
44. Experimental Characterization of Fe-C-Cr Steel
The retention of the significant amount of austenite at room temperature in SAE
52100 steel is associated with the effect of alloying elements, like chromium and
carbon. It has been shown in [8] that the chromium distribution over the austenite
grain in SAE 52100 steel is not homogeneous after cementite dissolution at 1133 K,
which affects the austenite stability with respect to bainite formation.
The measurements of the lattice parameter of the retained austenite in SAE
52100 steel after partial formation of lower bainite at different temperatures indicate
that there is a carbon enrichment of retained austenite (Figure 3.6).
0.7
0.8
0.9
1.0
1.1
1.2
0.0 0.2 0.4 0.6 0.8 1.0
Lower bainite volume fraction
Carboncontent,wt.%
483 K
503 K
533 K
553 K
573 K
Figure 3.6. Carbon content of the retained austenite as a function of lower bainite volume
fraction. The solid square represents the carbon content of austenite calculated from the
mass balance, when the volume fraction of lower bainite is zero. Dashed line shows the
expected carbon enrichment of austenite when no martensite forms on quenching.
It means that not all carbon precipitates in cementite within the ferritic plates, and
carbon diffuses into the austenite without precipitation of carbides either. It should
be noted that overestimation of the carbon content is likely to occur at low fractions
of bainite due to the formation of martensite upon quenching. The magnitude of this
effect can be estimated for a lower bainite fraction of zero. The austenite carbon
content calculated from the mass balance between ferrite and austenite (Figure 3.6,
36
45. Chapter 3
square) is lower than one obtained from the XRD analysis by more than 0.2 wt.%.
The values for austenite lattice parameter at lower bainite formation temperatures is
lower than the lattice parameter of retained austenite measured at room temperature,
which is an indication that actually more significant carbon enrichment of austenite
occurs during lower bainite formation than observed from the XRD analysis (Figure
3.6, dashed line).
3.4 Thermal stability of retained austenite
In the previous section the evolution of the volume fraction of retained
austenite in SAE 52100 steel is investigated. A thermal stability of the retained
austenite is also a very important issue for the dimensional stability of the bearings
[6]. In this section the stability range of retained austenite upon cooling and heating
is investigated using thermo-magnetic experiments. The thermal cycle from room
temperature to 1173 K and back is performed for specimens with lower bainitic
microstructure obtained after different holding times at 503 K. Figure 3.7 shows the
temperature dependence of the magnetization at a constant magnetic field of
0.79×106 A/m for two specimens: (a) soft-annealed and (b) annealed for 45 minutes at
503 K. The microstructure of the soft-annealed specimen consists of ferrite and a
fraction of 0.05 of spheroidized cementite, whereas the specimen annealed for 45 min
at 503 K is partially transformed to lower bainite and contains a significant fraction of
retained austenite. It is clear that the magnetization of the soft-annealed material
(Figure 3.7 (a)) decreases with increasing temperature; this is due to the increase in
thermal precession at the atomic level. The magnetization approaches zero at about
1050 K, above this temperature the ordered magnetic structure disappears, and the
material becomes paramagnetic [11]. The observed hysteresis of cooling and heating
curves occurs due to the phase transformation. As an example of typical M(T)
behavior the temperature dependence of the magnetization for a material containing
retained austenite, the specimen annealed for 45 min at 503 K is shown in Figure 3.7
37
46. Experimental Characterization of Fe-C-Cr Steel
(b) and (c). An increase of magnetization is observed during heating in the range
485 K–550 K, which is mainly due to the increase of the volume fraction of ferro-
magnetic phases, i.e. decomposition of retained austenite. At temperatures above
480 K the cementite becomes paramagnetic, and the difference in magnetization
during heating and cooling can be directly related to the volume fraction of retained
austenite, although the possible formation of the intermediate carbides can affect the
magnetization, as will be discussed below.
It should be noted that all specimens showing this increase in magnetization
present an interesting phenomenon: an “overshoot” of the heating curve with respect
to the cooling curve is observed at about 575 K (Figure 3.7 (b) and (c)), which is
known to be the Curie temperature of ε-carbides [12]. The observed overshoot can
likely be attributed to the formation of ε-carbides during the decomposition of
retained austenite, as reported in [13]. The intermediate ε-carbide could be further
transformed to ε’- (also known as η-) carbides and to cementite [13].
0.00
0.40
0.80
1.20
1.60
250 450 650 850 1050
Temperature, K
Magnetization,A/mx10
6
heating
cooling
(a)
38
47. Chapter 3
0.00
0.40
0.80
1.20
1.60
250 450 650 850 1050
Temperature, K
Magnetization,A/mx10
6
heating
cooling
(b)
1.10
1.20
1.30
1.40
475 575 675 775
Temperature, K
Magnetization,A/mx10
6
Δ
M C
M H
(c)
Figure 3.7. The temperature dependence (high temperature cycle (300 K → 1133 K → 300
K)) of magnetization under constant field 0.79 x 106 A/m for: (a) soft-annealed specimen
and (b) specimen transformed for 45 min at 503 K. (c) a close-up of (b) in order to illustrate
the calculation of thermal stability of retained austenite from the high temperature
magnetic measurements.
The decomposition process of γR is estimated using the following proposed
equation:
39
48. Experimental Characterization of Fe-C-Cr Steel
( )
1
( ) ΔR
H
γ
C
M T
f
M T
= −
+
, (3.1)
for .( )Δ< TT HM and CM are magnetization values obtained at the same
temperature from the heating and cooling curves, respectively. Δ is the maximum
overshoot between heating and cooling curves, for more detail see Figure 3.7 (c). It is
assumed that the decomposition of austenite starts with the formation of ε-carbides,
and the change in magnetization value during heating is a result of the increase in
volume fraction of ferro-magnetic phases, on the one hand, and the decrease in the
saturation magnetization of ε-carbides, on the other hand. In addition to the volume
fraction of γR at room temperature, these observations give important information
about the thermal stability of austenite. The temperature dependence of the volume
fraction of retained austenite calculated using Equation (3.1) is shown in Figure 3.8
and summarized in Figure 3.9.
0.00
0.05
0.10
0.15
0.20
380 430 480 530 580
Temperature, K
Volumefractionofaustenite
0 min
20 min
45 min
60 min
90 min
120 min
b
Figure 3.8. Temperature dependence of retained austenite fraction obtained from the high
temperature magnetic measurements.
40
49. Chapter 3
One can see that the starting temperature of austenite decomposition varies with
bainitic holding time, and is in the range from 480 K (45 min at 503 K) to 540 K
(120 min at 503 K). The end temperature of austenite decomposition is 580 K for all
holding times (Figure 3.9).
450
500
550
600
0 20 40 60 80 100 1
Time, min
Temperature,K
20
end
start
Figure 3.9. Start (triangles) and end (circles) temperatures of retained austenite
decomposition upon heating vs. bainite holding time.
Figure 3.10 shows the temperature dependence of the magnetization at a
constant magnetic field of 0.79×106 A/m for a thermal cycle from room temperature
to 10 K and back for the soft-annealed material and the specimen annealed for 45 min
at 503 K. It is shown that the magnetization of the soft-annealed material increases
with decreasing temperature, which is due to the increase in saturation of the
ferromagnetic phases. Cooling and heating curves are the same for the soft-annealed
material because it contains only ferrite and cementite. For the heat-treated
specimens an additional increase in magnetization is observed during cooling due to
the increase in the volume fraction of ferromagnetic phases during cooling, i.e.
retained austenite transforms to martensite. The maximum difference between
cooling and heating curves is observed for the specimen that has been annealed for
41
50. Experimental Characterization of Fe-C-Cr Steel
45 min at 503 K. A significant amount of austenite (0.09) is found to be stable down to
10 K.
1.00
1.10
1.20
1.30
1.40
1.50
1.60
0 50 100 150 200 250 300
Temperature, K
Magnetization,A/mx10
6
cooling
heating
soft-annealed
45 min at 503 K
Figure 3.10. The temperature dependence (low temperature cycle (300 K → 10 K → 300 K)
of magnetization under constant field of 0.79 x 106 A/m for soft-annealed material and
specimen annealed for 45 min at 503 K.
The essential information that can be obtained from the experiments described
here is the thermal stability of austenite upon cooling (γ → α') and upon heating (γ →
α + carbides). The austenite fraction as a function of temperature is calculated upon
heating (Equation 3.1) and cooling [14] for the specimen with the highest amount of
retained austenite at room temperature, and is shown in Figure 3.11. It is observed
that all retained austenite is decomposed into ferrite and cementite (possibly with the
formation of intermediate carbides) during heating, whereas during cooling to 10 K a
large amount of austenite remains untransformed.
One can see from Figure 3.10 and Figure 3.11 that the transformation of retained
austenite to martensite stops at around 110 K. This is likely an indication of the
presence of two types of retained austenite with different thermal stability against
martensite transformation. That is, stable film-type austenite is retained between
42
51. Chapter 3
bainitic plates, while relatively less stable blocky austenite is retained between
sheaves of bainite [4, 5]. The thermal stability of retained austenite is understood in
terms of the carbon content [9] and the size of austenite grains [15, 16].
0.00
0.04
0.08
0.12
0.16
0.20
0 100 200 300 400 500 600
Temperature, K
Volumefractionofaustenite
γ --> α'
γ --> α + carbides
Figure 3.11. Temperature dependence of volume fraction of retained austenite in specimen
held for 45 min at 503 K.
Both types of retained austenite are enriched with carbon to some extent during
the bainite formation at 503 K (Figure 3.6), since austenite contains about 0.25 wt.% of
silicon acting as an inhibitor for carbide precipitation. As the blocky type of retained
austenite has usually larger grain size than the film-type austenite [15], the carbon
enrichment in film-type austenite is expected to be more than in the blocky type [4,
5]. Furthermore, the small grain size of film-type retained austenite leads to
insufficient nucleation sites for martensite transformation and it thus also increases
the stability of retained austenite significantly. The film-type retained austenite
remains untransformed during cooling to 10 K. The temperature range in which the
austenite is stable, i.e. neither transforms to ferrite and carbides during heating nor to
martensite during cooling, is determined to be 220 K, from 230 K to 450 K after a
lower bainitic heat treatment at 503 K for 45 min.
43
52. Experimental Characterization of Fe-C-Cr Steel
3.5 Conclusions
In this chapter, the experimental characterization of the kinetics of lower bainite
formation and its morphology in SAE 52100 bearing steel, as well as the evolution
and thermal stability of retained austenite is investigated with optical and electron
microscopy, X-ray diffraction and thermo-magnetic measurements. A significant
fraction of austenite is retained in the material. It has been demonstrated that the
maximum of retained austenite volume fraction occurs as a combination of the
increasing carbon concentration in the austenite and of the decreasing volume
fraction of the residual austenite at bainite formation temperatures.
R
fγ
The thermal stability of austenite upon cooling and heating is investigated. The
temperature range in which the austenite is stable, i.e. neither transforms to ferrite
and carbides during heating nor to martensite during cooling, is from 230 K to 450 K
for the specimens held for 45 min at 503 K. The temperature at which retained
austenite starts to decompose to ferrite and carbides upon heating varies with the
bainitic holding time and is in the range from 480 K (45 min at 503 K) to 540 K (120
min at 503 K). The end temperature of austenite decomposition is 580 K for all
holding times. The transformation of austenite to martensite during cooling till 10 K
is not complete, the transformation stops at 110 K, which is an indication of the
presence of the very stable film-type austenite.
44
53. Chapter 3
3.6 References
1. G.E. Hollox, R.A. Hobbs, J.M. Hampshire: Wear, 1981, vol. 68, pp. 229-240.
2. F.C. Akbasoglu, D.V. Edmonds: Met. Trans. A, 1900, vol. 21A, pp. 889-893.
3. J.M. Hampshire, J.V. Nash, G.E. Hollox: Rolling Contact Fatigue Testing of Bearing
Steels, J.J.C. Hoo (Ed.), Philadelphia, 1982, pp. 47- 66.
4. H.K.D.H. Bhadeshia, D.V. Edmonds: Metal Sci., 1983, vol. 17, pp. 411-425.
5. H.K.D.H. Bhadeshia: Mater. Sci. Forum, 2005, vols. 500-501, pp. 63-74.
6. E.B. Mikus, T.J. Hughel, J.M. Gerby, A.C. Knudsen: Trans. ASM, 1960, vol. 52, pp.
307-315.
7. J.H. Gu, K.D. Chang, H.S. Fang, Z. G. Yang, B.Z. Bai: J. Iron Steel Int., 2004, vol. 11,
pp. 42-46.
8. L. Zhao, F.J. Vermolen, A. Wauthier, J. Sietsma: Met. Mater. Trans. A., 2006, vol.
37A, pp. 1841-1850.
9. R.W.K. Honeycombe, H.K.D.H. Bhadeshia: Steels. Microstructure and Properties,
London, Arnold, 1995, p.103.
10. H.K.D.H. Bhadeshia: Acta Met., 1980, vol. 28, pp. 1103-1114.
11. R.M. Bozorth: Ferromagnetism, D. van Nostrad Companny Inc., New York, 1961, p.
367.
12. A.E. Berkowitz: Magnetism and Metallurgy, A.E. Berkowitz, E. Kneller (Eds.),
Academic Press, New York, 1969, pp. 331-363.
13. B.K. Jha, N.S. Mishra: Mater. Sci. Eng. A, 1999, vol. 263, pp. 42-55.
14. L. Zhao, O. Tegus, E. Brück, N.H. van Dijk, S.O. Kruijver, J. Sietsma, S. van der
Zwaag: Int. Conf. on TRIP-Aided High Strength Ferrous Alloys, B.C. de Cooman
(Ed.), Aachen, Germany, 2002, pp. 71-74.
15. Y.K. Lee, H.C. Shin, Y.C. Jang, S.H. Kim, C.S. Choi: Scripta Mater., 2002, vol. 47,
pp. 805-809.
16. E. Jimenez-Melero, N.H. van Dijk, L. Zhao, J. Sietsma, S.E. Offerman, J.P. Wright,
S. van der Zwaag: Acta. Mater., 2007, vol. 55, pp. 6713-6723.
45
55. 4 Modeling of Lower Bainite Formation
in Fe–C–Cr Steel
In recent years, many investigations have been carried out on the modeling of
bainite formation. In the present work, two physical models proposed in literature
are implemented to model the formation of lower bainite in high carbon and
chromium steels (Fe – 1.01 wt.% C – 1.36 wt.% Cr, SAE 52100). In the first model, a
reconstructive approach is used. Nucleation of bainitic laths is considered in the
general framework of classical nucleation theory and a diffusional growth model is
used. In the second model, displacive growth of bainitic ferrite is assumed, where the
change in the bainite volume fraction is determined by the nucleation rate. Model
calculations are compared to experimentally obtained lower bainite fractions for SAE
52100 steel and a reasonable agreement is found for both models. The advantages
and disadvantages of the proposed models for the overall isothermal bainite
formation in high carbon steels are discussed, and it is concluded that the model
based on the displacive approach is the most appropriate for the description of lower
bainite formation in high-carbon steels.
56. Modeling of Lower Bainite Formation in Fe-C-Cr Steel
4.1 Introduction
Lower bainitic microstructures are of great importance for industrial applications
due to the optimal combination of strength and toughness. The main disadvantage
associated with the production of steels with a lower bainite microstructure is that it
is a very time-consuming process. To reduce the production time without loss of the
desired mechanical properties, a better understanding of bainite formation and a
suitable model of the overall transformation kinetics are required.
Bainite formation takes place at intermediate temperatures, lower than the
temperatures for pearlite formation and higher than that for martensite formation.
The morphology of bainite varies with the transformation temperature. The different
forms of bainite in isothermally transformed steels are well studied [1-3]. Isothermal
bainite is distinguished as either upper or lower bainite, depending on whether the
carbides are formed between individual bainitic ferrite laths or plates, or within
them. The carbides are usually cementite, although ε-carbides can also be present in a
bainitic microstructure [2, 4, 5]. In steels with a high concentration of Si or Al the
precipitation of cementite is inhibited and the formation of so-called carbide-free
bainite takes place [6-9]. In this case carbide-free bainite is in fact cementite-free
upper bainite, which microstructure usually consists of bainitic ferrite laths separated
by films of carbon enriched retained austenite.
Among all austenite decomposition reactions, bainite formation remains the least
understood. Bainite plays an important role among solid-solid phase transformations
because it exhibits features of both diffusive and displacive transformation
mechanisms. A number of morphological features and similarities with martensite
have led some authors to assume a displacive mechanism of bainite formation [10-
12]. On the other hand, the similarities with Widmanstätten ferrite have led other
authors to assume a diffusive or reconstructive mechanism for bainite formation [11,
13, 14]. In spite of the many experimental results available in literature, the bainite
formation still remains a subject of scientific controversy. The main points of the
controversy will be discussed below.
48
57. Chapter 4
According to the reconstructive approach [13, 14] the diffusion of the atoms
during bainite formation is essential. The carbon content of the bainitic ferrite is
determined by para-equilibrium at the α/γ interface, and carbon continuously
diffuses from the bainitic ferrite into the austenite during the growth of the bainitic
laths or plates. The bainite formation rate is thus determined by the diffusion of
carbon in austenite. As for the displacive approach [10, 12], bainite grows without
any diffusion of substitutional or interstitial elements (similar to martensite).
Although martensite nucleation is also diffusionless, there is carbon partitioning
during the nucleation of bainitic ferrite. In the displacive approach it is assumed that
the bainitic ferrite forms with the carbon content of the parent phase followed by fast
carbon rejection into the surrounding austenite.
In recent years many investigations performed with atom probe techniques have
shown [15-17] that the bulk concentration of substitutional alloying elements in the
bainitic ferrite is the same as that of the parent austenite. This finding is consistent
with both the reconstructive and the displacive approach, since both assume that
only carbon exhibits measurable long-distance diffusion during bainite formation.
Nevertheless, there is still no agreement in the literature regarding the initial carbon
content in ferrite, which is impossible to determine experimentally. The fact that at
low transformation temperatures the precipitation of cementite occurs inside the
bainitic ferrite favors the displacive idea that bainitic ferrite forms with carbon
supersaturation.
Another point of the controversy is the occurrence of surface relief introduced by
bainite growth. At first, this observation seems to support the displacive mechanism
of bainite formation, in which the formation of bainite causes an invariant plane
strain (IPS) [18]. However, Aaronson and co-authors [19] have shown that the
experimentally observed surface relief can also be explained from the reconstructive
point of view and that the surface relief is not always of IPS type, but also sometimes
tent-shaped relief occurs.
49
58. Modeling of Lower Bainite Formation in Fe-C-Cr Steel
In the present chapter bainite formation is investigated in the industrial alloyed
steel SAE 52100 with a high concentration of carbon and chromium (Fe-1.01 wt.% C–
1.36 wt.% Cr). An attempt to find a suitable physical model for lower bainite
formation in high carbon steel is made. Two models proposed in the literature with
different physical approaches and developed for low- to medium-carbon steels have
been implemented to describe the formation of lower bainite in high carbon steels.
Quidort and Brechet’s model [20, 21] based on the reconstructive approach is
discussed in Section 4.2, Van Bohemen and Sietsma’s model [22] based on the
displacive approach is presented in Section 4.3. In Section 4.4 the advantages and
disadvantages of the proposed models for the overall isothermal bainite formation in
high carbon steels are discussed.
4.2 Reconstructive model
In the literature there is a large variety of models for the kinetics of bainite
formation, but only few attempts are based on a physical mechanism. The kinetics
model proposed recently by Quidort and Brechet [20, 21], based on the reconstructive
approach, is discussed in the present section and has been implemented for the
description of the lower bainite formation in high carbon steel.
In this model it is assumed that:
1. The nucleation of bainite is controlled by carbon diffusion and can be described
with the classical nucleation theory.
2. The growth rate of bainite is controlled by carbon diffusion from ferrite to
austenite. A Trivedi model for diffusion-controlled growth is used to describe the
growth rate of bainite.
3. In low Si steels carbide precipitation accompanies bainite formation and creates
extra sinks for the carbon flow. In Quidort and Brechet’s model a quantitative
description of carbide precipitation is not included, but its accelerating effect on
50
59. Chapter 4
the overall bainite formation kinetics is incorporated in one of the fitting
parameters.
4. Three fitting parameters K1, K2 and t0 are used in order to adjust the modelling
results to the experimentally obtained bainite formation kinetics. In the present
model K1 and K2 are physical parameters accounting for the deviation from the
maximum growth rate of bainite, the cross-section area of a single bainite lath, the
initial nucleation-site density and the activation energy for diffusion. The
empirical parameter accounting for the “incubation time”, t0, is either directly
taken from the experimental results or can be found using one extra fitting
parameter K3.
4.2.1 Growth rate
In order to provide a physically based overall kinetics model for bainite
formation, a description of both the nucleation and growth kinetics of the new phase
is needed. For the growth rate of bainitic ferrite in Quidort and Brechet’s approach
[21] the simplified version of the Trivedi model [22] for diffusion-controlled growth
of plate precipitates is used, expressing the interface velocity for bainitic ferrite
by
0αv
( ) ( )(-Δ
γ
3C
0α C α
m
27
,
256
D
v x T G T
V
=
π σ
)Ωm * , (4.1)
where is an algebraic combination of the carbon supersaturation in austenite,
defined by:
Ω* Ω0
Ω
Ω
Ω Ω
0
*
2
0 0
2 1
1
2π π
=
− −
, (4.2)
51
60. Modeling of Lower Bainite Formation in Fe-C-Cr Steel
γα
γα αγ
Ω0
CC
C C
x x
x x
−
=
−
, (4.3)
where , and are the atom fractions of carbon in austenite (far away from
the interface), in austenite at the interface and in ferrite at the interface, respectively.
Cx γα
Cx αγ
Cx
( )γ
CD T is the diffusivity of carbon in austenite, ( )Δ mG T the maximum driving force
for ferrite formation, the molar volume of ferrite [α
mV 23], and σ the ferrite/austenite
interfacial energy per unit area. In Quidort and Brechet’s work a value of 0.2 Jm-2 was
taken as a rough estimate for the interfacial energy [21]. According to the data
presented in work of Tanaka, Aaronson and Enomoto [25-27] for different steels, the
interfacial energy varies from 0.02 to 0.07 Jm-2 in the temperature range from 1185–
750 K, respectively. In the present work the interfacial energy per unit area at lower
bainite formation temperatures is estimated from a linear extrapolation to low
temperature of the data presented in [25-27] (Figure 4.1) and shown in Table 4.1.
The maximum driving force ( )Δ mG T [10] for ferrite nucleation (Table 4.1) and
the interfacial carbon concentrations are calculated under the assumption that para-
equilibrium exists at the interface. Para-equilibrium is defined here as a constrained
local equilibrium in which only carbon partitions between the parent and the
product phase and there is no redistribution of substitutional elements [28].
As has been shown in [21], the diffusion-controlled model for growth gives a
satisfactory description of the temperature and carbon concentration dependence of
the growth rate of bainitic ferrite. The growth rate of bainitic ferrite is therefore
described according to the Trivedi diffusion-controlled approach. The input
parameters for the growth rate calculated with Equation (4.1) are listed in Table 4.1.
The obtained temperature dependence of the growth rate of bainitic ferrite in SAE
52100 steel will be used for further analysis in the next section.
52
61. Chapter 4
0
0.03
0.06
0.09
0.12
0.15
0.18
400 600 800 1000 1200
Temperature, K
Interfacialenergyσ,Jm
-2
Fe-C-Mn-Ni Fe-C-Mn
Fe-C-Mn-Co Fe-C-Mn-Si
Fe-C-Ni Fe-C
Fe-C-Co Fe-C-Si
Figure 4.1. The ferrite – austenite interfacial energy per unit area obtained in references
[25-27] for different alloys. The line is a linear extrapolation to low temperatures.
Table 4.1. The input parameters for the growth rate of bainitic ferrite calculated with
Equation (4.1).
T,
K
γ
CD ,
10-16 m2s-1
σ ,
10-2 Jm-2
Δ mG ,
Jmol-1
0αv ,
10-7 ms-1
483 0.2 10.5 -3620 0.4
503 0.6 10.1 -3460 0.9
533 2.1 9.5 -3210 3.0
553 4.7 9.1 -3045 6.1
573 9.9 8.7 -2880 11.9
4.2.2 Nucleation Rate
It has been shown in [20] that the nucleation rate of bainitic ferrite decreases
with decreasing temperature, which is inconsistent with a displacive interpretation of
the nucleation rate. The classical nucleation theory [29] is therefore used to describe
53
62. Modeling of Lower Bainite Formation in Fe-C-Cr Steel
the temperature dependence of the nucleation rate and the temperature dependence
is assumed to be controlled only by carbon diffusion and not by the driving force.
This is due to the fact that at the low temperatures at which bainite is usually formed,
the large driving force causes the activation energy for nucleation to be small
compared to the activation energy for diffusion and to RT. This results in a relation
for the nucleation rate, , given by:N&
B
0 exp
k T Q
N N
h R
⎛= −⎜
⎝ ⎠
& D
T
⎞
⎟ , (4.4)
where is the initial nucleation-site density,0N R the gas constant, T the
temperature, the Planck constant, the Boltzmann constant, and is the
activation energy representing the barrier to transfer carbon atoms across the
interface. It is assumed in [
h Bk DQ
20] that γ
DQ K= 2QC , where 2 0.33K = for medium carbon
steels (0.5 wt.% C) and γ
CQ is the activation energy for volume diffusion of carbon
calculated with the empirical equation [30]:
( )
2γ 5 5
C C160354 7.955 10 23 10Q x= − × + × Cx , (4.5)
where is the atom fraction of carbon in the austenite calculated using the
ThermoCalc software and equals to 0.039 at 1133 K in case of SAE 52100 steel, the rest
of carbon is precipitated in spheroidized cementite.
Cx
γ
CQ is in Jmol-1.
The value for comes from an Arrhenius analysis of nucleation rate data [2K 20,
27]. Therefore, the temperature dependence of the nucleation rate for SAE 52100 steel
has been deduced according to the procedure described in [20]. In the case of bainite
formation, the assumption of a constant linear growth rate and a constant nucleation
54
63. Chapter 4
rate results in n=2 in the Avrami equation ( ( )( )2
1 expf k T t= − − × ). Growth is
considered to occur mainly in one dimension assuming that the thickening of the
bainitic plates can be neglected compared to their lengthening. According to the
physical meaning of the fitting parameters of the Avrami equation, is
proportional to the product of the nucleation and the growth rates:
( )k T
( ) 1 0αk T C Nv= & , (4.6)
where C1 is a constant.
The temperature dependence of the nucleation rate can therefore be estimated
as the ratio ( ) 0αk T v . The coefficients ( )k T are obtained from an Avrami fit (Figure
4.2, n=2) of the experimentally determined bainite formation kinetics curves for
different temperatures measured by dilatometry (Chapter 3).
0.0
0.2
0.4
0.6
0.8
1.0
0 20 40 60
Time,
Fraction
80 100 120
min
483 K
503 K
533 K
553 K
573 K
Avrami fit
Figure 4.2. An Avrami fit to the experimental kinetics curves at different temperatures.
The open symbols represent the experimental results. Solid lines give the results of the
Avrami fit with n=2.
55
64. Modeling of Lower Bainite Formation in Fe-C-Cr Steel
Since the temperature dependence of the growth rate of bainitic ferrite can
be calculated with the Trivedi model (Equation (4.1), [
0αv
22]), we can obtain the
temperature dependence for the nucleation rate. The ratio ( ) 0αk T v as a function of
temperature for SAE 52100 steel is presented in Figure 4.3. It is clear that this
indicates that the nucleation rate decreases with decreasing temperature, which is
consistent with the diffusional approach.
0
2
4
6
8
10
12
460 480 500 520 540 560 580
Temperature, K
k/v0α
Figure 4.3. The temperature dependence of the nucleation rate for bainitic ferrite
estimated as the ratio between the Avrami coefficient k (when n fixed to be 2) and the
growth rate as calculated with Equation (4.1).
By taking the natural logarithm of Equations (4.4) and (4.6), a more convenient
graphical representation of nucleation rate as a function of temperature is obtained
(Figure 4.4). It should be noted that the temperature effect from the linear term in
Equation (4.4) is assumed to be negligible compared with the one from the exponent.
The slope of the curve equals to D /Q R− . The value obtained for from the
analysis in
DQ
Figure 4.4 is 40 kJmol-1, whereas the activation energy for volume
diffusion of carbon in austenite calculated with the Equation (4.5) equals 132 kJmol-1
56
65. Chapter 4
for SAE 52100 steel. Then the parameter is2K D
γ
C
40
0.30
132
Q
Q
= = for SAE 52100 steel,
which is close to the value obtained for medium carbon steels [20].
0.0
0.5
1.0
1.5
2.0
2.5
3.0
1.7 1.8 1.9 2.0 2.1
Temperature
-1
(K
-1
x 10
3
)
Ln(k/v0α)
Slope = -Q D /R
Figure 4.4. Estimation of the activation energy from the temperature dependence of
the nucleation rate for bainitic ferrite (
DQ
Figure 4.3).
4.2.3 Overall kinetics for bainitic ferrite formation
Finally, to obtain the relation between the fraction transformed, time and
temperature the equations for nucleation and growth of bainitic ferrite (Equations
(4.1) and (4.4)) are combined in an Avrami analysis and the isothermal overall
kinetics are described by
( )
γ
2B 2 C
1 0α 01 exp exp
k T K Q
f K v
h RT
⎛ ⎞⎛ ⎞
= − − − −⎜ ⎜ ⎟
⎝ ⎠⎝ ⎠
t t ⎟ , (4.7)
57
66. Modeling of Lower Bainite Formation in Fe-C-Cr Steel
where is the isothermal holding time, the incubation time. K1 is a fitting
parameter, which represents contributions from (1) possible deviation from the
maximum growth rate , (2) the cross-section area of a single bainite lath (in order
to translate the one-dimensional velocity into a volume fraction) and (3) the initial
nucleation-site density . In fact, K1 is equal to (Equation (4.6)), and K2 is
already known from the analysis in Section
t 0t
0αv
0N
0αv
1 0C N
4.2.2 and equals 0.30.
0.0
0.2
0.4
0.6
0.8
1.0
0 20 40 60 80 100 120
Time, min
Fraction
483 K
503 K
533 K
553 K
573 K
Model
Figure 4.5. The comparison between calculated and experimentally found bainite fractions
vs. isothermal holding time at different bainite holding temperatures. The open symbols
represent the experimental results. Solid lines give the calculated isothermal bainite
formation kinetics according to the Quidort and Brechet’s model.
The comparison between experimental and calculated results for isothermal lower
bainite formation is presented in Figure 4.5. It should be noted that kinetics curves
were calculated using Equation (4.7) rescaled by 0.95, since at bainite formation
temperatures the initial volume fraction of austenite at 1133 K is not 1 but 0.95 (the
rest is spheroidized cementite). The model gives a reasonable agreement between
experimental and calculated kinetics curves at different temperatures. It should be
noted that all calculated curves are fitted to the experimental results using a single
58
67. Chapter 4
adjustable parameter K1 = 0.004 μm-1, next to already known K2 = 0.30. The
incubation time t0 is taken from the experiment (different for each temperature), and
defined as the time at which a lower bainite volume fraction of 0.02 is detected.
4.3 Displacive model
Several kinetics models based on the displacive approach have been proposed
in the literature [31-34]. An extensive overview of available kinetics model for bainite
formation is given in [35]. It is shown that most displacive models give a reasonable
description of bainite formation only in high Si steel, where the precipitation of
cementite is inhibited and the formation of carbide-free bainite is expected. The
kinetics model proposed recently by Van Bohemen and Sietsma [22], based on the
displacive approach is discussed in the present section and implemented for the
description of the lower bainite formation in high carbon steel.
In this model:
1. The growth of bainite is assumed to be displacive, and the overall bainite
formation kinetics is determined by the nucleation rate.
2. No carbon enrichment of austenite is taken into account in the model, so it can be
applied to low Si steels.
3. Autocatalytic nucleation is taken into account.
4. The nucleation site density is assumed to be proportional to the driving force.
5. Two fitting parameters, λ and κ, are used in order to adjust the modelling results
to the experimentally obtained bainite formation kinetics. In the present model λ
is an empirical parameter representing autocatalytic nucleation and κ is a physical
rate parameter.
59
68. Modeling of Lower Bainite Formation in Fe-C-Cr Steel
4.3.1 Nucleation rate
In Van Bohemen and Sietsma’s model for bainite formation the nucleation rate
is expressed as:
( )( )0
*
1 1 expBk T Q
N N f f
h R
λ ⎛ ⎞= − + −⎜
⎝ ⎠
&
T
⎟ , (4.8)
where is the initial nucleation-site density,0N R the gas constant, T the
temperature, the Planck constant, the Boltzmann constant, λ the temperature-
independent parameter representing autocatalytic nucleation, f the volume fraction
of bainite, and the activation energy, which has two contributions: (1)
from the activation energy for diffusion and (2) from the activation energy for
nucleation .
h
*G
Bk
Δ* DQ Q G= + *
DQ
Δ
The difference between Equation (4.4) of the reconstructive approach and
Equation (4.8) of the displacive approach is, first, in Equation (4.8) autocatalytic
nucleation is incorporated using ( )1 fλ+ , and ( )1 f− accounts for the decrease in the
number of the potential nucleation sites with the increase of bainite volume fraction f.
Second, in the present model no extra assumption is made for the activation energy
, whereas in Quidort and Brechet’s model it has been assumed that >> ,
so that (Section
*Q DQ Δ *G
* DQ Q=
*
4.2.2). Since the current displacive model is developed for
low Si steels, in which the precipitation of carbides occurs, it is reasonable to assume
that is constant during isothermal bainite formation, but it is temperature
dependent due to the contribution from Δ .
Q
*G
The other important difference in Van Bohemen and Sietsma’s model from
other existing models in the literature [20, 31-35] is that the nucleation site density
is not an adjustable parameter but is estimated based on the theory of athermal
martensite formation, derived by Magee [
0N
36] as:
60
69. Chapter 4
(0
b
h
b
N T
V
α
= − )T , (4.9)
where is a constant inversely proportional to the austenite grain size, the
average volume of a bainite sub-unit, T the transformation temperature, Th the
highest temperature at which the displacive transformation can occur [
b
α bV
35, 37].
4.3.2 Overall kinetics for bainite formation
According to the displacive approach the growth of bainite is very fast and
since the average volume of a bainitic sub-unit is assumed to be constant, the change
in the volume fraction of bainite can be directly related to the nucleation rate as:
d d
d d
b
f N
V
t t
= . (4.10)
This differential equation has an analytical solution in the case that λ and are
constants during isothermal bainite formation, which is generally true for low Si
steels. By substituting Equations (4.8) and (4.9) in Equation (4.10) and using the
boundary condition , the solution can be written as:
*Q
( ) 00 ==tf
( )( )
( )( )
1 exp 1
exp 1 1
t
f
t
κ λ
λ κ λ
− − +
=
− + +
, (4.11)
where κ is a temperature-dependent rate parameter that can be written as:
61
70. Modeling of Lower Bainite Formation in Fe-C-Cr Steel
( )
*
expbB
h
k T Q
T T
h
κ α ⎛= − −⎜
⎝ ⎠RT
⎞
⎟ . (4.12)
The comparison of experimental results for the isothermal bainite formation at
different temperatures with the displacive approach is shown in Figure 4.6.
0.0
0.2
0.4
0.6
0.8
1.0
0 20 40 60 80 100 1
Time, min
Fraction
20
483 K
503 K
533 K
553 K
573 K
Model
Figure 4.6. The comparison between calculated and experimentally found bainite fractions
vs. isothermal holding time at different bainite holding temperatures. The open symbols
represent the experimental results. Solid lines give the calculated isothermal bainite
formation kinetics according to the Van Bohemen and Sietsma’s model.
It should be noted that kinetics curves calculated using Equation (4.11) are rescaled
by 0.95, since at bainite formation temperatures the volume fraction of austenite is
not 1 but 0.95 (the rest is spheroidized cementite). The fitting is somewhat better than
has been found with Quidort and Brechet’s model (Figure 4.5), especially taking into
account the fact that this model has two (λ and κ) instead of three (K1, K2, t0)
adjustable parameters.
All curves in Figure 4.6 were obtained by fitting Equation (4.11) to the
experimental results using only two parameters: the autocatalytic constant λ=70,
62
71. Chapter 4
which determines the S-shape of the kinetics curves and the rate constant , which is
temperature dependent and presented in
κ
κFigure 4.7. The increase of with the
temperature increase is consistent with the results from [22].
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
460 480 500 520 540 560 580
Temperature, K
Rateparameter,κx10
-3
,s
-1
Figure 4.7. The temperature dependence of the rate constant κ.
4.4 Discussion
In the previous sections two models with two different physical approaches,
displacive and reconstructive, for bainite formation are described, and they are both
applied to model lower bainite formation in high carbon and chromium steel (SAE
52100). Figure 4.5 and Figure 4.6 show the comparison between experimental and
calculated results. It can be seen that the fit with Van Bohemen and Sietsma’s model
seems to be slightly better, especially since no extra adjustable parameter to account
for the “incubation time” is required; the S-shape of kinetics curves is described by
the λ autocatalytic parameter.
It should be noted that all curves were fitted using MatLab 7.0 Curve Fitting
Tool with a non-linear least squares method. After fitting the R2 values for different
models and temperatures are compared (Table 4.2). R2 is a statistic measure that can
63
72. Modeling of Lower Bainite Formation in Fe-C-Cr Steel
give some information on how well the predicted (fitted) line approximates the real
data points. R2=1 indicates that the model perfectly fits the experimental data. It can
be seen from Table 4.2 that for each curve R2 value is closer to 1 for Van Bohemen
and Sietsma’s model.
Table 4.2. R2 values of fitted with different models bainite formation kinetics.
Temperature, K
Quidort and Brechet’s
model,
R2
Van Bohemen and Sietsma’s
model,
R2
483 0.946 0.952
503 0.954 0.973
533 0.984 0.990
553 0.977 0.994
573 0.968 0.990
In the present section the fitting parameters of both models are discussed and
the choice of the most suitable model for lower bainite formation in high carbon
steels is justified.
4.4.1 K1, K2, and t0 parameters in Quidort and Brechet’s reconstructive
model
As can be seen from Equation (4.7) three parameters are used in Quidort and
Brechet’s reconstructive model to adjust the predicted bainite fraction curves to the
experimental ones obtained from the dilatometry (Chapter 3). In the case of SAE
52100 steel for all investigated temperatures the fitting parameters are equal to
K1 = 0.004 μm-1 and K2 = 0.30 and “incubation times” t0 are taken from the
experimental results.
64
73. Chapter 4
The actual meaning of the K1 parameter in Quidort and Brechet’s model is not
specified in detail. Despite the fact that an exact expression for K1 has not been
presented, it is known that K1 is supposed to have at least three different
contributions: (1) deviation from the maximum growth rate calculated with Equation
(4.1), (2) the cross-section area of a single bainite lath or plate and (3) the initial
nucleation-site density. It is worth saying that it is difficult, if not impossible, to
separate these contributions [39]. In the present work it was found that
K1 = 0.004 μm-1 for SAE 52100 steel (Table 2.1). Quidort and Brechet [20] have shown
that the K1 parameter is lower in a high-alloyed steel (Fe–0.5C–4.9Ni, wt.%,
K1=0.140 μm-1) than in a low-alloyed one (Fe–0.5C–0.7Mn–0.3Cr–0.03Al, wt.%,
K1=0.285 μm-1), which indicates the larger deviation from the maximum growth rate
in high-alloyed steel. The much lower K1 value for SAE 52100 steel can be attributed,
first, to the higher carbon content, which will result in a slowing down effect (large
deviation from the maximum grown rate). Second, in Quidort and Brechet’s work the
formation of upper bainite has been studied; for upper bainite the size of bainitic
laths is usually bigger than that for lower bainite, as studied in the present work,
which will lead to an additional lowering of K1 parameter for SAE 52100 steel.
It is assumed that the nucleation rate of bainite is controlled by austenite grain
boundary diffusion of carbon. The K2 parameter accounting for the grain boundary
diffusion is estimated (before fitting Equation (4.7) to the experimental results) using
the temperature dependence of the nucleation rate. The nucleation rate is derived by
combining the experimentally obtained kinetics curves for lower bainite formation
(Chapter 3) and the calculated growth rates (Equation (4.1)). Similar to Quidort and
Brechet’s original work, the K2 parameter is found to be approximately 1/3.
The “incubation times” t0 are taken from the experimental results as the time at
which a bainite volume fraction of 0.02 has formed. The incubation time is a
relatively vague parameter in thermally activated processes; during this time after
the transformation temperature is reached the transformation does not start
immediately. Usually the incubation time is seen as a nucleation period, when
65
