Kinetics of bainite formation above and below Ms in high-Si steels
Author:Stefan van Bohemen (Tata Steel RD&T)
Co-authors:Jilt Sietsma (Delft University of Technology)Dave Hanlon (Tata Steel RD&T)
Modern Bainitic Steels Workshop, May 16th, 2012, Paris
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IntroductionHistorical background
Davenport & Bain (1930)
Eutectoid steel
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Dilatometry data in 1930 paper(Davenport & Bain)
Size ...
γ → αb above Ms
Ms ~ 230 ºC→
γ → α’
320 ºC
250 ºC
180 ºC
Troostite above Ms
and
Troostite below Ms
γ → αb below Ms
time
lengthchange
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TTT diagram in 1930 paperDavenport & Bain (1930)
γ → αb above Ms
γ → αb below Ms
Ms →
time
temperature
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Similar TTT diagrams Howard & Cohen (1948)
“Beginning of isothermal transformation on isothermal holding below Ms”
time
tem
pera
ture
Ms
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Outline• Model description• Application I: Bainite formation without martensite • Application II: Bainite formation above Ms, in the presence of martensite• Application III: Bainite formation below Ms, in the presence of martensite
Ms
T
t
III
III
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Model: nucleation
( )
: austenite grain size : highest temperature for displacive transformationh
hi
T TN
ddT
γ
γ
−∝
d *(1 ) (1 )exp d iN Qf ft kT
Nν λ ⎛ ⎞= − + −⎜ ⎟⎝ ⎠
Int. J. Mater. Res. (2008), 7, p739
Nucleation rate controls the transformation kinetics:
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Model: transformation kinetics
( )1m
d (1 )(1 )d
with exp exp bh
f f ft
QKZ T Td R kTγ
λ κ
δκ ν α
= − +
Γ ⎛ ⎞⎛ ⎞= − − −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
( )( )
1 exp (1 )exp (1 ) 1
tf
tκ λ
λ κ λ− − +
=− + +
Metall. Mater. Trans. A. (2010), 41, p285
λ : autocatalytic factorκ : rate parameter
1ln1
(1 )
ff
tλ
κ λ
⎛ ⎞−− ⎜ ⎟+⎝ ⎠=
+
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Model parameters
λ : autocatalytic factor, a parameter that is relevant for the nucleation behaviour
κ : rate parameter, dependent on:• dγ : austenite grain size• Qb : activation energy (empirical formula, Metall. Mater. Trans. A. (2010) )
• Th : bainite start temperature (empirical formula)
Part I: Bainite formation above Ms
Int. J. Mat. Res. (2012) DOI 10.3139/146.110744
γ →αb (+ γR)
t
T
A3
High-Si steel 0.29C-2.4Mn-1.8Si:- C-enrichment of the remaining austenite,- Some θ precipitates, - f θ is accounted for by adjusting the carbon concentration of bainitic ferrite.
Tiso
Ms
Taus Bähr805 Dilatometer
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Bainite kinetics above Ms
Model parameters:dγ = 22 µmλ = 24 (constant)
At t = 0 s:Qb = 75 kJ/molTh = 536 ºC
Th and Qb depend on Carbon content in remaining austenite!
Example, at 420ºC-300s: Qb = 126 kJ/mol ; Th = 424 ºC ; f = 0.75
Mainly the decrease in Th accounts for incomplete transformation
0.0
0.2
0.4
0.6
0.8
1.0
0 200 400 600 800 1000 1200
t (s)
f 370ºC
390ºC
420ºC
450ºC
480ºC
370 ºC
420 ºC 390 ºC450 ºC
480 ºC
300
340
380
420
460
500
540
580
620
1 10 100 1000t [s]
T [º
C]
calc. start-curve f = 0.03
calc. f = 0.50 (with C-enrichment of austenite)
calc. f = 0.50 (without C-enrichment of austenite)
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TTT diagram 0.29C-2.4Mn-1.8Si
Int. J. Mat. Res. (2012) DOI 10.3139/146.110744
Increase in kinetics in the range 325-360ºC:Transition to lower bainite?
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Part II: Q & P experiments
γ + α’→αb + α’ + γR
t
A3
Ms
Taus
P = 390 ºC
Q = 250-305 ºC
At TP = 390 ºC:• Bainite formation accelerated by the presence of martensite• Carbon partitioning• Tempering of martensite
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Time-Temperature
200
250
300
350
400
450
107 112 117 122 127
Time (s)
Tem
pera
ture
(ºC
)
Q305ºC - P390ºC Q295ºC - P390ºCQ280ºC - P390ºC Q250ºC - P390ºC9168 - 950ºC-SC-Q Hold 390ºC
M s ~ 310ºC
Martensite formation
Fully Martensitic
0
20
40
60
80
100
120
140
0 100 200 300 400
Temperature (°C)
Dila
tatio
n (m
icro
n)
Q280ºC - P390ºCMartensite formationheating martensitegamma expansion
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Temperature-Dilatation
Martensite
Bainite
280ºC
390ºCFully Martensitic
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Temperature-Dilatation
0
20
40
60
80
100
120
140
0 100 200 300 400Temperature (°C)
Dila
tatio
n (m
icro
n)
Q305ºC - P390ºC Q295ºC - P390ºCQ280ºC - P390ºC Q250ºC - P390ºCHold 390ºC 950ºC-Qheating martensite gamma expansion
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Fraction of Bainite at TP = 390 ºC
MartensiteVol.%
AusteniteVol.%
BainiteVol.%
FromDilatometry
FromXRD remainder
Q250-P390 73 15 13Q280-P390 52 14 34Q295-P390 30 19 51Q305-P390 6 20 74
Dilatometry Vol.% Martensite XRD Vol.% Austenite Remainder = Vol.% Bainite
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15t (s)
f
Q250ºC - P390ºCQ280ºC - P390ºCQ295ºC - P390ºCQ305ºC - P390ºC Q250ºC, f = 0.73
Q305ºC, f = 0.06
Q295ºC, f = 0.30
Q280ºC, f = 0.52200
250
300
350
400
450
107 112 117 122 127
Time (s)
Tem
pera
ture
(ºC
)
Q305ºC - P390ºC Q295ºC - P390ºCQ280ºC - P390ºC Q250ºC - P390ºC9168 - 950ºC-SC-Q Hold 390ºC
M s ~ 310ºC
Martensite formation
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Martensite formed during Quench
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700t (s)
f
390ºC without sub_Ms quenchf martensite
Q250ºC-P390ºC, ◊ = 110
390ºC, ◊⎦= 24
Q305ºC-P390ºC, ◊ = 30Q295ºC-P390ºC, ◊ = 60
Q280ºC-P390ºC, ◊ = 85
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Bainite kinetics at TP = 390 ºC after formation of different fractions of martensite
df/dt autocatalysis
κ (Th, dγ , Qb) =the same as previous
Only λ is adjusted!
λ is varied from 30 to 110 to account foraccelerated kinetics dueto previously formedmartensite
0
20
40
60
80
100
120
0.00 0.20 0.40 0.60 0.80 1.00
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Bainite kinetics at TP = 390 ºC relation between λ and fraction of martensite
λ
f α’
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Steven & Haynes (1956)“First” observation of accelerated bainite formation
“Start of bainite in the presence of 10% and 55% martensite”
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Part III: Bainite formation below Ms
γ + α’ → αb + α’ + γR
t
T
A3
Interrupted Q
Ms
Taus
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Bainite formation below Ms
0
20
40
60
80
100
120
140
0 100 200 300 400
Temperature (°C)
Dila
tatio
n (m
icro
n)
950ºC-Q Hold 325ºC-50mQ305ºC - 60m Q295ºC - 70mQ280ºC - 80m Q250ºC - 100m
Ms
200
250
300
350
400
450
107 112 117 122 127 132
Time (s)
Tem
pera
ture
(ºC
)
Q295ºC - 70m Q305ºC - 60mQ280ºC - 80m Q250ºC - 100m9168 - 950ºC-SC-Q Hold 325ºC-50m
Q(<Ms)-Hold
MsMartensite
BainiteFully
Martensitic
Cooling curves Dilatometry curves
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Fractions of Bainite below Ms
MartensiteVol.%
AusteniteVol.%
BainiteVol.%
FromDilatometry
FromXRD remainder
Q250 73 11 16Q280 52 11 37Q295 30 10 60Q305 6 9 85
Dilatometry Vol.% Martensite XRD Vol.% Austenite Remainder = Vol.% Bainite
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Bainite kinetics below Ms
κ (Th, dγ , Qb) = the same as previousλ ≈ 75
0.0
0.2
0.4
0.6
0.8
1.0
0 200 400 600 800 1000
t (s)
f
f martensite
Q250ºC, ξ = 75
325ºC, ξ = 75
Q305ºC, ξ = 75Q295ºC, ξ = 75
Q280ºC, ξ = 70
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TTT diagram
λ ≈ 75
λ ≈ 25
200
240
280
320
360
400
440
480
520
560
600
1 10 100 1000t [s]
T [º
C]
calc. start-curve f = 0.03 (Ref. [8])
calc. f = 0.50 (with C-enrichment of austenite)
50%
3%
75%
Upper Bainite
Lower Bainite
Martensite + Lower Bainite
+ Austenite
Ms
Bs
85%
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0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700t (s)
f
390ºC without sub_Ms quenchf martensite
Q250ºC-P390ºC, ◊ = 110
390ºC, ◊⎦= 24
Q305ºC-P390ºC, ◊ = 30Q295ºC-P390ºC, ◊ = 60
Q280ºC-P390ºC, ◊ = 85
df/dt autocatalysis