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