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Mat E 443 Ferrous MetallurgyIowa State University

R.E. Napolitano

Unit 2: Phase transformations in iron and steel

Fundamentals of nucleation and growth

Proeutectoid transformations

The eutectoid transformation

Overall transformation kinetics

Martensite transformation

Phase equilibria in the Fe-C system

Bainite transformation

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Mat E 443 Ferrous MetallurgyIowa State University

R.E. Napolitano

TTTCurves for isothermal transformation

time

T

50%10% 90%

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Mat E 443 Ferrous MetallurgyIowa State University

R.E. Napolitano

TTTCurves for isothermal transformation

T

50%10% 90%time

f= fraction transformed

0

1

f

T1

0.1

0.5

0.9

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Mat E 443 Ferrous MetallurgyIowa State University

R.E. Napolitano

TTTCurves for isothermal transformation

T

50%10% 90%time

0

1

f

T1

T2

T3

T4

T1T2

T3

T4

T5

T6

T5

T6

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Mat E 443 Ferrous MetallurgyIowa State University

R.E. Napolitano

Modeling the overall transformation kinetics

Nucleation rate

Growth rate

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Mat E 443 Ferrous MetallurgyIowa State University

R.E. Napolitano

Nucleation and growth

K

f

t

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Mat E 443 Ferrous MetallurgyIowa State University

R.E. Napolitano

KE

Nucleation and growth

f

t

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Mat E 443 Ferrous MetallurgyIowa State University

R.E. Napolitano

K

E

Nucleation and growth

f

t

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Mat E 443 Ferrous MetallurgyIowa State University

R.E. Napolitano

K

E

Nucleation and growth

f

t

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Mat E 443 Ferrous Metallurgy

Iowa State University

R.E. Napolitano

K

E

Nucleation and growth

f

t

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Mat E 443 Ferrous Metallurgy

Iowa State University

R.E. Napolitano

Nucleation and growth

K

Ef

t

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Mat E 443 Ferrous Metallurgy

Iowa State University

R.E. Napolitano

Nucleation and growth

f

t

E

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Mat E 443 Ferrous Metallurgy

Iowa State University

R.E. Napolitano

E

Nucleation and growthLets consider the cooling of a single phase

austenite through the intercritical regime.

f

t

f(t)

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Mat E 443 Ferrous Metallurgy

Iowa State University

R.E. Napolitano

Assumptions

Nucleation sites are randomly

distributed

Nucleation rate is constant

Growth rate is constant and

isotropic

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Mat E 443 Ferrous Metallurgy

Iowa State University

R.E. Napolitano

The transformed volume

!

!n

i

iexVV

1

2

3

4RV

iT!

!t

vdttRX

X! tv

3

3

4

tRtVi T!

!! !!n

i

n

i

iex tRtVtV1

3

1 3

4T

31

3

3

4vt

n

i

i!

! XT

-

!

!

!

tt

t

t0

4

4

1

3

4XT

XXT dvtNt 33

03

4 !

433

tvtVex

T!

This is the extended volume.

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Mat E 443 Ferrous Metallurgy

Iowa State University

R.E. Napolitano

The transformed volume

43

3tvNfex

T

!

!P The probability that any

randomly selected point lies inuntransformed volume.

fP ! 1 How is f related to fex?

ex

dffdf ! 1

! exdffdf

1

ex

ff ! 1ln 433

tvNT

!

!

43

3exp1

tvNfT

! 433

exp1 tvNf T

? Anktf ! exp1