Chapter 10 Phase transformations - University of...

Chapter 10-

ISSUES TO ADDRESS...• Transforming one phase into another takes time.

• How does the rate of transformation depend ontime and T?

1

• How can we slow down the transformation so thatwe can engineering non-equilibrium structures?

• Are the mechanical properties of non-equilibriumstructures better?

Feγ

(Austenite)

Eutectoid transformation

C FCC

Fe3C (cementite)

α (ferrite)

+(BCC)

CHAPTER 10:Phase transformations

Chapter 10-

Rates of solid state reactions

I- Nucleation – Formation of very small crystals (nuclei) of the new phase, which are capable of growing

II- Growth – Nuclei increase in size with disappearance of parent phase. Growth continues until equilibrium fraction (predicted by phase diagram) is reached

Phase transformation proceeds through 2 stages

Fra

ctio

n o

f tra

nsf

orm

atio

n, y

log (t)

0

0.5

1

t0.5

nucleation

Growth

Chapter 10- 2

• Fraction transformed depends on time.

fraction transformed time

y = 1− e−ktn

Avrami Eqn.

• Transformation rate depends on T – thermally activated

1 10 102 1040

50

100 135°

C11

9°C

113°

C10

2°C

88°C

43°Cy (%)

log (t) min

Ex: recrystallization of Cu

r = 1t0.5

= Ae−Q /RT

activation energy

• r often small (rate so slow): equilibrium not possible!

y

log (t)

Fixed T

0

0.5

1

t0.5

Fraction of transformation

Rate = 1

t0.5

Chapter 10- 33

• Can make it occur at: ...727ºC (cool it slowly) ...below 727ºC (“undercool” it!)

• Eutectoid transf. (Fe-C System):

αferrite

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.

7

L

γ austenite

γ+L

γ+Fe3C

Fe3C cementiteα+Fe3C

α+γ

L+Fe3C

(Fe) Co, wt% C

Eutectoid:

0.77

727°C

T(°C)

∆T

0.02

2

γ ⇒ α + Fe3C0.77wt%C

0.022wt%C6.7wt%C

Undercooling by ∆T: Ttransf. < 727ºC

Equil. cooling: Ttransf. = 727ºC

Adapted from Fig. 9.21,Callister 6e. (Fig. 9.21 adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)

Transformations & undercooling

Chapter 10- 4

γαααα

α

α

pearlite growth direction

Austenite (γ) grain boundary

cementite (Fe3C)ferrite (α)

γ

Diffusive flow of C needed

α

αγ γ

α

• Growth of pearlite from austenite:

• Reaction rateincreases with∆T.

Adapted from Fig. 9.13, Callister 6e.


Eutectoid transformation rate ~ ∆T

675°C (∆T smaller)

1 10 102 103time (s)

0

50

100

y (%

pea

rlit

e) 0

50

100

600°C (∆T larger)

650°C

% a

uste

nite

Chapter 10- 5

• Reaction rate is a result of nucleation and growthof crystals.

• Examples:

% Pearlite

0

50

100

Nucleation regime

Growth regime

log (time)t50

Nucleation rate increases w/ ∆T

Growth rate increases w/ T

Nucleation rate high

T just below TE T moderately below TE T way below TENucleation rate lowGrowth rate high

γ γ γ

pearlite colony

Nucleation rate med .Growth rate med. Growth rate low

Adapted fromFig. 10.1, Callister 6e.

Nucleation and growth

Chapter 10- 6

• Fe-C system, Co = 0.77wt%C• Transformation at T = 675C.

Adapted from Fig. 10.4,Callister 6e. (Fig. 10.4 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.)

Isothermaltransformation diagrams

400

500

600

700

1 10 102 103 104 105

0%pearlite

100%

50%

Austenite (stable) TE (727°C)Austenite (unstable)

Pearlite

T(°C)

100

50

01 102 104

T=675°C

y,

% t

ran

sfo

rmed

time (s)

time (s)

isothermal transformation at 675°C

Chapter 10- 7

• Eutectoid composition, Co = 0.77wt%C• Begin at T > 727C• Rapidly cool to 625C and hold isothermally.

Adapted from Fig. 10.5,Callister 6e. (Fig. 10.5 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.)

Ex: Cooling history Fe-C system

1 10 102 103 104 105 time (s)

500

600

700

T(°C)

γ γ

γγγγ

γ

Austenite (stable)

Pearlite

0%pearlite

100%

50%

TE (727°C)

Chapter 10- 8

10µm

- Smaller ∆T: colonies are larger

- Larger ∆T: colonies are smaller

• Ttransf just below TE--Larger T: diffusion is faster--Pearlite is coarser.

Two cases:• Ttransf well below TE

--Smaller T: diffusion is slower--Pearlite is finer.

Adapted from Fig. 10.6 (a) and (b),Callister 6e. (Fig. 10.6 from R.M. Ralls et al., An Introduction to Materials Science and Engineering, p. 361, John Wiley and Sons, Inc., New York, 1976.)

Pearlite morphology

Chapter 10- 9

Bainite reaction rate:

rbainite = e−Q / RT

• Bainite:--α lathes (strips) with long

rods of Fe3C--diffusion controlled.

• Isothermal Transf. Diagram

Adapted from Fig. 10.9,Callister 6e.(Fig. 10.9 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.)

(Adapted from Fig. 10.8, Callister, 6e. (Fig. 10.8 from Metals Handbook, 8th ed.,Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.)

Fe3C (cementite)

5 µm

α (ferrite)

Non-equil transformation products: Fe-C

10 103 105

time (s)10-1

400

600

800

T(°C)Austenite (stable)

200

P

B

TE

0% 100%

50%

100% bainitepearlite/bainite boundary

100% pearlite

A

A

Chapter 10- 10

60 µm

α (ferrite)

Fe3C (cementite)

• Spheroidite:--α crystals with spherical Fe3C--diffusion dependent.--heat bainite or pearlite for long times--reduces interfacial area (driving force)


Adapted from Fig. 10.9,Callister 6e.(Fig. 10.9 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.)

(Adapted from Fig. 10.10, Callister, 6e. (Fig. 10.10 copyright United States Steel Corporation, 1971.)

Other products: Fe-C system (1)

10 103 105time (s)10-1

400

600

800


200

P

B

TE

0% 100%

50%

A

A

Spheroidite100% spheroidite

100% spheroidite

Chapter 10- 11

• Martensite:--γ(FCC) to Martensite (BCT)


(Adapted from Fig. 10.12, Callister, 6e. (Fig. 10.12 courtesy United States Steel Corporation.)


xx x

xx

x potential C atom sites

Fe atom sites

(involves single atom jumps)

time (s)10 103 10510-1

400

600

800


200

P

B

TE

0%

100%50%

A

A

S

M + AM + A

M + A

0%50%90%

Martentite needlesAustenite

60 µ

m

• γ to M transformation..-- is rapid!-- % transf. depends on T only.

(Adapted from Fig. 10.11, Callister, 6e.

Other products: Fe-C system (2)

Chapter 10- 12


Cooling ex: Fe-C system (1)• Co = Ceutectoid• Three histories...

time (s)10 103 10510-1

400

600

800


200

P

B

0%

100%50%

A

S

M + AM + AM + A

0%50%90%

100% Bainite

A

100%A 100%B

Case I

Rapid cool to: 350°C

250°C

650°C

Hold for:

104s

102s

20s

Rapid cool to:

Troom

Troom

400°C

Hold for:

104s

102s

103s

Rapid cool to:

Troom

Troom

Troom

Chapter 10-

• Co = Ceutectoid• Three histories...

time (s)10 103 10510-1

400

600

800


200

P

B

0% 100%50%

A

S

M + AM + AM + A

0%50%90%

M + trace of A

A

100%A

Case II

Rapid cool to: 350°C

250°C

650°C

Hold for:

104s

102s

20s

Rapid cool to:

Troom

Troom

400°C

Hold for:

104s

102s

103s

Rapid cool to:

Troom

Troom

Troom

13


Cooling ex: Fe-C system (2)

Chapter 10- 14


Cooling ex: Fe-C system (3)Rapid cool to:

350°C

250°C

650°C

Hold for:

104s

102s

20s

Rapid cool to:

Troom

Troom

400°C

Hold for:

104s

102s

103s

Rapid cool to:

Troom

Troom

Troom

• Co = Ceutectoid• Three histories...

time (s)10 103 10510-1

400

600

800T(°C)

Austenite (stable)

200

P

B

0%

100%50%

A

S

M + AM + AM + A

0%50%90%

50%P, 50%B

A

50%P, 50%A

50%P, 50%A

100%A

50%P, 50%B

Case III

Chapter 10- 15

Adapted from Fig. 10.20, Callister 6e. (Fig. 10.20 based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.)

Adapted from Fig. 9.27,Callister6e. (Fig. 9.27 courtesy Republic Steel Corporation.)

Adapted from Fig. 9.30,Callister 6e. (Fig. 9.30 copyright 1971 by United States Steel Corporation.)

Mechanical prop: Fe-C system (1)• Effect of wt%C

• More wt%C: TS and YS increase, %EL decreases.wt%C0 0.5 1

0

50

100%EL

Imp

act

ener

gy

(Izo

d, f

t-lb

)

0

40

80

300

500

700

900

1100YS(MPa)TS(MPa)

wt%C0 0.5 1

hardness

0.7

7

0.7

7

Co>0.77wt%C Hypereutectoid

Co<0.77wt%C Hypoeutectoid

Pearlite (med)ferrite (soft)

Pearlite (med)Cementite

Hypo HyperHypo Hyper

(hard)

Chapter 10- 16

Adapted from Fig. 10.21, Callister 6e. (Fig. 10.21 based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, pp. 9 and 17.)

Mechanical prop: Fe-C system (2)• Fine vs coarse pearlite vs spheroidite

• Hardness: fine > coarse > spheroidite • %AR: fine < coarse < spheroidite

80

160

240

320

wt%C0 0.5 1

Bri

nell

hard

ness fine

pearlitecoarse pearlitespheroidite

0

30

60

90

wt%C0 0.5 1

Du

ctili

ty (%

AR

)

fine pearlite

coarse pearlite

spheroidite

Hypo Hyper Hypo Hyper

Chapter 10- 17

• Fine Pearlite vs Martensite:

• Hardness: fine pearlite << martensite.

Adapted from Fig. 10.23, Callister 6e. (Fig. 10.23 adapted from Edgar C. Bain, Functions of the Alloying Elements in Steel, American Society for Metals, 1939, p. 36; and R.A. Grange, C.R. Hribal, and L.F. Porter, Metall. Trans. A, Vol. 8A, p. 1776.)

Mechanical prop: Fe-C system (3)

0

200

wt%C0 0.5 1

400

600

Bri

nell

hard

ness martensite

fine pearlite

Hypo Hyper

Chapter 10- 18

• reduces brittleness of martensite,• reduces internal stress caused by quenching.

Adapted from Fig. 10.24, Callister 6e. (Fig. 10.24 copyright by United States Steel Corporation, 1971.)

Adapted from Fig. 10.25, Callister 6e. (Fig. 10.25 adapted from Fig. furnished courtesy of Republic Steel Corporation.)

Tempering martensite

• decreases TS, YS but increases %AR

YS(MPa)TS(MPa)

800

1000

1200

1400

1600

1800

304050

60

200 400 600Tempering T (°C)

%AR

TS

YS

%AR

9 µm

• produces extremely small Fe3C particles surrounded by α.

Chapter 10- 19

Austenite (γ)

Bainite (α + Fe3C plates/needles)

Pearlite (α + Fe3C layers + a proeutectoid phase)

Martensite (BCT phase diffusionless

transformation)

Tempered Martensite (α + very fine

Fe3C particles)

slow cool

moderate cool

rapid quench

reheat

Str

eng

th

Duc

tilit

yMartensite

T Martensite bainite

fine pearlite coarse pearlite

spheroidite

General Trends


Summary: processing options

Chapter 10-

Effect of alloying

Chapter 10-

Reading: Read all of Chapter 10; Review the learning objectives on page 299

Core Problems: 10: 1, 10, 1432

Self-help Problems: Review Example problem 10.1

0

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