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

• How does the rate of transformation depend on time and T?

1

• How can we slow down the transformation so that we can engineering non-equilibrium structures?• Are the mechanical properties of non-equilibrium structures better?

Fe

(Austenite)

Eutectoid transformation

C FCC

Fe3C (cementite)

(ferrite)

+(BCC)

CHAPTER 11:PHASE TRANSFORMATIONS

2

• Fraction transformed depends on time.

fraction transformed time

y1 e ktn

Avrami Eqn.

• Transformation rate depends on T.

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: equil not possible!

Adapted from Fig. 10.1, Callister 6e.

Adapted from Fig. 10.2, Callister 6e. (Fig. 10.2 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)

y

log (t)

Fixed T

0

0.5

1

t0.5

FRACTION OF TRANSFORMATION

33

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

• Eutectoid transf. (Fe-C System):

ferrite

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6

.7

L

austenite

+L

+Fe3C

Fe3C cementite+Fe3C

+

L+Fe3C

(Fe) Co, wt% C

Eutectoid:

0.7

7

727°C

T(°C)

T

0.0

22

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

4

pearlite growth direction

Austenite () grain boundary

cementite (Fe3C)

ferrite ()

Diffusive flow of C needed

• Growth of pearlite from austenite:

• Reaction rate increases with T.

Adapted from Fig. 9.13, Callister 6e.

Adapted from Fig. 10.3, Callister 6e.

EUTECTOID TRANSFORMATION RATE ~ T

675°C (T smaller)

1 10 102 103time (s)

0

50

100

y (

% p

earl

ite)

0

50

100

600°C (T larger)

650°C

% a

ust

enit

e

5

• Reaction rate is a result of nucleation and growth of 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 low

Growth rate high

pearlite colony

Nucleation rate med Growth rate med. Growth rate low

Adapted fromFig. 10.1, Callister 6e.

NUCLEATION AND GROWTH

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

ransf

orm

ed

time (s)

time (s)

isothermal transformation at 675°C

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)

Austenite (stable)

Pearlite

0%pearlite

100%

50%

TE (727°C)

8

10m

- 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

9

Bainite reaction rate:

rbainitee Q /RT

• Bainite: -- 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 m

(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% bainite

pearlite/bainite boundary100% pearlite

A

A

10

60 m

(ferrite)

Fe3C

(cementite)

• Spheroidite: -- crystals with spherical Fe3C --diffusion dependent. --heat bainite or pearlite for long times --reduces interfacial area (driving force)• 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. 10.10, 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

T(°C)Austenite (stable)

200

P

B

TE

0%

100%

50%

A

A

Spheroidite100% spheroidite

100% spheroidite

11

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

Adapted from Fig. 10.13, Callister 6e.

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

• Isothermal Transf. Diagram

xx x

xx

xpotential C atom sites

Fe atom sites

(involves single atom jumps)

time (s)10 103 10510-1

400

600

800

T(°C)Austenite (stable)

200

P

B

TE

0%

100%50%

A

A

S

M + AM + A

M + A

0%50%90%

Martentite needlesAustenite

60

m

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

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

OTHER PRODUCTS: Fe-C SYSTEM (2)

12

Adapted from Fig. 10.15, Callister 6e.

COOLING EX: Fe-C SYSTEM (1)• Co = Ceutectoid• Three histories...

time (s)10 103 10510-1

400

600

800

T(°C)Austenite (stable)

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

• Co = Ceutectoid• Three histories...

time (s)10 103 10510-1

400

600

800

T(°C)Austenite (stable)

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

Adapted from Fig. 10.15, Callister 6e.

COOLING EX: Fe-C SYSTEM (2)

14

Adapted from Fig. 10.15, Callister 6e.

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

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%C

0 0.5 10

50

100%EL

Impact

energ

y (

Izod,

ft-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)

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 pearlite

coarse pearlitespheroidite

0

30

60

90

wt%C0 0.5 1

Duct

ility

(%

AR

)

fine pearlite

coarse pearlite

spheroidite

Hypo Hyper Hypo Hyper

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

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

m

• produces extremely small Fe3C particles surrounded by

19

Austenite ()

Bainite ( + Fe3C plates/needles)

Pearlite ( + Fe3C layers + a proeutectoid phase)

Martensite (BCT phase diffusionless

transformation)

Tempered Martensite ( + very fine

Fe3C particles)

slow cool

moderate cool

rapid quench

reheat

Str

ength

Duct

ilit

yMartensite

T Martensite bainite

fine pearlite coarse pearlite

spheroidite

General Trends

Adapted from Fig. 10.27, Callister 6e.

SUMMARY: PROCESSING OPTIONS

20

• Particles impede dislocations.• Ex: Al-Cu system• Procedure: --Pt A: solution heat treat (get solid solution) --Pt B: quench to room temp. --Pt C: reheat to nucleate small crystals within crystals.• Other precipitation systems: • Cu-Be • Cu-Sn • Mg-Al

Pt A (sol’n heat treat)

Pt B

Pt C (precipitate )

Temp.

Time

Adapted from Fig. 11.22, Callister 6e. (Fig. 11.22 adapted from J.L. Murray, International Metals Review 30, p.5, 1985.)

Adapted from Fig. 11.20, Callister 6e.

PRECIPITATION HARDENING

300

400

500

600

700

0 10 20 30 40 50wt%Cu(Al)

L+L

+L

T(°C)

A

B

C

composition range needed for precipitation hardening

CuAl2

21

• 2014 Al Alloy:

• TS peaks with precipitation time.• Increasing T accelerates process.

• %EL reaches minimum with precipitation time.

Adapted from Fig. 11.25 (a) and (b), Callister 6e. (Fig. 11.25 adapted from Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker (Managing Ed.), American Society for Metals, 1979. p. 41.)

PRECIPITATE EFFECT ON TS, %EL

precipitation heat treat time (h)

tensi

le s

trength

(M

Pa)

300

400

500

2001min 1h 1day 1mo1yr

204°C

149°C

non-

equi

l. so

lid s

olut

ion

man

y sm

all

prec

ipita

tes

“ag

ed”

fe

wer

larg

e

pre

cipi

tate

s

“ove

rage

d”%

EL

(2in

sam

ple

)10

20

30

0 1min 1h 1day 1mo1yr

204°C 149°C

precipitation heat treat time (h)

22

• Peak-aged --avg. particle size = 64b --closer spaced particles efficiently stop dislocations.

Simulation courtesyof Volker Mohles,Institut für Materialphysik der Universitåt, Münster, Germany (http://www.uni-munster.de/physik/MP/mohles/). Used with permission.

SIMULATION: DISLOCATION MOTION PEAK AGED MATERIAL

Click on image tobegin simulation

23

• Over-aged --avg. particle size = 361b --more widely spaced particles not as effective.

Simulation courtesyof Volker Mohles,Institut für Materialphysik der Universitåt, Münster, Germany (http://www.uni-munster.de/physik/MP/mohles/). Used with permission.

SIMULATION: DISLOCATION MOTION

OVERAGED MATERIAL

Click on image tobegin simulation

24

• Hard precipitates are difficult to shear. Ex: Ceramics in metals (SiC in Iron or Aluminum).

Large shear stress needed to move dislocation toward precipitate and shear it.

Side View

Top View

Slipped part of slip plane

Unslipped part of slip plane

S

Dislocation “advances” but precipitates act as “pinning” sites with spacing S.

precipitate

• Result: y ~

1S

STRENGTHENING STRATEGY 3: PRECIPITATION STRENGTHENING

25

• View onto slip plane of Nimonic PE16• Precipitate volume fraction: 10%• Average precipitate size: 64 b (b = 1 atomic slip distance)

Simulation courtesy of Volker Mohles, Institut für Materialphysik der Universitåt, Münster, Germany (http://www.uni-munster.de/physik/MP/mohles/). Used with permission.

SIMULATION:PRECIPITATION STRENGTHENING

26

• Internal wing structure on Boeing 767

• Aluminum is strengthened with precipitates formed by alloying.

Adapted from Fig. 11.24, Callister 6e. (Fig. 11.24 is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)

Adapted from Fig. 11.0, Callister 5e. (Fig. 11.0 is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)

1.5m

APPLICATION:PRECIPITATION STRENGTHENING

Reading:

Core Problems:

Self-help Problems:

0

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