2012-05-20

1

Chapter 11 -

Chapter 11:Phase Transformations

School of Mechanical Engineering

Choi, Hae-Jin

Materials Science - Prof. Choi, Hae-Jin 1

Chapter 11 - 2

ISSUES TO ADDRESS...

• Transforming one phase into another takes time.

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

• Is it possible to slow down transformations so that non-equilibrium structures are formed?

• Are the mechanical properties of non-equilibriumstructures more desirable than equilibrium ones?

Fe

(Austenite)

Eutectoid transformation

C FCC

Fe3C(cementite)

(ferrite)

+

(BCC)

2012-05-20

2

Chapter 11 -

Phase Transformations

Nucleation – nuclei (seeds) act as templates on which crystals grow

– for nucleus to form rate of addition of atoms to nucleus must be faster than rate of loss

– once nucleated, growth proceeds until equilibrium is attained

3

Driving force to nucleate increases as we increase T– supercooling (eutectic, eutectoid)– superheating (peritectic)

Small supercooling slow nucleation rate - few nuclei - large crystals

Large supercooling rapid nucleation rate - many nuclei - small crystals

Chapter 11 -

Solidification: Nucleation Types

• Homogeneous nucleation– nuclei form in the bulk of liquid metal– requires considerable supercooling

(typically 80-300°C)

4

• Heterogeneous nucleation– much easier since stable “nucleating surface” is

already present — e.g., mold wall, impurities in liquid phase

– only very slight supercooling (0.1-10ºC)

2012-05-20

3

Chapter 11 -

Homogeneous Nucleation & Energy Effects

5

r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy)

GT = Total Free Energy= GS + GV

Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface)

24 rGS

= surface tension

Volume (Bulk) Free Energy –stabilizes the nuclei (releases energy)

GrGV3

3

4

volume unit

energy free volume G

Chapter 11 -

Solidification

6

TH

Tr

f

m

2

*

Note: Hf and are weakly dependent on T

r* decreases as T increases

For typical T r* ~ 10 nm

Hf = latent heat of solidification

Tm = melting temperature

= surface free energy

T = Tm - T = supercooling

r* = critical radius

2012-05-20

4

Chapter 11 -

Rate of Phase Transformations

7

Kinetics - study of reaction rates of phase transformations

• To determine reaction rate – measure degree of transformation as function of time (while holding temp constant)

measure propagation of sound waves –on single specimen

electrical conductivity measurements –on single specimen

X-ray diffraction – many specimens required

How is degree of transformation measured?

Chapter 11 -

Rate of Phase Transformation

Avrami equation => y = 1- exp (-kt n)

– k & n are transformation specific parameters

8

transformation complete

log tFra

ctio

n tr

ansf

orm

ed, y

Fixed T

fraction transformed

time

0.5

By convention rate = 1 / t0.5

Adapted from Fig. 11.10, Callister & Rethwisch 3e.

maximum rate reached – now amount unconverted decreases so rate slows

t0.5

rate increases as surface area increases & nuclei grow

2012-05-20

5

Chapter 11 -

Temperature Dependence of Transformation Rate

• For the recrystallization of Cu, since

rate = 1/t0.5

rate increases with increasing temperature

9

• Rate often so slow that attainment of equilibrium state not possible!

Adapted from Fig. 11.11, Callister & Rethwisch 3e.(Fig. 11.11 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)

135C 119C 113C 102C 88C 43C

1 10 102 104

Chapter 11 -

Transformations & Undercooling

10

• For transf. to occur, must cool to below 727°C (i.e., must “undercool”)

• Eutectoid transf. (Fe-Fe3C system): + Fe3C0.76 wt% C

0.022 wt% C6.7 wt% C

Fe 3

C (

cem

entit

e)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

(austenite)

+L

+Fe3C

+Fe3C

L+Fe3C

(Fe) C, wt%C

1148°C

T(°C)

ferrite

727°C

Eutectoid:Equil. Cooling: Ttransf. = 727ºCT

Undercooling by Ttransf. < 727C

0.7

6

0.0

22

Adapted from Fig. 10.28,Callister & Rethwisch 3e. (Fig. 10.28 adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)

2012-05-20

6

Chapter 11 -

The Fe-Fe3C Eutectoid Transformation

11

Coarse pearlite formed at higher temperatures – relatively soft

Fine pearlite formed at lower temperatures – relatively hard

• Transformation of austenite to pearlite:

Adapted from Fig. 10.15, Callister & Rethwisch 3e.

pearlite growth direction

Austenite ()grain boundary

cementite (Fe3C)

Ferrite ()

• For this transformation,rate increases with [Teutectoid – T ] (i.e., T). Adapted from

Fig. 11.12, Callister & Rethwisch 3e.

675°C (T smaller)

0

50y

(% p

earli

te)

600°C (T larger)

650°C

100

Diffusion of C during transformation

Carbon diffusion

Chapter 11 - 12

Generation of Isothermal Transformation Diagrams

Adapted from Fig. 11.13,Callister & Rethwisch 3e. (Fig. 11.13 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.)

• The Fe-Fe3C system, for Co = 0.76 wt% C• A transformation temperature of 675°C.

100

50

01 102 104

T = 675°C

y,

% t

rans

form

ed

time (s)

400

500

600

700

1 10 102 103 104 105

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

Pearlite

T(°C)

time (s)

isothermal transformation at 675°C

Consider:

2012-05-20

7

Chapter 11 - 13

Austenite-to-Pearlite Isothermal Transformation• Eutectoid composition, C0 = 0.76 wt% C• Begin at T > 727°C• Rapidly cool to 625°C• Hold T (625°C) constant (isothermal treatment)

Adapted from Fig. 11.14,Callister & Rethwisch 3e. (Fig. 11.14 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.)

400

500

600

700

Austenite (stable)TE (727C)

Austenite (unstable)

Pearlite

T(°C)

1 10 102 103 104 105

time (s)

Chapter 11 -

Transformations Involving Noneutectoid Compositions

14

Hypereutectoid composition – proeutectoid cementite

Consider C0 = 1.13 wt% C

TE (727°C)

T(°C)

time (s)

A

A

A+

C

P

1 10 102 103 104

500

700

900

600

800

A+

P

Adapted from Fig. 11.16, Callister & Rethwisch 3e.

Adapted from Fig. 10.28, Callister & Rethwisch 3e.

Fe 3

C (

cem

entit

e)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

(austenite)

+L

+Fe3C

+Fe3C

L+Fe3C

(Fe) C, wt%C

T(°C)

727°CT

0.7

6

0.0

22

1.13

2012-05-20

8

Chapter 11 -

Bainite: Another Fe-Fe3C Transformation Product

15

10 103 105

time (s)10-1

400

600

800

T(°C)Austenite (stable)

200

P

B

TEA

A

• Bainite:-- elongated Fe3C particles in

-ferrite matrix

-- diffusion controlled• Isothermal Transf. Diagram,

C0 = 0.76 wt% C

Adapted from Fig. 11.18, Callister & Rethwisch 3e.

Adapted from Fig. 11.17, Callister & Rethwisch 3e. (Fig. 11.17 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)

100% bainite

100% pearlite

Chapter 11 - 16

Spheroidite: Another Microstructure for the Fe-Fe3C System

• Spheroidite:-- Fe3C particles within an -ferrite matrix-- formation requires diffusion-- heat bainite or pearlite at temperature

just below eutectoid for long times-- driving force – reduction

of -ferrite/Fe3C interfacial area

Adapted from Fig. 11.19, Callister & Rethwisch 3e. (Fig. 11.19 copyright United States Steel Corporation, 1971.)

60 m

(ferrite)

(cementite)

Fe3C

2012-05-20

9

Chapter 11 - 17

Martensite: A Nonequilibrium Transformation Product

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

Adapted from Fig. 11.22, Callister & Rethwisch 3e. (Fig. 11.22 courtesy United States Steel Corporation.)

Adapted from Fig. 11.21, Callister & Rethwisch 3e.

Martensite needlesAustenite

60

m

xx x

xx

xpotential C atom sites

Fe atom sites

Adapted from Fig. 11.23, Callister & Rethwisch 3e.

• Isothermal Transf. Diagram

• to martensite (M) transformation..-- is rapid! (diffusionless)-- % transf. depends only on T to

which rapidly cooled

10 103 105 time (s)10-1

400

600

800

T(°C)Austenite (stable)

200

P

B

TEA

A

M + AM + A

M + A

0%50%90%

Chapter 11 -

Martensite Formation

(FCC) (BCC) + Fe3C

18

slow cooling

tempering

quench

M (BCT)

Martensite (M) – single phase

– has body centered tetragonal (BCT) crystal structure

Diffusionless transformation BCT if C0 > 0.15 wt% C

BCT few slip planes hard, brittle

2012-05-20

10

Chapter 11 -

Phase Transformations of AlloysEffect of adding other elements

Change transition temp.

Cr, Ni, Mo, Si, Mn

retard + Fe3C

reaction (and formation of

pearlite, bainite)

19

Adapted from Fig. 11.24, Callister & Rethwisch 3e.

Chapter 11 -

Continuous Cooling Transformation Diagrams

Conversion of isothermal transformation diagram to continuous cooling transformation diagram

20

Adapted from Fig. 11.26,Callister & Rethwisch 3e.

Cooling curve

2012-05-20

11

Chapter 11 -

Isothermal Heat Treatment Example Problems

On the isothermal transformation diagram for a 0.45 wt% C, Fe-C alloy, sketch and label the time-temperature paths to produce the following microstructures:a) 42% proeutectoid ferrite and 58% coarse

pearlite

b) 50% fine pearlite and 50% bainite

c) 100% martensite

d) 50% martensite and 50% austenite

21

Chapter 11 -

Solution to Part (a) of Example Problema) 42% proeutectoid ferrite and 58% coarse pearlite

22

Isothermally treat at ~ 680°C

-- all austenite transforms to proeutectoid and coarse pearlite.

A + B

A + P

A + A

BP

A50%

0

200

400

600

800

0.1 10 103 105

time (s)

M (start)M (50%)M (90%)

Adapted from Fig. 10.29,Callister 5e.

Fe-Fe3C phase diagram, for C0 = 0.45 wt% C

Wpearlite C0 0.022

0.76 0.022

= 0.45 0.0220.76 0.022

= 0.58

W = 1 0.58 = 0.42

T (°C)

2012-05-20

12

Chapter 11 -

Solution to Part (b) of Example Problem

b) 50% fine pearlite and 50% bainite

23

T (°C)

A + B

A + P

A + A

BP

A50%

0

200

400

600

800

0.1 10 103 105

time (s)

M (start)M (50%)M (90%)

Adapted from Fig. 10.29,Callister 5e.

Fe-Fe3C phase diagram, for C0 = 0.45 wt% C

Then isothermally treat at ~ 470°C

– all remaining austenite transforms to bainite.

Isothermally treat at ~ 590°C – 50% of austenite transforms

to fine pearlite.

Chapter 11 -

Solutions to Parts (c) & (d) of Example Problem

c) 100% martensite –rapidly quench to room temperature

24

d) 50% martensite

& 50% austenite

-- rapidly quench to ~ 290°C, hold at this T

T (°C)

A + B

A + P

A + A

BP

A50%

0

200

400

600

800

0.1 10 103 105

time (s)

M (start)M (50%)M (90%)

Adapted from Fig. 10.29,Callister 5e.

Fe-Fe3C phase diagram, for C0 = 0.45 wt% C

d)

c)

2012-05-20

13

Chapter 11 -

Mechanical Props: Influence of C Content

25

Adapted from Fig. 10.34, Callister & Rethwisch 3e.

• Increase C content: TS and YS increase, %EL decreases

C0 < 0.76 wt% C

Hypoeutectoid

Pearlite (med)ferrite (soft)

Adapted from Fig. 10.37, Callister & Rethwisch 3e.

C0 > 0.76 wt% C

Hypereutectoid

Pearlite (med)Cementite

(hard)

Adapted from Fig. 11.30, Callister & Rethwisch 3e. (Fig. 11.30 based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.)

300

500

700

900

1100YS(MPa)TS(MPa)

wt% C0 0.5 1

hardness

0.7

6

Hypo Hyper

wt% C0 0.5 1

0

50

100

%EL

Imp

act

en

erg

y (I

zod

, ft-

lb)

0

40

80

0.7

6

Hypo Hyper

Chapter 11 -

Mechanical Props: Fine Pearlite vs. Coarse Pearlite vs. Spheroidite

26

Adapted from Fig. 11.31, Callister & Rethwisch 3e. (Fig. 11.31 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.)

• Hardness:• %RA:

fine > coarse > spheroiditefine < coarse < spheroidite

80

160

240

320

wt%C0 0.5 1

Bri

ne

ll h

ard

ne

ss

fine pearlite

coarsepearlitespheroidite

Hypo Hyper

0

30

60

90

wt%C

Duc

tility

(%

RA

)

fine pearlite

coarsepearlite

spheroidite

Hypo Hyper

0 0.5 1

2012-05-20

14

Chapter 11 -

Mechanical Props: Fine Pearlite vs. Martensite

27

• Hardness: fine pearlite << martensite.

Adapted from Fig. 11.33, Callister & Rethwisch 3e. (Fig. 11.33 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.)

0

200

wt% C0 0.5 1

400

600

Bri

ne

ll h

ard

ne

ss martensite

fine pearlite

Hypo Hyper

Chapter 11 -

Tempered Martensite

28

• tempered martensite less brittle than martensite• tempering reduces internal stresses caused by quenching

Adapted from Fig. 11.34, Callister & Rethwisch 3e. (Fig. 11.34 copyright by United States Steel Corporation, 1971.)

• tempering decreases TS, YS but increases %RA• tempering produces extremely small Fe3C particles surrounded by

Adapted from Fig. 11.35, Callister & Rethwisch 3e. (Fig. 11.35 adapted from Fig. furnished courtesy of Republic Steel Corporation.)

9 m

YS(MPa)TS(MPa)

800

1000

1200

1400

1600

1800

30

40

50

60

200 400 600Tempering T (°C)

%RA

TS

YS

%RA

Heat treat martensite to form tempered martensite

2012-05-20

15

Chapter 11 -

Summary of Possible Transformations

29

Adapted from Fig. 11.37, Callister & Rethwisch 3e.

Austenite ()

Pearlite( + Fe3C layers + a proeutectoid phase)

slow cool

Bainite( + elong. Fe3C particles)

moderatecool

Martensite(BCT phase diffusionless

transformation)

rapid quench

Tempered Martensite ( + very fine

Fe3C particles)

reheat

Str

engt

h

Duc

tility

Martensite T Martensite

bainite fine pearlite

coarse pearlite spheroidite

General Trends

Chapter 11 - 30

Precipitation Hardening

0 10 20 30 40 50wt% Cu

L+L

+L

300

400

500

600

700

(Al)

T(°C)

composition range available for precipitation hardening

CuAl2

A

Adapted from Fig. 11.43, Callister & Rethwisch 3e. (Fig. 11.43 adapted from J.L. Murray, International Metals Review 30, p.5, 1985.)

• Particles impede dislocation motion.• Ex: Al-Cu system• Procedure:

Adapted from Fig. 11.41, Callister & Rethwisch 3e.

-- Pt B: quench to room temp.(retain solid solution)

-- Pt C: reheat to nucleatesmall particles within phase.

• Other alloys that precipitationharden:• Cu-Be• Cu-Sn• Mg-Al

Temp.

Time

-- Pt A: solution heat treat(get solid solution)

Pt A (sol’n heat treat)

B

Pt B

C

Pt C (precipitate

2012-05-20

16

Chapter 11 - 31

Influence of Precipitation Heat Treatment on TS, %EL• 2014 Al Alloy:

• Maxima on TS curves.• Increasing T accelerates

process.

precipitation heat treat time

tens

ile s

tren

gth

(MP

a)

200

300

400

1001min 1h 1day 1mo 1yr

204°C149°C

• Minima on %EL curves.

%E

L(2

in s

ampl

e)

10

20

30

01min 1h 1day 1mo 1yr

204°C 149°C

precipitation heat treat time

Chapter 11 - 32

Melting & Glass Transition Temps.What factors affect Tm and Tg?

• Both Tm and Tg increase with increasing chain stiffness

• Chain stiffness increased by presence of

1. Bulky sidegroups

2. Polar groups or sidegroups

3. Chain double bonds and aromatic chain groups

• Regularity of repeat unit arrangements – affects Tm only

32

Adapted from Fig. 11.47, Callister & Rethwisch 3e.

2012-05-20

17

Chapter 11 - 33

Thermoplastics vs. Thermosets

33

• Thermoplastics:-- little crosslinking-- ductile-- soften w/heating-- polyethylene

polypropylenepolycarbonatepolystyrene

• Thermosets:-- significant crosslinking

(10 to 50% of repeat units)-- hard and brittle-- do NOT soften w/heating-- vulcanized rubber, epoxies,

polyester resin, phenolic resin

Adapted from Fig. 11.48, Callister & Rethwisch 3e. (Fig. 11.48 is from F.W. Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley and Sons, Inc., 1984.)

Callister, Fig. 16.9

T

Molecular weight

Tg

Tmmobile liquid

viscousliquid

rubber

tough plastic

partially crystalline solid

crystalline solid

Chapter 11 - 34

Summary

• Heat treatments of Fe-C alloys produce microstructures including:

-- pearlite, bainite, spheroidite, martensite, tempered martensite

• Precipitation hardening--hardening, strengthening due to formation of

precipitate particles.--Al, Mg alloys precipitation hardenable.

• Polymer melting and glass transition temperatures