Chapter 11: Phase TransformationsPhase Transformationsweb.khu.ac.kr/~kpark/material/ch11r.pdf ·...

Chapter 11:Phase TransformationsPhase Transformations

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

Fe Eutectoid

transformation

Fe3C(cementite)

(Austenite)C FCC

(ferrite)

+(BCC)

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

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

• Are the mechanical properties of non-equilibrium

Chapter 11 - 1

structures more desirable than equilibrium ones?

Phase TransformationsNucleation

– 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 lossfaster than rate of loss– once nucleated, growth proceeds until equilibrium is attained

Driving force to nucleate increases as we increase TDriving 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 - 2

Solidification: Nucleation Typesyp

• Homogeneous nucleationHomogeneous nucleation– nuclei form in the bulk of liquid metal– requires considerable supercooling q p g

(typically 80-300°C)

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

already present — e.g., mold wall, impurities in y p g , , pliquid phase

– only very slight supercooling (0.1-10ºC)

Chapter 11 - 3

Homogeneous Nucleation & Energy EffectsSurface Free Energy- destabilizes the nuclei (it takes energy to make an interface)an interface)

24 rGS

= surface tension

GT = Total Free Energy

= surface tension

T gy= GS + GV

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

GrGV3

343

volume unitenergy free volume

G

Chapter 11 - 4

r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy) Adapted from Fig.11.2(b), Callister & Rethwisch 3e.

Solidification

T2r* = critical radius

THTr

f

m

2*

H l t t h t f lidifi tiTm = melting temperature= surface free energy

Hf = latent heat of solidificationT = Tm - T = supercooling

Note: Hf and are weakly dependent on T

r* decreases as T increases

For typical T r* ~ 10 nm

Chapter 11 - 5

Overall transformation rate:

T N G T N G

Chapter 11 - 6

Rate of Phase Transformations

Kinetics - study of reaction rates of phaseKinetics study of reaction rates of phase transformations

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

How is degree of transformation measured?

electrical conductivity measurements –i l i

X-ray diffraction – many specimens required

measure propagation of sound waves –on single specimen

on single specimen

Chapter 11 - 7

on single specimen

Rate of Phase Transformationtransformation complete

med

, yFixed T

trans

form Fixed T

0.5 maximum rate reached – now amount unconverted decreases so rate slows

ract

ion

t unconverted decreases so rate slows

t0.5

rate increases as surface area increases & nuclei grow

A i ti > 1 ( kt n)

log tFr

Adapted from Fig. 11.10, Callister & R th i h 3Avrami equation => y = 1- exp (-kt n)

fraction transformed

time

Rethwisch 3e.

– k & n are transformation specific parameterstransformed

B ti t 1 / tChapter 11 - 8

By convention rate = 1 / t0.5

Temperature Dependence of Transformation RateTransformation Rate

Adapted from Fig. 11.11, Callister & Rethwisch 3eRethwisch 3e.(Fig. 11.11 adapted from B.F. Decker and D. Harker, "Recrystallization in R ll d C " T

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

Rolled Copper", Trans AIME, 188, 1950, p. 888.)1 10 102 104

• For the recrystallization of Cu, since

rate = 1/t0.5

rate increases with increasing temperature

• Rate often so slow that attainment of equilibrium t t t ibl !

Chapter 11 - 9

state not possible!

Transformations & Undercoolingg

• For transf. to occur, must • Eutectoid transf. (Fe-Fe3C system): + Fe3C

0.76 wt% C0 022 t% C

6.7 wt% Ccool to below 727°C (i.e., must “undercool”)

0.022 wt% C

T(°C)1600

1400 L

T( C)Adapted from Fig. 10.28,Callister & Rethwisch 3e. (Fig. 10.28 adapted from Binary Alloy Phase

ntite

)

00

1200 (austenite)

+LL+Fe3C1148°C

Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)

(cem

en1000

800

+Fe3Cferrite

727°C

Eutectoid:Equil. Cooling: Ttransf. = 727ºC

Fe3C

600

400

+Fe3C727 C

TUndercooling by Ttransf. < 727C

.76

022

Chapter 11 - 10

4000 1 2 3 4 5 6 6.7(Fe) C, wt%C

0.0.0

The Fe-Fe3C Eutectoid Transformation3• Transformation of austenite to pearlite:

Austenite () cementite (Fe3C)Diffusion of C during transformation

Austenite ()grain boundary

cementite (Fe3C)Ferrite ()

during transformation

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

pearlite growth direction

• For this transformation,

rate increases with [T – T ] (i e T) 50ar

lite) 600°C

(T larger)650°C

100

Carbon diffusion

[Teutectoid – T ] (i.e., T). Adapted from Fig. 11.12, Callister & Rethwisch 3e.

675°C (T smaller)

0

50y

(% p

ea 650 C

Coarse pearlite formed at higher temperatures – relatively soft

Chapter 11 - 11

Fine pearlite formed at lower temperatures – relatively hard

Generation of Isothermal Transformation DiagramsDiagrams

• The Fe-Fe3C system, for Co = 0.76 wt% CConsider:

• A transformation temperature of 675°C.

100T = 675°Crm

ed

50

0

T = 675 C

y,

% tr

ansf

or

01 102 104% time (s)

Austenite (stable) T (727 C)T(°C)

Adapted from Fig. 11.13,Callister & ( f

600

700Austenite (stable) TE (727C)

Austenite (unstable)

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

500

600isothermal transformation at 675°C

Chapter 11 - 12

y , , p )400

1 10 102 103 104 105 time (s)

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

Austenite (stable)T(°C)700

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

T( C)

Adapted from Fig. 11.14,Callister & Rethwisch 3e. (Fig. 11.14 adapted from H. Boyer (Ed ) Atlas of Isothermal

600 Pearlite

(Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997,

500

p. 28.)400

1 10 102 103 104 105

Chapter 11 - 13

1 10 102 103 104 105

time (s)

Transformations Involving Noneutectoid CompositionsNoneutectoid Compositions

Consider C0 = 1 13 wt% CConsider C0 1.13 wt% CT(°C)900 1600

T(°C)

TE (727°C)A

A

A+C700

800

entit

e)

1400

1200

L

(austenite)

+LL+Fe3C

P

700

600 A+

P

3C (c

eme

1000

800 +Fe3C

727°CT

time (s)1 10 102 103 104

500 Fe3

600

4000 1 2 3 4 5 6 6.7

+Fe3C

(Fe) C %C

T

0.76

0.02

2

13( )Adapted from Fig. 11.16, Callister & Rethwisch 3e.


(Fe) C, wt%C1.

Chapter 11 - 14

Hypereutectoid composition – proeutectoid cementite

Bainite: Another Fe-Fe3C Transformation ProductTransformation Product

• Bainite:-- elongated Fe3C particles in

-ferrite matrix-- diffusion controlled

• Isothermal Transf. Diagram,Fe3C(cementite)

800

T(°C)Austenite (stable)

TEA

Isothermal Transf. Diagram, C0 = 0.76 wt% C

( )(ferrite)

600

T( C)P

TEA

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

5 m

100% bainite

100% pearlite

400 BA

( gHandbook, 8th ed., Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.)

100% bainite

10 103 10510-1

200

Chapter 11 - 15

10 10time (s)

10Adapted from Fig. 11.18, Callister & Rethwisch 3e.

Spheroidite: Another Microstructure for the Fe Fe C System

• Spheroidite:

for the Fe-Fe3C System

• Spheroidite:-- Fe3C particles within an -ferrite matrix-- formation requires diffusion

(ferrite)

-- heat bainite or pearlite at temperature just below eutectoid for long times

-- driving force – reduction (cementite)

Fe3C

of -ferrite/Fe3C interfacial area

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

Chapter 11 - 16

Martensite: A Nonequilibrium Transformation Product

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

Transformation Product( ) ( )

0 m

xx x

x

x potential C atom sites

Fe atom sites


60x xx

• Isothermal Transf. Diagram

Adapted from Fig. 11.22, Callister & R th i h 3 (Fi 11 22 t

Martensite needlesAustenite

600

800

T(°C)Austenite (stable)

PTEA

Rethwisch 3e. (Fig. 11.22 courtesy United States Steel Corporation.)

Adapted from Fig. 11.23, Callister & • to martensite (M) transformation..400

600

BARethwisch 3e.

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

which rapidly cooled200

A

M + AM + A

0%50%90%

Chapter 11 - 17

which rapidly cooled

10 103 105 time (s)10-1

M AM + A

90%

Martensite Formation

slow cooling (FCC) (BCC) + Fe3Cslow cooling

quench

tempering

q

M (BCT)

Martensite (M) – single phase – has body centered tetragonal (BCT)

crystal structure

Diffusionless transformation BCT if C0 > 0.15 wt% CBCT few slip planes hard, brittle

Chapter 11 - 18

BCT few slip planes hard, brittle

Phase Transformations of AlloysyEffect of adding other elements

Ch t iti tChange transition temp.

Cr, Ni, Mo, Si, MnCr, Ni, Mo, Si, Mn

retard + Fe3C reaction (and formation of (pearlite, bainite)

Chapter 11 - 19


Continuous Cooling T f ti DiTransformation Diagrams

C i f i th lConversion of isothermal transformation diagram to continuous cooling transformation diagramtransformation diagram

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

Cooling curve

Chapter 11 - 20

Isothermal Heat Treatment Example ProblemsProblems

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 ) p

pearliteb) 50% fine pearlite and 50% bainiteb) 50% fine pearlite and 50% bainitec) 100% martensited) 50% t it d 50% t itd) 50% martensite and 50% austenite

Chapter 11 - 21

Solution to Part (a) of Example ProblemProblem

a) 42% proeutectoid ferrite and 58% coarse pearliteFe-Fe3C phase diagram

Isothermally treat at ~ 680°C

all austenite transformsA + A

800

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

T (°C)-- all austenite transforms to proeutectoid and coarse pearlite. A + P

BP600

T ( C)

A + BB

A50%400 M (start)

Wpearlite C0 0.0220.76 0.022

200

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

= 0.45 0.022

0.76 0.022 = 0.58

0

200

Ad t d f

W = 1 0.58 = 0.42

Chapter 11 - 22

00.1 10 103 105

time (s)Adapted from Fig. 10.29,Callister 5e.

Solution to Part (b) of Example Problem

b) 50% fine pearlite and 50% bainiteProblem

Fe-Fe3C phase diagram

T (°C)A + A

800


Isothermally treat at ~ 590°C T ( C)

A + PBP600

y– 50% of austenite transforms

to fine pearlite.

A + BB

A50%400 M (start)

Then isothermally treat at ~ 470°C

all remaining austenite

200

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

– all remaining austenite transforms to bainite.

0

200

Ad t d f

Chapter 11 - 23

00.1 10 103 105


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

c) 100% martensite – rapidly quench to room temperature Fe-Fe3C phase diagramtemperature

d) 50% martensite T (°C)

A + A800


& 50% austenite-- rapidly quench to

290°C h ld t thi T

T ( C)

A + PBP600

~ 290°C, hold at this TA + B

B

A50%400 M (start)

200

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

0

200

Ad t d f

c)

Chapter 11 - 24

00.1 10 103 105


Mechanical Props: Influence of C Contentp

Pearlite (med)Pearlite (med)Cementite


C0 < 0.76 wt% CHypoeutectoid

Pearlite (med)ferrite (soft)


C0 > 0.76 wt% CHypereutectoid

Cementite(hard)

yp yp

Adapted from Fig. 1100YS(MPa)

TS(MPa) Hypo Hyper

100%EL

t-lb)

80Hypo Hyper

11.30, Callister & Rethwisch 3e. (Fig. 11.30 based on data from Metals Handbook: Heat

700

900hardness

50 gy (I

zod,

ft

40

Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals 1981 p 9 )300

50050

mpa

ct e

ner

0

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

Metals, 1981, p. 9.)

wt% C0 0.5 1

0.76 wt% C0 0.5 1

0 Im

0.76

Chapter 11 - 25

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

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

320 fine pearlite

Hypo Hyper 90

A)

spheroidite

Hypo Hyper

240

hard

ness coarse

pearlitespheroidite

60

ctili

ty (%

RA spheroidite

80

160

Brin

ell

0

30Duc

fine pearlite

coarsepearlite

Adapted from Fig. 11.31, Callister & Rethwisch 3e. (Fig. 11.31 based on • Hardness: fine > coarse > spheroidite

wt%C0 0.5 1 0wt%C0 0.5 1

( gdata from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, pp. 9 and 17.)

• %RA:fine coarse spheroiditefine < coarse < spheroidite

Chapter 11 - 26

Mechanical Props: Fine Pearlite vs. MartensiteMartensite

Hypo Hyper

Adapted from Fig. 11.33, Callister & Rethwisch 3e. (Fig. 11.33 adapted from Edgar C Bain400

600ha

rdne

ss martensite

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,

d L F P t M t ll T A200

400

Brin

ell

fine pearlite and L.F. Porter, Metall. Trans. A, Vol. 8A, p. 1776.)

0wt% C0 0.5 1

fine pearlite

• Hardness: fine pearlite << martensite.

Chapter 11 - 27

Tempered Martensitep• tempered martensite less brittle than martensiteHeat treat martensite to form tempered martensite

• tempering reduces internal stresses caused by quenching

YS(MPa)TS(MPa)

1800

Adapted from Fig. 11 34 C lli t &

Adapted from Fi 11 35 m

1600

1800

TS

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

Fig. 11.35, Callister & Rethwisch 3e. (Fig. 11.35 adapted from

9 m

1200

1400

5060

YS

Fig. furnished courtesy of Republic Steel Corporation.) 800

1000

304050

%RA%RA

• tempering produces extremely small Fe3C particles surrounded by

200 400 600Tempering T (°C)

Chapter 11 - 28• tempering decreases TS, YS but increases %RA

p g p y 3 p y

Summary of Possible TransformationsyAdapted from Fig. 11.37, Callister & R th i h 3

Austenite ()Rethwisch 3e.

slow cool

moderatecool

rapid quench

Pearlite( + Fe3C layers + a

Bainite( + elong. Fe3C particles)

Martensite(BCT phase

proeutectoid phase)( pdiffusionless

transformation)

reheatMartensite

Tempered

reheat

ngth

tility

Martensite T Martensite

bainite Martensite ( + very fine

Fe3C particles)

Stre

n

Duc

tfine pearlite coarse pearlite

spheroidite

Chapter 11 - 29

spheroiditeGeneral Trends

Precipitation Hardening

L700

T(°C) C Al

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

L+L

+L

500

600T( C) CuAl2

A

• Procedure:-- Pt A: solution heat treat

(get solid solution)

300

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

-- Pt C: reheat to nucleate

(get solid solution)C

0 10 20 30 40 50wt% Cu

300(Al)

composition range available for precipitation hardening

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

• Other alloys that precipitation

B

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

• Other alloys that precipitationharden:• Cu-Be

Temp.Pt A (sol’n heat treat)

Adapted from Fig

• Cu-Sn• Mg-Al Pt C (precipitate

Chapter 11 - 30


TimePt B

Influence of Precipitation Heat Treatment on TS %EL

• 2014 Al Alloy:

M i TS

Treatment on TS, %EL

Mi i %EL• Maxima on TS curves.• Increasing T accelerates

process

• Minima on %EL curves.

process.

h (M

Pa)

400

mpl

e)

20

30

e st

reng

th

200

300

204°C149°C

L(2

in s

a

10

20

204°C 149°C

precipitation heat treat time

tens

ile

100 1min 1h 1day 1mo 1yr

204°C%

EL

0 1min 1h 1day 1mo 1yr

204 C

precipitation heat treat time

Chapter 11 - 31Adapted from Fig. 11.45 (a) and (b), Callister & Rethwisch 3e. (Fig. 11.45 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.)

precipitation heat treat time precipitation heat treat time

Diff t h

Chapter 11 -

Coherent lattice Different phase appears.Uniform alloying elements

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

• Both Tm and Tg increase with increasing chain stiffness

• Chain stiffness increased by ypresence of1. Bulky sidegroups2 Polar groups or sidegroups2. Polar groups or sidegroups3. Chain double bonds and

aromatic chain groups

• Regularity of repeat unit arrangements – affects Tm only

Chapter 11 - 3333


Thermoplastics vs. Thermosets

• Thermoplastics:

p

Callister, T

i rubber-- little crosslinking-- ductile-- soften w/heating

,Fig. 16.9

T

Tmmobile liquid

viscousliquid

rubber

tough plastic

-- polyethylenepolypropylenepolycarbonate

Tgp

partially crystallinepolycarbonate

polystyrene

Th Molecular weight

crystalline solidcrystalline

solid

• Thermosets:-- significant crosslinking

(10 to 50% of repeat units)

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.)

Molecular weight

( p )-- hard and brittle-- do NOT soften w/heating-- vulcanized rubber epoxies

Chapter 11 - 3434

vulcanized rubber, epoxies,polyester resin, phenolic resin

Summary

• Heat treatments of Fe-C alloys produce microstructures

y

Heat treatments of Fe C alloys produce microstructures including:-- pearlite, bainite, spheroidite, martensite, tempered

t itmartensite• Precipitation hardening

--hardening, strengthening due to formation of a de g, s e g e g due o o a o oprecipitate particles.

--Al, Mg alloys precipitation hardenable.Pol mer melting and glass transition temperat res• Polymer melting and glass transition temperatures

Chapter 11 - 35

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