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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)
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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)
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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
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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
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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.)
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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:
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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
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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
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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
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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
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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)
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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)
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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
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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
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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
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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.
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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