Chapter 11:
Phase Transformations
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
Fe
g
(Austenite)
C
FCC
Fe C
3
Eutectoid
transformation (cementite)
+
a
(ferrite)
(BCC)
• How does the rate of transformation depend on
time and temperature ?
• Is it possible to slow down transformations so that
non-equilibrium structures are formed?
• Are the mechanical properties of non-equilibrium
structures more desirable than equilibrium ones?
Chapter 11 - 1
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
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 - 2
Solidification: Nucleation Types
• Homogeneous nucleation
– nuclei form in the bulk of liquid metal
– requires considerable supercooling
(typically 80-300°C)
• 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)
Chapter 11 - 3
Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
DGS = 4pr 2 g
g = surface tension
GT = Total Free Energy
= GS + GV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
4
DGV = pr 3 DGu
3
DGu =
volume free energy
unit volume
r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy)
Adapted from Fig.11.2(b), Callister & Rethwisch 4e.
Chapter 11 - 4
Solidification
- 2gTm
r* =
DHf DT
r* = critical radius
g = surface free energy
Tm = melting temperature
Hf = latent heat of solidification
T = Tm - T = supercooling
Note: Hf and g are weakly dependent on T

r*
decreases as T increases
For typical T
r* ~ 10 nm
Chapter 11 - 5
Rate of Phase Transformations
Kinetics - study of reaction rates of phase
transformations
• To determine reaction rate – measure degree
of transformation as function of time (while
holding temp constant)
How is degree of transformation measured?
X-ray diffraction – many specimens required
electrical conductivity measurements –
on single specimen
measure propagation of sound waves –
on single specimen
Chapter 11 - 6
Fraction transformed, y
Rate of Phase Transformation
transformation complete
Fixed T
maximum rate reached – now amount
unconverted decreases so rate slows
0.5
t0.5
rate increases as interfacial surface area
increases & nuclei grow
log t
Avrami equation => y = 1- exp (-kt n)
fraction
transformed
Adapted from
Fig. 11.10,
Callister &
Rethwisch 4e.
time
– k & n are transformation specific parameters
By convention
rate = 1 / t0.5
Chapter 11 - 7
Temperature Dependence of
Transformation Rate
135C 119C
1
10
113C 102C
102
88C
43C
104
Adapted from Fig.
11.11, Callister &
Rethwisch 4e.
(Fig. 11.11 adapted
from B.F. Decker and
D. Harker,
"Recrystallization in
Rolled Copper", Trans
AIME, 188, 1950, p.
888.)
• For the recrystallization of Cu, since
rate = 1/t0.5
rate increases with increasing temperature
• Rate often so slow that attainment of equilibrium
state not possible!
Chapter 11 - 8
Transformations & Undercooling
g  a + Fe3C
• Eutectoid transf. (Fe-Fe3C system):
0.76 wt% C
6.7 wt% C
• For transf. to occur, must
0.022 wt% C
cool to below 727°C
(i.e., must “undercool”)
T(°C)
1600
d
1200
L+Fe3C
1148°C
1000
g +Fe3C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
800
727°C
400
0
(Fe)
T
a +Fe3C
Undercooling by Ttransf. < 727C
0.76
600
0.022
a
ferrite
g +L
g
(austenite)
1
2
3
4
5
6
Fe3C (cementite)
L
1400
Adapted from Fig.
10.28,Callister & Rethwisch
4e. (Fig. 10.28 adapted from
Binary Alloy Phase
Diagrams, 2nd ed., Vol. 1,
T.B. Massalski (Ed.-inChief), ASM International,
Materials Park, OH, 1990.)
6.7
C, wt%C
Chapter 11 - 9
The Fe-Fe3C Eutectoid Transformation
• Transformation of austenite to pearlite:
Adapted from
Fig. 10.15,
Callister &
Rethwisch 4e.
a
a
g a
a
a
a
g
• For this transformation,
rate increases with
[Teutectoid – T ] (i.e., T).
cementite (Fe3C)
Ferrite (a)
a
g
pearlite
growth
direction
a
a
100
y (% pearlite)
Austenite (g)
grain
boundary
Diffusion of C
during transformation
600°C
(T larger)
50
0
650°C
675°C
(T smaller)
g
Carbon
diffusion
Adapted from
Fig. 11.12,
Callister &
Rethwisch 4e.
Coarse pearlite  formed at higher temperatures – relatively soft
Fine pearlite
 formed at lower temperatures – relatively hard
Chapter 11 - 10
Generation of Isothermal Transformation
Diagrams
Consider:
y,
% transformed
• The Fe-Fe3C system, for C0 = 0.76 wt% C
• A transformation temperature of 675°C.
100
T = 675°C
50
0
10 2
1
T(°C)
Austenite (stable)
10 4
time (s)
TE (727C)
700
Austenite
(unstable)
600
Pearlite
isothermal transformation at 675°C
500
400
1
10
10 2 10 3 10 4 10 5
time (s)
Adapted from Fig. 11.13,Callister &
Rethwisch 4e. (Fig. 11.13 adapted from H.
Boyer (Ed.) Atlas of Isothermal
Transformation and Cooling
Transformation Diagrams, American
Society for Metals, 1977, p. 369.)
Chapter 11 - 11
Austenite-to-Pearlite Isothermal Transformation
•
•
•
•
Eutectoid composition, C0 = 0.76 wt% C
Begin at T > 727ºC
Rapidly cool to 625ºC
Hold T (625ºC) constant (isothermal treatment)
T(ºC)
Austenite (stable)
700
Austenite
(unstable)
600
g
g
500
TE (727ºC)
Pearlite
g
g
g
Adapted from Fig.
11.14,Callister &
Rethwisch 4e. (Fig. 11.14
adapted from H. Boyer
(Ed.) Atlas of Isothermal
Transformation and
Cooling Transformation
Diagrams, American
Society for Metals, 1997,
p. 28.)
g
400
1
10
10 2
10 3
10 4
10 5
time (s)
Chapter 11 - 12
Transformations Involving
Noneutectoid Compositions
Consider C0 = 1.13 wt% C
T(°C)
T(°C)
900
d
A
+
1200
C
A
+
P
a
P
L+Fe3C
(austenite)
1000
g +Fe3C
800
600
500
1
g +L
g
10
102
103
time (s)
Adapted from Fig. 11.16,
Callister & Rethwisch 4e.
104
T
400
0
(Fe)
0.76
600
A
TE (727°C)
A
1.13
700
L
1400
0.022
800
1
727°C
a +Fe3C
2
3
4
5
Adapted from Fig. 10.28,
Callister & Rethwisch 4e.
6
Fe3C (cementite)
1600
6.7
C, wt%C
Hypereutectoid composition – proeutectoid cementite
Chapter 11 - 13
Bainite: Another Fe-Fe3C
Transformation Product
• Bainite:
-- elongated Fe3C particles in
a-ferrite matrix
-- diffusion controlled
• Isothermal Transf. Diagram,
C0 = 0.76 wt% C
800
Austenite (stable)
T(°C)
A
5 mm
100% pearlite
100% bainite
400
B
A
a (ferrite)
TE
P
600
Fe3C
(cementite)
Adapted from Fig. 11.17, Callister &
Rethwisch 4e. (Fig. 11.17 from Metals
Handbook, 8th ed., Vol. 8, Metallography,
Structures, and Phase Diagrams, American
Society for Metals, Materials Park, OH,
1973.)
200
10-1
10
103
Adapted from Fig. 11.18,
Callister & Rethwisch 4e.
105
time (s)
Chapter 11 - 14
Spheroidite: Another Microstructure
for the Fe-Fe3C System
a
-- Fe3C particles within an a-ferrite matrix (ferrite)
• Spheroidite:
-- formation requires diffusion
-- heat bainite or pearlite at temperature
Fe3C
just below eutectoid for long times (cementite)
-- driving force – reduction
of a-ferrite/Fe3C interfacial area
60 mm
Adapted from Fig. 11.19, Callister &
Rethwisch 4e. (Fig. 11.19 copyright
United States Steel Corporation,
1971.)
Chapter 11 - 15
Martensite: A Nonequilibrium
Transformation Product
• Martensite:
Fe atom
sites
x
x
x
x
x
60 mm
-- g(FCC) to Martensite (BCT)
potential
C atom sites
x
Adapted from Fig. 11.21,
Callister & Rethwisch 4e.
• Isothermal Transf. Diagram
800
Austenite (stable)
T(°C) A
400
10-1
Adapted from Fig. 11.22, Callister &
Rethwisch 4e. (Fig. 11.22 courtesy
United States Steel Corporation.)
• g to martensite (M) transformation.
B
A
200
TE
P
600
Adapted from
Fig. 11.23,
Callister &
Rethwisch 4e.
Martensite needles
Austenite
0%
50%
90%
M+A
M+A
M+A
10
103
105
-- is rapid! (diffusionless)
-- % transf. depends only on T to
which rapidly cooled
time (s)
Chapter 11 - 16
Martensite Formation
g (FCC)
slow cooling
a (BCC) + Fe3C
quench
M (BCT)
tempering
Martensite (M) – single phase
– has body centered tetragonal (BCT)
crystal structure
Diffusionless transformation
BCT  few slip planes
BCT if C0 > 0.15 wt% C
 hard, brittle
Chapter 11 - 17
Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard g  a + Fe3C
reaction (and formation of
pearlite, bainite)
Adapted from Fig. 11.24,
Callister & Rethwisch 4e.
Chapter 11 - 18
Continuous Cooling
Transformation Diagrams
Conversion of isothermal
transformation diagram to
continuous cooling
transformation diagram
Adapted from Fig. 11.26,
Callister & Rethwisch 4e.
Cooling curve
Chapter 11 - 19
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
Chapter 11 - 20
Solution to Part (a) of Example
Problem
a) 42% proeutectoid ferrite and 58% coarse pearlite
Isothermally treat at ~
680°C
Fe-Fe3C phase diagram,
for C0 = 0.45 wt% C
800
A
T (°C)
-- all austenite transforms
to proeutectoid a and
coarse pearlite.
Wpearlite =
C0 - 0.022
0.76 - 0.022
=
A+a
P
B
600
A+P
A+B
A
400
0.45 - 0.022
= 0.58
0.76 - 0.022
200
50%
M (start)
M (50%)
M (90%)
Wa ¢ = 1 - 0.58 = 0.42
Adapted from Fig. 11.50,
Callister & Rethwisch 4e.
0
0.1
10
103
time (s)
105
Chapter 11 - 21
Solution to Part (b) of Example
Problem
b) 50% fine pearlite and 50% bainite
Fe-Fe3C phase diagram,
for C0 = 0.45 wt% C
800
Isothermally treat at ~ 590°CT (°C)
– 50% of austenite transforms
to fine pearlite.
A
P
B
600
Then isothermally treat
at ~ 470°C
– all remaining austenite
transforms to bainite.
A+a
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
200
Adapted from Fig. 11.50,
Callister & Rethwisch 4e.
0
0.1
10
103
time (s)
105
Chapter 11 - 22
Solutions to Parts (c) & (d) of Example
Problem
c) 100% martensite – rapidly quench to room
Fe-Fe3C phase diagram,
temperature
for C0 = 0.45 wt% C
d) 50% martensite 800
T (°C)
& 50% austenite
-- rapidly quench to
~ 290°C, hold at this
temperature
A
A+a
P
B
600
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
d)
200
c)
Adapted from 11.50,
Callister & Rethwisch 4e.
0
0.1
10
103
time (s)
105
Chapter 11 - 23
Mechanical Props: Influence of C Content
Adapted from Fig. 10.34,
Callister & Rethwisch 4e.
TS(MPa)
1100
YS(MPa)
C0 < 0.76 wt% C
Hypoeutectoid
Hypo
Hyper
C0 > 0.76 wt% C
Hypereutectoid
Hypo
%EL
Adapted from Fig. 10.37,
Callister & Rethwisch 4e.
Hyper
80
100
900
hardness
40
700
50
500
0
0.5
1
wt% C
0
0
0.5
0.76
0
0.76
300
Impact energy (Izod, ft-lb)
Pearlite (med)
ferrite (soft)
Pearlite (med)
Cementite
(hard)
Adapted from Fig.
11.30, Callister &
Rethwisch 4e. (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.)
1
wt% C
• Increase C content: TS and YS increase, %EL decreases
Chapter 11 - 24
Mechanical Props: Fine Pearlite vs. Coarse
Pearlite vs. Spheroidite
Brinell hardness
320
Hyper
fine
pearlite
240
coarse
pearlite
spheroidite
160
80
0
• Hardness:
• %RA:
0.5
1
wt%C
90
Ductility (%RA)
Hypo
Hypo
spheroidite
60
coarse
pearlite
fine
pearlite
30
0
Hyper
0
fine > coarse > spheroidite
fine < coarse < spheroidite
0.5
1
wt%C
Adapted from Fig. 11.31, Callister &
Rethwisch 4e. (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.)
Chapter 11 - 25
Mechanical Props: Fine Pearlite vs.
Martensite
Brinell hardness
Hypo
600
Hyper
martensite
Adapted from Fig. 11.33, Callister
& Rethwisch 4e. (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.)
400
200
fine pearlite
0
0
0.5
1
wt% C
• Hardness: fine pearlite << martensite.
Chapter 11 - 26
Tempered Martensite
Heat treat martensite to form tempered martensite
• tempered martensite less brittle than martensite
• tempering reduces internal stresses caused by quenching
TS(MPa)
YS(MPa)
1800
Adapted from
Fig. 11.35,
1400
Callister &
Rethwisch 4e.
1200
(Fig. 11.35
adapted from
Fig. furnished 1000
courtesy of
Republic Steel
800
Corporation.)
200
TS
YS
60
50
%RA
40
30
%RA
400
9 mm
1600
Adapted from Fig.
11.34, Callister &
Rethwisch 4e. (Fig.
11.34 copyright by
United States Steel
Corporation, 1971.)
600
Tempering T (°C)
• tempering produces extremely small Fe3C particles surrounded by a.
• tempering decreases TS, YS but increases %RA
Chapter 11 - 27
Summary of Possible Transformations
Austenite (g)
slow
cool
Bainite
Strength
(a + Fe3C layers + a
proeutectoid phase)
(a + elong. Fe3C particles)
Martensite
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
General Trends
rapid
quench
Martensite
(BCT phase
diffusionless
transformation)
reheat
Ductility
Pearlite
moderate
cool
Adapted from
Fig. 11.37,
Callister &
Rethwisch 4e.
Tempered
Martensite
(a + very fine
Fe3C particles)
Chapter 11 - 28
Precipitation Hardening
• Particles impede dislocation motion.
700
• Ex: Al-Cu system
T(°C)
• Procedure:
600
a+L
-- Pt A: solution heat treat
(get a solid solution)
-- Pt B: quench to room temp.
(retain a solid solution)
-- Pt C: reheat to nucleate
small q particles within
a phase.
a
500
400
• Other alloys that precipitation
harden: Temp.
• Cu-Be
• Cu-Sn
• Mg-Al
Adapted from Fig.
11.41, Callister &
Rethwisch 4e.
Pt A (sol’n heat treat)
q+L
A
q
a+q
C
300
0 B 10
(Al)
CuAl2
L
20
30
40
50
wt% Cu
composition range
available for precipitation hardening
Adapted from Fig. 11.43, Callister & Rethwisch 4e.
(Fig. 11.43 adapted from J.L. Murray, International
Metals Review 30, p.5, 1985.)
Pt C (precipitate q)
Pt B
Time
Chapter 11 - 29
Influence of Precipitation Heat
Treatment on TS, %EL
• 2014 Al Alloy:
400
300
200
100
149°C
204°C
1min
1h 1day 1mo 1yr
precipitation heat treat time
• Minima on %EL curves.
%EL (2 in sample)
tensile strength (MPa)
• Maxima on TS curves.
• Increasing T accelerates
process.
30
20
10
0
204°C
149°C
1min
1h 1day 1mo 1yr
precipitation heat treat time
Adapted from Fig. 11.46 (a) and (b), Callister & Rethwisch 4e. (Fig. 11.46 adapted from Metals
Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker Chapter 11 - 30
(Managing Ed.), American Society for Metals, 1979. p. 41.)
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
Adapted from Fig. 11.48,
Callister & Rethwisch 4e.
Chapter 11 - 31
Thermoplastics vs. Thermosets
• Thermoplastics:
-- little crosslinking
-- ductile
-- soften w/heating
-- polyethylene
polypropylene
polycarbonate
polystyrene
• Thermosets:
T
viscous
liquid
mobile
liquid
Callister,
rubber
Fig. 16.9
tough
plastic
crystalline
solid
partially
crystalline
solid
Molecular weight
Adapted from Fig. 11.49, Callister & Rethwisch 4e. (Fig.
-- significant crosslinking
11.49 is from F.W. Billmeyer, Jr., Textbook of Polymer
(10 to 50% of repeat units) Science, 3rd ed., John Wiley and Sons, Inc., 1984.)
-- hard and brittle
-- do NOT soften w/heating
-- vulcanized rubber, epoxies,
polyester resin, phenolic resin
Chapter 11 - 32
Tm
Tg
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
Chapter 11 - 33
ANNOUNCEMENTS
Reading:
Core Problems:
Self-help Problems:
Chapter 11 - 34