Chapter 10: Phase Transformations

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Chapter 10:
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 10 - 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 10 - 2
Solidification: Nucleation Types
• Homogeneous nucleation
– nuclei form in the bulk of liquid metal
– requires considerable supercooling
(typically 80-300ºC)
• 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 10 - 3
Homogeneous Nucleation & Energy Effects
Surface Free Energy - destabilizes
the nuclei (it takes energy to make
an interface)
GS  4r 2 g
g = surface tension
GT = Total Free Energy
= GS + GV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
4
GV  r 3 G
3
G 
volume free energy
unit volume
r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy)
Adapted from Fig.10.2(b), Callister & Rethwisch 8e.
Chapter 10 - 4
Solidification
 2gTm
r* 
Hf T
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 10 - 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 10 - 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 surface area increases
& nuclei grow
log t
Avrami equation => y = 1- exp (-kt n)
fraction
transformed
Adapted from
Fig. 10.10,
Callister &
Rethwisch 8e.
time
– k & n are transformation specific parameters
By convention
rate = 1 / t0.5
Chapter 10 - 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.
10.11, Callister &
Rethwisch 8e.
(Fig. 10.11 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 10 - 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 727ºC
(i.e., must “undercool”)
T(ºC)
1600
d
1200
L+Fe3C
1148ºC
1000
g +Fe3C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
800
727ºC
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.
9.24,Callister & Rethwisch
8e. (Fig. 9.24 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 10 - 9
The Fe-Fe3C Eutectoid Transformation
• Transformation of austenite to pearlite:
Adapted from
Fig. 9.15,
Callister &
Rethwisch 8e.
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
600ºC
(T larger)
50
0
650ºC
675ºC
(T smaller)
g
Carbon
diffusion
Adapted from
Fig. 10.12,
Callister &
Rethwisch 8e.
Coarse pearlite  formed at higher temperatures – relatively soft
Fine pearlite
 formed at lower temperatures – relatively hard
Chapter 10 - 10
Generation of Isothermal Transformation
Diagrams
Consider:
y,
% transformed
• The Fe-Fe3C system, for C0 = 0.76 wt% C
• A transformation temperature of 675ºC.
100
T = 675ºC
50
0
10 2
1
T(ºC)
Austenite (stable)
10 4
time (s)
TE (727ºC)
700
Austenite
(unstable)
600
Pearlite
isothermal transformation at 675ºC
500
400
1
10
10 2 10 3 10 4 10 5
time (s)
Adapted from Fig. 10.13,Callister &
Rethwisch 8e. (Fig. 10.13 adapted from H.
Boyer (Ed.) Atlas of Isothermal
Transformation and Cooling
Transformation Diagrams, American
Society for Metals, 1977, p. 369.)
Chapter 10 - 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.
10.14,Callister &
Rethwisch 8e. (Fig. 10.14
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 10 - 12
Transformations Involving
Noneutectoid Compositions
Consider C0 = 1.13 wt% C
T(ºC)
T(ºC)
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. 10.16,
Callister & Rethwisch 8e.
104
T
400
0
(Fe)
0.76
600
A
TE (727ºC)
A
1.13
700
L
1400
0.022
800
1
727ºC
a +Fe3C
2
3
4
5
Adapted from Fig. 9.24,
Callister & Rethwisch 8e.
6
Fe3C (cementite)
1600
6.7
C, wt%C
Hypereutectoid composition – proeutectoid cementite
Chapter 10 - 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(ºC)
A
5 mm
100% pearlite
100% bainite
400
B
A
a (ferrite)
TE
P
600
Fe3C
(cementite)
Adapted from Fig. 10.17, Callister &
Rethwisch 8e. (Fig. 10.17 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. 10.18,
Callister & Rethwisch 8e.
105
time (s)
Chapter 10 - 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. 10.19, Callister &
Rethwisch 8e. (Fig. 10.19 copyright
United States Steel Corporation,
1971.)
Chapter 10 - 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. 10.20,
Callister & Rethwisch 8e.
• Isothermal Transf. Diagram
800
Austenite (stable)
T(ºC)
A
400
10-1
Adapted from Fig. 10.21, Callister &
Rethwisch 8e. (Fig. 10.21 courtesy
United States Steel Corporation.)
• g to martensite (M) transformation..
B
A
200
TE
P
600
Adapted from
Fig. 10.22,
Callister &
Rethwisch 8e.
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 10 - 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 10 - 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. 10.23,
Callister & Rethwisch 8e.
Chapter 10 - 18
Continuous Cooling
Transformation Diagrams
Conversion of isothermal
transformation diagram to
continuous cooling
transformation diagram
Adapted from Fig. 10.25,
Callister & Rethwisch 8e.
Cooling curve
Chapter 10 - 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 10 - 20
Solution to Part (a) of Example
Problem
a) 42% proeutectoid ferrite and 58% coarse pearlite
Fe-Fe3C phase diagram,
for C0 = 0.45 wt% C
Isothermally treat at ~ 680ºC
800
-- all austenite transforms
to proeutectoid a and
coarse pearlite.
Wpearlite 
C0  0.022
0.76  0.022
=
A
T (ºC)
A+a
P
B
600
A+P
A+B
A
400
0.45  0.022
= 0.58
0.76  0.022
50%
M (start)
M (50%)
M (90%)
200
Wa  = 1  0.58 = 0.42
Adapted from
Fig. 10.29,
Callister 5e.
0
0.1
10
103
time (s)
105
Chapter 10 - 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 ~ 590ºC T (ºC)
– 50% of austenite transforms
to fine pearlite.
A
P
B
600
Then isothermally treat
at ~ 470ºC
– 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. 10.29,
Callister 5e.
0
0.1
10
103
time (s)
105
Chapter 10 - 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 (ºC)
& 50% austenite
-- rapidly quench to
~ 290ºC, 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
Fig. 10.29,
Callister 5e.
0
0.1
10
103
time (s)
105
Chapter 10 - 23
Mechanical Props: Influence of C Content
Adapted from Fig. 9.30,
Callister & Rethwisch 8e.
TS(MPa)
1100
YS(MPa)
C0 < 0.76 wt% C
Hypoeutectoid
Hypo
Hyper
C0 > 0.76 wt% C
Hypereutectoid
Hypo
%EL
Adapted from Fig. 9.33,
Callister & Rethwisch 8e.
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.
10.29, Callister &
Rethwisch 8e. (Fig.
10.29 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 10 - 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. 10.30, Callister &
Rethwisch 8e. (Fig. 10.30 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 10 - 25
Mechanical Props: Fine Pearlite vs.
Martensite
Brinell hardness
Hypo
600
Hyper
martensite
Adapted from Fig. 10.32,
Callister & Rethwisch 8e. (Fig.
10.32 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 10 - 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. 10.34,
1400
Callister &
Rethwisch 8e.
1200
(Fig. 10.34
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.
10.33, Callister &
Rethwisch 8e. (Fig.
10.33 copyright by
United States Steel
Corporation, 1971.)
600
Tempering T (ºC)
• tempering produces extremely small Fe3C particles surrounded by a.
• tempering decreases TS, YS but increases %RA
Chapter 10 - 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. 10.36,
Callister &
Rethwisch 8e.
Tempered
Martensite
(a + very fine
Fe3C particles)
Chapter 10 - 28
ANNOUNCEMENTS
Reading:
Core Problems:
Self-help Problems:
Chapter 10 - 29
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