Chapter 10: Phase Transformations
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
Fe
γ
(Austenite)
C
FCC
Fe C
3
Eutectoid
transformation (cementite)
+
α
(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
Two pressure-temperature phase
diagrams are shown: for H2O (top) and
CO2 (bottom). Phase transformations
occur when phase boundaries (the red
curves) on these plots are crossed as
temperatures and/or pressure is
changed. For example, ice melts
(transformations to liquid water) upon
heating, which corresponds to crossing
the solid-liquid phase boundary, as
represented by the arrow on the H2O
phase diagram.
Similarly, upon passing
across the solid-gas phase
boundary of the CO2 phase
diagram, dry ice (solid CO2)
sublimates (transforms into
gaseous CO2). Again, as
arrow delineates this phase
transformation. (Changing
pressure)
Chapter 10 - 2
[10.2, 10.3] 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 ΔT (Tm-T)
– supercooling (eutectic, eutectoid) (p.341)
– superheating (peritectic)
Small supercooling  slow nucleation rate - few nuclei - large crystals
Large supercooling  rapid nucleation rate - many nuclei - small crystals
Chapter 10 - 3
[10.3] Solidification: Nucleation Types
• Homogeneous nucleation
– nuclei form in the bulk of liquid metal
– requires considerable supercooling (ΔT)
(typically 80-300°C)
• Heterogeneous (異種的) nucleation
– much easier since stable “nucleating surface” is
already present — e.g., mold wall, impurities in
liquid phase
– only very slight supercooling (0.1-10°C)
Chapter 10 - 4
Fig. 10.1 Schematic diagram showing the nucleation of a spherical
solid particle in a liquid.
Chapter 10 - 5
Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
γ = surface tension
ΔGT = Total Free Energy
= ΔGS + ΔGV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
r* = critical nucleus: for r < r* nuclei shrink; for r > r* nuclei grow (to reduce energy)
Adapted from Fig. 10.2(b), Callister & Rethwisch 10e.
Chapter 10 - 6
4 3
2𝛾𝛾
(10.1)
(10.3)
𝜋𝜋𝑟𝑟 ∆𝐺𝐺𝑣𝑣 + 4𝜋𝜋𝑟𝑟 2 𝛾𝛾
𝑟𝑟 ∗ = −
3
∆𝐺𝐺𝑣𝑣
3
16𝜋𝜋𝛾𝛾
𝑑𝑑 ∆𝐺𝐺
4
(10.4)
∆𝐺𝐺 ∗ =
= 𝜋𝜋∆𝐺𝐺𝑣𝑣 3𝑟𝑟 2 + 4𝜋𝜋𝜋𝜋 2𝑟𝑟 = 0 (10.2)
2
3 ∆𝐺𝐺𝑣𝑣
𝑑𝑑𝑑𝑑
3
∆𝐺𝐺 =
Fig. 10.2 (a) Schematic curves for volume free energy and surface free
energy contributions to the total free energy change attending the
formation of a spherical embryo/nucleus during solidification. (b)
Schematic plot of free energy versus embryo/nucleus, on which is shown
the critical free energy change (△G*) and the critical nucleus radius (r*).
Chapter 10 - 7
∆𝐻𝐻𝑓𝑓 𝑇𝑇𝑚𝑚 − 𝑇𝑇
(10.5)
∆𝐺𝐺𝑣𝑣 =
𝑇𝑇𝑚𝑚
16𝜋𝜋𝛾𝛾 3
16𝜋𝜋𝛾𝛾 3 𝑇𝑇𝑚𝑚2
∗
∆𝐺𝐺 =
=
2
3 ∆𝐺𝐺𝑣𝑣
3∆𝐻𝐻𝑓𝑓2
2𝛾𝛾
2𝛾𝛾𝑇𝑇𝑚𝑚
𝑟𝑟 = −
= −
∆𝐺𝐺𝑣𝑣
∆𝐻𝐻𝑓𝑓
1
𝑇𝑇𝑚𝑚 − 𝑇𝑇 2 (10.7)
∗
1
𝑇𝑇𝑚𝑚 − 𝑇𝑇
(10.6)
Fig. 10.3 Schematic total free energy versus embryo/nucleus radius
curves for two different temperatures. The critical free energy change
(△G*) and the critical nucleus radius (r*) are indicated for each
temperature.
Chapter 10 - 8
Solidification
r* = critical radius
γ = surface free energy
(10.6)
Tm = melting temperature
ΔHf = latent(潛在的)heat of solidification
ΔT = Tm - T = supercooling
Note: ΔHf and γ are weakly dependent on ΔT
∴
r*
decreases as ΔT increases
For typical ΔT
r* ~ 10 nm
Chapter 10 - 9
∗
∆𝐺𝐺
𝑛𝑛∗ = 𝐾𝐾1 𝑒𝑒𝑒𝑒𝑒𝑒 −
𝑘𝑘𝑘𝑘
(5.8)
∆𝐺𝐺 ∗
𝑄𝑄𝑑𝑑
𝑒𝑒𝑒𝑒𝑒𝑒 −
(10.8) 𝑁𝑁̇ = 𝐾𝐾3 𝑛𝑛 𝑣𝑣𝑑𝑑 = 𝐾𝐾1 𝐾𝐾2 𝐾𝐾3 𝑒𝑒𝑒𝑒𝑒𝑒 −
𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘
𝑄𝑄𝑑𝑑
(10.10)
𝑣𝑣𝑑𝑑 = 𝐾𝐾2 𝑒𝑒𝑒𝑒𝑒𝑒 −
(10.9) ∆ T: supercooling
𝑘𝑘𝑘𝑘
Or undercooling
∗
Fig. 10.4 For solidification, schematic plots of (a) number of stable
nuclei 𝑛𝑛∗ versus temperature, (b) frequency of atomic attachment 𝑣𝑣𝑑𝑑
versus temperature, and (c) nucleation rate 𝑁𝑁̇ versus temperature
(the dashed curves are reproduced from parts a and b)
Chapter 10 - 10
Chapter 10 - 11
Ex. Prob. 10.1
Computation of Critical Nucleus Radius and Activation Free Energy
(a) For the solidification of pure gold, calculate the critical radius r* and the
activation free energy ΔG* if nucleation is homogeneous. Values for the
latent heat of fusion ∆𝐻𝐻𝑓𝑓 and surface free energy 𝛾𝛾 are -1.16 x 109 J/m3 and
0.132 J/m2, respectively. Use the supercooling value found in Table 10.1.
(b) Now calculate the number of atoms found in a nucleus of critical size.
Assume a lattice parameter of a=0.413 nm for solid gold at its melting
temperature. Gold structure is FCC.
(10.11)
(b)
𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣
o
∆
T=230
K
(a) 𝑇𝑇𝑚𝑚 =1064 C,
#unit cells/particle =
𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣
2𝛾𝛾𝑇𝑇
1
4 ∗3
𝜋𝜋𝑟𝑟
𝑟𝑟 ∗ = − 𝑚𝑚
=1.32nm
3
𝑇𝑇𝑚𝑚 −𝑇𝑇
∆𝐻𝐻𝑓𝑓
=
= 137 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
3
𝑎𝑎
atoms
Eq. (10.7)
137
x
4
=
548
16𝜋𝜋𝛾𝛾 3 𝑇𝑇𝑚𝑚2
1
critical nucleus
∗
−19 𝐽𝐽
∆𝐺𝐺 =
=
9.64
×
10
𝑇𝑇𝑚𝑚 − 𝑇𝑇 2
3∆𝐻𝐻𝑓𝑓2
Solution
Chapter 10 - 12
Heterogeneous Nucleation
𝛾𝛾𝐼𝐼𝐼𝐼 = 𝛾𝛾𝑆𝑆𝐼𝐼 + 𝛾𝛾𝑆𝑆𝐿𝐿 cos 𝜃𝜃
2𝛾𝛾𝑆𝑆𝑆𝑆
𝑟𝑟 ∗ = −
∆𝐺𝐺𝑣𝑣
(10.13)
(10.12)
3
16𝜋𝜋𝛾𝛾
𝑆𝑆𝑆𝑆
∆𝐺𝐺 ∗ =
𝑆𝑆 𝜃𝜃
2
3∆𝐺𝐺𝑣𝑣
(10.14)
Fig. 10.5 Heterogeneous nucleation of a solid from a liquid. The solidsurface(γSI), solid-liquid (γ SL, and liquid-surface(γ IL), interfacial
energies are prepresented by vectors. The wetting angle (θ) is also
shown.
Chapter 10 - 13
3
16𝜋𝜋𝛾𝛾
𝑆𝑆𝑆𝑆
∆𝐺𝐺 ∗ =
𝑆𝑆 𝜃𝜃
3∆𝐺𝐺𝑣𝑣2
(10.14)
∗
∗
∆𝐺𝐺ℎ𝑒𝑒𝑒𝑒
= ∆𝐺𝐺ℎ𝑜𝑜𝑜𝑜
𝑆𝑆 𝜃𝜃
0 < 𝑆𝑆 𝜃𝜃 < 1
(10.15)
Fig. 10.6 Schematic free energy versus embryo/nucleus radius plot
on which are presented curves for both homogeneous and
heterogeneous nucleation. Critical free energies and the critical
radius are also shown.
Chapter 10 - 14
Fig. 10.7 Nucleation rate versus
temperature for both homogeneous
and heterogeneous nucleation.
Degree of super-cooling (△T) for
each is also shown.
Chapter 10 - 15
Growth rate (𝐺𝐺)̇
𝐺𝐺̇ = 𝐶𝐶 𝑒𝑒𝑒𝑒𝑒𝑒 −
𝑄𝑄
𝑘𝑘𝑘𝑘
(10.16)
Fig. 10.8 Schematic plot showing curves for nucleation
rate (N), growth rate (G), and overall transformation
rate versus temperature.
Chapter 10 - 16
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 - 17
Fig. 10.9 Schematic plots of (a) transformation rate versus
temperature and (b) logarithm time [to some degree (e.g., 0.5
fraction) of transformation] versus temperature. The curves in
both (a) and (b) are generated from the same set of data-that
is, for horizontal axes, the time [scaled logarithmically in the
(b) plot] is just the reciprocal of the rate from plot (a).
Chapter 10 - 18
Fraction transformed, y
Rate of Phase Transformation
transformation complete
Fixed T
0.5
Avrami equation
(10.17)
maximum rate reached – now amount
unconverted decreases so rate slows
rate increases as interfacial surface area
t0.5 increases & nuclei grow
Fig. 10.10 Plot of
log t
fraction reacted versus
the logarithm of time
typical of many solid=> y = 1- exp (-kt n)
state transformations
fraction
time
in which temperature
transformed
is held constant.
– k & n are transformation specific parameters
By convention
rate = 1 / t0.5
(10.18)
Chapter 10 - 19
Temperature Dependence of Transformation Rate
135°C 119°C
1
10
113°C 102°C
102
88°C
43°C
104
• For the recrystallization of Cu, since
rate = 1/t0.5
Fig. 10.11 Percent
recrystallization as a
function of time and at
constant temperature
for pure copper.
rate increases with increasing temperature
• Rate often so slow that attainment of equilibrium
state not possible!
Chapter 10 - 20
Ex. Prob. 10.2
Rate of Recrystallization Computation
It is known that the kinetics of recrystallization for some alloy obeys the
Avrami equation and that the value of n is 3.1. if the fraction recrystallized is
y=0.30 after t=20 min, determine the rate of recrystallization.
Solution
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =
1
𝑡𝑡0.5
(10.18)
y = 1 − 𝑒𝑒𝑒𝑒𝑒𝑒 −𝑘𝑘𝑡𝑡
𝑡𝑡0.5
𝑛𝑛
𝑙𝑙𝑙𝑙 1 − 0.5
= −
𝑘𝑘
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =
1
𝑡𝑡0.5
(10.17)
1/𝑛𝑛
𝑙𝑙𝑙𝑙 1 − 𝑦𝑦
𝑘𝑘 = −
= 3.30 × 10−5 𝑚𝑚𝑚𝑚𝑚𝑚−3.1
𝑛𝑛
𝑡𝑡
= 24.8 𝑚𝑚𝑚𝑚𝑚𝑚
= 4.0 × 10−2 𝑚𝑚𝑚𝑚𝑚𝑚−1
Chapter 10 - 21
[10.5] Transformations & Undercooling
γ ⇒ α + Fe3C
• Eutectoid transf. (Fe-Fe3C system):
0.76 wt% C
6.7 wt% C
• For transf. to occur, must
cool to below 727oC
(i.e., must “undercool”)
T(°C)
1600
0.022 wt% C
𝛾𝛾 0.76𝑤𝑤𝑤𝑤𝑤 𝐶𝐶
𝑐𝑐𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜
ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
𝛼𝛼 0.022𝑤𝑤𝑤𝑤𝑤 𝐶𝐶 + 𝐹𝐹𝐹𝐹3 𝐶𝐶 6.7𝑤𝑤𝑤𝑤𝑤 𝐶𝐶
(10.19)
Fig. 9.24, Callister &
Rethwisch 10e.
δ
L+Fe3C
1148°C
1000
γ +Fe3C
Eutectoid:
Equil. Cooling: Ttransf. =727°C
800
727°C
400
0
(Fe)
0.76
600
0.022
α
ferrite
γ +L
γ
(austenite)
ΔT
α +Fe3C
Undercooling by Ttransf. < 727°C
1
2
3
4
5
6
Fe3C (cementite)
L
1400
1200
[Adapted from Binary Alloy Phase
Diagrams, 2nd edition, Vol. 1, T. B.
Massalski (Editor-in-Chief), 1990.
Reprinted by permission of ASM
International, Materials Park, OH.]
6.7
C, wt%C
Chapter 10 - 22
The Fe-Fe3C Eutectoid Transformation
• Transformation of austenite to pearlite:
Adapted from
Fig. 9.15,
Callister &
Rethwisch 10e.
α
α
γ α
α
α
α
γ
• For this transformation,
rate increases with
[Teutectoid – T ] (i.e., ΔT).
Fig. 10.12 For an iron-carbon alloy of
eutectoid composition (0.76 wt% C),
isothermal fraction reacted versus
the logarithm of time for the austenite
to pearlite transformation.
cementite (Fe3C)
Ferrite (α)
α
γ
pearlite
growth
direction
α
γ
α
100
y (% pearlite)
Austenite (γ)
grain
boundary
Diffusion of C
during transformation
600°C
(ΔT larger)
50
Carbon
diffusion
650°C
675°C
(ΔT smaller)
0
Coarse pearlite  formed at higher temperatures – relatively soft
Fine pearlite
 formed at lower temperatures – relatively hard
Chapter 10 - 23
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 = 675°C
50
0
10 2
1
T(°C)
Austenite (stable)
10 4
time (s)
Fig. 10.13 Demonstration of
how an isothermal
transformation diagram
(bottom) is generated from
percentage transformation
versus logarithm of time
measurements (top).
TE (727°C)
700
Austenite
(unstable)
600
Pearlite
isothermal transformation at 675oC
500
400
1
10
10 2 10 3 10 4 10 5
time (s)
Chapter 10 - 24
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)
T(ºC)
Austenite (stable)
700
Austenite
(unstable)
600
γ
γ
500
TE (727°C)
Pearlite
γ
γ
γ
Fig. 10.14 Isothermal
transformation diagram for
a eutectoid iron carbon
alloy, with superimposed
isothermal heat treatment
curve (ABCD).
Microstructures before,
during, and after the
austenite-to- perlite
transformation are shown.
γ
400
1
10
10 2
10 3
10 4
10 5
time (s)
Chapter 10 - 25
Fig. 10.14 Isothermal transformation diagram for a eutectoid iron
carbon alloy, with superimposed isothermal heat treatment curve
(ABCD). Microstructures before, during, and after the austeniteto- perlite transformation are shown.
Chapter 10 - 26
Fig. 10.15 Photomicrographs of (a) coarse pearlite and (b)
fine pearlite. 3000X.
Chapter 10 - 27
Transformations Involving Noneutectoid Compositions
Consider C0 = 1.13 wt% C
T(°C)
T(°C)
900
δ
A
1200
C
C
+
P
+
a
P
10
γ +Fe3C
1000
600
500
102
103
time (s)
104
Fig. 10.16 Isothermal transformation diagram
for a 1.13 wt% C iron-carbon alloy: A,
austenite; C, proeutectoid cementite; P,
pearlite.
L+Fe3C
(austenite)
proeutectoid cementite
800
C
1
γ +L
γ
727°C
α +Fe3C
400
0
(Fe)
0.76
600
A
TE (727°C)
A
1.13
+
700
L
1400
0.022
800
1
pearlite
2
3
4
Fig. 9.24, Callister & Rethwisch 10e.
5
6
Fe3C (cementite)
1600
6.7
C, wt%C
[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol.
1, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by
permission of ASM International, Materials Park, OH.]
Hypereutectoid composition – proeutectoid cementite
Chapter 10 - 28
Bainite: Another Fe-Fe3C Transformation Product
• Bainite:
-- elongated Fe3C particles in
α-ferrite matrix
-- diffusion controlled
• Isothermal Transf. Diagram,
C0 = 0.76 wt% C
800
Austenite (stable)
T(oC)
A
Fe3C
(cementite)
TE
P
600
α (ferrite)
5 μm
100% pearlite
Fig. 10.17, Callister & Rethwisch 10e.
(From Metals Handbook, Vol. 8, 8th edition,
Metallography, Structures and Phase Diagrams,
1973. Reproduced by permission of ASM
International, Materials Park, OH.)
100% bainite
400
B
A
200
10-1
10
103
Fig. 10.18, Callister & Rethwisch 10e. [Adapted
from H. Boyer (Editor), Atlas of Isothermal Transformation
and Cooling Transformation Diagrams, 1977. Reproduced
by permission of ASM International, Materials Park, OH.]
105
Fig. 10.18 Isothermal transformation diagram for an
iron-carbon alloy of eutectoid composition, including
austenite-to-pearlite (A-P) and austenite-to-bainite
(A-B) transformations.
time (s)
Chapter 10 - 29
Fig. 10.17 Transformation electron micrograph showing the structure
of bainite. A grain of bainite passes from lower left to upper right
corners; it consists of elongated and needle-shape particles of Fe3C
within a ferrite matrix. The phase surrounding the bainite is martensite.
Chapter 10 - 30
Fig. 10.18 Isothermal transformation diagram for an iron-carbon alloy
of eutectoid composition, including austenite-to-pearlite (A-P) and
austenite-to-bainite (A-B) transformations.
Chapter 10 - 31
Spheroidite: Another Microstructure for the
Fe-Fe3C System
α
-- Fe3C particles within an α-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 α-ferrite/Fe3C interfacial area
60 μm
Fig. 10.19, Callister &
Rethwisch 10e.
(Copyright United States Steel
Corporation, 1971.)
Fig. 10.19 Photomicrograph of a steel
having a spheroidite microstructure.
The small particles are cementite; the
continuous phase is α-ferrite. 1000X.
Chapter 10 - 32
Fig. 10.19 Photomicrograph of a steel
having a spheroidite microstructure.
The small particles are cementite; the
continuous phase is α-ferrite. 1000X.
Fig. 10.20 Photomicrograph of a pearlitic
steel that has partially transformed to
spheroidite. 1000X.
Chapter 10 - 33
Martensite: A Nonequilibrium Transformation Product
• Martensite:
Fe atom
sites
x
x
x
60 μm
-- γ(FCC) to Martensite (BCT)
potential
C atom sites
x
x
x
Adapted from Fig. 10.21,
Callister & Rethwisch 10e.
• Isothermal Transf. Diagram
800
Austenite (stable)
T(°C) A
400
10-1
Fig. 10.22, Callister & Rethwisch 10e.
(Courtesy United States Steel Corporation.)
• γ to martensite (M) transformation.
B
A
200
TE
P
600
Adapted from
Fig. 10.23,
Callister &
Rethwisch 10e.
Martensite needles
Austenite
0%
50%
90%
M+A
M+A
M+A
10
103
105
-- is rapid! (diffusionless)
-- % transformation depends only
on T to which rapidly cooled
time (s)
Chapter 10 - 34
Fig. 10.21 The body-centered
tetragonal (BCT) unit cell for
martensite steel showing iron
atoms (circles) and sites that
may be occupied by carbon
atoms (Xs). For this tetragonal
(四角形的)unit cell, c>a.
Fig. 10.22 Photomicrograph showing the
martensite microstructure. The needleshape grains are the martensite phase,
and the white regions are austenite that
failed to transform during the rapid
quench. 1220X.
Chapter 10 - 35
Fig. 10.23 The complete
isothermal transformation
diagram for an ironcarbon alloy of eutectoid
composition: A, austenite;
B, bainite; M, martensite;
P, pearlite.
Chapter 10 - 36
Martensite Formation
Austenite
slow cooling
γ (FCC)
Pearlite
α (BCC) + Fe3C
quench
M (BCT)
tempering
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
Chapter 10 - 37
Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard γ  α + Fe3C
reaction (and formation of
pearlite, bainite)
Fig. 10.24 Isothermal
transformation diagram for
an alloy steel (type 4340):
A, austenite; B, bainite; M,
martensite; P, pearlite; F,
proeutectoid ferrite.
Chapter 10 - 38
Ex. Prob. 10.3
Microstructural Determinations for Three Isothermal Heat Treatments
(a) Rapidly cool to 350oC (660o F), hold for 104 s, and quench to room temperature.
(b) Rapidly cool to 250oC (480o F), hold for 100 s, and quench to room temperature.
(c) Rapidly cool to 650oC (1200oF), hold for 20 s, rapidly cool to 400oC (750oF), hold
for 103 s, and quench to room temperature.
Solution
Chapter 10 - 39
Fig. 10.25 Isothermal
transformation diagram for
an iron-carbon alloy of
eutectoid composition and
the isothermal heat
treatments (a), (b), and (c)
in Ex. Prob. 10.3.
Chapter 10 - 40
[10.6] Continuous Cooling Transformation Diagrams
Conversion of isothermal
transformation diagram to
continuous cooling
transformation diagram
For continuous cooling, the
time required for a reaction to
begin and end is delayed.
Thus the isothermal curves
are shifted to longer times and
lower temperatures, as
indicated in Fig. 10.26.
Fig. 10.26 Superimposition of
isothermal and continuouscooling transformation
diagrams for a eutectoid ironcarbon alloy.
Cooling curve
Chapter 10 - 41
Fig. 10.27 Moderately
rapid and slow cooling
curves superimposed on a
continuous-cooling
transformation diagram for
a eutectoid iron-carbon
alloy.
Chapter 10 - 42
Fig. 10.28 Continuouscooling transformation
diagram for a eutectoid
iron-carbon alloy and
superimposed cooling
curves, demonstrating
the dependence of the
final microstructure on
the transformations that
occur during cooling.
Chapter 10 - 43
Fig. 10.24
Fig. 10.29 Continuous-cooling
transformation diagram for an
alloy steel (type 4340) and
several superimposed cooling
curves demonstrating
dependence of the final
microstructure of this alloy on
the transformations that occur
during cooling.
Chapter 10 - 44
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 - 45
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 α and
coarse pearlite.
A
T (oC)
A+α
P
B
600
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
200
See Fig. 10.29 and
Eqs. (9.20), (9.21)
0
0.1
10
103
time (s)
105
Chapter 10 - 46
Solution to Part (b) of Example
Problem
b) 50% fine pearlite and 50% bainite
Fe-Fe3C phase diagram,
for C0 = 0.45 wt% C
590oC
800
Isothermally treat at ~
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+α
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
200
Figure 10.40, Callister & Rethwisch 10e. (Adapted from
Atlas of Time-Temperature Diagrams for Irons and Steels, G. F.
Vander Voort, Editor, 1991. Reprinted by permission of ASM
International, Materials Park, OH.)
0
0.1
10
103
time (s)
105
Chapter 10 - 47
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 o800
T ( C)
& 50% austenite
-- rapidly quench to
~ 290°C, hold at this
temperature
A
A+α
P
B
600
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
d)
200
c)
Figure 10.40, Callister & Rethwisch 10e. (Adapted from
Atlas of Time-Temperature Diagrams for Irons and Steels, G. F.
Vander Voort, Editor, 1991. Reprinted by permission of ASM
International, Materials Park, OH.)
0
0.1
10
103
time (s)
105
Chapter 10 - 48
[10.7] Mechanical Properties: Influence of C Content
Pearlite (med)
Cementite
(hard)
Fig. 9.30, Callister & Rethwisch 10e.
(Courtesy of Republic Steel Corporation.)
C0 < 0.76 wt% C
Hypoeutectoid
Hypo
Hyper
1100
C0 > 0.76 wt% C
Hypereutectoid
Hypo
%EL
Fig. 9.33, Callister & Rethwisch 10e.
(Copyright 1971 by United States Steel
Corporation.)
Hyper
80
100
900
hardness
TS(MPa)
40
700
50
500
0.5
1
wt% C
0
0
0.5
0.76
0
YS(MPa)
0.76
300
0
Impact energy (Izod, ft-lb)
Pearlite (med)
ferrite (soft)
Fig. 10.30, Callister &
Rethwisch 10e.
[Data taken from Metals
Handbook: Heat Treating,
Vol. 4, 9th edition, V.
Masseria (Managing
Editor), 1981. Reproduced
by permission of ASM
International, Materials
Park, OH.]
1
wt% C
• Increase C content: TS and YS increase, %EL decreases
Chapter 10 - 49
Fig. 10.30 (a) Yield strength, tensile strength, and Brinell hardness
versus carbon concentration for plain carbon steels consisting of fine
pearlite. (b) Ductility (%EL and %RA) and Izod impact energy versus
carbon concentration for plain carbon steels having microstructures
consisting of fine pearlite.
Chapter 10 - 50
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
0.5
1
wt%C
fine > coarse > spheroidite
fine < coarse < spheroidite
Fig. 10.31 (a) Brinell and Rockwell hardness as a function of carbon
concentration for plain carbon steels having fine and coarse pearlite as well
as spheroidite microstructure. (b) Ductility (%RA) as a function of carbon
concentration for plain carbon steels having fine and coarse pearlite as well
as spheroidite microstructure.
Chapter 10 - 51
Fig. 10.32 (a) Brinell hardness and tensile strength and (b) Ductility
(%RA) (at room temperature) as a function of isothermal transformation
temperature for an iron-carbon alloy of eutectoid composition, taken over
the temperature range at which bainite and pearlite microstructures form.
Chapter 10 - 52
Mechanical Props: Fine Pearlite vs. Martensite
Brinell hardness
Hypo
600
Hyper
martensite
Fig. 10.33, Callister & Rethwisch 10e.
(Adapted from Edgar C. Bain, Functions of the
Alloying Elements in Steel, 1939; and R. A.
Grange, C. R. Hribal, and L. F. Porter, Metall.
Trans. A, Vol. 8A. Reproduced by permission
of ASM International, Materials Park, OH.)
400
200
fine pearlite
0
0
0.5
1
wt% C
• Hardness: fine pearlite << martensite.
Chapter 10 - 53
Fig. 10.33 Hardness (at room
temperature) as a function of
carbon concentration for plan
carbon martensite, tempered
martensitic [temperature at
371oC(700oF)], and pearlitic
steels.
Chapter 10 - 54
[10.8] 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
Fig. 10.35,
Callister &
Rethwisch 10e.
(Adapted from Edgar
C. Bain, Functions of
the Alloying
Elements in Steel,
1939. Reproduced
by permission of
ASM International,
Materials Park, OH.)
1400
TS
9 μm
1600
YS
1200
1000
60
50
%RA
40
30
%RA
800
200
400
600
Tempering T (°C)
Fig. 10.34 Electron
micrograph of
tempered martensite.
Tempering was
carried out at
594OC(1100OF). The
small particles are the
cementite phase; the
matrix phase is α–
ferrite. 9300X.
(10.20)
𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 BCT, single phase
→ 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝛼𝛼 + 𝐹𝐹𝐹𝐹3 𝐶𝐶 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
• tempering produces extremely small Fe3C particles surrounded by α.
• tempering decreases TS, YS but increases %RA
Chapter 10 - 55
Fig. 10.35 Tensile and yield
strengths and ductility (%RA)
(at room temperature) versus
tempering temperature for an
oil-quenched alloy steel (type
4340).
Chapter 10 - 56
Fig. 10.36 Hardness (at room temperature) versus tempering
time for a water-quenched eutectoid plain carbon (1080) steel.
Chapter 10 - 57
[10.9] Summary of Possible Transformations
Austenite (γ)
slow
cool
moderate
cool
Fig. 10.37 Possible
transformations involving the
decomposition of austenite.
rapid quench
Diffusionless
transformation
Bainite
Martensite
(α + Fe3C layers + a
proeutectoid phase)
(α + elong. Fe3C particles)
(BCT phase
diffusionless
transformation)
Martensite
Tempered Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
Ductility
Strength
Pearlite
reheat
Tempered
Martensite
(α + very fine
Fe3C particles)
General Trends
Chapter 10 - 58
Chapter 10 - 59
Ex. Prob. 10.4
Determination of Properties for a Eutectoid Fe-Fe3C Alloy Subjected
to an Isothermal Heat Treatment
Determine the tensile strength and ductility(%RA) of a eutectoid FeFe3C alloy has been subjected to heat treatment (c) in example
problem10.3.
Solution
(10.21)
𝑇𝑇𝑇𝑇 = 𝑊𝑊𝑝𝑝 𝑇𝑇𝑇𝑇𝑝𝑝 + 𝑊𝑊𝑏𝑏 𝑇𝑇𝑇𝑇𝑏𝑏
= 0.5(950)+0.5(1300)= 1125𝑀𝑀𝑀𝑀𝑀𝑀
%𝑅𝑅𝑅𝑅 = 𝑊𝑊𝑝𝑝 %𝑅𝑅𝑅𝑅𝑝𝑝 + 𝑊𝑊𝑏𝑏 %𝑅𝑅𝑅𝑅𝑏𝑏
= 0.5(32%)+0.5(52%) = 42%𝑅𝑅𝑅𝑅
Chapter 10 - 60
Fig. 10.25 Isothermal
transformation diagram for
an iron-carbon alloy of
eutectoid composition and
the isothermal heat
treatments (a), (b), and (c)
in Ex. Prob. 10.3.
Chapter 10 - 61
Materials of importance 10.1
Shape-memory alloys
Fig. Time-lapse photograph
that demonstrates the shapememory effect. A wire of a
shape-memory alloy (Nitinol)
has been bent and treated
such that its memory shape
spells are word Nitinol. The
wire is then deformed and,
upon heating (by passage of
electric current) springs back
to its predetermined shape;
this shape recovery process
is recorded on the
photograph.
Chapter 10 - 62
Fig. 10.38 Diagram illustrating the shape-memory effect. The insets are
schematic representations of the crystal structure at the four stages. Ms and Mf
denote temperatures at which the martensitic transformation begins and ends,
respectively. Likewise for the austenite transformation, As and Af represent the
respective beginning and end transformation temperatures.
Chapter 10 - 63
Fig. 10.39 Typical stress-strain-temperature behavior of a shape-memory alloy,
demonstrating its thermoelastic behavior. Specimen deformation, corresponding to the
curve from A to B, is carried out at a temperature below that at which the martensitic
transformation is complete (i.e., Mf of Fig.10.38). Release of the applied stress (also at
Mf) is represented by the curve BC. Subsequent heating to above the completed
austenite-transformation temperature (Af, Fig. 10.38) causes the deformed piece to
resume its original shape (along the curve from point C to point D).
Chapter 10 - 64
Summary
• Heat treatments of Fe-C alloys produce microstructures
including:
-- pearlite, bainite, spheroidite, martensite, tempered
martensite
• Rate of Phase transformation given by Avrami Equation
-- strong function of temperature
-- Isothermal transformation diagrams
Chapter 10 - 65