Chapter 10 Phase transformation in metals
Basic concepts
The kinetics of solid-state reactions
Isothermal transformation diagrams
Basic concepts
Phase transformation takes time to occur
Types of phase transformation
• Simple diffusion-dependent transformation -- no
change in either the number or composition of the
phases present
• Diffusion-dependent transformation -- change in
composition and the number of phases present
• Diffusionless, martensitic transformation
1
Fraction transformed, y
The kinetics of solid-state reactions
All out of material - done
Fixed T
0.5
maximum rate reached – now amount
unconverted decreases so rate slows
t0.5
rate increases as surface area increases
& nuclei grow
log t
Avrami rate equation => y = 1- exp (-ktn)
fraction
transformed
• k & n fit for specific sample
By convention
t: time
r = 1 / t0.5
The kinetics of solid-state reactions (continue)
1
135°C 119°C
113°C 102°C
10
102
88°C
43°C
104
In general, rate increases as T ↑
r = 1/t0.5 = A e -Q/RT
• R = gas constant
• T = temperature (K)
• A = preexponential factor
• Q = activation energy
Arrhenius
expression
• r often small: equilibrium not possible!
2
Eutectoid transformation rate
• Growth of pearlite from austenite:
Austenite (γ)
grain
boundary
α
α
γ α
α
α
α
Adapted from
Fig. 9.15,
Callister 7e.
γ
cementite (Fe3C)
Ferrite (α)
α
γ
γ
α
pearlite
growth
direction
• Recrystallization
rate increases
with ΔT.
Course pearlite
Fine pearlite
Diffusive flow
of C needed
α
y (% pearlite)
100
600°C
(ΔT larger)
50
650°C
675°C
(ΔT smaller)
Adapted from
Fig. 10.12,
Callister 7e.
0
formed at higher T - softer
formed at low T - harder
Nucleation and growth
• Reaction rate is a result of nucleation and growth
of crystals.
100
% Pearlite
Nucleation rate increases with ΔT
Growth
regime
50 Nucleation
Growth rate increases with T
regime
t 0.5
0
log (time)
Adapted from
Fig. 10.10, Callister 7e.
• Examples:
γ
pearlite
colony
T just below TE
Nucleation rate low
Growth rate high
γ
T moderately below TE
Nucleation rate med .
Growth rate med.
γ
T way below TE
Nucleation rate high
Growth rate low
3
Transformations & undercooling
γ ⇒ α + Fe3C
• Eutectoid transf. (Fe-C System):
• Can make it occur at:
0.76 wt% C
6.7 wt% C
0.022 wt% C
...727ºC (cool it slowly)
...below 727ºC (“undercool” it!)
T(°C)
1600
δ
γ+L
γ
1200
(austenite)
1000
γ +Fe3C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
800
727°C
0.022
600
400
0
(Fe)
ΔT
α +Fe3C
Undercooling by ΔTtransf. < 727°C
0.76
α
ferrite
L+Fe3C
1148°C
1
2
3
4
5
6
Fe3C (cementite)
L
1400
6.7
Co , wt%C
Isothermal transformation diagrams
Iron-iron carbide
eutectoid reaction
• C0=0.77wt%C
• Transformation at
T=6750C
Time-temptransformation
(T-T-T) plots
4
Pearlite morphology
TTransf is just below Teu
T larger, ΔT small -Coarse grains
TTransf is far below Teu
T small, ΔT large --fine
grains
Finer
Coarser
Effect of cooling history in Fe-C system
• Eutectoid composition, Co = 0.76 wt% C
• Begin at T > 727°C
• Rapidly cool to 625°C and hold isothermally.
T(°C)
Austenite (stable)
700
600
γ
Adapted from Fig.
10.14,Callister 7e.
(Fig. 10.14 adapted from
H. Boyer (Ed.) Atlas of
Isothermal Transformation
and Cooling
Transformation Diagrams,
American Society for
Metals, 1997, p. 28.)
Pearlite
γ
%
1
10 0
γ
γ
50% rlite
p ea
0%
γ
γ
500
400
TE (727°C)
Austenite
(unstable)
10
10 2
10 3
10 4
10 5
time (s)
5
Non-equilibrium transformation products: Fe-C
• Bainite:
--α lathes (strips) with long
rods of Fe3C
--diffusion controlled.
• Isothermal Transf. Diagram
800
Austenite (stable)
T(°C)
A
Fe3C
(cementite)
TE
P
600
α (ferrite)
5 μm
100% pearlite
pearlite/bainite boundary
100% bainite
400
B
A
103
%
10
100
10-1
50%
0%
200
105
time (s)
Spheroidite: Fe-C System
• Spheroidite:
α
(ferrite)
--α grains with spherical Fe3C
--diffusion dependent.
--heat bainite or pearlite for long times
Fe3C
--reduces interfacial area (driving force) (cementite)
60 μm
6
Martensite: Fe-C system
• Martensite:
--γ(FCC) to Martensite (BCT)
(involves single atom jumps)
x
x
x
x
potential
C atom sites
60 μm
Fe atom
sites
x
x
(Adapted from Fig.
10.20, Callister, 7e.
• Isothermal Transf. Diagram
800
Austenite (stable)
T(°C)
A
600
400
B
A
0%
200
10-1
Martensite needles
Austenite
TE
P
50
%
0%
50%
90%
M+A
M+A
M+A
10
• γ to M transformation..
10
0%
103
-- is rapid!
-- % transf. depends on T only.
105 time (s)
Martensite formation
slow cooling
γ (FCC)
quench
M (BCT)
α (BCC) + Fe3C
tempering
M = martensite is body centered tetragonal (BCT)
Diffusionless transformation
BCT
few slip planes
BCT if C > 0.15 wt%
hard, brittle
7
Example
Dynamic phase transformations
On the isothermal transformation diagram for 0.45
wt% C Fe-C alloy, sketch and label the timetemperature paths to produce the following
microstructures:
a) 50% fine pearlite and 50% bainite
b) 100% martensite
c) 50% martensite and 50% austenite
8
Example problem for Co = 0.45 wt%
a) 50% fine pearlite and 50% bainite
first make pearlite T (°C) 800
then bainite
A+α
A
P
B
600
fine pearlite
∴ lower T
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
200
0
0.1
10
103
105
time (s)
Example problem for Co = 0.45 wt%
b) 100 % martensite – quench = rapid cool
c) 50 % martensite
800
A+α
and 50 %
A
T
(°C)
austenite
P
B
600
A+P
A+B
A
400
50%
M (start)
M (50%)
M (90%)
d)
200
Adapted from
Fig. 10.29,
Callister 5e.
c)
0
0.1
10
103
time (s)
105
9