Chapter 10 -
1
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
• How does the rate of transformation depend on
time and T ?
• How can we slow down the transformation so that
we can engineering non-equilibrium structures?
• Are the mechanical properties of non-equilibrium
structures better?
Chapter 10:Phase Transformations
Chapter 10 -
2
Phase Transformations
Nucleation
–nuclei (seeds) act as template to grow crystals
–for nucleus to form rate of addition of atoms tonucleus must be faster than rate of loss
–once nucleated, grow until reach equilibrium
Driving force to nucleate increases as we increase T
–supercooling (eutectic, eutectoid)
–superheating (peritectic)
Small supercooling few nuclei - large crystals
Large supercooling rapid nucleation - many nuclei,
small crystals
Chapter 10 -
3
Solidification: Nucleation Processes
•Homogeneous nucleation
–nuclei form in the bulk of liquid metal
–requires supercooling (typically 80-300°C max)
•Heterogeneous nucleation
–much easier since stable “nucleus” is alreadypresent
•Could be wall of mold or impurities in the liquidphase
–allows solidification with only 0.1-10ºCsupercooling
Chapter 10 -
4
r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)
Adapted from Fig.10.2(b), Callister 7e.
Homogeneous Nucleation & Energy Effects
GT = Total Free Energy
= GS + GV
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
= surface tension
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
Chapter 10 -
5
Solidification
Note: HS = strong function of T
= weak function of T
r* decreases as T increases
For typical T r* ca. 100Å
HS = latent heat of solidification
Tm = melting temperature
= surface free energy
T = Tm - T = supercooling
r* = critical radius
Chapter 10 -
6
Rate of Phase Transformations
Kinetics - measure approach to equilibrium vs.time
•Hold temperature constant & measureconversion vs. time
sound waves – one sample
electrical conductivity – follow one sample
X-ray diffraction – have to do many samples
How is conversion measured?
Chapter 10 -
7
Rate of Phase Transformation
Avrami rate equation => y = 1- exp (-ktn)
–k & n fit for specific sample
All out of material - done
log t
Fraction transformed, y
Fixed T
fractiontransformed
time
0.5
By convention r = 1 / t0.5
Adapted fromFig. 10.10,
Callister 7e.
maximum rate reached – now amount
unconverted decreases so rate slows
t0.5
rate increases as surface area increases & nuclei grow
Chapter 10 -
8
Rate of Phase Transformations
•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
Arrheniusexpression
• r often small: equilibrium not possible!
Adapted from Fig.10.11, Callister 7e.(Fig. 10.11 adaptedfrom B.F. Decker andD. Harker,"Recrystallization inRolled Copper", TransAIME, 188, 1950, p.888.)
135C
119C
113C
102C
88C
43C
1
10
102
104
Chapter 10 -
9
Eutectoid Transformation Rate
Course pearlite formed at higher T - softer
Fine pearlite formed at low T - harder
Diffusive flow
of C needed
• Growth of pearlite from austenite:
Adapted fromFig. 9.15,Callister 7e.
pearlite
growth
direction
Austenite ()
grain
boundary
cementite (Fe3C)
Ferrite ()
• Recrystallization
rate increases
with T.
Adapted fromFig. 10.12,Callister 7e.
675°C
(T smaller)
0
50
y (% pearlite)
600°C
(T larger)
650°C
100
Chapter 10 -
10
• Reaction rate is a result of nucleation and growth
of crystals.
• Examples:
Adapted from
Fig. 10.10, Callister 7e.
Nucleation and Growth
% Pearlite
0
50
100
Nucleation
regime
Growth
regime
log (time)
t
0.5
Nucleation rate increases with T
Growth rate increases with T
T just below
TE
Nucleation rate low
Growth rate high
pearlite
colony
T moderately below
TE
Nucleation rate med
Growth rate med.
Nucleation rate high
T way below
TE
Growth rate low
Chapter 10 -
11
Transformations & Undercooling
•
Can make it occur at:
...727ºC (cool it slowly)
...below 727ºC (“undercool” it!)
•
Eutectoid
transf. (Fe-C System):
+
Fe3C
0.76 wt% C
0.022 wt% C
6.7 wt% C
Fe3C (cementite)
1600
1400
1200
1000
800
600
400
0
1
2
3
4
5
6
6.7
L
(austenite)
+L
+Fe3C
+Fe3C
L+Fe3C
(Fe)
Co , wt%C
1148°C
T(°C)
ferrite
727°C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
T
Undercooling by Ttransf. < 727C
0.76
0.022
Adapted from Fig.9.24,Callister 7e. (Fig. 9.24adapted from Binary AlloyPhase Diagrams, 2nd ed.,Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International,Materials Park, OH, 1990.)
Chapter 10 -
12
Adapted from Fig. 10.13,Callister 7e.
(Fig. 10.13 adapted from H. Boyer (Ed.)Atlas of Isothermal Transformation andCooling Transformation Diagrams,American Society for Metals, 1977, p.369.)
Isothermal Transformation Diagrams
• Fe-C system, Co = 0.76 wt% C
• Transformation at T = 675°C.
100
50
0
1
10
2
10
4
T = 675°C
y,
% transformed
time (s)
400
500
600
700
1
10
10
2
10
3
10
4
10
5
0%pearlite
100%
50%
Austenite (stable)
TE (727C)
Austenite
(unstable)
Pearlite
T(°C)
time (s)
isothermal transformation at 675°C
Chapter 10 -
13
• Eutectoid composition, Co = 0.76 wt% C
• Begin at T > 727°C
• Rapidly cool to 625°C and hold isothermally.
Adapted from Fig.10.14,Callister 7e.
(Fig. 10.14 adapted fromH. Boyer (Ed.) Atlas ofIsothermal Transformationand CoolingTransformation Diagrams,American Society forMetals, 1997, p. 28.)
Effect of Cooling History in Fe-C System
400
500
600
700
0%pearlite
100%
50%
Austenite (stable)
TE (727C)
Austenite
(unstable)
Pearlite
T(°C)
1
10
10
2
10
3
10
4
10
5
time (s)
Chapter 10 -
14
Transformations withProeutectoid Materials
Hypereutectoid composition – proeutectoid cementite
CO = 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. 10.16,Callister 7e.
Adapted from Fig. 9.24,Callister 7e.
Fe3C (cementite)
1600
1400
1200
1000
800
600
400
0
1
2
3
4
5
6
6.7
L
(austenite)
+L
+Fe3C
+Fe3C
L+Fe3C
(Fe)
Co , wt%C
T(°C)
727°C
T
0.76
0.022
1.13
Chapter 10 -
15
Non-Equilibrium TransformationProducts: Fe-C
• Bainite:
-- lathes (strips) with long
rods of Fe3C
--diffusion controlled.
• Isothermal Transf. Diagram
Adapted from Fig. 10.18, Callister 7e.
(Fig. 10.18 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and CoolingTransformation Diagrams, American Society for Metals, 1997, p. 28.)
(Adapted from Fig. 10.17, Callister, 7e. (Fig.10.17 from Metals Handbook, 8th ed.,
Vol. 8, Metallography, Structures, and PhaseDiagrams, American Society for Metals,Materials Park, OH, 1973.)
Fe3C
(cementite)
5 m
(ferrite)
10
10
3
10
5
time (s)
10
-1
400
600
800
T(°C)
Austenite (stable)
200
P
B
TE
0%
100%
50%
pearlite/bainite boundary
A
A
100% bainite
100% pearlite
Chapter 10 -
16
• Spheroidite:
-- grains with spherical Fe3C
--diffusion dependent.
--heat bainite or pearlite for long times
--reduces interfacial area (driving force)
Spheroidite: Fe-C System
(Adapted from Fig. 10.19, Callister, 7e.(Fig. 10.19 copyright United StatesSteel Corporation, 1971.)
60 m
(ferrite)
(cementite)
Fe3C
Chapter 10 -
17
• Martensite:
--(FCC) to Martensite (BCT)
Adapted fromFig. 10.22,Callister 7e.
(Adapted from Fig. 10.21, Callister, 7e.(Fig. 10.21 courtesy United StatesSteel Corporation.)
• Isothermal Transf. Diagram
• to M transformation..
-- is rapid!
-- % transf. depends on T only.
(Adapted from Fig.10.20, Callister, 7e.
Martensite: Fe-C System
Martensite needles
Austenite
60 m
10
10
3
10
5
time (s)
10
-1
400
600
800
T(°C)
Austenite (stable)
200
P
B
TE
0%
100%
50%
A
A
M + A
M + A
M + A
0%
50%
90%
x
x
x
x
x
x
potential
C atom sites
Fe atom
sites
(involves single atom jumps)
Chapter 10 -
18
(FCC) (BCC) + Fe3C
Martensite Formation
slow cooling
tempering
quench
M (BCT)
M = martensite is body centered tetragonal (BCT)
Diffusionless transformation BCT if C > 0.15 wt%
BCT few slip planes hard, brittle
Chapter 10 -
19
Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard + Fe3C
transformation
Adapted from Fig. 10.23, Callister 7e.
Chapter 10 -
20
Adapted fromFig. 10.25,
Callister 7e.
Cooling Curve
plot temp vs. time
Chapter 10 -
21
Dynamic Phase Transformations
On the isothermal transformation diagram for0.45 wt% C Fe-C alloy, sketch and label thetime-temperature paths to produce thefollowing microstructures:
a)42% proeutectoid ferrite and 58% coarsepearlite
b)50% fine pearlite and 50% bainite
c)100% martensite
d)50% martensite and 50% austenite
Chapter 10 -
22
A + B
A + P
A +
A
B
P
A
50%
0
200
400
600
800
0.1
10
103
105
time (s)
M (start)
M (50%)
M (90%)
Example Problem for Co = 0.45 wt%
a)42% proeutectoid ferrite and 58% coarse pearlite
first make ferrite
then pearlite
course pearlite
higher T
Adapted fromFig. 10.29,
Callister 5e.
T (°C)
Chapter 10 -
23
b)50% fine pearlite and 50% bainite
first make pearlite
then bainite
fine pearlite
lower T
T (°C)
A + B
A + P
A +
A
B
P
A
50%
0
200
400
600
800
0.1
10
103
105
time (s)
M (start)
M (50%)
M (90%)
Example Problem for Co = 0.45 wt%
Adapted fromFig. 10.29,
Callister 5e.
Chapter 10 -
24
A + B
A + P
A +
A
B
P
A
50%
0
200
400
600
800
0.1
10
103
105
time (s)
M (start)
M (50%)
M (90%)
Example Problem for Co = 0.45 wt%
c)100 % martensite – quench = rapid cool
d)50 % martensite
and 50 %austenite
d)
c)
Adapted fromFig. 10.29,
Callister 5e.
T (°C)
Chapter 10 -
25
Mechanical Prop: Fe-C System (1)
Adapted from Fig.10.29, Callister 7e.(Fig. 10.29 based ondata from MetalsHandbook: HeatTreating, Vol. 4, 9thed., V. Masseria(Managing Ed.),American Society forMetals, 1981, p. 9.)
Adapted from Fig. 9.30,Callister
7e. (Fig. 9.30 courtesy RepublicSteel Corporation.)
Adapted from Fig. 9.33,Callister 7e.(Fig. 9.33 copyright 1971 by UnitedStates Steel Corporation.)
• More wt% C: TS and YS increase
, %EL decreases.
• Effect of wt% C
Co < 0.76 wt% C
Hypoeutectoid
Pearlite (med)
ferrite (soft)
Co > 0.76 wt% C
Hypereutectoid
Pearlite (med)
C
ementite
(hard)
300
500
700
900
1100
YS(MPa)
TS(MPa)
wt% C
0
0.5
1
hardness
0.76
Hypo
Hyper
wt% C
0
0.5
1
0
50
100
%EL
Impact energy (Izod, ft-lb)
0
40
80
0.76
Hypo
Hyper
Chapter 10 -
26
Mechanical Prop: Fe-C System (2)
Adapted from Fig. 10.30, Callister 7e.(Fig. 10.30 based on data from MetalsHandbook: Heat Treating, Vol. 4, 9thed., V. Masseria (Managing Ed.),American Society for Metals, 1981, pp.9 and 17.)
• Fine vs coarse pearlite vs spheroidite
• Hardness:
• %RA:
fine > coarse > spheroidite
fine < coarse < spheroidite
80
160
240
320
wt%C
0
0.5
1
Brinell hardness
fine
pearlite
coarse
pearlite
spheroidite
Hypo
Hyper
0
30
60
90
wt%C
Ductility (%AR)
fine
pearlite
coarse
pearlite
spheroidite
Hypo
Hyper
0
0.5
1
Chapter 10 -
27
Mechanical Prop: Fe-C System (3)
• Fine Pearlite vs Martensite:
• Hardness: fine pearlite << martensite.
Adapted from Fig. 10.32,Callister 7e. (Fig. 10.32 adaptedfrom Edgar C. Bain, Functions ofthe 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% C
0
0.5
1
400
600
Brinell hardness
martensite
fine pearlite
Hypo
Hyper
Chapter 10 -
28
Tempering Martensite
• reduces brittleness of martensite,
• reduces internal stress caused by quenching.
Adapted fromFig. 10.33,Callister 7e.(Fig. 10.33copyright byUnited StatesSteelCorporation,1971.)
•
decreases TS, YS but increases %RA
•
produces extremely small Fe3C particles surrounded by
Adapted fromFig. 10.34,Callister 7e.(Fig. 10.34adapted fromFig. furnishedcourtesy ofRepublic SteelCorporation.)
9 m
YS(MPa)
TS(MPa)
800
1000
1200
1400
1600
1800
30
40
50
60
200
400
600
Tempering T (°C)
%RA
TS
YS
%RA
Chapter 10 -
29
Summary: Processing Options
Adapted fromFig. 10.36,Callister 7e.
Austenite ()
Bainite
( + Fe3C plates/needles)
Pearlite
( + Fe3C layers + a
proeutectoid phase)
Martensite
(BCT phase
diffusionless
transformation)
Tempered
Martensite
( + very fine
Fe3C particles)
slow
cool
moderate
cool
rapid
quench
reheat
Strength
Ductility
Martensite
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
General Trends
Chapter 10 -
30
Core Problems:
Self-help Problems:
ANNOUNCEMENTS
Reading: