Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the...
-
Upload
duane-owens -
Category
Documents
-
view
218 -
download
0
Transcript of Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the...
![Page 1: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/1.jpg)
Phase Transformation Chapter 9
![Page 2: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/2.jpg)
Shiva-Parvati, Chola Bronze
Ball State University
Q: How was the statue made?
A: Invest casting
Liquid-to-solid transformation
An example of phase transformation
![Page 3: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/3.jpg)
Czochralski crystal pulling technique
How does one produce single crystal of Si for electronic applications?
![Page 4: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/4.jpg)
Quenching of steel componentsa solid->solid phase transformation
How does one harden a steel component?
![Page 5: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/5.jpg)
Liquid
solid
ifica
tion
evaporation
sublimation
Solid
gas
mel
ting
condensation
Solid state phase
transformationSolid 21
![Page 6: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/6.jpg)
Thermodynamic driving force for a phase transformation?
Decrease in Gibbs free energy
Liquid-> solid
gs - gl = g = -ve
![Page 7: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/7.jpg)
ggL
gS
gS < gL
gL < gSLiquid is
stable
TmT
Gibbs free energy as a function of temperature, Problem 2.3
gL
gS
g
Solid is stable
Tfreezing
sT
g
p
T
c
T
g p
p
2
2
Fig. 9.1
![Page 8: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/8.jpg)
How does solidification begins?
Usually at the walls of the container
Why?
To be discussed later.
Heterogeneous nucleation.
![Page 9: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/9.jpg)
Spherical ball of solid of radius R in the middle of the liquid at a temperature below Tm
Homogeneous nucleation
gL = free energy of liquid per unit volumegS = free energy of solid
per unit volume
r
g = gS - gL
![Page 10: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/10.jpg)
Change in free energy of the system due to formation of the solid ball of radius r :
r
)(3
4 3Ls ggrf
+ve: barrier to nucleation 24 r
)(3
4 3Ls ggr
rr*
f
gp 24 r+
![Page 11: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/11.jpg)
grf 3
3
4
24 r
gr 3
3
4
rr*
f
gp 24 r+Solid balls of radius r < r* cannot grow as it will lead to increase in the free energy of the system !!!
Solid balls of radii r > r* will grow
r* is known as the CRITICAL RADIUS OF HOMOGENEOUS NUCLEATION
![Page 12: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/12.jpg)
grf 3
3
4 24 r
gr 3
3
4
rr*
f
gp 24 r+
0*
rrr
f
gr
2*
*f
2
3
)(3
16*
gf
Eqn. 9.5
Eqn. 9.4
![Page 13: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/13.jpg)
T
g
Tm
gL
gS
T
g (T)
LS ggg )()()( TsTThTg
)()( mThTh )()( mTsTs
0)()()( mmmm TsTThTg
m
mm T
ThTs
)()(
)()()( mm TsTThTg
m
mm T
ThTTh
)()(
)( mm
m ThT
TT
mm
hT
TTg
)( Eqn.
9.7
Driving force for solidification
![Page 14: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/14.jpg)
grf 3
3
4 gp 24 r+
gr
2*
2
3
)(3
16*
gf
)(3
4)( 3 TgrTf gp 24 r+
f
rm
m
hT
TTg
)(
m
m
hT
Tr
2*
22
23
)()(3
16*
m
m
hT
Tf
Eqn. 9.8
Eqn. 9.7
Fig. 9.3
r1*
f1*
f2*
r2*
T1T2 <
![Page 15: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/15.jpg)
15
S
VG=S+V
RR*
Nucleation Capillary Rise
Unstable Equilibrium Stable Equilibrium
H*
S
E=S+VV
H
Comparison of Nucleation & Capillary Rise
![Page 16: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/16.jpg)
16
Nucleation Capillary Rise
Driving Force Volume free energy (R3)
Surface energy (H)
Opposing Force
Surface energy (R2)
Volumetric gravitational potential (H2)
Equilibrium Unstable Stable
R. Prasad, “On Capillary Rise and Nucleation”, Journal of Chemical Education, Vol. 85, No. 10, October 2008, p1389
![Page 17: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/17.jpg)
17
Journal of Chemical Education, Vol. 85, No. 10, October 2008, p1389
![Page 18: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/18.jpg)
18
Nucleation is often aided by some preexisting surfaces, e.g., container walls, grain boundaries etc.
Such nucleation is called HETEROGENEOUS NUCLEATION
HETEROGENEOUS NUCLEATION
Pepsi experiment
![Page 19: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/19.jpg)
19
Orthophosphoric Acid Demonstration
Homogeneous vs. heterogeneous nucleation
Cloud seeding and artificial rain
Phosphoric acid, used in many soft drinks (primarily cola), has been linked to lower bone density in epidemiological studies.
-Wikipedia
![Page 20: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/20.jpg)
20
![Page 21: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/21.jpg)
Critical particle
Fig. 9.4
Formation of critical nucleus by statistical fluctuation
Atoms surrounding the critical particle
Diffuse jump of a surrounding atom to the critical particle makes it a nucleation
![Page 22: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/22.jpg)
![Page 23: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/23.jpg)
AAAGVf caphet )(
)cos1(
2
cos14
)(3
4
22
2
3
RA
RA
SRVcap4
coscos32)(
3 S
cos
![Page 24: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/24.jpg)
Plot of S()
![Page 25: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/25.jpg)
![Page 26: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/26.jpg)
RT
fNN t
*exp*
s*= no. of liquid phase atoms facing the critical sized particle
Hd = activation energy for diffusive jump from liquid to the solid phase = atomic vibration frequency
The rate of successful addition of an atom to a critical sized paticle
RT
Hsv dexp*' Eqn. 9.10
Eqn. 9.9
![Page 27: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/27.jpg)
Rate of nucleation, I , (m3 s-
1)
With decreasing T
1. Driving force increases
2. Atomic mobility decreases
= No. of nucleation events per m3 per sec
= number of critical clusters per unit volume (N*)x
rate of successful addition of an atom to the critical cluster (’)
T
I
Tm
![Page 28: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/28.jpg)
Growth
Increase in the size of a product particle after it has nucleated
dt
drU
T
U
![Page 29: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/29.jpg)
Overall Transformation Kinetics
),( IUfdT
dX
U
I
dX/dt
TI : Nucleation rate (m-3
s-1)
U : Growth rate (ms-1)
dt
dr
Overall transformation rate (fraction trans-formed per second, s-1)
X=fraction of product phase
![Page 30: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/30.jpg)
Fraction transformed as a function of time
ts tf
X
t
Slow due to very few nuclei
Slow due to final impingement
![Page 31: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/31.jpg)
TTT Diagram for liquid-to-solid transformation
TStable liquid
UnderCooled liquid
crystal
Crystallization begins
L+
Crystallization ends
dX/dt
T
log t
X
log tts tf
0
1
Tm C-curves
![Page 32: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/32.jpg)
L+
TStable liquid
UnderCooled liquid
log t
Tm
TTT Diagram for liquid-to-solid transformation
U
I
T
Coarse grained crystals
Fine grained crystals
glass
![Page 33: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/33.jpg)
T
log t
ts metals
ts SiO2
RT
HfsNI d
t
*exp*
22
23
)()(3
16*
m
m
hT
Tf
Hd ∝ log (viscosity)
Metals: high hm, low viscosity
SiO2: low hm, high viscosity
Silica glassMetallic glass
Eqn. 9.11
Eqn. 9.8
![Page 34: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/34.jpg)
Cooling rate 106 ºC s-1
Inert gas pressure
Molten alloy
Heater coil
Quartz tube
Rotating cooledmetal drum
Jet of molten metal
Ribbon ofglassy metal
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
Melt Spinning for metallic glass ribbons
![Page 35: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/35.jpg)
L+
T
log t
Tm
TTmTg
Log (viscosity Pa-s)
12
18
crystal
Stable liquid
Undercooled liquid
glass
30
Fig. 9.17
![Page 36: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/36.jpg)
Tm
Specific volume Stable liquid
Undercooled liquid
Fast cool
Slow cool
Tgs
Tgf
crystal
Fig. 9.18
T
![Page 37: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/37.jpg)
log t
U
I
T
L+
TStable liquidUndercooled liquid
Tm
devitrification
time
T
Glass ceramics
nucleation
growth
glass
Glass ceramic
Liquid
glass crystal
Very fine crystals
TU
TIFig. 9.16
![Page 38: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/38.jpg)
Corning’s new digital hot plates with PyroceramTM tops.
Corningware PyroceramTM heat resistant cookware
ROBAX® was heated until red-hot. Then cold water was
poured on the glass ceramic from above - with NO
breakage.
![Page 39: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/39.jpg)
Czochralski crystal pulling technique for
single crystal Si
SSPL: Solid State Physics Laboratory, N. Delhi
J. Czochralski, (1885-1953)
Polish Metallurgist
![Page 40: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/40.jpg)
A
Steel
Hardness
Rockwell C
15 0.8
Wt% C Micro-structureCoarsepearlite
finepearlite
bainiteTempered martensite
martensite
0.8
0.8
0.8
0.8
30
45
55
65
Heattreatment
Annealing
normalizing
austempering
tempering
quenching
B
C
D
E
TABLE 9.2
![Page 41: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/41.jpg)
HEAT TREATMENT
Heating a material to a high temperature,
holding it at that temperature for certain
length of time followed by cooling at a
specified rate is called heat treatment
![Page 42: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/42.jpg)
A
N
AT
TQ
heati
ng
holding
time
T
Annealing Furnace cooling RC 15
Normalizing Air cooling RC 30
Quenching Water cooling RC 65
Tempering Heating after quench RC 55
Austempering Quench to an inter- RC 45mediate temp and hold
![Page 43: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/43.jpg)
Eutectoid Reaction
CFeCo
3725
0.8 0.02
6.67
cool
Pearlite
Ammount of Fe3C in PearliteRed Tie Line below eutectoid temp
pearliteCFf
3 02.067.6
02.08.0
117.065.6
78.0
![Page 44: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/44.jpg)
Phase diagrams do not have any information about time or rates of transformations.
We need TTT diagram for
austenite-> pearlite
transformation
![Page 45: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/45.jpg)
Stable austenite
unstable austenite
TTT diagram for eutectoid steel
start
finish
![Page 46: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/46.jpg)
Stable austenite
unstable austenite
start
finishAnnealing:coarse pearliteNormalizin
g:fine pearlite
U
I
TTTT diagram for eutectoid steel
![Page 47: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/47.jpg)
Callister
![Page 48: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/48.jpg)
Stable austenite
unstable austenite
start
finish
TTT diagram for eutectoid steel
A+M
M
Ms
Mf
Ms : Martensite start temperature
Mf : Martensite finish temperature
’: martensite (M)
' coolingrapid
QUENCHING
Hardness RC 65
Extremely rapid, no C-curves
![Page 49: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/49.jpg)
BCT
Amount of martensite formed does not depend upon time, only on temperature.Atoms move only a fraction of atomic distance during the transformation:
1. Diffusionless (no long-range diffusion)2. Shear (one-to-one correspondence between and ’ atoms) 3. No composition change
Martensitic transformation
![Page 50: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/50.jpg)
Problem 3.1
BCT unit cell of (austenite)
414.12 a
c
BCT unit cell of ’ (martensite)
08.100.1 a
c
0% C (BCC)
1.2 % C
Contract ~ 20%
Expand ~ 12%
Martensitic transformation (contd.)
Fig. 9.12
![Page 51: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/51.jpg)
Hardness of martensite as a function of C content
Wt % Carbon →
20
40
60
0.2 0.4 0.6
Hard
ness
, R
C
Hardness of martensite depends mainly on C content and not on other alloying additions
Fig. 9.13
Martensitic transformation (contd.)
![Page 52: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/52.jpg)
A
N
AT
TQ
heati
ng
T
![Page 53: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/53.jpg)
Heating of quenched steel below the eutectoid temperature, holding for a specified time followed by ar cooling.
TEMPERING
CFetempering3
T<TE
?
![Page 54: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/54.jpg)
Tempering (contd.)
+Fe3C PEARLITE
A distribution of fine particles of Fe3C in matrix known as TEMPERED MARTENSITE.
Hardness more than fine pearlite, ductility more than martensite.
Hardness and ductility controlled by tempering temperature and time.
Higher T or t -> higher ductility, lower strength
![Page 55: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/55.jpg)
Tempering Continued
Callister
![Page 56: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/56.jpg)
AustemperingBainite
Short needles of Fe3C embedded in plates of ferrite
![Page 57: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/57.jpg)
Problems in Quenching
Quench Cracks
High rate of cooling:
surface cooler than interior
Surface forms martensite before the interior
Austenite
martensite
Volume expansion
When interior transforms, the hard outer martensitic shell constrains this expansion leading to residual stresses
![Page 58: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/58.jpg)
But how to shift the C-curve to higher times?
Solution to Quench cracks
Shift the C-curve to the right (higher times)
More time at the nose
Slower quenching (oil quench) can give martensite
![Page 59: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/59.jpg)
By alloying
All alloying elements in steel (Cr, Mn, Mo, Ni, Ti, W, V) etc shift the C-curves to the right.
Exception: Co
Substitutional diffusion of alloying elements is slower than the interstitial diffusion of C
![Page 60: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/60.jpg)
Plain C steel
Alloy steel
Alloying shifts the C-curves to the right.Separate C-curves for pearlite and bainite
Fig. 9.10
![Page 61: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/61.jpg)
Hardenability
Ability or ease of hardening a steel by formation of martensite using as slow quenching as possible
Alloying elements in steels shift the C-curve to the right
Alloy steels have higher hardenability than plain C steels.
![Page 62: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/62.jpg)
Hardnenability Hardness
Ability or ease of hardening a steel
Resistance to plastic deformation as measured by indentation
Only applicable to steels
Applicable to all materials
Alloying additions increase the hardenability of steels but not the hardness.
C increases both hardenability and hardness of steels.
![Page 63: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/63.jpg)
High Speed steel
Alloy steels used for cutting tools operated at high speeds
Cutting at high speeds lead to excessive heating of cutting tools
This is equivalent to unintended tempering of the tools leading to loss of hardness and cutting edge
Alloying by W gives fine distribution of hard WC particles which counters this reduction in hardness: such steels are known as high speed steels.
![Page 64: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/64.jpg)
+
: solid solution of Cu in FCC Al: intermetallic compound CuAl2
4
Tsolvus
supersaturated saturated +
FCC FCC Tetragonal
4 wt%Cu 0.5 wt%Cu 54 wt%Cu
Precipitation of in
![Page 65: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/65.jpg)
Stable
unstable Tsolvus
As-quenched
start finsh
+
Aging
TTT diagram of precipitation of in
A fine distribution of precipitates in matrix causes hardening
Completion of precipitation corresponds to peak hardness
![Page 66: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/66.jpg)
-grains
As quenched
-grains +
Aged
Peak aged
Dense distribution of fine
overaged
Sparse distribution of coarse
Driving force for coarsening
/ interfacial energy
![Page 67: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/67.jpg)
0.1 1 10 100
hardness
Aging time
(days)
180ºC
100ºC 20ºC
Aging temperature
Peak hardness is less at higher aging temperaturePeak hardness is obtained in shorter time at higher aging temperature
Fig. 9.15
![Page 68: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/68.jpg)
U
I
T Stable
unstable
As-quenched
start finsh
+
Aging
Tsolvus
1
hardness
180ºC
100ºC 20ºC
100 ºC
180 ºC
![Page 69: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/69.jpg)
Recovery, Recrystallization and grain growth
Following slides are courtsey
Prof. S.K Gupta (SKG)
Or Prof. Anandh Subramaniam (AS)
![Page 70: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/70.jpg)
Cold work
↑ dislocation density
↑ point defect density
Plastic deformation in the temperature range above(0.3 – 0.5)
Tm → COLD WORK
Point defects and dislocations have strain energy associated with them
(1 -10) % of the energy expended in plastic deformation is stored in the form of strain energy
)1010(~
)1010(~
1412
ndislocatio
96
ndislocatio
materialStrongermaterialAnnealed workCold
AS
![Page 71: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/71.jpg)
Cold work↑ Hardness
↑ Strength
↑ Electrical resistance
↓ Ductility
AS
![Page 72: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/72.jpg)
Cold work Anneal
Recrystallization
Recovery
Grain growth
AS
![Page 73: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/73.jpg)
Recovery, Recrystallization and Grain Growth
During recovery
1. Point Defects come to Equilibrium
2. Dislocations of opposite sign lying on a slip plane annihilate each other
(This does not lead to substantial decrease in the dislocation density)
SKG
![Page 74: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/74.jpg)
POLYGONIZATION
Bent crystal
Low angle grain boundaries
Polygonization
AS
![Page 75: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/75.jpg)
Recrystallization
Strained grains Strain-free grains
Driving force for the Process =
Stored strain energy of dislocations
SKG
![Page 76: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/76.jpg)
Recrystallization Temperature:
Temperature at which the 50% of the cold-worked material recrystallizes in one hour
Usually around 0.4 Tm (m.p in K)
SKG
![Page 77: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/77.jpg)
Factors that affect the recrystallization temperature:
1. Degree of cold work
2. Initial Grain Size
3. Temperature of cold working
4. Purity or composition of metal
Solute Drag Effect
Pinning Action of Second Phase Particle
SKG
![Page 78: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/78.jpg)
Solute Drag Effect
SKG
![Page 79: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/79.jpg)
Grain Boundary Pinning
SKG
![Page 80: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/80.jpg)
Grain Growth
Increase in average grain size following recrystallization
Driving Force reduction in grain boundary
energy
Impurities retard the process
SKG
![Page 81: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/81.jpg)
Grain growth
Globally► Driven by reduction in grain boundary energy
Locally► Driven by bond maximization (coordination number
maximization)
AS
![Page 82: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/82.jpg)
Bonded to4 atoms
Bonded to 3 atoms
Direction of grainboundary migration
Boundary moves towards itscentre of curvature
JUMP
AS
![Page 83: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/83.jpg)
Hot Work and Cold Work
Hot Work Plastic deformation above TRecrystallization
Cold Work Plastic deformation below TRecrystallization
Col
d W
ork
Hot
Wor
k
Recrystallization temperature (~ 0.4 Tm)
AS
![Page 84: Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e8f5503460f94b930cb/html5/thumbnails/84.jpg)
Cold work Recovery Recrystallization Grain growth
Tensile strength
Ductility
Electical conductivityInternal stress
Fig. 9.19
%CW Annealing Temperature
AS