admission in India 2015

1. MCA Admission in India
BY:
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2. Short Course on solidification at IISc October – November
NTNU
2012
Lars Arnberg, NTNU
2
1. Introduction – basic concepts 29/10
1. Nucleation - grain refinement 31/10
Crystal morphology
3. Interface stability 5/11
Cells and dendrites
4. Three phase solidification 7/11
Segregation
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3. NTNU
Solidification, Lecture 1
3
Introduction / Basic concepts
Simple heat flow during solidification
Mushy Zone
Columnar / equiaxed solidification
Curvature effects
Phase diagrams – solute redistribution
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4. Microstructur4e NTNU
Solidification of metals is a crystallisation process
Microstructure development
Depends on
Microstructure
Composition (constitution)
Concentration, C
Crystal types, phases
Phase diagram, k, m
Crystal morphology
Casting conditions
Crystal size
Chemical composition
Growth rate, V
Temperature gradient, G
Cooling rate, G*V
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5. Micr5ostructure NTNU
Increasing concentration
Increasing constitutional
undercooling (DTc)
Increasing morphological
instability
Increasing cooling rate (G*V)
Structure refinement
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6. NTNU
Heat flow
6
dT
dt
dfs
dt
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
A
v
q
=-c
+DH
dT
dt
A
vc
=-q
+dfs
dt
DH
c
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7. NTNU
Mushy zone
7
a
Alloys will solidify over a
temperature Interval, ΔTf
M. Z. is where solidification
occurs
Depending on freezing
range and temp gradient
a=
DTf
G
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8. NTNU
Controlled solidification
8
a: Bridgman furnace
Independent control of G & V.
G & V constant
b: Directional chill casting
G & V time dependant
dT/dt = GV
s=Kt1/2
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998 admission.edhole.com

9. NTNU
Growth modes
morphology & temperature distribution
9
Directional
Growth of
columnar
crystals
Free growth
of equiaxed
crystals
Positive G Negative G
Pure metal
Alloy
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998 admission.edhole.com

10. Structure of castings
10 NTNU
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11. Capillary effects; solid/liquid interface NTNU
 Undercooling
 Curvature
2/r for sphere
 Gibbs Thomson
~ 10-7 Km
K dA
dV
=
11
Solidification microstructures
given by competition between:
•Curvature : tends to maximise scale
•Diffusion: tends to minimise scale
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
DT=KG
G =
s
Dsf
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12. NTNU
Phase digram, solute redistribution
12
C0
DT0
Cs DC0
l
s
T
Cl
Tl
Ts
• Eutectic phase diagram
• Lower solubility
of alloying elements
in s than in l
• k=Cs/Cl<1 (distribution
coefficient)
• m= dTl/dC<0
• k and m constants if solidus
& liquidus lines are straight
C
D=-mDC0
T0
C0
=-m
(1-k)
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13. 13
Al-Fe Al-Mg
Al-Mn
Al-Si
Eutectic Al
phase diagrams
for important
alloying
elements
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14. 14
Al-Fe
k=0.03
AlMg
k=0.44
Al-Mn
k=0.90
Al-Si
k=0.14
Al phase
diagrams with
different
partition
coefficients
k=Cs/Cl
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15. NTNU
Summary/ Conclusions
15
 Solidification is accomplished by external cooling of a melt. Needed for
decreasing the temperature and removing latent heat of fusion
Metals solidify at a distinct freezing point, alloys have a solidification
interval (freezing range)
 Solidification microstructure will depend on both composition, (C0)
constitution (k, m) and process (G, V)
 Control of V and G will differ between casting processes
 Solidification will occur in mushy zone. Extent of MZ will depend on
temperature gradient and freezing range
 Crystal may grow directionally as columnar grains (G>0) or freely from
an undercooled melt as equiaxed grains (G<0)
 Creation of s/l interface will require undercooling. ΔTr will increase
with increased curvature (small crystal radii)
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16. NTNU
Summary/ Conclusions
16
 Scale of solidification microstructure will be determined by diffusion
(decreasing) and curvature (increasing)
 Solidification of alloys means redistribution of solute between s and l.
Determined by distribution coefficient, k.
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17. NTNU
Symbols
17
C: concentration G: temperature gradient, dT/dx K/m
k: distribution coefficient k=Cs/Cl Δsf: entropy of fusion, J/(m3K)
m: liquidus slope, dT/dC σ: solid/liquid interface energy, J/m2
V: growth rate m/s Cl: liquid concentration
T: temperature: K Cs: solid concentration
ΔT: undercooling, K C0: Initial alloy concentration
q: heat flux W/m2
A: area m2
V: volume m3
t: time, s
ΔH: heat of fusion J/m3
c: heat capacity: J/(m3K)
fs: fraction solid
ΔTf: freezing range, K admission.edhole.com