Simultaneous Transformation Kinetics Avrami theory Adapted for many reactions occurring together...
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Simultaneous Transformation Kinetics • Avrami theory • Adapted for many reactions occurring together • Ferrite, Widmanstatten ferrite, pearlite…. • Complex carbide-precipitation reactions • Competition between inter- and intra- granularly nucleated reactions • Some difficulties
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Transcript of Simultaneous Transformation Kinetics Avrami theory Adapted for many reactions occurring together...
Simultaneous Transformation Kinetics
• Avrami theory
• Adapted for many reactions occurring together
• Ferrite, Widmanstatten ferrite, pearlite….
• Complex carbide-precipitation reactions
• Competition between inter- and intra-granularly nucleated reactions
• Some difficulties
DISPLACIVE
RECONSTRUCTIVE
0.00 0.25 0.50 0.75 1.00
0.00
0.25
0.50
0.75
1.00 Allotriomorphic Widmanstatten Pearlite
PREDICTED FRACTION
MEASURED FRACTIONJones & Bhadeshia, 1996
CONSTRAINED UNCONSTRAINED
7407006606205800.0
0.2
0.4
0.6
0.8
1.0
Temperature / °C
0.0
0.2
0.4
0.6
0.8
1.0
PEARLITE
11 K/min
101 K/min
w
Jones & Bhadeshia, 1996
100 microns austenite grain size
Temperature / °C
PEARLITE
11 K/min
101 K/min
w
Jones & Bhadeshia, 1996
30 microns austenite grain size
0.0
0.2
0.4
0.6
0.8
1.0
7607206806406000.0
0.2
0.4
0.6
0.8
1.0
0 75 150 225 3000.00
0.25
0.50
0.75
1.00
Time / s
β+ β
Robson, Jones & Bhadeshia, 1996
0.001 0.01 0.1 1 10 100 1000 104500
550
600
650
700
Time /h
0.1% Laves
2% M23
C6
0.1% M2X
(b)
Steel F (10Cr1MoV)
Robson & Bhadeshia, 1996
0.1 1 10 100 1000 104500
550
600
650
700
750
800
Time /h
1% M23
C6
1% M2C
M23
C6 observed
M2X
observed
Baker & Nutting 2.25Cr1Mo Steel
Robson & Bhadeshia, 1996
10 100 1000 104450
500
550
600
650
700
0.25% Predicted0.25% Calculated by Hald
Time /h
(a)
Robson & Bhadeshia, 1996
NF 616
-350
-300
-250
-200
-150
-100
-50
0
50
400 500 600 700 800 900 1000
EquilibriumNon equilibrium
Temperature /degCRobson & Bhadeshia, 1996
Driving force for M2X precipitation
0
0.005
0.01
0.015
0.02
0.025
500 550 600 650 700 750 800
M23
C6
Laves PhaseM
2X
Temperature /degC
Steel F (10CrMoV)
Robson & Bhadeshia, 1996
-500
-450
-400
-350
-300
-250
-200
-150
-100
500 550 600 650 700
2.25Cr1Mo10CrMoV
Temperature /degC
M2X precipitation
Robson & Bhadeshia, 1996
-450
-400
-350
-300
-250
-200
-150
500 550 600 650 700 750
2.25Cr1Mo10CrMoV
Temperature /degCRobson & Bhadeshia, 1996
M23C6 precipitation
-100
-80
-60
-40
-20
0
20
500 550 600 650 700 750
10CrMoV 2.25Cr1Mo
Temperature /degC
Laves phase precipitation
Robson & Bhadeshia, 1996
-500
-400
-300
-200
-100
0
100
750 800 850 900 950 1000 1050 1100
DG M2X
DG M23C6
DG LavesDG M2X
Temperature /K
Delta G /J/mol
Steel F, Free Energy Changes
Robson & Bhadeshia, 1996
dVØ=µ1°VØV∂dVeØt1 t2
ba
dVØ=µ1°VØ+VµV∂dVeØdVµ=µ1°VØ+VµV∂dVeµ
Kasuya, Ichikawa, Fuji and Bhadeshia, 1999
Kasuya, Ichikawa, Fuji and Bhadeshia, 1999
0 100 200 300 400 500 6000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time / s
Prestrain
0.0
0.18
0.360.63
Singh & Bhadeshia, 1996
Singh & Bhadeshia, 1996
0 100 200 300 400 500 6000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time / s
Prestrain
0.0
0.63
Singh & Bhadeshia, 1996
0.0 0.2 0.4 0.6300
350
400
Prestrain
Ms of the alloy
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
Prestrain
500 oC
475 oC
450 oC
400 oC
V(x∞ÆC°xÆ∞C)=DC@xC@zjz§V(x∞ÆMn°xÆ∞Mn)=DMn@xMn@zjz§V(x∞ÆC°xÆ∞C)=DC@xC@zjz§V(x∞ÆMn°xÆ∞Mn)=DMn@xMn@zjz§DC¿DMnDC¿DMn
