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
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
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
0.001 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
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