simulation of ppprecipitation kinetics in c+n...
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Chair of Materials Technology Institute of Materials
Simulation of precipitation p pkinetics in C+N Steels
Laís Mújicaa,b, Sebastian Webera,c, Werner Theisena
a) Ruhr-Universität Bochum, Lehrstuhl Werkstofftechnik b) Max-Planck Institut für Eisenforschung, Düsseldorf
c) Helmholtz-Zentrum Berlin
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Aachen, September 2009
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Outline
• Description to the system
• Nucleation of precipitates
• Diffusion calculations
• Conclusion
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Description of the systemDescription of the system
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Introduction
• Twinning induced plasticity
austenitic matrix
• Usually are Fe-Mn-C or Fe-Mn-Al-Si systems with low corrosion
i tresistance
• Use of carbon and nitrogen as interstitial to give strengthinterstitial to give strength
• Manganese, Chromium • TWIP steels exhibit exceptional pdeformability and strength
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1500L
• TWIP, fully austenitic materialG
1200C]
A
F+A
material
• Find out the appropriate amount of each element
L+A
900ure
[° A
• Direct austenitic solidificationA+M23C6900
mper
at A+M23C6+M2(C,N)
A+σ
• Avoid N2 degassing
• Avoid precipitates
23 6
600
Tem A+σ
M23C6+M2(C,N) • Optimize chromium and manganese contents
3000 0.2 0.4 0.6 0.8 1.0
(C+N) [wt%]
12Cr-20Mn-CN C/N=0.75 P=1 bar TCALC TCFE5
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(C+N) [wt%] TCALC -TCFE5
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Composition
Content wt% Interstitials
F M C C N C+N C/NFe Mn Cr C N C+N C/N
bal. 20.0 12.0 0.24 0.32 0.56 0.75
bal. 25.0 12.0 0.30 0.40 0.70 0.75
bal. 30.0 12.0 0.30 0.40 0.70 0.75bal. 30.0 12.0 0.30 0.40 0.70 0.75
Ingot castingH i 50% T 1150°CHammering: ε= 50%, T= 1150°CSolution annealing: T= 1150°CQuenching in water
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Material properties
1000 25Mn12CrCN 0°
600
800
30Mn12CrCN 0° 20Mn12CrCN 0°
Pa]
400
600
tres
s [M
P0
200St
0 20 40 60 80 100
Elongation [%]
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• Optimum C/N ratio1600
Precipitates
L
L+A
G
Optimum C/N ratio
• Isopleths to verify the austenite field
1400
600
[°C]
A
L+Astability
• Total interstitial 1200
ature
[
A+M2(C,N) A+M23C6
content constant
• Tendency to form 800
1000
mper
a
A+M23C6+M2(C,N)
ycarbides and nitrides
600
800
Te
• Intercrystalline corrosion
0 1 2 3 4 5
012345 W(N)x10-3
(C)W
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NucleationNucleation
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• Chemical potential of the
FundamentalsChemical potential of the nucleus is controlled by the surrounding matrixBinary system Fe-Ni
• Change of chemical potentials are related to the tangent to the Gibbs gfree energy curve of the matrix
• Difference between tangent and G nucleusdefines the driving force of the transformation parallel tangent
Source: G. Inden. Notes
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• Dependent not only on driving
Fundamentals• Dependent not only on driving
force but on the surface energy
C iti l di h l ti σπ 24 r
• Critical radius where nucleation is possible
GrrrG Δ+Δ 32 44)( πσπNucleusEmbryos
− σ2
VGrrrG Δ+=Δ3
4)( πσπ
r
Vcrit G
rΔ
=
34 • Heterogeneous nucleation: VGr Δ3
34π • Heterogeneous nucleation:
foreign bodies promote nucleation
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Nucleation - Driving force
FCC (γ) M23C6 • ΔGV is calculated f
0,6
C6
DGM(M23C6)
Nucleation
from TCALC, where the matrix phase
0,4
ce M
23C
Nucleation thermodynamically
favored
active, the nucleant dormant and
0,2
ng fo
rc
No nucleation
dormant and the other phases suspended
0,0Driv
i
suspended
600 700 800 900 1000-0,2
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Temperature [°C]
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0 / 2
Nucleus critical radio
F G i σ = 0.4 J/m2
Vm = 6.35x10-6 m3/mol• From ΔGV is
estimated the critical radius10-9]
• Asymptotic behavior due to th i it t 10-10di
us [m
]
the proximity to driving force equal to 0
10-11
10
tical
rad
10 11
Crit
550 600 650 700 750 800 850 900 950
10-12
T t [°C]
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Temperature [°C]
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Nucleus composition0 68 0 175
• Nucleus composition is higher in Fe as 0,64
0,68
fr]
Cr Mn 0,174
0,175
gtemperature increases0,60
Mn)
[wt-f
r) [w
t-fr]
0,172
0,173
• Nucleus composition is higher in Mn
0,56
M23
C6,M
M23
C6,C
r
0 170
0,171
higher in Mn and Cr as temperature decreases
0,52 w(M
w(M
0,169
0,170
decreases600 700 800 900 1000
0,48
Temperature [°C]
0,168
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p [ ]
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Diffusion calculations
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• DICTRA
Problem set-up• DICTRA
• Single cell calculations:
• FCC(γ) - M23C6
• 20Mn12Cr0.24C0.32N, Nucleus, Nr=5 nm ,
1atm
• Geometric grid
r=5 nm
• Circular geometry
SSOL4 MOB2Matrix, M • SSOL4-MOB2
• Isothermal conditions
Matrix, Mr=5 µm
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Problem set-up
• For each temperature, the correspondent composition of the nucleus is incorporated as an input
• For all the calculations the nucleus radius of 5 nm is set as a parameter
• The matrix composition is the original of the substrate
I th l t i id f 0 8 d 20 i t • In the nucleus, a geometric grid f=0.8 and 20 points was used. In the matrix, a geometric grid f= 1.25 and 60 points was employed
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M23C6 Growth
0,01
0,1• 850°CΔT 1 10 7
1E-4
1E-3
mol
-fr] ΔTmin= 1x10-7s
ΔTmax= 1x105 s
1E-6
1E-5
M23
C6) [
m
1E-8
1E-7
inn(
M
10-9 10-7 10-5 10-3 10-1 101 103 105 1071E-9
Time [s]
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Time [s]
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M23C6 Growth10-5
• Based on the composition, equilibrium is
10-5
850°Cequilibrium is reached up to 1x108s
10-6
ter [
m]
10-7
Dia
met
10-8
10-8 10-6 10-4 10-2 100 102 104 106 108
10 8
Ti [ ]
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Time [s]
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Elements diffusion
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Carbon
• Carbon
T=0s T=1e2 s T=1e4 s T=1e6 sT 1 8
diffuses form the fcc matrix towards the
0,1T=1e8 s
ol-fr
]
carbide
x(C
) [m
o
0,01
x
10-9 10-8 10-7 10-6 10-5
Distance [m]
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Nitrogen • Nitrogen content is diminished in 0 014 is diminished in the surroundings of th bid
0,012
0,014
the carbide.
• Concentration of N is increased in
0,008
0,010
ol-fr
]
N is increased in the outer part of the cell.
0,004
0,006
x(N
) [m
o
• Agreement with Ab initiocalculations on 0 000
0,002
x
T=0s T=1e2s T=1e4s T=1e6sT=1e8s calculations on
M23C6 destabilization by N
1E-9 1E-8 1E-7 1E-6 1E-5
0,000
Distance [m]
T 1e8s
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by NDistance [m]
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Chromium
• Chromium diffuses form the fcc matrix
0,5 T=0s T=1e2s T=1e4s T=1e8s
the fcc matrix towards the carbide
0,4
ol-fr
]
T=1e6s
• Outer part of M23C6 is Cr-rich0 2
0,3
(Cr)
[mo
rich
0,1
0,2x(
1E-9 1E-8 1E-7 1E-6 1E-5
,
Distance [m]
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Distance [m]
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Chromium
0,13
0,12l-fr]
0,11
(Cr)
[mo
0,10
T=0s T=1e-3s T=1e-2s T=1e-1s T=1s
x(
6E-9 8E-9 1E-8 1,2E-8 1,4E-8
Distance [m] Source: W. Theisen, H. Berns.
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Ferritic materials
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Manganese
• Manganese content is i d i h
0 19
0,20
increased in the surroundings of the carbide.
0 17
0,18
0,19
ol-fr
]
• Concentration of Mn is i d i th
0,16
0,17
(Mn)
[mo
increased in the outer part of the cell.0,14
0,15x( T=0s T=1e2s T=1e4s T=1e6sT 1e8s
1E-9 1E-8 1E-7 1E-6 1E-50,13
Distance [m]
T=1e8s
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Distance [m]
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Carbide growthKinetic analysisKinetic analysis
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• Appropriate Appropriate criteria to construct the TTT diagrams from diagrams from the simulation results of 20M 12C ll20Mn12Cr alloy
• Comparison with experimental experimental data
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Source: V. Gavriljuk, H. Berns. High Nitrogen Steels
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i i Critical time – Linear intersection approach
Kinetics
-2
fr)]
log(mol-fr) Linear Fit of log(mol-fr) Linear Fit of log(mol-fr)
pp
-4
og(m
ol-
-6
l-fr)
[Lo
-8
Log(
mo
-8 -6 -4 -2 0 2 4 6 8-10
L
L (ti ) [L ( )]
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Log(time) [Log(s)]
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KineticsCritical time – 2nd derivative approachCritical time 2 derivative approach
-2)] log(mol-fr)Boltzmann of log(mol-fr)
-4
g(m
ol-fr
) Boltzmann of log(mol-fr)
-6
-fr) [
Log
-8
Log(
mol
-
-8 -6 -4 -2 0 2 4 6 8-10
L (ti ) [L ( )]
L
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Log(time) [Log(s)]
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Critical time – 2nd derivative approach
0,50
0,75 Derivative Y1
0,25
0,50
ol-fr
))m
e))2
0 25
0,00
(Log
(mo
(Log
(tim
-0,50
-0,25
d2 ( d(
-8 -6 -4 -2 0 2 4 6 8-0,75
Log(time) [Log(s)]
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Log(time) [Log(s)]
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1000Consolidated
intercept derivative
900
re [°
C]
800
pera
tuTe
m
100 101 102 103 104700
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Critical time [s]
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Conclusions• Assuming homogeneous nucleation of M23C6 in the austenitic
matrix Fe-20Mn-12Cr-0.24c-0.32N, it is thermodynamically
ffavored at temperatures over 900°C
• Assuming homogeneous nucleation of M23C6 in the austenitic Assuming homogeneous nucleation of M23C6 in the austenitic
matrix Fe-20Mn-12Cr-0.24c-0.32N, the critical temperature for
precipitation is 850°Cp p
• It is possible to construct TTT diagrams based on Dictra
calculations. The results can be more conservative than the
experimental ones constructed on the basis of changes of
Thermo-Calc Anwendertreffen – September 2009 - Laís Mújica 32
macroscopic properties.
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EXPERIMENTAL-CURRENT AND FURTHER WORK:
I th l h t t t t f l i A t T (700• Isothermal heat treatment of samples in Ar at Temp (700-900°C each 50°C) followed by water quenching
• Oxalic acid electrolytic etching – ASTM 262/98 –Susceptibility to Intergranular Attack in Austenitic Stainless Steels
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Thank you very much for Thank you very much for your attentiony
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