Kplus Kplus Modelling of Kinetics in Multi- Component, Multi-Phase, Multi- Particle Systems: Application E. Kozeschnik J. Svoboda F.D. Fischer Institute for Materials Science, Welding and Forming, Graz University of Technology Materials Center Leoben, Austria Academy of Sciences, Brno, Czech Republic Institute of Metal Physics, University of Mining, Leoben , Austria Erich Schmid Institute of Materials Science, Austrian Academy of Sciences , Austria Institute of Mechanics, University of Mining, Leoben , Austria
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Modelling of Kinetics in Multi- Component, Multi-Phase, Multi- Particle Systems: Application E. Kozeschnik J. Svoboda F.D. Fischer Institute for Materials.
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KplusKplus
Modelling of Kinetics in Multi-Component, Multi-Phase, Multi-Particle Systems: Application
E. KozeschnikJ. SvobodaF.D. Fischer
Institute for Materials Science, Welding and Forming, Graz University of TechnologyMaterials Center Leoben, Austria
Academy of Sciences, Brno, Czech RepublicInstitute of Metal Physics, University of Mining, Leoben , Austria
Erich Schmid Institute of Materials Science, Austrian Academy of Sciences , AustriaInstitute of Mechanics, University of Mining, Leoben , Austria
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Contents
• Model formulation
• Computer Implementation
• Algorithm flow-chart
• Application to– Nucleation, growth and coarsening of
cementite in steel– TTP Diagram for gamma_prime in Ni-base – Complex experimental tool steel
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
The modeling team (2001-2006) ...
• J. Svoboda– Academy of Sciences, Czech Republic, CZ
• F.D. Fischer– Institute of Mechanics, University of Leoben, A
• E. KozeschnikB. Sonderegger (2004-)– Institute for Materials Science, Welding and Forming, Graz
University of Technology, A
Task: Model development and implementation for precipitation kinetics in multi-component, multi-phase, multi-particle systems
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Idea …
• System with spherical precipitates of different size, composition and phase type in multi-component matrix.
• Evolution equations from Onsager thermodynamic extremal principle: System develops with constrained maximum Gibbs Free Energy dissipation.
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Model formulation: Growth …
• Gibbs Free Energy
• Maximum Gibbs Free Energy Dissipation with constraint
∑∑ ∑ ∑== = =
γπρ+⎟⎠
⎞⎜⎝
⎛μ+λ
πρ+μ=
m
1k
2k
n
1i
m
1kki
n
1ikik
3k
i0i0 4c3
4NG
kk y
Q
y
G&∂∂
−=∂∂
21
kikk cry ,=
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Gibbs Free Energy dissipation …
1. Diffusion through matrix
2. Interface movement
3. Diffusion in precipitates
∑=
=m
k k
kk
MQ
1
22
2
4 ρπρ &
€
Q3 =RT
ckiDki0
ρ k
∫i=1
n
∑k=1
m
∑ 4πr2 jki2 dr =
4πRTρ k5 ˙ c ki
2
45ckiDkii=1
n
∑k=1
m
∑
∑∑∑∑∫= == =
+−≈=
m
k
n
i ii
kikikikkki
m
k
n
i
Z
ii Dc
cccRTdrJr
Dc
RTQ
k1 1 00
20
322
1 1 001
)3/)((44
&& ρρρππ
ρ
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Results: Growth
• Linear system of equations in , and :r&c&
∑++
=
=pn
jijij ByA
1
1
kjkikk vcry ,, &&=
kjv
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Multi-component nucleation
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
kT
GexpNZJ
*
c*
sΔ
β ⎟⎠⎞
⎜⎝⎛−=
texpJJ s
τ
2
1
*2
2
2
1
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂Δ∂−
=ir
GkT
Zπ
⎟⎟⎠
⎞⎜⎜⎝
⎛ −== ∑
=
m
i iMi
Mi
Pi
**
Dc
)cc(rA/r
1
2
2*
4 Ωπβ
22
1
Z*βτ =
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Thermo-Kinetic software: MatCalc
• Equilibrium (CALPHAD)
• Diffusion (MOBILITY)
• Phase trans-formations
E. Kozeschnik, B. Buchmayr, “MatCalc – A simulation tool for multicomponent thermodynamics, diffusion and phase transformation kinetics”, in: ‘Mathematical
Modelling of Weld Phenomena 5’, Institute of Materials, London, Book 734, 2001;349.
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Calculation: flow-chart
Pre-Proc.: Initialize and set up parameters
for
all p
reci
pita
tes
Nucleation? Add precipitate class
Growth Evaluate
Dissolution? Remove prec. classnext
tim
e st
ep
Post-Proc.: Evaluate results
KplusKplus
Example I
Nucleation – Growth - Coarsening
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Start MatCalc ...
Live demo ...
• Cementite precipitation in Fe-0.1%C• 100 precipitate classes• Automatic interfacial energy
KplusKplus
Example II
TTP-diagram
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
γ’-precipitation in Ni-base alloy
• Ni-13at%Al
• 200 classes
• =17 mJ/m2
• Cooling rates: 0,01 – 1000 °/s
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
400
500
600
700
800
900
1e0 1e1 1e2 1e3 1e4
time [s]
γ’-precipitation in Ni-base alloy
0.1% 1%10% 25%
50%75%
KplusKplus
Example III
Complex systems ...
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
A Comprehensive Treatment of Precipitation Kinetics
in Complex Materials
B. Sonderegger1,6,M. Bischof2, E. Kozeschnik1 H. Leitner2, H. Clemens2, J. Svoboda4, F.D. Fischer3,5
1: Institute for Materials Science, Welding and Forming, Graz, University of Technology, Austria2: Dept. of Physical Metallurgy and Materials Testing, Montanuniversität Leoben, Austria3: Institute of Mechanics, Montanuniversität Leoben, Austria4: Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Brno, Czech Republic5: Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Leoben, Austria6: Materials Center Leoben, Leoben, Austria
Presentation given at „Solid-solid Phase Transformations in Inorganic Materials“, Phoenix, AZ, USA, 2005
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Outline
Introduction
Experimental
Numerical Results
Conclusion!!
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Outline Complex material
• Experimental Results
Improved Understanding of Precipitation Kinetics
• Numerical Simulations
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Testmelt
C Cr Mo V Ni Al Co Si Mn Fe
1.4 2.6 1.4 0.3 6.0 5.0 1.8 0.4 0.2 bal
Composition (at%)
Carbides (MC, M2C, M3C, M6C, M23C6)
Intermetallic Phases (NiAl, B2 ordering)
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Experimental Investigations
1 10 1001E-5
1E-4
1E-3
0,01
0,1 A D G I
f / 1/nm
R / nm
Casting, Austenitising, HTUp to 10000min
APFIM
SANS
TEM
M. Bischof et al.: „An advanced approach to the characterisation of precipitates in steels“, 4:45pm, Room Pueblo/Sonora
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Experimental - Numerical
1 10 1001E-5
1E-4
1E-3
0,01
0,1 A D G I
f / 1/nm
R / nm
Numerical Simulation:
APFIM
SANS
TEM
www.matcalc.tugraz.at
“MatCalc—a simulation tool for multicomponent thermodynamics, diffusion and phase transformation kinetics.”Kozeschnik E, Buchmayr B., Mathematical mod. of weld phenomena 5. London Institute of Materials; 2001. p. 349– 61
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Simulation Starting Conditions
• Database: extended TCFE3+Mobility
• Chemical Composition (10 Elements)
• Phases: MC, M2C, M3C, M6C, M23C6, NiAl
• Matrix: Grain Size, Subgrain Size etc. (Number of Nucleation sites)
• Interfacial Energies • Chemical driving forces• Chemical potentials
• Exact Heat Treatment conditions from casting to annealing (610°C, up to 10000min (167h))
Calculated from thermodyn. Databases
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Equilibrium Analysis
Precipitates after
austenitising
(990°C)
Precipitates after HT
(10000min)
(610°C)
MX MX
M6C M6C
M2C? M2C
M23C6
NiAl
No M3C
Decrease of G(M6C): G=G0-2600 [J/mol]
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02
Calculation with improved database
Improved Database
M6C: 1,5mol%, d=580nm
MX: 0,2mol%, d=60 nm
M2C: very few primary
G(M6C)=G0-2600 [J/mol]
IWS, Graz University of Technology, Austria / Materials Center Leoben E. Kozeschnik, 2005-09-02