E. Kozeschnik
http://matcalc.at
Thermo-kinetics based materials
modeling with MatCalc – Functionality
and integration
Outline
•
•
General information
Thermodynamic engine
• Equilibrium and non-equilibrium thermodynamics
• Phase diagrams
• Non-equilibrium driving forces
• Precipitation modeling
• SFFK-Model for multi-component precipitation simulation.
• Interfacial energy modeling
• GBB approach for interfacial energies
• Size effect and diffuse interfaces
• Through-process modeling – first results
• Sub-structure evolution – Yield point simulation
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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MatCalc general information
MatCalc, the Materials Calculator
• Project start: 1993, TU Graz
• Coordinator: E. Kozeschnik
• Institute of Materials Science and Technology
Vienna University of Technology
• http://matcalc.at
• General structure
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•
•
•
•
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Language: C++
Platform: Qt
GUI, command line and libraries (API)
Data export and import functionality
Advanced scripting language
Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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http://matcalc.at
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Software architecture
Win
Mac
Linux
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MatCalc thermodynamic engine
MatCalc thermodynamic engine
• Thermodynamic data (Gibbs energy) from
proprietary/general CALPHAD databases
• Unencrypted (text based)
 Thermodynamics + Mobility
 Physical properties (density etc.)
• Full: Al, Fe, Ni. Demo: Mg, Ti, TiAl, SMA, Mo …
• Thermodynamic engine
• Multi-component multi-phase Gibbs energy
•
•
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minimizer
Unconstrained and compositionally constrained
equilibrum
Phase boundary search (phase diagrams)
Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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MatCalc thermodynamic engine
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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MatCalc thermodynamic engine
• Phase diagrams (from tutorial t8)
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Precipitation modeling
Precipitates …
Various types of
precipitates in
tempered martensite
(C-extraction replica
in TEM)
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Precipitates …
TEM image:
TiC in steel
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Precipitates …
g‘-precipitates in Ni-base superalloy UDIMET 720Li
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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SFFK model for precipitate growth …
Multi-component
-> Mean-field
approximation of
precipitation problem
n
m
µ

l
g
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… components
… precipitates
… chemical potential
… radius
… mechanical energy
… interfacial energy
Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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SFFK model for precipitate growth …
Gibbs energy of a system with n components and m precipitates
Gibbs energy
of the matrix
Bulk free energies
of all precipitates
Energy contribution of the
precipitate matrix interface
Free energy dissipation:
Dissipation by interface movement
Dissipation by diffusion inside the precipitate
Dissipation by diffusion inside the matrix
E. Kozeschnik, J. Svoboda, F. D. Fischer, CALPHAD, 28 (4), 2005, 379-382.
J. Svoboda, F. D. Fischer, P. Fratzl and E. Kozeschnik, Mater. Sci. Eng. A, 2004, 385 (1-2) 166-174.
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Onsager‘s thermodynamic extremal principle
• Lars Onsager (1931), Norwegian Chemical
Engineer.
• Nobel Prize in 1968 for reciprocal relations. In
this paper, formulation of the TEP.
A thermodynamic system evolves along
the particular kinetic path, where
maximum entropy is produced
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Onsager‘s thermodynamic extremal principle
• Lars Onsager (1931), Norwegian Chemical
Engineer.
• Nobel Prize in 1968 for reciprocal relations. In
this paper, formulation of the TEP.
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Numerical integration …
for all precipitates
next time step
Pre-Proc.: Initialize and set up parameters
Nucleation?
Add precipitate class
Growth
Evaluate
Dissolution?
Remove prec. class
Post-Proc.: Evaluate results
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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http://matcalc.at
Thermo-kinetic software MatCalc
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Typical output of prec.-simulations
Cementite (Fe3C) formation in Fe0.4wt% C
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Heat treatment of X38 CrMoV 5-3
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Ni-base superalloy UDIMET 720 Li
R. Radis et al., Acta Mater. 57 (2009) 5739-5747.
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Ni-base superalloy UDIMET 720 Li
R. Radis et al., Acta Mater. 57 (2009) 57395747.
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Through-process modeling
Through-process modeling
Processing -> Microstructure -> Property
Process simulation
Microstructure
modeling
Mechanical modeling
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Example: Yield-point modeling
• State parameter-based approach
• Grain size (distribution)
• Substructure
 Internal / Wall dislocations, subgrain size, misorientation,
aspect ratio
 Evolution equations for state parameters instead of
constitutive/empirical laws
Simulate
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Example: Yield-point modeling (ABC)
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Example: Yield-point modeling (ABC)
• Advantages:
• Simple, only 3 parameters. Easy calibration
• Strain-rate sensitive
• Physical mechanisms reflected in formulation:
Dislocation generation
Dynamic recovery
dr G× b3 2
= 2 ×C × Dd
r - req2
dt
kB ×T
(
)
Static recovery
• Shortcomings:
• Current ABC formulation is one-parameter model
• Advanced model (2-param.) under development
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Summary
Some recent developments …
• Major steps towards predictive simulation of
precipitation
• Multi-component SFFK Model -> MatCalc (2004-2006)
• Prediction of interfacial energies-> GBB model (20062008)
Correction of sharp IE -> size effect (2007-2009)
Entropy correction for IE -> diffuse interfaces (2008-…)
(Quenched-in) excess vacancies (2009-2011-…)
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•
•
• Recent ongoing work / new subjects
• Solute trapping of vacancies / interstitials (2010-)
• Deformation-induced effects on precipitation (2011-)
• Microstructure evolution (ReXX, Recovery, disl. …)
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Interfacial energy modeling
• Introduction into classical nucleation theory
• The concept of nucleation barriers.
• Steady state nucleation rates and time
dependence
• Nucleation in multi-component systems
• Multi-component extension of CNT
• Treatment of interfacial energies
• Generalized nearest-neighbor broken-bond model
• Corrections to planar sharp interfacial energies
 Size correction and diffuse interfaces
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Richard Becker: 1931
• The nearest-neighbor broken-bond model
R. Becker, Ann. Phys., 1938,
Vol. 32, pp. 128-140
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Ansatz
• Two blocks of matter
• Count bonds in initial and final configuration
g E
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new
AB
E
broken
AA
E
broken
BB
Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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NNBB model
• Bond counting:
nS ZS
E
=
× eAA
2
nS ZS
broken
EBB =
× eBB
2
broken
AA
new
EAB
= nS ZS × eAB
é
ù
1
g = nS zS êeAB - (e AA + e BB )ú
ë
û
2
• nS … number of surface atoms/area
zS … number of bonds across interface
eAA … bond energy between two A-atoms
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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NNBB model
• We have
é
ù
1
g = nS zS × êe AB - (eAA + eBB )ú
ë
û
2
• On the other hand:
é
ù
1
DH = zL N × êeAB - (eAA + eBB )ú
ë
û
2
• N … Avogadro number
ZL … coordination number for nearest neighbors
DH … enthalpy of mixing
nS zS
g=
DH
NzL
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Structural factor …
• Structural factor: Take into account nextnearest neigbors
• Value is approximately
z S ,eff
 0.328bcc / 0.329 fcc
z L ,eff
g
nS z S ,eff
Nz L ,eff
DH
• Implemented in
MatCalc 5.21
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Interfacial energy prediction: Size
correction and diffuse interfaces ...
Size effect and diffuse interfaces ...
• Take into account
• size of precipitate
• diffuse interface
nS z S
g  
DH
Nz L
B. Sonderegger and E. Kozeschnik, Scripta Mater. 60 (2009) 635-638.
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Size effect...
• Less broken inter-atomic bonds, if precipitate
is small
B. Sonderegger and E. Kozeschnik, Scripta Mater. 60 (2009) 635-638.
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Diffuse interfaces ...
• Take into account
entropic
contributions
 1
B. Sonderegger and E. Kozeschnik, Metal. Mater. Trans 41A (2010) 3262-3269.
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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Diffuse interfaces ...
B. Sonderegger and E. Kozeschnik, Metal. Mater. Trans 41A (2010) 3262-3269.
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Ernst Kozeschnik, MatCalc – The Materials Calculator , Rolduc Abdij, Kerkrade, Netherlands
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