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Modelling of Kinetics in Multi-Component, Multi-Phase, Multi-Particle Systems: Application

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

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Modelling of Kinetics in Multi-Component, Multi-Phase, Multi-Particle Systems: Application

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  1. 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

  2. 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

  3. 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

  4. 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.

  5. Model formulation: Growth … • Gibbs Free Energy • Maximum Gibbs Free Energy Dissipation with constraint

  6. Gibbs Free Energy dissipation … • Diffusion through matrix • Interface movement • Diffusion in precipitates

  7. Results: Growth • Linear system of equations in , and :

  8. Multi-component nucleation

  9. 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.

  10. Matrix phase Precipitate 1 Precipitate 2 • Microstructure - f(t,T) • dislocation density • grain size • sub-grain size … Precipitate 3 … • Precipitate props • s, lk , Mintf • nucleation site(s) • … Software implementation Overall composition bulk dislocations grain boundaries sub-grain boundaries other particles +

  11. next time step for allprecipitates Nucleation? Add precipitate class Growth Evaluate Dissolution? Remove prec. class Post-Proc.: Evaluate results Calculation: flow-chart Pre-Proc.: Initialize and set up parameters

  12. Example I Nucleation – Growth - Coarsening

  13. Live demo ... • Cementite precipitation in Fe-0.1%C • 100 precipitate classes • Automatic interfacial energy Start MatCalc ...

  14. Example II TTP-diagram

  15. g’-precipitation in Ni-base alloy • Ni-13at%Al • 200 classes • s=17 mJ/m2 • Cooling rates: 0,01 – 1000 °/s

  16. 900 800 700 600 500 400 1e0 1e1 1e2 1e3 1e4 time [s] g’-precipitation in Ni-base alloy 0.1% 1% 25% 10% 50% 75%

  17. Example III Complex systems ...

  18. 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, Austria 2: Dept. of Physical Metallurgy and Materials Testing, Montanuniversität Leoben, Austria 3: Institute of Mechanics, Montanuniversität Leoben, Austria 4: Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Brno, Czech Republic 5: Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Leoben, Austria 6: Materials Center Leoben, Leoben, Austria Presentation given at „Solid-solid Phase Transformations in Inorganic Materials“, Phoenix, AZ, USA, 2005

  19. Outline Introduction Experimental Numerical Results ! ! Conclusion

  20. Outline Complex material • Experimental Results • Numerical Simulations Improved Understanding of Precipitation Kinetics

  21. Introduction Precipitation Hardening in Steels Intermetallic Phases (e.g maraging steels) Carbides,Nitrides Testmelt

  22. Testmelt Composition (at%) Carbides (MC, M2C, M3C, M6C, M23C6) Intermetallic Phases (NiAl, B2 ordering)

  23. Experimental Investigations APFIM Casting, Austenitising, HT Up to 10000min SANS TEM M. Bischof et al.: „An advanced approach to the characterisation of precipitates in steels“, 4:45pm, Room Pueblo/Sonora

  24. Experimental - Numerical APFIM Numerical Simulation: SANS 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 TEM

  25. 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 Calculated from thermodyn. Databases • Exact Heat Treatment conditions from casting to annealing • (610°C, up to 10000min (167h))

  26. Equilibrium Analysis Decrease of G(M6C): G=G0-2600 [J/mol]

  27. Calculation with improved database G(M6C)=G0-2600 [J/mol] M6C: 1,5mol%, d=580nm MX: 0,2mol%, d=60 nm M2C: very few primary Improved Database

  28. Identification of Precipitates cast + aust HT NiAl M2C Cementite MX : too small M23C6 M6C SANS (HT 10000min)

  29. Identification of Precipitates cast + aust HT • M23C6: • nucleation too fast • r stays too small • f growing too fast Variation of G? Matrix Parameters? Correction of g! Increase of g: Lower Nucleation Rate Slower increase of f Faster increase of r

  30. g(M23C6) HT All numerical results agree with experimental findings (within statistical errors)

  31. Summary and Conclusions Simulated full heat treatment of a very complex system (10 Elements, 6 phases) Correct Equlibrium Calculations Very good results of kinetic simulation Fit of 2 parameters were sufficient to meet ~ 20-30 single measurement points Experiments get easier to interpret Simulation results get improved Further development of thermodynamic databases

  32. http://matcalc.tugraz.at

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