Thermo-kinetics based materials modeling with MatCalc Functionality and integration

Transcription

1 Thermo-kinetics based materials modeling with MatCalc Functionality and integration E. Kozeschnik

2 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 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 2

3 MatCalc general information

4 MatCalc, the Materials Calculator Project start: 1993, TU Graz Coordinator: E. Kozeschnik Institute of Materials Science and Technology Vienna University of Technology General structure 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 4

5 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 5

6 Software architecture Win Mac Linux Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 6

7 MatCalc thermodynamic engine

8 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 minimizer Unconstrained and compositionally constrained equilibrum Phase boundary search (phase diagrams) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 8

9 MatCalc thermodynamic engine Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 9

10 MatCalc thermodynamic engine Phase diagrams (from tutorial t8) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 10

11 Precipitation modeling

12 Precipitates Various types of precipitates in tempered martensite (C-extraction replica in TEM) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 12

13 Precipitates TEM image: TiC in steel Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 13

14 Precipitates g -precipitates in Ni-base superalloy UDIMET 720Li Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 14

15 SFFK model for precipitate growth Multi-component -> Mean-field approximation of precipitation problem n components m precipitates µ chemical potential radius l mechanical energy g interfacial energy Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 15

16 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, J. Svoboda, F. D. Fischer, P. Fratzl and E. Kozeschnik, Mater. Sci. Eng. A, 2004, 385 (1-2) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 16

17 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 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 17

18 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 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 18

19 next time step for all precipitates Numerical integration Pre-Proc.: Initialize and set up parameters Nucleation? Add precipitate class Growth Dissolution? Evaluate Remove prec. class Post-Proc.: Evaluate results Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 19

20 Thermo-kinetic software MatCalc Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 20

21 Typical output of prec.-simulations Cementite (Fe 3 C) - formation in Fe- 0.4wt% C Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 21

22 Heat treatment of X38 CrMoV Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 22

23 Ni-base superalloy UDIMET 720 Li R. Radis et al., Acta Mater. 57 (2009) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 23

24 Ni-base superalloy UDIMET 720 Li R. Radis et al., Acta Mater. 57 (2009) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 24

25 Through-process modeling

26 Through-process modeling Processing -> Microstructure -> Property Process simulation Microstructure modeling Mechanical modeling Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 26

27 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 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 27

28 Example: Yield-point modeling (ABC) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 28

29 Example: Yield-point modeling (ABC) Advantages: Simple, only 3 parameters. Easy calibration Strain-rate sensitive Physical mechanisms reflected in formulation: Dislocation generation dr - dt = 2 C D d G b 3 ( 2) k B T r 2 - r eq Dynamic recovery Static recovery Shortcomings: Current ABC formulation is one-parameter model Advanced model (2-param.) under development Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 29

30 Summary

31 Some recent developments Major steps towards predictive simulation of precipitation Multi-component SFFK Model -> MatCalc ( ) Prediction of interfacial energies-> GBB model ( ) Correction of sharp IE -> size effect ( ) Entropy correction for IE -> diffuse interfaces (2008- ) (Quenched-in) excess vacancies ( ) Recent ongoing work / new subjects Solute trapping of vacancies / interstitials (2010-) Deformation-induced effects on precipitation (2011-) Microstructure evolution (ReXX, Recovery, disl. ) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 31

32 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 32

33 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 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 33

34 Richard Becker: 1931 The nearest-neighbor broken-bond model R. Becker, Ann. Phys., 1938, Vol. 32, pp Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 34

35 Ansatz Two blocks of matter Count bonds in initial and final configuration g E new AB E broken AA E broken BB Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 35

36 NNBB model Bond counting: E broken AA = n SZ S 2 e AA E broken BB = n SZ S 2 e BB é g = n S z S ë ê e AB e AA +e BB E new AB = n S Z S e AB ( ) n S number of surface atoms/area z S number of bonds across interface e AA bond energy between two A-atoms ù û ú Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 36

37 NNBB model We have é g = n S z S e AB e +e AA BB ë ê ( ) ù û ú On the other hand: é DH = z L N e AB e +e AA BB ë ê ( ) N Avogadro number Z L coordination number for nearest neighbors DH enthalpy of mixing g = n Sz S Nz L DH ù û ú Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 37

38 Structural factor Structural factor: Take into account nextnearest neigbors ns zs, eff g DH Value is approximately Nz z z S, eff L, eff bcc Implemented in MatCalc 5.21 / fcc L, eff Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 38

39 Interfacial energy prediction: Size correction and diffuse interfaces...

40 Size effect and diffuse interfaces... Take into account size of precipitate diffuse interface g n S z Nz S L DH B. Sonderegger and E. Kozeschnik, Scripta Mater. 60 (2009) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 40

41 Size effect... Less broken inter-atomic bonds, if precipitate is small B. Sonderegger and E. Kozeschnik, Scripta Mater. 60 (2009) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 41

42 Diffuse interfaces... Take into account entropic contributions 1 B. Sonderegger and E. Kozeschnik, Metal. Mater. Trans 41A (2010) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 42

43 Diffuse interfaces... B. Sonderegger and E. Kozeschnik, Metal. Mater. Trans 41A (2010) Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 43