http://matcalc.at Thermo-kinetics based materials modeling with MatCalc Functionality and integration E. Kozeschnik
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 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 2
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 Language: C++ Platform: Qt GUI, command line and libraries (API) Data export and import functionality Advanced scripting language 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 4
http://matcalc.at 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 5
Software architecture Win Mac Linux 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 6
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 minimizer Unconstrained and compositionally constrained equilibrum Phase boundary search (phase diagrams) 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 8
MatCalc thermodynamic engine 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 9
MatCalc thermodynamic engine Phase diagrams (from tutorial t8) 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 10
Precipitation modeling
Precipitates Various types of precipitates in tempered martensite (C-extraction replica in TEM) 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 12
Precipitates TEM image: TiC in steel 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 13
Precipitates g -precipitates in Ni-base superalloy UDIMET 720Li 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 14
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 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 15
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. 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 16
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 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 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. 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 18
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 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 19
http://matcalc.at Thermo-kinetic software MatCalc 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 20
Typical output of prec.-simulations Cementite (Fe 3 C) - formation in Fe- 0.4wt% C 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 21
Heat treatment of X38 CrMoV 5-3 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 22
Ni-base superalloy UDIMET 720 Li R. Radis et al., Acta Mater. 57 (2009) 5739-5747. 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 23
Ni-base superalloy UDIMET 720 Li R. Radis et al., Acta Mater. 57 (2009) 5739-5747. 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 24
Through-process modeling
Through-process modeling Processing -> Microstructure -> Property Process simulation Microstructure modeling Mechanical modeling 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 26
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 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 27
Example: Yield-point modeling (ABC) 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 28
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 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 29
Summary
Some recent developments Major steps towards predictive simulation of precipitation Multi-component SFFK Model -> MatCalc (2004-2006) Prediction of interfacial energies-> GBB model (2006-2008) Correction of sharp IE -> size effect (2007-2009) Entropy correction for IE -> diffuse interfaces (2008- ) (Quenched-in) excess vacancies (2009-2011- ) Recent ongoing work / new subjects Solute trapping of vacancies / interstitials (2010-) Deformation-induced effects on precipitation (2011-) Microstructure evolution (ReXX, Recovery, disl. ) 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 31
26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 32
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 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 33
Richard Becker: 1931 The nearest-neighbor broken-bond model R. Becker, Ann. Phys., 1938, Vol. 32, pp. 128-140 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 34
Ansatz Two blocks of matter Count bonds in initial and final configuration g E new AB E broken AA E broken BB 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 35
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 - 1 2 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 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 36
NNBB model We have é g = n S z S e AB - 1 2 e +e AA BB ë ê ( ) ù û ú On the other hand: é DH = z L N e AB - 1 2 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 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 37
Structural factor Structural factor: Take into account nextnearest neigbors ns zs, eff g DH Value is approximately Nz z z S, eff L, eff 0.328 bcc Implemented in MatCalc 5.21 / 0.329 fcc L, eff 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 38
Interfacial energy prediction: Size correction and diffuse interfaces...
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) 635-638. 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 40
Size effect... Less broken inter-atomic bonds, if precipitate is small B. Sonderegger and E. Kozeschnik, Scripta Mater. 60 (2009) 635-638. 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 41
Diffuse interfaces... Take into account entropic contributions 1 B. Sonderegger and E. Kozeschnik, Metal. Mater. Trans 41A (2010) 3262-3269. 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 42
Diffuse interfaces... B. Sonderegger and E. Kozeschnik, Metal. Mater. Trans 41A (2010) 3262-3269. 26.06.2014 Ernst Kozeschnik, MatCalc The Materials Calculator, Rolduc Abdij, Kerkrade, Netherlands 43