Modelling of long-term phase stability in Ni-based superalloys based on thermodynamic and kinetic CALPHAD calculations

Transcription

1 Modelling of long-term phase stability in Ni-based superalloys based on thermodynamic and kinetic CALPHAD calculations R. Rettig, R. F. Singer Institute of Science and Technology of Metals (WTM) DFG-Research Training Group 1229 Department of Materials Science and Engineering University of Erlangen, Germany ThermoCalc User Meeting Aachen 10 th 11 th September 2009 Folie 1

2 1. Introduction Folie 2

3 Single crystal alloy development 2 µm 50 µm content / wt-% Rhenium Ruthenium René N6 René N5 CMSX-10 CMSX-4 4 PWA René N2 CMSX-2 0 1st 2nd 3rd 4th 5th generation Re solid solution strengthening enhancement of TCP-phase formation influencing / -misfit A. Volek (2002) Ru solid solution strengthening reduction of TCP-phase formation reverse partitioning Folie 3

4 Precipitation of TCP phases in superalloys phase P R prototype Cr 46 Fe 54 Mo 6 Co 7 Cr 18 Mo 42 Ni 40 Cr 18 Mo 31 Co 51 Mg crystal structure tetragonal rhomoedral orthorombic rhomboedric / hexagonal hexagonal TCP TCP phases are detrimental to mechanical properties: depletion of solid solution strengtheners Neumeier (2009) crack initiation sites Folie 4

5 3. Basics of precipitation modelling Folie 5

6 Challenges for a precipitation model Aims fully multicomponent modelling (> 8 alloying elements) use of CALPHAD thermodynamics and kinetics considering multiphase growth and dissolution Challenges many details of the precipitation are still unknown online coupling with CALPHAD calculations generates additional computational costs Folie 6

7 Calculation of Phase Diagrams (CALPHAD) Basic principle: minimization of Gibbs energy computation of thermodynamic properties of very complex systems on physical basis phase fraction / mol-% G G G G 1,0 0,8 0,6 0,4 0,2 0,0 general thermodynamics fcc 0 ln 0 ideal xs mix mix example CMSX-4 database TTNi7 P temperature / C ' G xg RT x x G i G xx L x x xs k mix i j ij i j i ji k G x i k L ij xs i i i i mix disordered phase k CALPHAD database for all elements i, j Gibbs free energy molar fraction of element i interaction parameter (i,j) of k-th order Folie 7

8 Validation of thermodynamic database TTNi7 Superalloy database melting temp. meas. / C no Re and Ru with Re 1450 with Ru liquidus Shao05 Fuchs02 Sponseller96 Copland01 Dharwadkar92 this work melting temp. sim. / C ' solvus meas. / C no Re and Ru with Re with Ru -solvus Shao05 Fuchs02 Sponseller96 Copland01 Dharwadkar92 this work Caron ' solvus sim. / C R. Rettig, A. Heckl, S. Neumeier, F. Pyczak, M. Göken, R.F. Singer. Defect and Diffusion Forum (2009) Folie 8

9 ThermoCalc in precipitation modelling Phase fractions in equilibrium CALPHAD methods allow 100 simple calculation of phase fractions transition temperatures can be calculated phase fractions of precipitates in equilibrium can be calculated V i / mol-% ,1 P T / C alloy CMSX-4 (3 wt-% Re) ' L Folie 9

10 ThermoCalc in precipitation modelling Driving forces of precipitation driving force of precipitation is a thermodynamic property driving forces can be used as an input to precipitation models via TQ / TC-API libraries G m / kj/mol T / C alloy SRR300D (3 wt-% Re) P Folie 10

11 DICTRA in precipitation modelling Kinetics of precipitation DICTRA performs 1D diffusion simulations diffusional growth of precipitates can be simulated simulation of moving boundary problems of multicomponent systems is numerically tricky concentration Cr / wt-% Ni-Cr60 3 h 28 h 278 h 833 h position / µm Folie 11

12 4. A more sophisticated precipitation model Folie 12

13 A multicomponent, multiphase precipitation model Basic idea of model 1. nucleation of precipitates 2. Diffusional growth of precipitates G G s c r * v r TCP matrix G V r Folie 13

14 A multicomponent, multiphase precipitation model Idea of model Loop for all timesteps Driving force from CALPHAD Loop for all precipitate types Nucleation rate timestep 1 New nucleation Growth of all existing particles Total removal of solute from matrix Loop for all particles Growth rate using CALPHAD Volume change Solute removal from matrix based on ideas from T. Sourmail, PhD (2002), Univ. of Cambridge red: New concepts developed in the present work Folie 14

15 A multicomponent, multiphase precipitation model Idea of model Loop for all timesteps Driving force from CALPHAD Loop for all precipitate types Nucleation rate timestep 1 timestep 2 New nucleation Growth of all existing particles Total removal of solute from matrix Loop for all particles Growth rate using CALPHAD Volume change Solute removal from matrix based on ideas from T. Sourmail, PhD (2002), Univ. of Cambridge red: New concepts developed in the present work Folie 15

16 A multicomponent, multiphase precipitation model Idea of model Loop for all timesteps Driving force from CALPHAD Loop for all precipitate types Nucleation rate timestep 1 timestep 2 timestep 3 New nucleation Growth of all existing particles Total removal of solute from matrix Loop for all particles Growth rate using CALPHAD Volume change Solute removal from matrix based on ideas from T. Sourmail, PhD (2002), Univ. of Cambridge red: New concepts developed in the present work Folie 16

17 Algorithm for precipitation model Loop for all timesteps Loop for all precipitate types Driving force from CALPHAD Nucleation rate New nucleation Growth of all existing particles Total removal of solute from matrix Loop for all particles Growth rate using CALPHAD Volume change Solute removal from matrix Folie 17

18 Nucleation model Activation energy for nucleation classical (unary or binary) nucleation G G G S * activation energy strain energy interface energy G V f * 16 f Nucleation rate * N N 0 nucleation rate saturation of available nucleation sites number of nucleates available nucleation sites G t 3 3 GV GS chemical driving force -> CALPHAD factor for heterogeneous nucleation dn r G Gt N0 exp exp dt kt kt dn N dn dt N0 dt 1 r activation energy for atomic migration vibration frequency H. Sieurin et al. (2007) dn r dt 2 not constricted nucleation rate Folie 18

19 Algorithm for precipitation model Loop for all timesteps Loop for all precipitate types Driving force from CALPHAD Nucleation rate New nucleation Growth of all existing particles Total removal of solute from matrix Loop for all particles Growth rate using CALPHAD Volume change Solute removal from matrix Folie 19

20 Interfaces in a multicomponent system Interface concentrations defined by the operating tieline multicomponent moving boundary problem i element i c P Precipitate i c I v Matrix i c M c P, c I are NOT fixed to mass-balance tieline equations defining v, c P, c I : i i flux balances Ji v cp ci i i local equilibrium cp ci multicomponent diffusion n1 J D c i ij j j1 - mass-balance tieline: different growth rates for all elements due to different diffusivities => flux-balance-tieline has to be found (all elements have identical growth rates) J i µ () c D ij n Q. Chen et al. (2008) flux of element i at interface chemical potential diffusion coefficient matrix number of elements Folie 20

21 5. Examples of application Folie 21

22 Application of the precipitation model Impact of alloy composition on precipitation screening of alloy instability with ThermoCalc influence of residual segregation in the dendrite core influence of ruthenium on TCP-phase precipitation Folie 22

23 Screening of alloy instability Traditional PHACOMP / New-PHACOMP method PHACOMP: electron vacancy density N v New-PHACOMP: energy niveau of 3d orbitals M d N N x v v, i i i from A. Volek (2002) Folie 23

24 Screening of alloy instability CALPHAD method as an efficient alternative number of samples 5 TCP no TCP TCP not observed TCP observed Simulated amount of TCP / mol-% experimental data A. Volek (2002) TCP simulated / mol-% 4 Experiment yes yes yes 3 yes yes h at 950 C, 1050 C, 1150 C? no no no MC2 MC533 MC534 MC544 MC645 MC653 CMSX-10M René N6 Alloy #11 experimental data: Caron (2000) Superalloys Folie 24

25 Effect of residual segregation Dendritic solidification of superalloys as-cast segregation DICTRA-simulation of heat treatment Re residual segregation Re W 1315 C t / h Neumeier (2009) experimental data: M. Lamm (2007) Folie 25

26 Effect of residual segregation Modelling of TCP-phase precipitation in the dendrite as-cast state heat treated state 1200 interdendritic region dendrite core 1200 dendrite core T / C homogeneous alloy T / C homogeneous alloy interdendritic region 1 vol-% P t / h 1 vol-% P t / h in accordance with experimental results alloy TMS-121 (Re-containing superalloy) Folie 26

27 Suppression of TCP-phases with Ruthenium Thermodynamics and driving forces 3 0 % Ru 2.5 % Ru 6 V TCP / mol-% 2 1 P G m / kj/mol % Ru 0 % Ru T / C equilibrium phase fractions T / C thermodynamic driving force alloys TMS-121 (0 wt-% Ru) and TMS-138 (3 wt-% Ru) Folie 27

28 Suppression of TCP-phases with Ruthenium Kinetics of precipitation Ru changes growth kinetics partly due to change in interface energy T / C interdendr. region 1000 dendrite core vol-% P t / h T / C 0 % Ru % Ru vol-% P t / h experimental data: Sato et al. (2006) Scripta Mat alloys TMS-121 (0 wt-% Ru) and TMS-138 (3 wt-% Ru) Folie 28

29 6. Summary Folie 29

30 Conclusions and Outlook Conclusions: multicomponent precipitation model including CALPHAD calculations has been developed the new model can be applied for prediction of TTT-diagrams and precipitation sequences reliable prediction of model parameters remains an important issue many details of TCP-phase precipitation are still unknown Folie 30

31 We are grateful for a grant from the German Science Foundation (DFG) in the framework of the DFG-Graduiertenkolleg (Research Training Group) 1229/1 Stable and Metastable Multiphase Systems for High Temperature Applications at the Universities of Erlangen and Bayreuth. Folie 31