Numerical optimization of solution heat treatments of single crystal nickel-based superalloys: Methods and validation

Transcription

1 Numerical optimization of solution heat treatments of single crystal nickel-based superalloys: Methods and validation R. Rettig, F. Müller, R.F. Singer Materials Science, University of Erlangen, Germany ThermoCalc User Meeting Aachen, Germany, 11 th 12 th September 214

2 Agenda Nickel-based superalloys: metallic high temperature materials Solution heat treatment of superalloys Validation of thermodynamic and kinetic databases Fast calculation of property maps of microstructures Summary 2 SFB/Transregio 13

3 Combined cycle power plant efficiency (211): ca. 6% (33 g CO 2 / kwh) aim 22: ca. 63% (3 g CO 2 / kwh) Siemens AG 1st stage blade 25 mm, 4,3 kg 1 MW 5 Hz 1 t 1 C 3 yrs 1.,- $ Siemens AG plant control gas turbine heat recovery steam generator condensor generator steam turbine 3 Keppel, Alstom, Cooretec Workshop, 26 SFB/Transregio 13

4 efficiency / % Carnot-efficiency / % efficiency increase Efficiency of fossile power plants Development of efficiency Relation of efficiency and process temperature gas (CC) brown coal plans year of entry into service turbine outlet temperature is 5 C material improvement process temperature / C data according to Siemens AG and DPG (25) efficiency increase is always related to higher material temperatures 4 SFB/Transregio 13

5 max. service temperature / C Development of nickel-based superalloys Harada et al. (23) IGTC MarM247 CMSX-4 TMS-162 single crystals directionally solidified Waspalloy forged IN792 conventionally cast (globulitic) year of development temperature capability of nickel-based superalloys (breaking after 1 h at 137 MPa) 5 SFB/Transregio 13

6 Turbine blades 2 cm 5 cm 1 st stage, SGT5-4F, Siemens AG polycrystalline directionally solidified single crystalline 6 SFB/Transregio 13

7 Turbine blades 1 mm 2 cm 5 cm 1 st stage, SGT5-4F, Siemens AG polycrystalline directionally solidified single crystalline 7 SFB/Transregio 13

8 Agenda Nickel-based superalloys: metallic high temperature materials Solution heat treatment of superalloys Validation of thermodynamic and kinetic databases Fast calculation of property maps of microstructures Summary 8 SFB/Transregio 13

9 segregation coefficient Heat treatment cycle for superalloys Aims: reduction of dendritic segregation T solution heat treatment 134 C, 16 h dendritic segregation (ASTRA1-2) 4 3 standard heat treatment (CMSX-4) typical values for Re-containing alloys t 2 Re solution heat treatment time / h Heckl, Rettig, Singer, Adv. Mater. Res. 278 (211) 9 SFB/Transregio 13

10 Heat treatment cycle for superalloys Aims: reduction of dendritic segregation dissolution of eutectic phases solution heat treatment eutectic phases T 134 C, 16 h 3 µm typical values for Re-containing alloys t typical directionally solidified microstructure 1 SFB/Transregio 13

11 Heat treatment cycle for superalloys Aims: reduction of dendritic segregation dissolution of eutectic phases precipitation of well-defined cubic -phase particles -phase particles solution heat treatment T 134 C, 16 h -precipitation aging 114 C, 2 h 87 C, 24 h -matrix 5 µm typical values for Re-containing alloys t typical coherent / - microstructure 11 SFB/Transregio 13

12 Agenda Nickel-based superalloys: metallic high temperature materials Solution heat treatment of superalloys Validation of thermodynamic and kinetic databases Fast calculation of property maps of microstructures Summary 12 SFB/Transregio 13

13 melting temp. meas. / C ' solvus meas. / C Verification of commercial database TTNi7 liquidus -solvus no Re and Ru with Re 145 with Ru 14 no Re and Ru with Re with Ru Shao5 Fuchs2 Sponseller96 Copland1 Dharwadkar92 this work melting temp. sim. / C 12 1 Shao5 Fuchs2 Sponseller96 Copland1 Dharwadkar92 this work Caron ' solvus sim. / C Rettig, Heckl, Neumeier, Pyczak, Göken, Singer, Defect Diffus. Forum (29) 13 SFB/Transregio 13

14 composition ' / at-% composition ' / at-% composition / at-% composition / at-% and -phase composition calculated with TTNi7 Cr 1 Co Al 1 Mo Ru 1 Ti Ta 1 Re,1, temperature / C Al 1 Ti Co Cr temperature / C 1 Ru 1 Ta Mo Rettig et al. Defect Diffus. Forum (29),1,1 Re temperature / C temperature / C good agreement bad agreement 14 SFB/Transregio 13

15 Agenda Nickel-based superalloys: metallic high temperature materials Solution heat treatment of superalloys Validation of thermodynamic and kinetic databases Fast calculation of property maps of microstructures Summary 15 SFB/Transregio 13

16 Thermodynamic properties of the microstructure CMSX y-position / µm Cr / wt-% measured as-cast microsegregation 45 3 Re / wt-% calculated solidus temperature distribution => incipient melting prediction Tsolidus / C 6 y-position / µm y-position / µm SFB/Transregio 13 Rettig et al., Model. Sim. Mat. Sci. Eng.(214)

17 Efficient calculation of microstructure maps Difficulty: The calculation of a typical 25 x 25 pixel map takes around 1h Application in evaluation of heat treatment simulations requires calculation times smaller than 5 minutes Solution: Application of surrogate models ( nonlinear interpolation ) Algorithm: Rettig, Singer, Modelling and Simulation in Materials Science and Engineering (214) 17 SFB/Transregio 13

18 Re-content / wt-% Surrogate modelling Aim: Replacement of a computationally expensive CALPHAD-property function by a cheaper one ( model of the model ) Important methods: Response Surface Models ( polynomial fitting ) Artifical Neural Networks Inverse Distance Weighting Kriging method % 44% 43% an open-source library is available for MATLAB (DACE-library, University of Denmark) Mo-content / wt-% -content at 11 C (CMSX-4) non-linear fitting of the CALPHAD-property functions based on a small number of nodes 18 SFB/Transregio 13

19 y-position / µm Classification of the microstructure reference point Al-difference to ref. point / wt-% Rettig et al., MSMSE(214) Classification by magnitude of the compositional distance vector relative to a reference point 19 SFB/Transregio 13

20 y-position / µm y-position / µm Classification of the microstructure reference point Al-difference to ref. point / wt-% Rettig et al., MSMSE(214) reference point unsimilar distance vector to ref. point / wt-% Classification by magnitude of the compositional distance vector relative to a reference point similar 2 SFB/Transregio 13

21 Rettig et al., MSMSE(214) Classification of the microstructure reference point 15 r m ila si 3 45 un y-position / µm 45 6 r ila sim Al-difference to ref. point / wt-% 6 reference point 75 y-position / µm distance vector to ref. point / wt-% Classification by magnitude of the compositional distance vector relative to a reference point y-position / µm 6 45 Classes SFB/Transregio

22 Rettig et al., MSMSE(214) Classification of the microstructure reference point reference point 3 15 m ila r si 45 6 un y-position / µm 6 r ila sim Al-difference to ref. point / wt-% 75 y-position / µm distance vector to ref. point / wt-% Classification by magnitude of the compositional distance vector relative to a reference point y-position / µm 22 8 random nodes 45 per class 3 15 y-position / µm Classes 3 SFB/Transregio

23 multiple calculation speed-up 99.5% interpol. error quantile / C single calculation speed-up Algorithm parameters Rettig et al., MSMSE(214) number of classes number of classes number of design points per class number of design points per class Optimum parameters: 8 nodes per class 15 classes number of classes 23 Achieved speed-up: around 3 for a single calculation around 3 for repeated calculations 8 4 SFB/Transregio number of design points per class

24 y-position / µm y-position / µm frequency Application: -solvus temperature distribution in CMSX '-solvus temp. / C Response Surface model Kriging (Gauss-variogram) interpolation error / C 24 Quality of the interpolation: interpolation error is below 1 C for most areas slightly larger errors in the interdendritic regions Rettig et al., Model. Sim. Mat. Sci. Eng.(214) SFB/Transregio interpol. error / C

25 Agenda Nickel-based superalloys: metallic high temperature materials Solution heat treatment of superalloys Validation of thermodynamic and kinetic databases Fast calculation of property maps of microstructures Summary 25 SFB/Transregio 13

26 Summary Development of a high-performance algorithm for the calculation of microstructure mappings New possibility for the post-processing of phase-field simulations predicting the homogenization during solution heat treatments The Kriging-method has a high general potential for improving speed when applying the CALPHAD-method 26 SFB/Transregio 13