modelling of long-term phase stability in ni-based...
TRANSCRIPT
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Modelling of long-term phase stabilityin 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 – Aachen10th – 11th September 2009
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1. Introduction
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1st 2nd 3rd 4th 5th0
2
4
6
8
10
12
14
cont
ent /
wt-%
generation
Rhenium Ruthenium
Re• solid solution strengthening• enhancement of TCP-phaseformation• influencing /‘-misfit
Ru• solid solution strengthening• reduction of TCP-phase formation• reverse partitioning
‘
PWA1483René N2CMSX-2
René N5CMSX-4
René N6CMSX-10
50 µm
2 µm
A. Volek (2002)
Single crystal alloy development
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Precipitation of TCP phases in superalloys
hexagonalrhomboedric / hexagonal
orthorombicrhomoedraltetragonalcrystalstructure
MgCr18Mo31Co51Cr18Mo42Ni40Mo6Co7Cr46Fe54prototype
RPphase
Neumeier (2009)
TCP phases are detrimental to mechanical properties:
• depletion of solid solution strengtheners
• crack initiation sites
TCP
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3. Basics of precipitation modelling
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Challenges for a precipitation modelAims• 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
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Calculation of Phase Diagrams (CALPHAD)
0 ideal xsmix mixG G G G 0 lnfcc xs
i i i i mixi
G x G RT x x G kxs k
mix i j ij i ji j i k
G x x L x x
Basic principle: minimization of Gibbs energy
general thermodynamics disordered phase
CALPHAD database for all elements i, j
computation of thermodynamic properties of very complex systems on physical basis
database TTNi7
600 800 1000 1200 14000,0
0,2
0,4
0,6
0,8
1,0
P
'
phas
e fr
actio
n / m
ol-%
temperature / °C
example CMSX-4
Gix
kijL
Gibbs free energy
molar fraction of element i
interaction parameter (i,j) of k-th order
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Validation of thermodynamic database TTNi7Superalloy database
liquidus ‘-solvus
1300 1350 1400 14501300
1350
1400
1450 with Ruwith Reno Re and Ru
Shao05 Fuchs02 Sponseller96 Copland01 Dharwadkar92 this workm
eltin
g te
mp.
mea
s. /
°C
melting temp. sim. / °C800 1000 1200 1400
800
1000
1200
1400
with Ruwith Reno Re and Ru
Shao05 Fuchs02 Sponseller96 Copland01 Dharwadkar92 this work Caron00
' so
lvus
mea
s. /
°C' solvus sim. / °C
R. Rettig, A. Heckl, S. Neumeier, F. Pyczak, M. Göken, R.F. Singer. Defect and Diffusion Forum289-292 (2009) 101-108
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ThermoCalc in precipitation modellingPhase fractions in equilibrium
alloy CMSX-4 (3 wt-% Re)
• CALPHAD methods allowsimple calculation of phasefractions
• transition temperaturescan be calculated
• phase fractions ofprecipitates in equilibriumcan be calculated
600 800 1000 1200 14000,1
1
10
100
'L
P
V i / m
ol-%
T / °C
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ThermoCalc in precipitation modellingDriving forces of precipitation
alloy SRR300D (3 wt-% Re)
• driving force of precipitation is a thermodynamic property
• driving forces can be usedas an input to precipitationmodels via TQ / TC-API libraries
800 900 1000 1100 12000
2
4
6
P
Gm /
kJ/m
olT / °C
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DICTRA in precipitation modellingKinetics of precipitation
0 20 40 60 80 100404550556065707580
conc
entra
tion
Cr /
wt-%
position / µm
3 h 28 h 278 h 833 h
Ni-Cr60• DICTRA performs 1Ddiffusion simulations
• diffusional growth ofprecipitates can be simulated
• simulation of moving boundary problems of multicomponent systems is numerically tricky
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4. A more sophisticated precipitation model
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A multicomponent, multiphase precipitation modelBasic idea of model
r
GGs
GV
1. nucleation of precipitates 2. Diffusional growth of precipitates
r
c
TCP matrix
vr*
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A multicomponent, multiphase precipitation modelIdea of model
Loop for all timesteps
timestep 1
based on ideas from T. Sourmail, PhD (2002), Univ. of Cambridge
Loop for all precipitatetypes
New nucleation
Growth of all existingparticles
Total removal of solute from matrix
Driving force from CALPHAD
Nucleation rate
Loop for all particles
Growth rate using CALPHAD
Volume change
Solute removal from matrix
red: New concepts developed in the present work
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A multicomponent, multiphase precipitation modelIdea of model
Loop for all timesteps
timestep 1
timestep 2
based on ideas from T. Sourmail, PhD (2002), Univ. of Cambridge
Loop for all precipitatetypes
New nucleation
Growth of all existingparticles
Total removal of solute from matrix
Driving force from CALPHAD
Nucleation rate
Loop for all particles
Growth rate using CALPHAD
Volume change
Solute removal from matrix
red: New concepts developed in the present work
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A multicomponent, multiphase precipitation modelIdea of model
Loop for all timesteps
timestep 1
timestep 2timestep 3
based on ideas from T. Sourmail, PhD (2002), Univ. of Cambridge
Loop for all precipitatetypes
New nucleation
Growth of all existingparticles
Total removal of solute from matrix
Driving force from CALPHAD
Nucleation rate
Loop for all particles
Growth rate using CALPHAD
Volume change
Solute removal from matrix
red: New concepts developed in the present work
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Algorithm for precipitation model
Loop for all timesteps
Loop for all precipitatetypes
New nucleation
Growth of all existingparticles
Total removal of solute from matrix
Driving force from CALPHAD
Nucleation rate
Loop for all particles
Growth rate using CALPHAD
Volume change
Solute removal from matrix
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Nucleation modelActivation energy for nucleation
3*
216
3V S
G fG G
*G
f VGSG
classical (unary or binary) nucleation
activation energy
strain energy chemical driving force -> CALPHAD
interface energy factor for heterogeneous nucleation
Nucleation rate *
0 exp exp tr GdN GNdt kT kT
0
1 rdNdN Ndt N dt
nucleation rate
saturation of available nucleation sites
rdNdt
N0N
tG
number of nucleates
available nucleation sites
activation energy for atomic migrationvibration frequency
not constricted nucleation rate
H. Sieurin et al. (2007)
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Algorithm for precipitation model
Loop for all timesteps
Loop for all precipitatetypes
New nucleation
Growth of all existingparticles
Total removal of solute from matrix
Driving force from CALPHAD
Nucleation rate
Loop for all particles
Growth rate using CALPHAD
Volume change
Solute removal from matrix
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Interfaces in a multicomponent systemInterface concentrations defined by the operating tieline
multicomponent moving boundary problemiPc
iMc
iIc
vPrecipitate Matrix
element icP, cI are NOT fixed to mass-balance tieline
equations defining v, cP, cI:
flux balances i ii P IJ v c c
local equilibrium i iP Ic c
1
1
n
i ij jj
J D c
multicomponentdiffusion
- 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)
flux of element i at interface
chemical potential
diffusion coefficient matrix
number of elementsijD
( )µ ciJ
n
Q. Chen et al. (2008)
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5. Examples of application
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Application of the precipitation modelImpact 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
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Traditional PHACOMP / New-PHACOMP methodScreening of alloy instability
from A. Volek (2002)
, ·v v i ii
N N x PHACOMP: electron vacancy density Nv
New-PHACOMP: energy niveau of 3d orbitals Md
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Screening of alloy instabilityCALPHAD method as an efficient alternative
experimental data A. Volek (2002)
0 5 10 150
1
2
3
4
5 TCPno TCP
TCP not observed
TCP observed
num
ber o
f sam
ples
Simulated amount of TCP / mol-%
experimental data: Caron (2000) Superalloys
MC2MC53
3MC53
4MC54
4MC64
5MC65
3CMSX-10
MRen
é N6
Alloy #
11
0
1
2
3
4 Experimentyes
yes
yesyes
nono
yes
no
?TCP
sim
ulat
ed /
mol
-%
200h at 950 °C, 1050 °C, 1150 °C
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Effect of residual segregationDendritic solidification of superalloys
Neumeier (2009)
Re
experimental data: M. Lamm (2007)
DICTRA-simulation of heat treatmentas-cast segregation
1315 °C
0 5 10 15 20 250.00
0.25
0.50
0.75
1.00
W
Re
resi
dual
seg
rega
tion
t / h
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Effect of residual segregationModelling of TCP-phase precipitation in the dendrite
alloy TMS-121 (Re-containing superalloy)
as-cast state heat treated state
in accordance with experimental results
100 101 102 103 104 105900
1000
1100
1200
1 vol-% P
interdendritic regiondendrite core
homogeneous alloy
T / °
C
t / h 100 101 102 103 104 105900
1000
1100
1200
1 vol-% P
homogeneous alloy
dendrite core
interdendritic region
T / °
Ct / h
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Suppression of TCP-phases with RutheniumThermodynamics and driving forces
equilibrium phase fractions thermodynamic driving force
alloys TMS-121 (0 wt-% Ru) and TMS-138 (3 wt-% Ru)
800 900 1000 1100 12000
2
4
6
2.5 % Ru 0 % Ru
Gm /
kJ/m
olT / °C
900 1000 1100 12000
1
2
32.5 % Ru
0 % Ru
P
V TCP /
mol
-%
T / °C
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Suppression of TCP-phases with RutheniumKinetics of precipitation
alloys TMS-121 (0 wt-% Ru) and TMS-138 (3 wt-% Ru)
experimental data: Sato et al. (2006) Scripta Mat 1679-1684
1 10 100 1000 10000900
1000
1100
1200
1 vol-% Pdendrite core
interdendr. region
T / °
C
t / h1 10 100 1000 10000
900
1000
1100
12002.5 % Ru
0 % Ru
1 vol-% P
T / °
Ct / h
Ru changes growth kinetics partly due to change in interface energy
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6. Summary
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Conclusions and OutlookConclusions: • multicomponent precipitation model including CALPHAD calculations has been developed
• the new model can be applied for predictionof TTT-diagrams and precipitation sequences
• reliable prediction of model parameters remainsan important issue
• many details of TCP-phase precipitation are stillunknown
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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.