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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.