Modeling:(i)thermalsprayrapidsolidification(ii)partially‐moltenparticleimpact

MarkusBussmannMechanical&IndustrialEngineering

CentreforAdvancedCoatingTechnologies(CACT)UniversityofToronto

(i)thermalsprayrapidsolidification

Bob(Haibo)Liu,PhD

MarkusBussmann,JavadMostaghimi

3/22

Thermal Spray Coating

  ThermalsprayingYSZ(yttriastabilizedzirconia)  sprayingdistance:50mm  velocity:125±20m/s  particlediameter:45‐75µm  splatthickness:2µm  coolingrate:~106K/s

100 µm

4/22

SEM of a TBC cross-section

N.P.Padtureetal.,Science296,280,2002

5/22

YSZ phase diagram

6/22

CACT equilibrium model

  assumesapurematerialsolidifyingat  goodpredictionofoverallsplatshape/

morphology  nomicrostructureprediction

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Tm

7/22

Rapid solidification

  non‐equilibriumormeta/unstable  highinterfacevelocity  undercooling  non‐uniformdistributionofsolute  differentsolidphases

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(Ti <Tm)

8/22

Objective

  developamodeltopredict:

 microstructure,including:grainsize,morphology,transformation,duringrapidsolidification

  concentrationdistribution  accuratesolidificationvelocity

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YSZ

T.Chraskaetal,ThinSolidFilms40,397,2001

10/22

Alloy 625 – Ni-based alloy

11/22

Alloy 625

12/22

1D Interface Tracking Method

G.‐X.Wangetal,Mater.Manuf.Process19,259,2004

13/22

T & C eqns + ICs + BCs

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∂Tj∂t

=α j∇2Tj

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∂T(0,t)

∂x= h T(0,t)−T∞[ ]

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∂T(b,t)

∂x= 0

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T(x,0)=To

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∂CL∂t

=DL∇2CL

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∂C(0,t)

∂x=∂C(b,t)

∂x= 0

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C(x,0)= Co

G.‐X.Wangetal,Mater.Manuf.Process19,259,2004

14/22

interface conditions

  energyconservation:

  massconservation:

  fromphasediagram:

  undercooling:

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ρLViL= Ks∂TS∂x

i

−KL∂TL∂x

i

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CL −CS( )Vi =−DL∂CL∂x

i

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CS = kfCL

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Ti =Tm +m ⋅CL −Vi /µ

15/22

parabolic model

  everythingsofaristraditional  why?–becausethediffusionequationsarebasedon:

  Fourier’sLaw:

  Fick’sLaw:

  buttheseassumeaninfinite“diffusivespeed”  i.e.asuddenchangeinTorCisinstantaneouslyfelt

everywhereinadomain

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J =−k∇T

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Jc =−D∇C

16/22

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a0

finite diffusive speed vd

:inter‐atomicspacing

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νd =D /a0

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νn

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νd

:diffusivespeed

:solid/liquidinterfacevelocity

non‐equilibriumdiffusion: Liquid Solid

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νn

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τD=D /νd2

leadstoa“relaxationtime”

17/22

vd vs vn ?

globalequilibrium:T=const,C=const

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νn = 0

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νn <<νd localequilibrium:steadystates

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νn ~ νd

diffusionallocalequilibrium:parabolicequations(non‐equilibriumpartitioncoefficientkattheinterface)

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νn <νd

diffusionalnon‐equilibrium:hyperbolicequations

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νn >νd

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CS = CL = C0 (partitionless)

S.L.Sobolev,Phys.Rev.E55,6845,1997

18/22

  Cattaneodevisedmodifiedlawsin1948:

  Fourier’sLaw:

  Fick’sLaw:

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τ∂Jdt

+ J =−k∇T

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τD∂JC∂t

+ Jc =−D∇C

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hyperbolic model

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∂T

∂t+ τ

∂2T

∂t2=α∇2T

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∂T(0,t)

∂x= h T(0,t)−T∞[ ]

€

∂T(b,t)

∂x= 0

€

T(x,0)=To

€

∂CL∂t

+ τD∂2CL∂t2

=D∇2CL

€

∂C(0,t)

∂x=∂C(b,t)

∂x= 0

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C(x,0)= Co

20/22

hyperbolic interface BCs

  energyconservation:

  massconservation:

  fromphasediagram:

  undercooling:

€

(τ∂

∂t+1)ρLViL= Ks

∂TS∂x

i

−KL∂TL∂x

i

€

CL −CS( )Vi + τD∂

∂t((CL −Cs)Vi )=−DL

∂CL∂x

i

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CS = kfCL

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Ti =Tm +m ⋅CL −Vi /µ

22/22

planar vs cellular interface morphology

23/22

two indications of grain size

  1)ifplanar,thengrainsizeisdeterminedbytheinitialnucleationdensity,whichisafunctionofinitialundercooling(nucleationtemperature)

T.Chraskaetal,ThinSolidFilms40,397,2001

24/22

  2)ifcellular,thegraintipsarecurved;curvaturecanbedeterminedviastabilitytheory;andcurvaturedeterminesgrainsize(KGTmodel)

25/22

Results

  solvedthehyperbolicTandCequationsusingthesamerelaxationtime

  solutionmethod:MacCormack’spredictor‐correctorscheme

  pureAl–temperatureonly  YSZ–8wt%yttria  Alloy625–Ni‐21wt%Cralloy

26/22

Al – temperature only

27/22

YSZ interface velocity

28/22

YSZ solid-side concentration

29/22

YSZ liquid side gradients

30/22

YSZ grain radius

Upper limit

Lower limit

#

Grain morphology transformation

31/22

grain radius for Alloy 625

(ii)partiallymoltenparticleimpact

Tommy(Cheming)Wu,MASc

MarkusBussmann,JavadMostaghimi

33/22

Semi-Molten Droplets?

  Insufficientheatingofoxidation‐sensitivematerials(e.g.MCrAlY)

  Compositecoatings(e.g.WC‐Co–carbidesinacobaltmatrix)

WC WC WC

WC WC

WC

WC

WC

WC

WC

WC

SolidCore

LiquidShell

LiquidCoMatrix

C.J.Lietal.,MaterialsScienceandTechnology,2004

35/22

YSZ cross-section

36/22

Ni cross-section

37/22

model

38/22

model

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IB method of Uhlmann

40/22

Validation

axisymmetricflowpastasolidsphere,atvariousRe

42/22

43/22

YSZ sims

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Spread – 100 µm, 100 m/s

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Spread – 50 µm, 100 m/s