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
€
(Ti <Tm)
8/22
Objective
developamodeltopredict:
microstructure,including:grainsize,morphology,transformation,duringrapidsolidification
concentrationdistribution accuratesolidificationvelocity
9/22
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
€
∂Tj∂t
=α j∇2Tj
€
∂T(0,t)
∂x= h T(0,t)−T∞[ ]
€
∂T(b,t)
∂x= 0
€
T(x,0)=To
€
∂CL∂t
=DL∇2CL
€
∂C(0,t)
∂x=∂C(b,t)
∂x= 0
€
C(x,0)= Co
G.‐X.Wangetal,Mater.Manuf.Process19,259,2004
14/22
interface conditions
energyconservation:
massconservation:
fromphasediagram:
undercooling:
€
ρLViL= Ks∂TS∂x
i
−KL∂TL∂x
i
€
CL −CS( )Vi =−DL∂CL∂x
i
€
CS = kfCL
€
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
€
Jc =−D∇C
16/22
€
a0
finite diffusive speed vd
:inter‐atomicspacing
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νd =D /a0
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νn
€
νd
:diffusivespeed
:solid/liquidinterfacevelocity
non‐equilibriumdiffusion: Liquid Solid
€
νn
€
τD=D /νd2
leadstoa“relaxationtime”
17/22
vd vs vn ?
globalequilibrium:T=const,C=const
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νn = 0
€
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
€
τD∂JC∂t
+ Jc =−D∇C
19/22
hyperbolic model
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∂T
∂t+ τ
∂2T
∂t2=α∇2T
€
∂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
€
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
€
CS = kfCL
€
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
39/22
IB method of Uhlmann
40/22
Validation
axisymmetricflowpastasolidsphere,atvariousRe
42/22
43/22
YSZ sims
49/22
Spread – 100 µm, 100 m/s
50/22
Spread – 50 µm, 100 m/s