Modeling: (i) thermal spray rapid solidification (ii) partially molten particle impact Markus Bussmann Mechanical & Industrial Engineering Centre for Advanced Coating Technologies (CACT) University of Toronto
(i) thermal spray rapid solidification Bob (Haibo) Liu, PhD Markus Bussmann, Javad Mostaghimi
Thermal Spray Coating Thermal spraying YSZ (yttria stabilized zirconia) spraying distance: 50 mm velocity: 125 ± 20 m/s particle diameter: 45 75 µm splat thickness: 2 µm cooling rate: ~ 10 6 K/s 100 µm 3/22
SEM of a TBC cross-section N.P. Padture et al., Science 296, 280, 2002 4/22
YSZ phase diagram 5/22
CACT equilibrium model assumes a pure material solidifying at good prediction of overall splat shape/ morphology no microstructure prediction T m 6/22
Rapid solidification non equilibrium or meta/unstable high interface velocity undercooling (T i <T m ) non uniform distribution of solute different solid phases 7/22
Objective develop a model to predict: microstructure, including: grain size, morphology, transformation, during rapid solidification concentration distribution accurate solidification velocity 8/22
YSZ T. Chraska et al, Thin Solid Films 40, 397, 2001 9/22
Alloy 625 Ni-based alloy 10/22
Alloy 625 11/22
1D Interface Tracking Method G. X. Wang et al, Mater. Manuf. Process 19, 259, 2004 12/22
T & C eqns + ICs + BCs T j t =α j 2 T j T(x,0) =T o T(0,t) x T(b,t) x = h[ T(0,t) T ] = 0 C L t = D L 2 C L C(x,0) = C o C(0,t) x = C(b,t) x = 0 G. X. Wang et al, Mater. Manuf. Process 19, 259, 2004 13/22
interface conditions energy conservation : T ρ L V i L = K S T s K L L x i x i mass conservation : ( C C L C S )V i = D L L x i from phase diagram : C S = k f C L undercooling : T i =T m + m C L V i /µ 14/22
parabolic model everything so far is traditional why? because the diffusion equations are based on: Fourier s Law: J = k T Fick s Law: J c = D C but these assume an infinite diffusive speed i.e. a sudden change in T or C is instantaneously felt everywhere in a domain 15/22
finite diffusive speed v d Liquid Solid non equilibrium diffusion: ν d = D /a 0 : diffusive speed ν d a 0 ν n : inter atomic spacing : solid/liquid interface velocity ν n leads to a relaxation time τ 2 D= D /ν d 16/22
v d vs v n? ν n = 0 global equilibrium: T=const, C=const ν n <<ν d local equilibrium: steady states ν n <ν d ν n ~ ν d diffusional local equilibrium: parabolic equations (non equilibrium partition coefficient k at the interface) diffusional non equilibrium: hyperbolic equations ν n >ν d C S = C L = C 0 (partitionless) S.L. Sobolev, Phys. Rev. E 55, 6845, 1997 17/22
Cattaneo devised modified laws in 1948: Fourier s Law: τ J dt + J = k T Fick s Law: τ D J C t + J c = D C 18/22
hyperbolic model T t + τ 2 T t 2 =α 2 T C L t + τ D 2 C L t 2 = D 2 C L T(x,0) =T o T(0,t) x T(b,t) x = h[ T(0,t) T ] = 0 C(x,0) = C o C(0,t) x = C(b,t) x = 0 19/22
hyperbolic interface BCs energy conservation : mass conservation : (τ t +1)ρ L V i L = K T S T s K L L x i x i ( C L C S )V i + τ D t ((C C L C s )V i ) = D L L x i from phase diagram : C S = k f C L undercooling : T i =T m + m C L V i /µ 20/22
planar vs cellular interface morphology 22/22
two indications of grain size 1) if planar, then grain size is determined by the initial nucleation density, which is a function of initial undercooling (nucleation temperature) T. Chraska et al, Thin Solid Films 40, 397, 2001 23/22
2) if cellular, the grain tips are curved; curvature can be determined via stability theory; and curvature determines grain size (KGT model) 24/22
Results solved the hyperbolic T and C equations using the same relaxation time solution method: MacCormack s predictorcorrector scheme pure Al temperature only YSZ 8 wt% yttria Alloy 625 Ni 21 wt% Cr alloy 25/22
Al temperature only 26/22
YSZ interface velocity 27/22
YSZ solid-side concentration 28/22
YSZ liquid side gradients 29/22
YSZ grain radius Upper limit Lower limit Grain morphology transformation 30/22
grain radius for Alloy 625 31/22
(ii) partially molten particle impact Tommy (Cheming) Wu, MASc Markus Bussmann, Javad Mostaghimi
Semi-Molten Droplets? Insufficient heating of oxidation sensitive materials (e.g. MCrAlY) Liquid Shell Solid Core Composite coatings (e.g. WC Co carbides in a cobalt matrix) Liquid Co Matrix WC WC WC WC WC WC WC WC WC WC WC 33/22
C.J. Li et al., Materials Science and Technology, 2004
YSZ cross-section 35/22
Ni cross-section 36/22
model 37/22
model 38/22
IB method of Uhlmann 39/22
Validation axisymmetric flow past a solid sphere, at various Re 40/22
42/22
YSZ sims 43/22
Spread 100 µm, 100 m/s 49/22
Spread 50 µm, 100 m/s 50/22