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Modeling the Formation of Thermal Spray Coatings on Substrates with Arbitrary Shapes

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Abstract

The main focus of this study is on simulation of coating formation on substrates with arbitrary shapes. For this purpose, several substrate geometries shaped as inclined step, cylinder and sphere are considered. The stress analysis for these complex coating geometries is also performed. The formation of Nickel coatings on various shapes of stainless-steel substrates and Yttria-Stabilized Zirconia (YSZ) on NiCrAlY in the atmospheric plasma spray (APS) process is investigated. The topography of the coatings, as well as their microstructure, e.g., porosity, average thickness and average roughness, are evaluated. An algorithm, which is based on the Monte-Carlo stochastic model, is employed in this work. The parameters of the droplets impacting the surface, including their velocity, temperature and size, are predicted through the use of this stochastic model. Simulation results show that on the inclined part of the step or peripheral parts of the cylinder/sphere, the coating porosity is considerably lower than the flat parts, while the roughness is remarkably higher. A significant difference between the coating temperature and that of the substrate leads to the formation of residual thermal stresses. These stresses are analyzed using the object oriented finite-element (OOF) software, which utilizes an adaptive meshing technique and finite-element method to calculate residual thermal stresses. The maximum stress in the coatings occurs at the interface between the coating and the substrate. The coatings' topography and microstructure are compared with those of the experiments.

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Abbreviations

C :

Specific heat; stiffness tensor

d :

Diameter of splat

D :

Diameter of droplet

f :

Volume fraction

F :

External forces in linear elastic theory; cumulative probability distribution function

g :

Probability density function

h :

Thickness

H f :

Latent heat of fusion

K :

Stiffness tensor

P :

Porosity

R A :

Average surface roughness

S :

Random variate

t :

Time

T :

Temperature

U :

Gun speed

u :

Displacement vector

V :

Particle speed

c :

Coating

cell :

Cell

e :

Equivalent

el :

Elastic

g :

Gap

gun :

Gun

i :

Discretized x-direction

j :

Discretized y-direction

k :

Discretized z-direction

m :

Material

mat :

Material

max:

Maximum

sub:

Substrate

x :

Orthogonal coordinate

y :

Orthogonal coordinate

z :

Orthogonal coordinate

α :

Thermal expansion factor

γ :

Surface tension

δ :

Liquid–solid contact angle

ε :

Strain tensor

η :

Dummy variable

λ :

Thermal diffusivity

μ :

Mean value of probability density function

ν :

Kinematic viscosity

ξ :

Spread factor

ρ :

Density

σ :

Standard deviation of probability density function; stress in linear elastic theory

Pe:

Peclet number \(\left( {{\text{Pe}} = {\raise0.7ex\hbox{${{\text{VD}}}$} \!\mathord{\left/ {\vphantom {{{\text{VD}}} \lambda }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\lambda $}}} \right)\)

Re:

Reynolds number \(\left( {{\text{Re}} = {\raise0.7ex\hbox{${VD}$} \!\mathord{\left/ {\vphantom {{VD} \nu }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\nu $}}} \right)\)

Ste:

Stefan number \(\left( {{\text{Ste}} - = {\raise0.7ex\hbox{${C\left( {T - T_{{{\text{sub}}}} } \right)}$} \!\mathord{\left/ {\vphantom {{C\left( {T - T_{{{\text{sub}}}} } \right)} {H_{f} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${H_{f} }$}}} \right)\)

We:

Weber number \(\left( {{\text{We}} = {\raise0.7ex\hbox{${\rho V^{2} D}$} \!\mathord{\left/ {\vphantom {{\rho V^{2} D} \gamma }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\gamma $}}} \right)\)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Behrouz Haghighi & Mohammad Passandideh-Fard

  2. Centre for Advanced Coating Technologies (CACT), University of Toronto, Toronto, Canada

    Mohammad Passandideh-Fard & Javad Mostaghimi

Authors
  1. Behrouz Haghighi
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  2. Mohammad Passandideh-Fard
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  3. Javad Mostaghimi
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Correspondence to Javad Mostaghimi.

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This article is an invited paper selected from presentations at the 2023 International Thermal Spray Conference, held May 22–25, 2023, in Québec City, Canada, and has been expanded from the original presentation. The issue was organized by Giovanni Bolelli, University of Modena and Reggio Emilia (Lead Editor); Emine Bakan, Forschungszentrum Jülich GmbH; Partha Pratim Bandyopadhyay, Indian Institute of Technology, Karaghpur; Šárka Houdková, University of West Bohemia; Yuji Ichikawa, Tohoku University; Heli Koivuluoto, Tampere University; Yuk-Chiu Lau, General Electric Power (Retired); Hua Li, Ningbo Institute of Materials Technology and Engineering, CAS; Dheepa Srinivasan, Pratt & Whitney; and Filofteia-Laura Toma, Fraunhofer Institute for Material and Beam Technology.

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Haghighi, B., Passandideh-Fard, M. & Mostaghimi, J. Modeling the Formation of Thermal Spray Coatings on Substrates with Arbitrary Shapes. J Therm Spray Tech 33, 551–571 (2024). https://doi.org/10.1007/s11666-023-01691-2

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