Abstract
Most existing thermal barrier coating (TBC) studies do not account for the depletion of Al in the BC and growth of mixed oxides (MOs). In this complementary study, we modify and extend our earlier (Lim and Meguid in Mater Des, 2019. https://doi.org/10.1016/j.matdes.2018.107543) coupled finite volume (FV)–finite element (FE) formulations to incorporate diffusion reactions of Al and Cr in the BC. The modified/expanded FV–FE formulations are supported by the introduction of appropriate diffusion–reaction equations and high temperature oxidation model. Three aspects of the work were accordingly examined. Firstly, the FV model is used to describe the diffusion and reaction of Al and O2 in the formation of α-Al2O3. The β-phase rate of depletion predicted by the model agrees well with experimental findings. Secondly, the diffusion of Cr through the TGO that leads to the formation of an external layer of MOs is simulated using the FV model. Our simulations reveal that MOs form in the early stage of thermal exposure, although there are sufficient Al in the BC to sustain the growth of α-Al2O3 phase. We reasoned this to the formation of internal oxides and diffusion cell in the BC. Lastly, we studied the effect of roughness on β-phase depletion and growth of TGO (α-Al2O3 + MOs). We show that β-phase in the peak of undulation depletes faster and the interface between the β + γ phase and γ phase in the BC straightens over time. Furthermore, our results reveal that MOs tend to form in the valley of undulation due to the shorter diffusion path.
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Abbreviations
- \( C_{{O_{2} }} \), \( C_{\text{Al}} \) and \( C_{\text{Cr}} \) :
-
Concentration of O2, Al and Cr, respectively
- \( C_{{\upbeta,{\text{limit}}}} \) :
-
Concentration of Al at which β + γ two phase structure of BC transforms into a single γ-phase
- \( C_{{{\text{Al}},{\text{crit}}}} \) :
-
Critical-healing concentration of Al
- \( D_{{{\text{O}}_{2} ,{\text{TGO}}}} \) :
-
Diffusivity of O2 in TGO
- \( D_{{{\text{O}}_{2} ,{\text{BC}}}} \) :
-
Diffusivity of O2 in BC
- \( D_{{{\text{Al}},\upgamma}} \) :
-
Diffusivity of Al in γ-phase of BC
- \( D_{{{\text{Al}},\upbeta}} \) :
-
Diffusivity of Al in β-phase of BC
- \( D_{{{\text{Cr}},\upgamma}} \) :
-
Diffusivity of Cr in γ-phase of BC
- \( D_{{{\text{Cr}},{\text{TGO}}}} \) :
-
Diffusivity of Cr in TGO
- \( t_{\text{BC}} \) :
-
Thickness of BC
- \( N_{{{\text{M}}_{2} {\text{O}}_{3} }} \) :
-
Maximum number of moles of M2O3 that can be formed in each control volume cell (M = Al or Cr)
- \( \rho_{{{\text{M}}_{2} {\text{O}}_{3} }} \) :
-
Density of oxide M2O3 (M = Al or Cr)
- \( m_{{{\text{M}}_{2} {\text{O}}_{3} }} \) :
-
Molar mass of oxide M2O3 (M = Al or Cr)
- \( V_{CV} \) :
-
Volume of control volume or cell
- \( n \) :
-
Volume fraction of oxide formed in control volume
- tcell, and wcell :
-
Thickness and width of diffusion cell
- h and w :
-
Height and width of mixed oxide formed
- \( \bar{h}\,{\text{and}}\,\bar{w} \) :
-
Normalised height and width of mixed oxides
- T :
-
Temperature
- W and A :
-
Wavelength and Amplitude of sinusoidal undulation
- Ux and Uy :
-
Displacement in the x-direction and y-direction
- σ yy :
-
Out of plane stresses
- BC:
-
Bond coat
- FE:
-
Finite element
- FV:
-
Finite volume
- MOs:
-
Mixed oxides
- TBC:
-
Thermal barrier coating
- TC:
-
Top coat
- TGO:
-
Thermally grown oxide
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Lim, L.Y., Meguid, S.A. Modeling and characterisation of depletion of aluminium in bond coat and growth of mixed oxides in thermal barrier coatings. Int J Mech Mater Des 16, 667–683 (2020). https://doi.org/10.1007/s10999-019-09482-w
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DOI: https://doi.org/10.1007/s10999-019-09482-w