https://orcid.org/0000-0001-8861-4231
Abstract
Calcium-magnesium alumino-silicate (CMAS) infiltration and attack are difficult to simulate at real-world rates. To better understand the sensitivity of the process to engine operating parameters and CMAS chemical composition, a systems-based reduced order infiltration model that incorporates combustion gas properties, TBC microstructural properties, thermal barrier coating (TBC) heat transfer properties, and CMAS physical properties was developed. The aim was to predict the time to delamination for aircraft engines operating in non-benign environments. The penetration depths reached by a synthetic four-element CMAS mixture within a clean TBC were calculated by finite difference method. Engine operating conditions and TBC top coat types were varied to study the effects on the penetration depths and times. A larger difference between operating temperature and cold shock temperature was found to increase the risk of Mode I delamination. An increase in engine operating temperature had little effect on the critical penetration depth, but significantly influenced the actual penetration depth and time. An increase in electron beam - physical vapor deposition (EB-PVD) TBC taper angle resulted in a decrease in the critical penetration depths, suggesting a greater risk of Mode I delamination. The time taken to reach the actual penetration depth increased with operating time, until the TBC was consumed, at which point penetration time decreased with operating temperature due to lower melt viscosity.
References
1.
Saarimäki
, J.
, 2018
, Cracks in Superalloys
, Vol. 1897
, Linköping University Electronic Press, Linkoping, Sweden
.2.
Wenmann
, C.
, 2021
, “Erosion Behaviour of Thermal Barrier Coatings
,” Ph.D. dissertation
, Linköping University
, Linköping, Sweden
.https://www.diva-portal.org/smash/get/diva2:1568054/FULLTEXT01.pdf3.
Guo
, S.
, and Kagawa
, Y.
, 2007
, “Isothermal and Cycle Properties of EB-PVD Yttria-Partially-Stabilized Zirconia Thermal Barrier Coatings at 1150 and 1300 C
,” Ceram. Int.
, 33
(3
), pp. 373
–378
.10.1016/j.ceramint.2005.10.0054.
Feuerstein
, A.
, Knapp
, J.
, Taylor
, T.
, Ashary
, A.
, Bolcavage
, A.
, and Hitchman
, N.
, 2008
, “Technical and Economical Aspects of Current Thermal Barrier Coating Systems for Gas Turbine Engines by Thermal Spray and EBPVD: A Review
,” J. Therm. Spray Technol.
, 17
(2
), pp. 199
–213
.10.1007/s11666-007-9148-y5.
Krämer
, S.
, Faulhaber
, S.
, Chambers
, M.
, Clarke
, D. R.
, Levi
, C. G.
, Hutchinson
, J. W.
, and Evans
, A. G.
, 2008
, “Mechanisms of Cracking and Delamination Within Thick Thermal Barrier Systems in Aero-Engines Subject to Calcium-Magnesium-Alumino-Silicate (CMAS) Penetration
,” Mater. Sci. Eng. A
, 490
(1–2
), pp. 26
–35
.10.1016/j.msea.2008.01.0066.
Wellman
, R.
, Whitman
, G.
, and Nicholls
, J. R.
, 2010
, “CMAS Corrosion of EB PVD TBCs: Identifying the Minimum Level to Initiate Damage
,” Int. J. Refractory Met. Hard Mater.
, 28
(1
), pp. 124
–132
.10.1016/j.ijrmhm.2009.07.0057.
Vidal-Setif
, M. H.
, Chellah
, N.
, Rio
, C.
, Sanchez
, C.
, and Lavigne
, O.
, 2012
, “Calcium–Magnesium–Alumino-Silicate (CMAS) Degradation of EB-PVD Thermal Barrier Coatings: Characterization of CMAS Damage on Ex-Service High Pressure Blade TBCs
,” Surf. Coat. Technol.
, 208
, pp. 39
–45
.10.1016/j.surfcoat.2012.07.0748.
Peng
, H.
, Wang
, L.
, Guo
, L.
, Miao
, W.
, Guo
, H.
, and Gong
, S.
, 2012
, “Degradation of EB-PVD Thermal Barrier Coatings Caused by CMAS Deposits
,” Prog. Nat. Sci. Mater. Int.
, 22
(5
), pp. 461
–467
.10.1016/j.pnsc.2012.06.0079.
Krause
, A. R.
, Garces
, H. F.
, Dwivedi
, G.
, Ortiz
, A. L.
, Sampath
, S.
, and Padture
, N.
, 2016
, “Calcia-Magnesia-Alumino-Silicate (CMAS)-Induced Degradation and Failure of Air Plasma Sprayed Yttria-Stabilized Zirconia Thermal Barrier Coatings
,” Acta Mater.
, 105
, pp. 355
–366
.10.1016/j.actamat.2015.12.04410.
Bernard
, B.
, Quet
, A.
, Bianchi
, L.
, Joulia
, A.
, Malié
, A.
, Schick
, V.
, and Rémy
, B.
, 2017
, “Thermal Insulation Properties of YSZ Coatings: Suspension Plasma Spraying (SPS) Versus Electron Beam Physical Vapor Deposition (EB-PVD) and Atmospheric Plasma Spraying (APS)
,” Surf. Coat. Technol.
, 318
, pp. 122
–128
.10.1016/j.surfcoat.2016.06.01011.
Smialek
, J. L.
, 1991
, “The Chemistry of Saudi Arabian Sand: A Deposition Problem on Helicopter Turbine Airfoils
,” Gordon Conference on Corrosion
, New London, NH, July 14, Paper No. NAS 1.15, p. 105234
.https://www.researchgate.net/publication/23608470_The_chemistry_of_Saudi_Arabian_sand_-_A_deposition_problem_on_helicopter_turbine_airfoils12.
Nicholls
, J. R.
, Lawson
, K. J.
, Rickerby
, D. S.
, and Morrel
, P.
, 1998
, “Advanced Processing of TBC's for Reduced Thermal Conductivity
,” Rolls-Royce plc
, Aslborg, Denmark
.13.
Rätzer-Scheibe
, H.-J.
, Schulz
, U.
, and Krell
, T.
, 2006
, “The Effect of Coating Thickness on the Thermal Conductivity of EB-PVD PYSZ Thermal Barrier Coatings
,” Surf. Coat. Technol.
, 200
(18–19
), pp. 5636
–5644
.10.1016/j.surfcoat.2005.07.10914.
Qiu
, S.-Y.
, Wu
, C. W.
, Huang
, C. G.
, Ma
, Y.
, and Guo
, H. B.
, 2021
, “Microstructure Dependence of Effective Thermal Conductivity of EB-PVD TBCs
,” Materials
, 14
(8
), p. 1838
.10.3390/ma1408183815.
Pisani
, L.
, 2011
, “Simple Expression for the Tortuosity of Porous Media
,” Transp. Porous Media
, 88
(2
), pp. 193
–203
.10.1007/s11242-011-9734-916.
Kumar
, R.
, Rommel
, S.
, Jiang
, C.
, and Jordan
, E. H.
, 2022
, “Effect of CMAS Viscosity on the Infiltration Depth in Thermal Barrier Coatings of Different Microstructures
,” Surf. Coat. Technol.
, 432
, p. 128039
.10.1016/j.surfcoat.2021.12803917.
Bojdo
, N.
, and Filippone
, A.
, 2019
, “A Simple Model to Assess the Role of Dust Composition and Size on Deposition in Rotorcraft Engines
,” Aerospace
, 6
(4
), p. 44
.10.3390/aerospace604004418.
Zhao
, H.
, Levi
, C. G.
, and Wadley
, H. N. G.
, 2014
, “Molten Silicate Interactions With Thermal Barrier Coatings
,” Surf. Coat. Technol.
, 251
, pp. 74
–86
.10.1016/j.surfcoat.2014.04.00719.
Mechnich
, P.
, and Braue
, W.
, 2015
, “Solid‐State CMAS Corrosion of an EB‐PVD YSZ Coated Turbine Blade: Zr4+ Partitioning and Phase Evolution
,” J. Am. Ceram. Soc.
, 98
(1
), pp. 296
–302
.10.1111/jace.1324120.
Mercer
, C.
, Faulhaber
, S.
, Evans
, A. G.
, and Darolia
, R.
, 2005
, “A Delamination Mechanism for Thermal Barrier Coatings Subject to Calcium–Magnesium– Alumino-Silicate (CMAS) Infiltration
,” Acta Mater.
, 53
(4
), pp. 1029
–1039
.10.1016/j.actamat.2004.11.02821.
Cai
, Z.
, Jiang
, J.
, Wang
, W.
, Liu
, Y.
, and Cao
, Z.
, 2019
, “CMAS Penetration-Induced Cracking Behavior in the Ceramic Top Coat of APS TBCs
,” Ceram. Int.
, 45
(11
), pp. 14366
–14375
.10.1016/j.ceramint.2019.04.15222.
Zhao
, L. G.
, Lu
, T. J.
, and Fleck
, N. A.
, 2000
, “Crack Channelling and Spalling in a Plate Due to Thermal Shock Loading
,” J. Mech. Phys. Solids
, 48
(5
), pp. 867
–897
.10.1016/S0022-5096(99)00064-223.
Dong
, H.
, Wang
, H.
, Cai
, Z.
, Wang
, W.
, and Liu
, Y.
, 2024
, “Peridynamics–FEM Coupling for Interfacial Delamination Effected by Vertical Crack Density in Thermal Barrier Coatings
,” Int. J. Appl.
, 16
(1
), p. 2450005
.10.1142/S175882512450005424.
Gauntner
, D. J.
, and Sucec
, J.
, 1978
, “Method for Calculating Convective Heat-Transfer Coefficients Over Turbine Vane Surfaces
,” NASA Technical Publication, Washington, DC, No. E-9324
.https://ntrs.nasa.gov/api/citations/19780009395/downloads/19780009395.pdf25.
Wiesner
, V. L.
, and Bansal
, N. P.
, 2015
, “Mechanical and Thermal Properties of Calcium–Magnesium Aluminosilicate (CMAS) Glass
,” J. Eur. Ceram. Soc.
, 35
(10
), pp. 2907
–2914
.10.1016/j.jeurceramsoc.2015.03.03226.
Krämer
, S.
, Yang
, J.
, Levi
, C. G.
, and Johnson
, C. A.
, 2006
, “Thermochemical Interaction of Thermal Barrier Coatings With Molten CaO–MgO–Al2O3–SiO2 (CMAS) Deposits
,” J. Am. Ceram. Soc.
, 89
(10
), pp. 3167
–3175
.10.1111/j.1551-2916.2006.01209.x27.
Cavainolo
, B. A.
, Kinzel
, M. P.
, Naraparaju
, R.
, and Kabir
, M. R.
, 2023
, “Simulating CMAS Infiltration of an EB-PVD Thermal Barrier Coating Using the Volume-of-Fluid Method
,” AIAA
Paper No. 2023–4427.10.2514/6.2023-442728.
Mauro
, J. C.
, Yue
, Y.
, Ellison
, A. J.
, Gupta
, P. K.
, and Allan
, D. C.
, 2009
, “Viscosity of Glass-Forming Liquids
,” Proc. Natl. Acad. Sci.
, 106
(47
), pp. 19780
–19784
.10.1073/pnas.091170510629.
Dong
, J.
, Zhang
, D.
, and Gan
, L.
, 2019
, “An Empirical Formula for Accurate Calculation of Liquidus Temperature of Blast Furnace Slags in SiO2–Al2O3–CaO–MgO System
,” Ironmaking Steelmaking
, 46
(1
), pp. 71
–74
.10.1080/03019233.2017.134054530.
Kelton
, K. F.
, 2017
, “Kinetic and Structural Fragility—a Correlation Between Structures and Dynamics in Metallic Liquids and Glasses
,” J. Phys. Condens. Matter
, 29
(2
), p. 023002
.10.1088/0953-8984/29/2/02300231.
Avramov
, I.
, 2007
, “Viscosity Activation Energy' Physics and Chemistry of Glasses
,” Eur. J. Glass Sci. Technol. Part B
, 48
(1
), pp. 61
–63
.https://www.ingentaconnect.com/contentone/sgt/ejgst/2007/00000048/00000001/art0000832.
Wiesner
, V. L.
, and Bansal
, N. P.
, 2014
, “Crystallization Kinetics of Calcium–Magnesium Aluminosilicate (CMAS) Glass
,” Surf. Coat. Technol.
, 259
, pp. 608
–615
.10.1016/j.surfcoat.2014.10.02333.
Levi
, C. G.
, Hutchinson
, J. W.
, Vidal-Sétif
, M. H.
, and Johnson
, C. A.
, 2012
, “Environmental Degradation of Thermal-Barrier Coatings by Molten Deposits
,” MRS Bull.
, 37
(10
), pp. 932
–941
.10.1557/mrs.2012.23034.
Naraparaju
, R.
, Gomez Chavez
, J. J.
, Niemeyer
, P.
, Hess
, K.-U.
, Song
, W.
, Dingwell
, D. B.
, Lokachari
, S.
, Ramana
, C. V.
, and Schulz
, U.
, 2019
, “Estimation of CMAS Infiltration Depth in EB-PVD TBCs: A New Constraint Model Supported With Experimental Approach
,” J. Eur. Ceram. Soc.
, 39
(9
), pp. 2936
–2945
.10.1016/j.jeurceramsoc.2019.02.04035.
Naraparaju
, R.
, Hüttermann
, M.
, Schulz
, U.
, and Mechnich
, P.
, 2017
, “Tailoring the EB-PVD Columnar Microstructure to Mitigate the Infiltration of CMAS in 7YSZ Thermal Barrier Coatings
,” J. Eur. Ceram. Soc.
, 37
(1
), pp. 261
–270
.10.1016/j.jeurceramsoc.2016.07.02736.
Kabir
, M. R.
, Sirigiri
, A. K.
, Naraparaju
, R.
, and Schulz
, U.
, 2019
, “Flow Kinetics of Molten Silicates Through Thermal Barrier Coating: A Numerical Study
,” Coatings
, 9
(5
), p. 332
.10.3390/coatings905033237.
Johari
, A. D.
, and Rahman
, M. M.
, 2015
, “A Review of Advance Thermal Barrier Coating Architecture
,” The 3rd National Graduate Conference (Nat Grad 2015)
, Universiti Tenaga Nasional
, Putrajaya, Malaysia, Apr. 8–9
.https://www.researchgate.net/publication/304719080_A_review_of_advance_thermal_barrier_coating_architecture38.
Krause
, A. R.
, Senturk
, B. S.
, Garces
, H. F.
, Dwivedi
, G.
, Ortiz
, A. L.
, Sampath
, S.
, and Padture
, N. P.
, 2014
, “2ZrO2 Y2O3 Thermal Barrier Coatings Resistant to Degradation by Molten CMAS: Part I Optical Basicity Considerations and Processing
,” J. Am. Ceram. Soc.
, 97
(12
), pp. 3943
–3949
.10.1111/jace.1321039.
Gleeson
, B.
, 2006
, “Thermal Barrier Coatings for Aeroengine Applications
,” J. Propul. Power
, 22
(2
), pp. 375
–383
.10.2514/1.2073440.
Lima
, R. S.
, 2020
, “Perspectives on Thermal Gradients in Porous ZrO2-7–8 wt.% Y2O3 (YSZ) Thermal Barrier Coatings (TBCs) Manufactured by Air Plasma Spray (APS)
,” Coatings
, 10
(9
), p. 812
.10.3390/coatings1009081241.
Kumar
, V.
, and Kandasubramanian
, B.
, 2016
, “Processing and Design Methodologies for Advanced and Novel Thermal Barrier Coatings for Engineering Applications
,” Particuology
, 27
, pp. 1
–28
.10.1016/j.partic.2016.01.00742.
Chen
, X.
, 2006
, “Calcium–Magnesium–Alumina–Silicate (CMAS) Delamination Mechanisms in EB-PVD Thermal Barrier Coatings
,” Surf. Coat. Technol.
, 200
(11
), pp. 3418
–3427
.10.1016/j.surfcoat.2004.12.02943.
Wilke
, C. R.
, 1950
, “A Viscosity Equation for Gas Mixtures
,” J. Chem. Phys.
, 18
(4
), pp. 517
–519
.10.1063/1.174767344.
Reid
, R. C.
, Prausnitz
, J. M.
, and Sherwood
, T. K.
, 1977
, The Properties of Gases and Liquids
, 3rd ed., McGraw-Hill
, New York
.45.
Maitland
, G.
, Rigby
, M.
, Smith
, E.
, Wakeham
, W.
, and Henderson
, D.
, 1983
, “Intermolecular Forces: Their Origin and Determination
,” Phys. Today
, 36(4), pp. 57
–58
.10.1063/1.291558746.
Hirschfelder
, J. O.
, Curtiss
, C. F.
, and Bird
, R. B.
, 1964
, The Molecular Theory of Gases and Liquids
, Wiley
, Hoboken, NJ.47.
Guggenheim
, E. A.
, 1960
, Elements of the Kinetic Theory of Gases
, Vol. 1
, Pergamon Press
, Oxford, UK
.48.
Chapman
, S.
, and Cowling
, T. G.
, 1990
, The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases
, Cambridge University Press
, Cambridge, UK
.49.
Nieto
, A.
, Agrawal
, R.
, Bravo
, L.
, Hofmeister-Mock
, C.
, Pepi
, M.
, and Ghoshal
, A.
, 2021
, “Calcia–Magnesia–Alumina–Silicate (CMAS) Attack Mechanisms and Roadmap Towards Sandphobic Thermal and Environmental Barrier Coatings
,” Int. Mater. Rev.
, 66
(7
), pp. 451
–492
.10.1080/09506608.2020.182441450.
Webster
, R. I.
, and Opila
, E. J.
, 2022
, “Viscosity of CaO-MgO-Al2O3-SiO2 (CMAS) Melts: Experimental Measurements and Comparison to Model Calculations
,” J. Non-Cryst. Solids
, 584
, p. 121508
.10.1016/j.jnoncrysol.2022.12150851.
Wellman
, R. G.
, and Nicholls
, J. R.
, 2007
, “A Review of the Erosion of Thermal Barrier Coatings
,” J. Phys. D Appl. Phys.
, 40
(16
), pp. R293
–R305
.10.1088/0022-3727/40/16/R0152.
Altun
, Ö.
, and Böke
, Y.
, 2009
, “Effect of the Microstructure of EB-PVD Thermal Barrier Coatings on the Thermal Conductivity and the Methods to Reduce the Thermal Conductivity
,” Arch. Mater. Sci.
, 48
, p. 48
.https://www.researchgate.net/publication/44567623_Effect_of_the_microstructure_of_EB-PVD_thermal_barrier_coatings_on_the_thermal_conductivity_and_the_methods_to_reduce_the_thermal_conductivity53.
Kakuda
, T. R.
, Limarga
, M. A.
, Bennett
, T. D.
, and Clarke
, D. R.
, 2009
, “Evolution of Thermal Properties of EB-PVD 7YSZ Thermal Barrier Coatings
,” Acta Mater.
, 57
(8
), pp. 2583
–2591
.10.1016/j.actamat.2009.02.019Copyright © 2025 by ASME
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