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Modeling Residual Stress Development in Thermal Spray Coatings: Current Status and Way Forward

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Abstract

An overview of analytical and numerical methods for prediction of residual stresses in thermal spray coatings is presented. The various sources and mechanisms underlying residual stress development in thermal spray coatings are discussed, then the various difficulties associated with experimental residual stress measurement in thermal spray coatings are highlighted. The various analytical and numerical models used for prediction of residual stresses in thermal spray coatings are thoroughly discussed. While analytical models for prediction of postdeposition thermal mismatch stresses are fully developed, analytical quenching and peening stress models still require extensive development. Various schemes for prediction of residual stresses using the finite element method are identified. The results of the various numerical and analytical models are critically analyzed, and their accuracy and validity, when compared with experiments, are discussed. Issues regarding the accuracy and applicability of the models for predicting residual stresses in thermal spray coatings are highlighted, and several suggestions for future development of the models are given.

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References

  1. F.J. Hermanek, Thermal Spray Terminology and Company Origins, ASM international, Materials Park, OH, 2001

    Google Scholar 

  2. P.L. Fauchais, J.V.R. Heberlein, and M. Boulos, Thermal Spray Fundamentals: From Powder to Part, Springer, Berlin, 2014

    Book  Google Scholar 

  3. R.B. Heimann, Plasma-Spray Coating: Principles and Applications, Wiley, New York, 2008

    Google Scholar 

  4. Begriffe and Einteilung, DIN EN 657; Thermal Spray—Terminology and Classification, Springer, Berlin, Heidelberg, 1994

    Google Scholar 

  5. L. Pawlowski, The Science and Engineering of Thermal Spray Coatings, Wiley, New York, 2008

    Book  Google Scholar 

  6. A. McDonald, Analysis of Thermal Spraying in the Industries of Western Canada. In International Thermal Spray Conference and Exposition (ITSC), ASM, 2015.

  7. M. Gaona, R.S. Lima, and B.R. Marple, Influence of Particle Temperature and Velocity on the Microstructure and Mechanical Behaviour of High Velocity Oxy-Fuel (HVOF)-Sprayed Nanostructured Titania Coatings, J. Mater. Process. Technol., 2008, 198(1-3), p 426-435

    Article  Google Scholar 

  8. T.S. Sidhu, S. Prakash, and R.D. Agrawal, Studies on the Properties of High-Velocity Oxy-Fuel Thermal Spray Coatings for Higher Temperature Applications, Mater. Sci., 2005, 41(6), p 805-823

    Article  Google Scholar 

  9. D. Cheng, G. Trapaga, J.W. McKelliget, and E.J. Lavernia, Mathematical Modeling of High Velocity Oxygen Fuel Thermal Spraying: An Overview, Key Eng. Mater., 2001, 197, p 1-26

    Article  Google Scholar 

  10. H. Herman, Plasma-Sprayed Coatings. Scientific American; (USA), 1988.

  11. M. Oksa, E. Turunen, T. Suhonen, T. Varis, and S.-P. Hannula, Optimization and Characterization of High Velocity Oxy-Fuel Sprayed Coatings: Techniques, Mater. Appl. Coat. Mol. Divers. Preserv. Int., 2011, 1(1), p 17-52

    Google Scholar 

  12. Handbook of Residual Stress and Deformation of Steel. ASM International, 2002.

  13. T.W. Clyne and S.C. Gill, Residual Stresses in Thermal Spray Coatings and Their Effect on Interfacial Adhesion: A Review of Recent Work, J. Therm. Spray Technol., 1996, 5(4), p 401-418

    Article  Google Scholar 

  14. N.P. Padture, M. Gell, and E.H. Jordan, Thermal Barrier Coatings for Gas-Turbine Engine Applications, Sci. Am. Assoc. Adv. Sci., 2002, 296(5566), p 280-284

    Google Scholar 

  15. A. Nusair Khan, J. Lu, and H. Liao, Effect of Residual Stresses on Air Plasma Sprayed Thermal Barrier Coatings, Surf. Coat. Technol., 2003, 168(2-3), p 291-299

    Article  Google Scholar 

  16. J. Zhu, H. Xie, Z. Hu, P. Chen, and Q. Zhang, Residual Stress in Thermal Spray Coatings Measured by Curvature Based on 3D Digital Image Correlation Technique, Surf. Coat. Technol., 2011, 206(6), p 1396-1402

    Article  Google Scholar 

  17. P. Araujo, D. Chicot, M. Staia, and J. Lesage, Residual Stresses and Adhesion of Thermal Spray Coatings, Surf. Eng., 2005, 21(1), p 35-40

    Article  Google Scholar 

  18. Z. Xue, A.G. Evans, and J.W. Hutchinson, Delamination Susceptibility of Coatings Under High Thermal Flux, J. Appl. Mech. Am. Soc. Mech. Eng., 2009, 76(4), p 41008

    Article  Google Scholar 

  19. V. Teixeira, M. Andritschky, W. Fischer, H.P. Buchkremer, and D. Stöver, Effects of Deposition Temperature and Thermal Cycling on Residual Stress State in Zirconia-Based Thermal Barrier Coatings, Surf. Coat. Technol., 1999, 1999(120-121), p 103-111

    Article  Google Scholar 

  20. K. Khor and Y. Gu, Effects of Residual Stress on the Performance of Plasma Sprayed Functionally Graded ZrO2/NiCoCrAlY Coatings, Mater. Sci. Eng. A, 2000, 277(1-2), p 64-76

    Article  Google Scholar 

  21. S. Kuroda, T. Dendo, and S. Kitahara, Quenching Stress in Plasma Sprayed Coatings and Its Correlation with the Deposit Microstructure, J. Therm. Spray Technol., 1995, 4(1), p 75-84

    Article  Google Scholar 

  22. R. Gadow, M.J. Riegert-Escribano, and M. Buchmann, Residual Stress Analysis in Thermally Sprayed Layer Composites, Using the Hole Milling and Drilling Method, J. Therm. Spray Technol., 2005, 14(March), p 100-108

    Article  Google Scholar 

  23. M.H. Staia, E. Ramos, A. Carrasquero, A. Roman, J. Lesage, D. Chicot, and G. Mesmacque, Effect of Substrate Roughness Induced by Grit Blasting upon Adhesion of WC-17% Co Thermal Sprayed Coatings, Thin Solid Films, 2000, 377, p 657-664

    Article  Google Scholar 

  24. J. Matejicek, S. Sampath, D. Gilmore, and R. Neiser, In Situ Measurement of Residual Stresses and Elastic Moduli in Thermal Sprayed Coatings: Part 2: Processing Effects on Properties of Mo Coatings, Acta Mater., 2003, 51(3), p 873-885

    Article  Google Scholar 

  25. Y. Song, Z. Lv, Y. Liu, X. Zhuan, and T.J. Wang, Effects of Coating Spray Speed and Convective Heat Transfer on Transient Thermal Stress in Thermal Barrier Coating System during the Cooling Process of Fabrication, Appl. Surf. Sci., 2015, 2015(324), p 627-633

    Article  Google Scholar 

  26. J. Zhu, W. Chen, and H. Xie, Simulation of Residual Stresses and Their Effects on Thermal Barrier Coating Systems Using Finite Element Method, Sci. China Phys. Mech. Astron., 2014, 58(3), p 1-10

    Google Scholar 

  27. S.C. Gill and T.W. Clyne, Stress Distributions and Material Response in Thermal Spraying of Metallic and Ceramic Deposits, Metall. Trans. B, 1990, 21(2), p 377-385

    Article  Google Scholar 

  28. A.M. Limarga, R. Vaßen, and D.R. Clarke, Stress Distributions in Plasma-Sprayed Thermal Barrier Coatings Under Thermal Cycling in a Temperature Gradient, J. Appl. Mech., 2011, 78(1), p 11003

    Article  Google Scholar 

  29. R.T.R. McGrann, D.J. Greving, J.R. Shadley, E.F. Rybicki, T.L. Kruecke, and B.E. Bodger, The Effect of Coating Residual Stress on the Fatigue Life of Thermal Spray-Coated Steel and Aluminum, Surf. Coat. Technol., 1998, 108-109, p 59-64

    Article  Google Scholar 

  30. P. Araujo, D. Chicot, M. Staia, and J. Lesage, Residual Stresses and Adhesion of Thermal Spray Coatings, Surf. Eng., 2013, 21, p 35-40

    Article  Google Scholar 

  31. J. Mostaghimi, S. Chandra, R. Ghafouri-Azar, and A. Dolatabadi, Modeling Thermal Spray Coating Processes: A Powerful Tool in Design and Optimization, Surf. Coat. Technol., 2003, 2003(163-164), p 1-11

    Article  Google Scholar 

  32. R. Ghafouri-Azar, J. Mostaghimi, and S. Chandra, Modeling Development of Residual Stresses in Thermal Spray Coatings, Comput. Mater. Sci., 2006, 35(1), p 13-26

    Article  Google Scholar 

  33. J. Prehm, Coupled Coating Formation Simulation in Thermal Spray Processes Using CFD and FEM, CFD Lett., 2011, 1(1), p 89-99

    Google Scholar 

  34. S. Takeuchi, M. Ito, and K. Takeda, Modelling of Residual Stress in Plasma-Sprayed Coatings: Effect of Substrate Temperature, Surf. Coat. Technol., 1990, 1990(43-44), p 426-435

    Article  Google Scholar 

  35. S. Kuroda, Y. Tashiro, H. Yumoto, S. Taira, H. Fukanuma, and S. Tobe, Peening Action and Residual Stresses in High-Velocity Oxygen Fuel Thermal Spraying of 316L Stainless Steel, J. Therm. Spray Technol., 2001, 10(2), p 367-374

    Article  Google Scholar 

  36. S. Sampath, X. Jiang, J. Matejicek, L. Prchlik, A. Kulkarni, and A. Vaidya, Role of Thermal Spray Processing Method on the Microstructure, Residual Stress and Properties of Coatings: An Integrated Study for Ni-5 wt%Al Bond Coats, Mater. Sci. Eng. A, 2004, 364(1-2), p 216-231

    Article  Google Scholar 

  37. T.-G. Wang, S.-S. Zhao, W.-G. Hua, J.-B. Li, J. Gong, and C. Sun, Estimation of Residual Stress and Its Effects on the Mechanical Properties of Detonation Gun Sprayed WC–Co Coatings, Mater. Sci. Eng. A, 2010, 527(3), p 454-461

    Article  Google Scholar 

  38. K. Al-Athel, K. Loeffel, H. Liu, and L. Anand, Modeling Decohesion of a Top-Coat from a Thermally-Growing Oxide in a Thermal Barrier Coating, Surf. Coat. Technol., 2013, 2013(222), p 68-78

    Article  Google Scholar 

  39. A.A. Abubakar, S.S. Akhtar, and A.F.M. Arif, Phase Field Modeling of V2O5 Hot Corrosion Kinetics in Thermal Barrier Coatings, Comput. Mater. Sci., 2015, 2015(99), p 105-116

    Article  Google Scholar 

  40. K.A. Khor, Z.L. Dong, and Y.W. Gu, Plasma Sprayed Functionally Graded Thermal Barrier Coatings, Mater. Lett., 1999, 38(6), p 437-444

    Article  Google Scholar 

  41. A.A. Abubakar, S.S. Akhtar, A.F.M. Arif, and J. Mostaghimi, The Effect of Porosity on the Hot Corrosion Failure of Thermal Barrier Coatings, Model. Simul. Mater. Sci. Eng., 2015, 23(7), p 75001

    Article  Google Scholar 

  42. V. Luzin, K. Spencer, and M.-X. Zhang, Residual Stress and Thermo-Mechanical Properties of Cold Spray Metal Coatings, Acta Mater., 2011, 59(3), p 1259-1270

    Article  Google Scholar 

  43. B. Klusemann, R. Denzer, and B. Svendsen, Microstructure-Based Modeling of Residual Stresses in WC-12Co-Sprayed Coatings, J. Therm. Spray Technol., 2011, 21(1), p 96-107

    Article  Google Scholar 

  44. O.P. Oladijo, A.M. Venter, L.A. Cornish, and N. Sacks, X-Ray Diffraction Measurement of Residual Stress in WC-Co Thermally Sprayed Coatings onto Metal Substrates, Surf. Coat. Technol., 2012, 206(23), p 4725-4729

    Article  Google Scholar 

  45. B.S. Yilbas and A.F.M. Arif, Residual Stress Analysis for HVOF Diamalloy 1005 Coating on Ti–6Al–4V Alloy, Surf. Coat. Technol., 2007, 202(3), p 559-568

    Article  Google Scholar 

  46. J. Matejicek, S. Sampath, and J. Dubsky, X-Ray Residual Stress Measurement in Metallic and Ceramic Plasma Sprayed Coatings, J. Therm. Spray Technol., 1998, 7(4), p 489-496

    Article  Google Scholar 

  47. O. Kesler, J. Matejicek, S. Sampath, S. Suresh, T. Gnaeupel-Herold, P.C. Brand, and H.J. Prask, Measurement of Residual Stress in Plasma-Sprayed Metallic, Ceramic and Composite Coatings, Mater. Sci. Eng. A, 1998, 257(2), p 215-224

    Article  Google Scholar 

  48. J. Pina, A. Dias, and J.L. Lebrun, Study by X-Ray Diffraction and Mechanical Analysis of the Residual Stress Generation during Thermal Spraying, Mater. Sci. Eng. A, 2003, 347(1), p 21-31

    Article  Google Scholar 

  49. Y.-C. Yang and E. Chang, Measurements of Residual Stresses in Plasma-Sprayed Hydroxyapatite Coatings on Titanium Alloy, Surf. Coat. Technol., 2005, 190(1), p 122-131

    Article  Google Scholar 

  50. T.C. Totemeier and J.K. Wright, Residual Stress Determination in Thermally Sprayed Coatings—A Comparison of Curvature Models and X-Ray Techniques, Surf. Coat. Technol., 2006, 200(12), p 3955-3962

    Article  Google Scholar 

  51. C. Lyphout, P. Nylén, A. Manescu, and T. Pirling, Residual Stresses Distribution through Thick HVOF Sprayed Inconel 718 Coatings, J. Therm. Spray Technol., 2008, 17(5-6), p 915-923

    Article  Google Scholar 

  52. R. Kingswell, K.T. Scott, B. Sorensen, Measurement of Residual Stress in Plasma Sprayed Ceramic Coatings. in Proceedings of 2nd Plasma-Technik Symposium, Plasma-Technik, Wohlen, Switzerland, 1991, p 377-388.

  53. G.G. Stoney, The Tension of Metallic Films Deposited by Electrolysis, Proc. R. Soc. London Ser. A Contain. Pap. Math. Phys. Character, 1909, 82(553), p 172-175

    Article  Google Scholar 

  54. A. Brenner and S. Senderoff, Calculation of Stress in Electrodeposits from the Curvature of a Plated Strip, J. Res. Natl. Bur. Stand. (1934), 1949, 42(2), p 105

    Article  Google Scholar 

  55. M. Mutter, G. Mauer, R. Mücke, R. Vaßen, H.C. Back, and J. Gibmeier, Investigations on the Initial Stress Evolution During Atmospheric Plasma Spraying of YSZ by In Situ Curvature Measurement, J. Therm. Spray Technol., 2016, 25(4), p 672-683

    Article  Google Scholar 

  56. S. Sampath, V. Srinivasan, A. Valarezo, A. Vaidya, and T. Streibl, Sensing, Control, and In Situ Measurement of Coating Properties: An Integrated Approach Toward Establishing Process-Property Correlations, J. Therm. Spray Technol., 2009, 18(2), p 243-255

    Article  Google Scholar 

  57. X. Zhang, M. Watanabe, and S. Kuroda, Effects of Processing Conditions on the Mechanical Properties and Deformation Behaviors of Plasma-Sprayed Thermal Barrier Coatings: Evaluation of Residual Stresses and Mechanical Properties of Thermal Barrier Coatings on the Basis of in Situ Curvature Measurement under a Wide Range of Spray Parameters, Acta Mater., 2013, 61(4), p 1037-1047

    Article  Google Scholar 

  58. F.A. Kandil, J.D. Lord, A.T. Fry, and P. V Grant, A Review of Residual Stress Measurement Methods, A Guide to Technical Selection, NPL, Report MATC, 2001, 4.

  59. T. Valente, C. Bartuli, M. Sebastiani, and A. Loreto, Implementation and Development of the Incremental Hole Drilling Method for the Measurement of Residual Stress in Thermal Spray Coatings, J. Therm. Spray Technol., 2005, 14(4), p 462-470

    Article  Google Scholar 

  60. G. Montay, A. Cherouat, A. Nussair, and J. Lu, Residual Stresses in Coating Technology, J. Mater. Sci. Technol., 2004, 20, p 81-84

    Google Scholar 

  61. M. Escribano and R. Gadow, Residual Stress Measurement and Modeling for Ceramic Layer Composites. in 27th International Cocoa Beach Conference on Advanced Ceramics and Composites: A, W.M. Kriven and H.-T. Lin, Eds., (USA), 2003, p 615-622.

  62. M. Buchmann, R. Gadow, and J. Tabellion, Experimental and Numerical Residual Stress Analysis of Layer Coated Composites, Mater. Sci. Eng. A, 2000, 288(2), p 154-159

    Article  Google Scholar 

  63. K. Berreth, M. Buchmann, R. Gadow, J. Tabellion, Evaluation of Residual Stresses in Thermal Sprayed Coatings. in Proceedings of International Thermal Spray Conference, Düsseldorf, 1999.

  64. Y.Y. Santana, J.G. La Barbera-Sosa, M.H. Staia, J. Lesage, E.S. Puchi-Cabrera, D. Chicot, and E. Bemporad, Measurement of Residual Stress in Thermal Spray Coatings by the Incremental Hole Drilling Method, Surf. Coat. Technol., 2006, 201(5), p 2092-2098

    Article  Google Scholar 

  65. E. Held and J. Gibmeier, Application of the Incremental Hole-Drilling Method on Thick Film Systems—An Approximate Evaluation Approach, Exp. Mech., 2015, 55(3), p 499-507

    Article  Google Scholar 

  66. P. Grant, J. Lord, P. Whitehead, and A.T. Fry, The Application of Fine Increment Hole Drilling for Measuring Machining-Induced Residual Stresses, Appl. Mech. Mater., 2005, 3, p 105-110

    Article  Google Scholar 

  67. S. Kuroda and T.W. Clyne, The Quenching Stress in Thermally Sprayed Coatings, Thin Solid Films, 1991, 200(1), p 49-66

    Article  Google Scholar 

  68. S. Widjaja, A.M. Limarga, and T.H. Yip, Modeling of Residual Stresses in a Plasma-Sprayed Zirconia/Alumina Functionally Graded-Thermal Barrier Coating, Thin Solid Films, 2003, 434(1-2), p 216-227

    Article  Google Scholar 

  69. S. Kuroda, T. Fukushima, and S. Kitahara, Significance of Quenching Stress in the Cohesion and Adhesion of Thermally Sprayed Coatings, J. Therm. Spray Technol., 1992, 1(4), p 325-332

    Article  Google Scholar 

  70. H.-J. Kim and Y.-G. Kweon, Elastic Modulus of Plasma-Sprayed Coatings Determined by Indentation and Bend Tests, Thin Solid Films, 1999, 342(1-2), p 201-206

    Article  Google Scholar 

  71. Y. Tan, A. Shyam, W.B. Choi, E. Lara-Curzio, and S. Sampath, Anisotropic Elastic Properties of Thermal Spray Coatings Determined via Resonant Ultrasound Spectroscopy, Acta Mater., 2010, 58(16), p 5305-5315

    Article  Google Scholar 

  72. T. Valente, C. Bartuli, M. Sebastiani, and F. Casadei, Finite Element Analysis of Residual Stress in Plasma-Sprayed Ceramic Coatings, Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl., 2004, 218(4), p 321-330

    Google Scholar 

  73. J. Stokes and L. Looney, Predicting Quenching and Cooling Stresses within HVOF Deposits, J. Therm. Spray Technol., 2008, 17(5-6), p 908-914

    Article  Google Scholar 

  74. J. Matejicek and S. Sampath, In Situ Measurement of Residual Stresses and Elastic Moduli in Thermal Sprayed Coatings: Part 1: Apparatus and Analysis, Acta Mater., 2003, 51(3), p 863-872

    Article  Google Scholar 

  75. H. Liao, P. Vaslin, Y. Yang, and C. Coddet, Determination of Residual Stress Distribution from in Situ Curvature Measurements for Thermally Sprayed WC/Co Coatings, J. Therm. Spray Technol., 1997, 6(2), p 235-241

    Article  Google Scholar 

  76. K.G. Soderberg and A.K. Graham, Stress in Electrodeposits Its Significance, Proc. Am. Electroplat. Soc., 1947, 34, p 74-79

    Google Scholar 

  77. S. Timoshenko, Analysis of Bi-Metal Thermostats, J. Opt. Soc. Am. Opt. Soc. Am., 1925, 11(3), p 233

    Article  Google Scholar 

  78. C.H. Hsueh and A.G. Evans, Residual Stresses in Meta/Ceramic Bonded Strips, J. Am. Ceram. Soc., 1985, 68(5), p 241-248

    Article  Google Scholar 

  79. H.C. Liu and S.P. Murarka, Elastic and Viscoelastic Analysis of Stress in Thin Films, J. Appl. Phys., 1992, 72(8), p 3458

    Article  Google Scholar 

  80. L.F. Francis, A.V. Mccormick, D.M. Vaessen, and J.A. Payne, Development and Measurement of Stress in Polymer Coatings, J. Mater. Sci., 2002, 37(22), p 4717-4731

    Article  Google Scholar 

  81. Z.Q. Jiang, Y. Huang, and A. Chandra, Thermal Stresses in Layered Electronic Assemblies, J. Electron. Packag. Am. Soc. Mech. Eng., 1997, 119(2), p 127

    Article  Google Scholar 

  82. K.D. Cowley and P.W.R. Beaumont, The Measurement and Prediction of Residual Stresses in Carbon-Fibre/Polymer Composites, Compos. Sci. Technol., 1997, 57(11), p 1445-1455

    Article  Google Scholar 

  83. G.P. Cherepanov, On the Theory of Thermal Stresses in a Thin Bonding Layer, J. Appl. Phys., 1995, 78(11), p 6826

    Article  Google Scholar 

  84. Y. Wen and C. Basaran, An Analytical Model for Thermal Stress Analysis of Multi-Layered Microelectronic Packaging, Mech. Mater., 2004, 36(4), p 369-385

    Article  Google Scholar 

  85. C.-H. Hsueh, Modeling of Elastic Deformation of Multilayers due to Residual Stresses and External Bending, J. Appl. Phys., 2002, 91(12), p 9652

    Article  Google Scholar 

  86. X.C. Zhang, B.S. Xu, H.D. Wang, and Y.X. Wu, An Analytical Model for Predicting Thermal Residual Stresses in Multilayer Coating Systems, Thin Solid Films, 2005, 488(1-2), p 274-282

    Article  Google Scholar 

  87. P.H. Townsend, D.M. Barnett, and T.A. Brunner, Elastic Relationships in Layered Composite Media with Approximation for the Case of Thin Films on a Thick Substrate, J. Appl. Phys., 1987, 62(11), p 4438

    Article  Google Scholar 

  88. C.H. Hsueh and S. Lee, Modeling of Elastic Thermal Stresses in Two Materials Joined by a Graded Layer, Compos. Part B Eng., 2003, 34(8), p 747-752

    Article  Google Scholar 

  89. X.C. Zhang, B.S. Xu, H.D. Wang, Y. Jiang, and Y.X. Wu, Modeling of Thermal Residual Stresses in Multilayer Coatings with Graded Properties and Compositions, Thin Solid Films, 2006, 497(1-2), p 223-231

    Article  Google Scholar 

  90. X.-Y. Gong and D.R. Clarke, On the Measurement of Strain in Coatings Formed on a Wrinkled Elastic Substrate, Oxid. Met., 1998, 50(5-6), p 355-376

    Article  Google Scholar 

  91. C.H. Hsueh and E.R. Fuller, Analytical Modeling of Oxide Thickness Effects on Residual Stresses in Thermal Barrier Coatings, Scr. Mater., 2000, 42(8), p 781-787

    Article  Google Scholar 

  92. X.C. Zhang, B.S. Xu, H.D. Wang, and Y.X. Wu, Effects of Oxide Thickness, Al2O3 Interlayer and Interface Asperity on Residual Stresses in Thermal Barrier Coatings, Mater. Des., 2006, 27(10), p 989-996

    Article  Google Scholar 

  93. M. Song, Y. Ma, and S. Gong, Analysis of Residual Stress Distribution along Interface Asperity of Thermal Barrier Coating System on Macro Curved Surface, Prog. Nat. Sci. Mater. Int., 2011, 21(3), p 262-267

    Article  Google Scholar 

  94. Y.C. Tsui and T.W. Clyne, An Analytical Model for Predicting Residual Stresses in Progressively Deposited Coatings Part 1: Planar Geometry, Thin Solid Films, 1997, 306(1), p 23-33

    Article  Google Scholar 

  95. G. Bolelli, V. Cannillo, L. Lusvarghi, R. Rosa, A. Valarezo, W.B. Choi, R. Dey, C. Weyant, and S. Sampath, Functionally Graded WC–Co/NiAl HVOF Coatings for Damage Tolerance, Wear and Corrosion Protection, Surf. Coat. Technol., 2012, 206(8-9), p 2585-2601

    Article  Google Scholar 

  96. Y.C. Tsui and T.W. Clyne, An Analytical Model for Predicting Residual Stresses in Progressively Deposited Coatings Part 2: Cylindrical Geometry, Thin Solid Films, 1997, 306(1), p 34-51

    Article  Google Scholar 

  97. L. Wu, J. Zhu, and H. Xie, Numerical and Experimental Investigation of Residual Stress in Thermal Barrier Coatings during APS Process, J. Therm. Spray Technol., 2014, 23(4), p 653-665

    Article  Google Scholar 

  98. J. Liu, R. Bolot, and S. Costil, Residual Stresses and Final Deformation of an Alumina Coating: Modeling and Measurement, Surf. Coat. Technol., 2015, 2014(268), p 241-246

    Article  Google Scholar 

  99. Z. Gan, H.W. Ng, and A. Devasenapathi, Deposition-Induced Residual Stresses in Plasma-Sprayed Coatings, Surf. Coat. Technol., 2004, 187(2-3), p 307-319

    Article  Google Scholar 

  100. G. Qian, T. Nakamura, and C.C. Berndt, Effects of Thermal Gradient and Residual Stresses on Thermal Barrier Coating Fracture, Mech. Mater., 1998, 27(2), p 91-110

    Article  Google Scholar 

  101. F. Kroupa, Nonlinear Behavior in Compression and Tension of Thermally Sprayed Ceramic Coatings, J. Therm. Spray Technol., 2007, 16(1), p 84-95

    Article  Google Scholar 

  102. R. Musalek, J. Matejicek, M. Vilemova, and O. Kovarik, Non-Linear Mechanical Behavior of Plasma Sprayed Alumina Under Mechanical and Thermal Loading, J. Therm. Spray Technol., 2010, 19(1), p 422-428

    Article  Google Scholar 

  103. Y. Liu, T. Nakamura, V. Srinivasan, A. Vaidya, A. Gouldstone, and S. Sampath, Non-Linear Elastic Properties of Plasma-Sprayed Zirconia Coatings and Associated Relationships with Processing Conditions, Acta Mater., 2007, 55(14), p 4667-4678

    Article  Google Scholar 

  104. S.C. Gill and T.W. Clyne, Thermomechanical Modeling of the Development of Residual Stress During Thermal Spraying. in 2nd Plasma Technik Symposium, ed by A.R.N. and S.S. H. Eschenauer, P. Huber. Plasma Technik 3, 1991, p 227-238.

  105. S.C. Gill and T.W. Clyne, Property Data Evaluation for the Modeling of Residual Stress Development during Vacuum Plasma Spray Deposition. in 1st European Conf. on Adv. Mats. and Procs. (Euromat’89), ed by H. Exner (Deutsh. Gesell. f. Metallk.), 1990, p 1221-1230.

  106. G.A. Keramidas, E.C. Ting, and A. Finite, Element Formulation for Thermal Stress Analysis. Part I: Variational Formulation, Nucl. Eng. Des., 1976, 39(2-3), p 267-275

    Article  Google Scholar 

  107. T.R. Chandrupatla, A.D. Belegundu, T. Ramesh, and C. Ray, Introduction to Finite Elements in Engineering, Prentice Hall, Upper Saddle River, 1997, p 279-300

    Google Scholar 

  108. Y. Jiang, B.S. Xu, H.D. Wang, and Y.H. Lu, Finite Element Modeling of Residual Stress around Holes in the Thermal Barrier Coatings, Comput. Mater. Sci., 2010, 49(3), p 603-608

    Article  Google Scholar 

  109. J. Stokes and L. Looney, Residual Stress in HVOF Thermally Sprayed Thick Deposits, Surf. Coat. Technol., 2004, 177-178, p 18-23

    Article  Google Scholar 

  110. X.C. Zhang, B.S. Xu, H.D. Wang, and Y.X. Wu, Modeling of the Residual Stresses in Plasma-Spraying Functionally Graded ZrO2/NiCoCrAlY Coatings Using Finite Element Method, Mater. Des., 2006, 27(4), p 308-315

    Article  Google Scholar 

  111. M. Buchmann and R. Gadow, Estimation of Residual Stresses from the Simulation of the Deposition Process of Ceramic Coatings on Light Metal Cylinder Liners. in 25th Annual Conference on Composites, Advanced Ceramics, Materials, and Structures, eds by B. M. Singh and T. Jessen (USA), 2001, p 67-74.

  112. M. Wenzelburger, M. Escribano, and R. Gadow, Modeling of Thermally Sprayed Coatings on Light Metal Substrates: Layer Growth and Residual Stress Formation, Surf. Coat Technol., 2004, 2004(181), p 429-435

    Article  Google Scholar 

  113. M. Wenzelburger, M.J. Riegert-Escribano, and R. Gadow, Methods of Residual Stress Analysis in Layer Composites and Their Application, Mech. Prop. Perform. Enginnering Ceram. Compos, Ceram. Eng. Sci. Proc., 2009, 26(2), p 371-379

    Google Scholar 

  114. H. Zhao, J. Zhang, Z. Wang, P. Lin, and Z. Wang, Adhesion and Residual Stress of Plasma Sprayed Alumina-Titania Coatings, J. Adhes. Sci. Technol., 2015, 29(10), p 991-1001

    Article  Google Scholar 

  115. P. Fogarassy, F. Turquier, and A. Lodini, Residual Stress in Plasma Sprayed Zirconia on Cylindrical Components, Mech. Mater., 2003, 35(7), p 633-640

    Article  Google Scholar 

  116. E. Lugscheider and R. Nickel, Finite Element Simulation of a Coating Formation on a Turbine Blade during Plasma Spraying, Surf. Coat. Technol., 2003, 2003(174-175), p 475-481

    Article  Google Scholar 

  117. M. Lee, B. Lee, J. Lim, and M. Kim, Residual Stress Analysis of the Thermal Barrier Coating System by Considering the Plasma Spraying Process, J. Mech. Sci. Technol., 2014, 28(6), p 2161-2168

    Article  Google Scholar 

  118. L. Wang, Y. Wang, X.G. Sun, J.Q. He, Z.Y. Pan, and C.H. Wang, Finite Element Simulation of Residual Stress of Double-Ceramic-Layer La2Zr2O7/8YSZ Thermal Barrier Coatings Using Birth and Death Element Technique, Comput. Mater. Sci., 2012, 2012(53), p 117-127

    Article  Google Scholar 

  119. P. Bengtsson and C. Persson, Modelled and Measured Residual Stresses in Plasma Sprayed Thermal Barrier Coatings, Surf. Coat. Technol., 1997, 92(1-2), p 78-86

    Article  Google Scholar 

  120. L.R. Alejano and A. Bobet, Drucker-Prager Criterion, Rock Mech. Rock Eng., 2012, 45(6), p 995-999

    Article  Google Scholar 

  121. H.W. Ng and Z. Gan, A Finite Element Analysis Technique for Predicting as-Sprayed Residual Stresses Generated by the Plasma Spray Coating Process, Finite Elem. Anal. Des., 2005, 41, p 1235-1254

    Article  Google Scholar 

  122. J. Zimmerman, Finite Element Modelling of the Residual Stresses Induced in Thermally Deposited Coatings, Arch. Metall. Mater., 2014, 59(2), p 593-599

    Article  Google Scholar 

  123. J. Zimmerman, Z. Lindemann, D. Golański, T. Chmielewski, and W. Włosiński, Modeling Residual Stresses Generated in Ti Coatings Thermally Sprayed on Al2O3 Substrates, Bull. Pol. Acad. Sci. Tech. Sci., 2013, 61(2), p 515-525

    Google Scholar 

  124. P. Bansal, P.H. Shipway, and S.B. Leen, Residual Stresses in High-Velocity Oxy-Fuel Thermally Sprayed Coatings—Modelling the Effect of Particle Velocity and Temperature during the Spraying Process, Acta Mater., 2007, 2007(55), p 5089-5101

    Article  Google Scholar 

  125. P. Bansal, P.H. Shipway, and S.B. Leen, Effect of Particle Impact on Residual Stress Development in HVOF Sprayed Coatings, J. Therm. Spray Technol., 2006, 15(4), p 570-575

    Article  Google Scholar 

  126. M. Elhoriny, M. Wenzelburger, A. Killinger, R. Gadow, Experimental Investigation and Finite Element Simulation of Residual Stress Development in Thermally Sprayed Coatings. in International Thermal Spray Conference and Exposition, (Long Beach, California, USA), 2015

  127. S.J. Hollister and B.A. Riemer, Digital-Image-Based Finite Element Analysis for Bone Microstructure Using Conjugate Gradient and Gaussian Filter Techniques. in SPIE’s 1993 International Symposium on Optics, Imaging, and Instrumentation, eds by J.N. Wilson, D.C. Wilson, International Society for Optics and Photonics, 1993, p 95-106.

  128. K. Terada, T. Miura, and N. Kikuchi, Digital Image-Based Modeling Applied to the Homogenization Analysis of Composite Materials, Comput. Mech., 1997, 20(4), p 331-346

    Article  Google Scholar 

  129. S.A. Langer, E.R. Fuller, and W.C. Carter, OOF: An Image-Based Finite-Element Analysis of Material Microstructures, Comput. Sci. Eng., 2001, 3(3), p 15-23

    Article  Google Scholar 

  130. C.-H. Hsueh, J.A. Haynes, M.J. Lance, P.F. Becher, M.K. Ferber, E.R. Fuller, S.A. Langer, W.C. Carter, and W.R. Cannon, Effects of Interface Roughness on Residual Stresses in Thermal Barrier Coatings, J. Am. Ceram. Soc., 1999, 82(4), p 1073-1075

    Article  Google Scholar 

  131. R. Berthelsen, D. Tomath, R. Denzer, and A. Menzel, Finite Element Simulation of Coating-Induced Heat Transfer: Application to Thermal Spraying Processes, Meccanica, 2016, 51(2), p 291-307

    Article  Google Scholar 

  132. A. Farrokhpanah, M. Bussmann, and J. Mostaghimi, A New Smoothed Particle Hydrodynamics (SPH) Formulation for Modelling Heat Conduction with Solidification and Melting, arXiv Prepr. arXiv1608.04400, 2016.

  133. R. Das and P.W. Cleary, Three-Dimensional Modelling of Coupled Flow Dynamics, Heat Transfer and Residual Stress Generation in Arc Welding Processes Using the Mesh-Free SPH Method, J. Comput. Sci., 2016, 16, p 200-216

    Article  Google Scholar 

  134. P. Profizi, A. Combescure, and K. Ogawa, SPH Modeling of Adhesion in Fast Dynamics: Application to the Cold Spray Process, Comptes Rendus Mécanique, 2016, 344(4), p 211-224

    Article  Google Scholar 

  135. J. Lu, J. Qian, and W. Han, Discrete Gradient Method in Solid Mechanics, Int. J. Numer. Methods Eng., 2008, 74(4), p 619-641

    Article  Google Scholar 

  136. J. Lu and J. Qian, Discrete Gradient Method over Polygon Mesh, Int. J. Numer. Methods Eng., 2009, 78(5), p 505-527

    Article  Google Scholar 

  137. E.B. Chin, J.-B. Lasserre, and N. Sukumar, Modeling Crack Discontinuities without Element Partitioning in the Extended Finite Element Method, Int. J. Numer. Methods Eng., 2016, 110, p 1021-1048

    Article  Google Scholar 

  138. B.L. Talamini and R. Radovitzky, A Parallel Discontinuous Galerkin/Cohesive-Zone Computational Framework for the Simulation of Fracture in Shear-Flexible Shells, Elsevier, Comput. Methods Appl. Mech. Eng., 2016

    Google Scholar 

  139. S. Rezaei, S. Wulfinghoff, and S. Reese, Prediction of Fracture in Grain Boundaries of Nano-coatings Using Cohesive Zone Elements, PAMM, 2016, 16(1), p 163-164

    Article  Google Scholar 

  140. V. Kouznetsova, M.G.D. Geers, and W.A.M. Brekelmans, Multi-scale Constitutive Modelling of Heterogeneous Materials with a Gradient-Enhanced Computational Homogenization Scheme, Int. J. Numer. Methods Eng., 2002, 54(8), p 1235-1260

    Article  Google Scholar 

  141. M.G.D. Geers, V.G. Kouznetsova, and W.A.M. Brekelmans, Multi-Scale Computational Homogenization: Trends and Challenges, J. Comput. Appl. Math., 2010, 234(7), p 2175-2182

    Article  Google Scholar 

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Acknowledgments

The authors would like to acknowledge the support provided by King Fahd University of Petroleum & Minerals (KFUPM) in funding this work through project FT161016.

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Authors and Affiliations

  1. Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Abba A. Abubakar, Abul Fazal M. Arif, Khaled S. Al-Athel & S. Sohail Akhtar

  2. Mechanical Engineering Department, University of Toronto, Toronto, Canada

    Javad Mostaghimi

Authors
  1. Abba A. Abubakar
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  2. Abul Fazal M. Arif
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  3. Khaled S. Al-Athel
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  4. S. Sohail Akhtar
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Correspondence to Abul Fazal M. Arif.

Appendix

Appendix

See Table 3.

Table 3 An overview of the previous models used for the prediction of residual stresses developed in thermal spray coatings
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Abubakar, A.A., Arif, A.F.M., Al-Athel, K.S. et al. Modeling Residual Stress Development in Thermal Spray Coatings: Current Status and Way Forward. J Therm Spray Tech 26, 1115–1145 (2017). https://doi.org/10.1007/s11666-017-0590-1

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