مروری بر مکانیزم های واماندگی و شبیه سازی المان محدود پوشش های سدحرارتی پلاسما اسپری

نوع مقاله : مقاله مروری

نویسندگان

1 دانشجوی دکتری، گروه مهندسی مکانیک، دانشگاه زنجان، زنجان، ایران

2 استاد، گروه مهندسی مکانیک، دانشگاه زنجان، زنجان، ایران

/amnc.2019.7.27.6

چکیده

درک مسائل واماندگی پوشش‌های سدحرارتی در ارزیابی قابلیت و دوام آن‌ها بسیار ضروری است. از این پوشش‌ها در شرایط کاری دمای بالا و گرادیان‌های شدید حرارتی استفاده می‌شود. در این مقاله، مروری بر مکانیزم‌های واماندگی پوشش‌های سدحرارتی پلاسما اسپری تحت بارگذاری‌های مختلف حرارتی و مکانیکی، انجام شده است. از آنجاییکه هزینه‌های روش‌های آزمایشگاهی، در شرایط کاری پوشش‌ها، بسیار بالا بوده و محدودیت‌های بسیاری برای این روش‌ها در شرایط عملکرد آن‌ها وجود دارد، این روش‌ها نمی‌توانند شرایط واقعی TBC را به‌خوبی منعکس کنند. از این رو مدل‌سازی المان محدود نقش مهمی در مطالعه‌ی این مسائل داشته و انتظار می‌رود با استفاده از این روش‌ها الگوهای واماندگی TBC تحت شرایط واقعی تعیین شود. در این مقاله همچنین روش‌های کاربردی و جدید مدل‌سازی المان محدود جهت شبیه‌سازی مکانیزم‌های واماندگی پوشش‌های سد حرارتی تحت بارهای حرارتی و مکانیکی مورد بحث و بررسی قرار گرفته است. از جمله این روش‌ها می-توان به روش‌های مجازی بازشدگی ترک، المان محدود توسعه یافته و مدل ناحیه چسبنده اشاره کرد. ضمناً، مقایسه‌ا‌ی بین روش‌های المان محدود ذکر شده و مزایا و محدودیت‌های آن‌ها، در مسائل واماندگی پوشش‌ها صورت گرفته است.

کلیدواژه‌ها

موضوعات


[1] V. Sankar, P. B. Ramkumar, D. Sebastian, D. Joseph, J. Jose, and A. Kurian, “Optimized Thermal Barrier Coating for Gas Turbine Blades,” Mater. Today Proc., vol. 11, pp. 912–919, 2019.
[2] عزیزی‌‌فر ا.، پورسعیدی ا. و رحیمی ج.، بررسی اثر پوشش‌‌های سدحرارتی بر توزیع دما و فرکانس پره‌‌های متحرک ردیف دوم در توربین‌‌های گازی GEF9، چهارمین کنفرانس ملی و دومین کنفرانس بین المللی پژوهش‌‌های کاربردی در مهندسی برق، مکانیک و مکاترونیک، تهران، ایران، 1395.
[3] H. Xu and H. Guo, Thermal barrier coatings. Elsevier, 2011.
[4] L. Wang et al., “Modeling of thermal properties and failure of thermal barrier coatings with the use of finite element methods: A review,” J. Eur. Ceram. Soc., vol. 36, no. 6, pp. 1313–1331, 2016.
[5] A. Shanian, A. S. Milani, N. Vermaak, K. Bertoldi, T. Scarinci, and M. Gerendas, “A combined finite element-multiple criteria optimization approach for materials selection of gas turbine components,” J. Appl. Mech., vol. 79, no. 6, p. 61019, 2012.
[6] J.-H. Qiao, R. Bolot, H. Liao, P. Bertrand, and C. Coddet, “A 3D finite-difference model for the effective thermal conductivity of thermal barrier coatings produced by plasma spraying,” Int. J. Therm. Sci., vol. 65, pp. 120–126, 2013.
[7] X. Ma, F. Wu, J. Roth, M. Gell, and E. H. Jordan, “Low thermal conductivity thermal barrier coating deposited by the solution plasma spray process,” Surf. Coatings Technol., vol. 201, no. 7, pp. 4447–4452, 2006.
[8] D. R. Clarke, “Materials selection guidelines for low thermal conductivity thermal barrier coatings,” Surf. Coatings Technol., vol. 163, pp. 67–74, 2003.
[9] G. Bertrand, P. Bertrand, P. Roy, C. Rio, and R. Mevrel, “Low conductivity plasma sprayed thermal barrier coating using hollow psz spheres: Correlation between thermophysical properties and microstructure,” Surf. Coatings Technol., vol. 202, no. 10, pp. 1994–2001, 2008.
[10] N. P. Bansal and D. Zhu, “Effects of doping on thermal conductivity of pyrochlore oxides for advanced thermal barrier coatings,” Mater. Sci. Eng. A, vol. 459, no. 1–2, pp. 192–195, 2007.
[11] X. C. Zhang, B. S. Xu, H. D. Wang, Y. Jiang, and Y. X. Wu, “Prediction of three-dimensional residual stresses in the multilayer coating-based systems with cylindrical geometry,” Compos. Sci. Technol., vol. 66, no. 13, pp. 2249–2256, 2006.
[12] 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, vol. 497, no. 1–2, pp. 223–231, 2006.
[13] X. Wu et al., “Size effect of thermal shock crack patterns in ceramics and numerical predictions,” J. Eur. Ceram. Soc., vol. 35, no. 4, pp. 1263–1271, 2015.
[14] F. Sen, O. Sayman, M. Toparli, and E. Celik, “Stress analysis of high temperature ZrO2 insulation coatings on Ag using finite element method,” J. Mater. Process. Technol., vol. 180, no. 1–3, pp. 239–245, 2006.
[15] W. G. Mao, Y. C. Zhou, L. Yang, and X. H. Yu, “Modeling of residual stresses variation with thermal cycling in thermal barrier coatings,” Mech. Mater., vol. 38, no. 12, pp. 1118–1127, 2006.
[16] G. Lee, A. Atkinson, and A. Selçuk, “Development of residual stress and damage in thermal barrier coatings,” Surf. Coatings Technol., vol. 201, no. 7, pp. 3931–3936, 2006.
[17] A. N. Khan, J. Lu, and H. Liao, “Effect of residual stresses on air plasma sprayed thermal barrier coatings,” Surf. Coatings Technol., vol. 168, no. 2–3, pp. 291–299, 2003.
[18] محمدی م. و پورسعیدی ا.، ارزیابی آزمایشگاهی و المان محدود تنش ناشی از اعمال پوشش سد حرارتی، اولین کنفرانس ملی مکانیک محاسباتی و تجربی، دانشگاه شهید رجائی، تهران، ایران، 1397.
[19] V. Teixeira, M. Andritschky, W. Fischer, H. . Buchkremer, and D. Stöver, “Analysis of residual stresses in thermal barrier coatings,” J. Mater. Process. Technol., vol. 92, pp. 209–216, 1999.
[20] G. Qian, T. Nakamura, and C. C. Berndt, “Effects of thermal gradient and residual stresses on thermal barrier coating fracture,” Mech. Mater., vol. 27, no. 2, pp. 91–110, 1998.
[21] M. Ranjbar-Far, J. Absi, G. Mariaux, and F. Dubois, “Simulation of the effect of material properties and interface roughness on the stress distribution in thermal barrier coatings using finite element method,” Mater. Des., vol. 31, no. 2, pp. 772–781, 2010.
[22] M. Ranjbar-Far, J. Absi, S. Shahidi, and G. Mariaux, “Impact of the non-homogenous temperature distribution and the coatings process modeling on the thermal barrier coatings system,” Mater. Des., vol. 32, no. 2, pp. 728–735, 2011.
[23] K. Sfar, J. Aktaa, and D. Munz, “Numerical investigation of residual stress fields and crack behavior in TBC systems,” Mater. Sci. Eng. A, vol. 333, no. 1–2, pp. 351–360, 2002.
[24] W. Zhu, M. Cai, L. Yang, J. W. Guo, Y. C. Zhou, and C. Lu, “The effect of morphology of thermally grown oxide on the stress field in a turbine blade with thermal barrier coatings,” Surf. Coatings Technol., vol. 276, pp. 160–167, 2015.
[25] M. Bäker, “Finite element simulation of interface cracks in thermal barrier coatings,” Comput. Mater. Sci., vol. 64, pp. 79–83, 2012.
[26] M. Białas, “Finite element analysis of stress distribution in thermal barrier coatings,” Surf. Coatings Technol., vol. 202, no. 24, pp. 6002–6010, 2008.
[27] A. Moridi, M. Azadi, and G. H. Farrahi, “Thermo-mechanical stress analysis of thermal barrier coating system considering thickness and roughness effects,” Surf. Coatings Technol., vol. 243, pp. 91–99, 2014.
[28] M. Ranjbar-far, J. Absi, G. Mariaux, and D. S. Smith, “Crack propagation modeling on the interfaces of thermal barrier coating system with different thickness of the oxide layer and different interface morphologies,” Mater. Des., vol. 32, no. 10, pp. 4961–4969, 2011.
[29] M. Ranjbar-Far, J. Absi, and G. Mariaux, “Finite element modeling of the different failure mechanisms of a plasma sprayed thermal barrier coatings system,” J. Therm. Spray Technol., vol. 21, no. 6, pp. 1234–1244, 2012.
[30] H. Ebrahimi and S. Nakhodchi, “Thermal fatigue testing and simulation of an APS TBC system in presence of a constant bending load,” Int. J. Fatigue, vol. 96, pp. 1–9, 2017.
[31] M. Baker, J. Rosler, and M. Volgmann, “Stress State and Failure Mechanisms of Thermal Barrier Coatings : Role of Creep in Thermally,” vol. 49, pp. 3659–3670, 2001.
[32] A. M. Freborg, B. L. Ferguson, W. J. Brindley, and G. J. Petrus, “Modeling oxidation induced stresses in thermal barrier coatings,” Mater. Sci. Eng. A, vol. 245, no. 2, pp. 182–190, 1998.
[33] W. G. Mao, J. P. Jiang, Y. C. Zhou, and C. Lu, “Effects of substrate curvature radius, deposition temperature and coating thickness on the residual stress field of cylindrical thermal barrier coatings,” Surf. Coatings Technol., vol. 205, no. 8–9, pp. 3093–3102, 2011.
[34] M.-J. Pindera, J. Aboudi, and S. M. Arnold, “The effect of interface roughness and oxide film thickness on the inelastic response of thermal barrier coatings to thermal cycling,” Mater. Sci. Eng. A, vol. 284, no. 1–2, pp. 158–175, 2000.
[35] W. X. Zhang, X. L. Fan, and T. J. Wang, “The surface cracking behavior in air plasma sprayed thermal barrier coating system incorporating interface roughness effect,” Appl. Surf. Sci., vol. 258, no. 2, pp. 811–817, 2011.
[36] M. Ahrens, R. Vaßen, and D. Stöver, “Stress distributions in plasma-sprayed thermal barrier coatings as a function of interface roughness and oxide scale thickness,” Surf. Coatings Technol., vol. 161, no. 1, pp. 26–35, 2002.
[37] R. Eriksson, S. Sjöström, H. Brodin, S. Johansson, L. Östergren, and X. H. Li, “TBC bond coat-top coat interface roughness: Influence on fatigue life and modelling aspects,” Surf. Coatings Technol., vol. 236, pp. 230–238, 2013.
[38] Q. M. Yu and Q. He, “Effect of material properties on residual stress distribution in thermal barrier coatings,” Ceram. Int., vol. 44, no. 3, pp. 3371–3380, 2018.
[39] N. Nayebpashaee, S. H. Seyedein, M. R. Aboutalebi, H. Sarpoolaky, and S. M. M. Hadavi, Finite element simulation of residual stress and failure mechanism in plasma sprayed thermal barrier coatings using actual microstructure as the representative volume, vol. 291. Elsevier B.V., 2016.
[40] M. Gupta, K. Skogsberg, and P. Nylén, “Influence of topcoat-bondcoat interface roughness on stresses and lifetime in thermal barrier coatings,” J. Therm. Spray Technol., vol. 23, no. 1–2, pp. 170–181, 2014.
[41] C. Hsueh et al., “Effects of Interface Roughness on Residual Stresses in Thermal Barrier Coatings,” J. Am. Ceram. Soc., vol. 82, no. 4, pp. 1073–1075, 1999.
[42] B. Zhou and K. Kokini, “Effect of pre-existing surface crack morphology on the interfacial thermal fracture of thermal barrier coatings: a numerical study,” Mater. Sci. Eng. A, vol. 348, no. 1–2, pp. 271–279, 2003.
[43] A. K. Ray and R. W. Steinbrech, “Crack propagation studies of thermal barrier coatings under bending,” J. Eur. Ceram. Soc., vol. 19, no. 12, pp. 2097–2109, 1999.
[44] M. Jinnestrand and H. Brodin, “Crack initiation and propagation in air plasma sprayed thermal barrier coatings, testing and mathematical modelling of low cycle fatigue behaviour,” Mater. Sci. Eng. A, vol. 379, no. 1–2, pp. 45–57, 2004.
[45] Z. X. Chen, L. H. Qian, and S. J. Zhu, “Determination and analysis of crack growth resistance in plasma-sprayed thermal barrier coatings,” Eng. Fract. Mech., vol. 77, no. 11, pp. 2136–2144, 2010.
[46] E. Schumann, C. Sarioglu, J. R. Blachere, F. S. Pettit, and G. H. Meier, “High-Temperature Stress Measurements During the Oxidation of NiAl,” Oxid. Met., vol. 53, pp. 259–272, 2000.
[47] Y. Z. Liu, X. B. Hu, Y. L. Zhu, H. Wei, V. P. Dravid, and W. W. Zhang, “Effects of isothermal oxidation on microstructure and mechanical properties of thermal barrier coatings,” Ceram. Int., 2019.
[48] D. M. and Lipkin and D. R. Clarke, “Measurement of the stress in oxide scales formed by oxidation of alumina-forming alloys,” Oxid. Met., vol. 45, no. 3–4, pp. 267–280, 1996.
[49] K. W. Schlichting, K. Vaidyanathan, Y. H. Sohn, E. H. Jordan, M. Gell, and N. P. Padture, “Application of Cr3+ photoluminescence piezo-spectroscopy to plasma-sprayed thermal barrier coatings for residual stress measurement,” Mater. Sci. Eng. A, vol. 291, no. 1–2, pp. 68–77, 2000.
[50] D. R. Clarke and W. Pompe, “Critical radius for interface separation of a compressively stressed film from a rough surface,” Acta Mater., vol. 47, no. 6, pp. 1749–1756, 1999.
[51] C. H. Hsueh, P. F. Becher, E. R. Fuller, S. A. Langer, and W. C. Carter, “Surface-roughness induced residual stresses in thermal barrier coatings: computer simulations,” in Materials science forum, 1999, vol. 308, pp. 442–449.
[52] K. W. Schlichting, N. P. Padture, E. H. Jordan, and M. Gell, “Failure modes in plasma-sprayed thermal barrier coatings,” Mater. Sci. Eng. A, vol. 342, no. 1–2, pp. 120–130, 2003.
[53] A. Rabiei and A. G. Evans, “Failure mechanisms associated with the thermally grown oxide in plasma-sprayed thermal barrier coatings,” Acta Mater., vol. 48, no. 15, pp. 3963–3976, 2000.
[54] K. Torkashvand, E. Poursaeidi, and M. Mohammadi, “Effect of TGO thickness on the thermal barrier coatings life under thermal shock and thermal cycle loading,” Ceram. Int., vol. 44, no. 8, pp. 9283–9293, 2018.
[55] N. P. Padture, M. Gell, and E. H. Jordan, “Thermal barrier coatings for gas-turbine engine applications,” Science (80-. )., vol. 296, no. 5566, pp. 280–284, 2002.
[56] محمدی م.، پورسعیدی ا. و ترکاشوند ک.، بررسی تجربی و عددی واماندگی پوشش‌‌های سد حرارتی تحت بارگذاری حرارتی، بیست و هفتمین همایش سالانه بین المللی مکانیک ایران، دانشگاه تربیت مدرس و دانشگاه تهران، تهران، ایران، 1398.
[57] K. Torkashvand and E. Poursaeidi, “Effect of temperature and ceramic bonding on BC oxidation behavior in plasma-sprayed thermal barrier coatings,” Surf. Coatings Technol., 2018.
[58] M. Bäker, J. Rösler, and G. Heinze, “A parametric study of the stress state of thermal barrier coatings Part II: Cooling stresses,” Acta Mater., vol. 53, no. 2, pp. 469–476, 2005.
[59] E. A. G. Shillington and D. R. Clarke, “Spalling failure of a thermal barrier coating associated with aluminum depletion in the bond-coat,” Acta Mater., vol. 47, no. 4, pp. 1297–1305, 1999.
[60] R. J. Christensen, D. M. Lipkin, D. R. Clarke, and K. Murphy, “Nondestructive evaluation of the oxidation stresses through thermal barrier coatings using Cr3+ piezospectroscopy,” Appl. Phys. Lett., vol. 69, no. 24, pp. 3754–3756, 1996.
[61] C. Bargraser et al., “Life approximation of thermal barrier coatings via quantitative microstructural analysis,” Mater. Sci. Eng. A, vol. 549, pp. 76–81, 2012.
[62] D. Zhu, S. R. Choi, and R. A. Miller, “Development and thermal fatigue testing of ceramic thermal barrier coatings,” Surf. Coatings Technol., vol. 188, pp. 146–152, 2004.
[63] P. K. Wright and A. G. Evans, “Mechanisms governing the performance of thermal barrier coatings,” Curr. Opin. Solid State Mater. Sci., vol. 4, no. 3, pp. 255–265, 1999.
[64] O. Trunova, T. Beck, R. Herzog, R. W. Steinbrech, and L. Singheiser, “Damage mechanisms and lifetime behavior of plasma sprayed thermal barrier coating systems for gas turbines—Part I: Experiments,” Surf. Coatings Technol., vol. 202, no. 20, pp. 5027–5032, 2008.
[65] A. G. Evans, D. R. Mumm, J. W. Hutchinson, G. H. Meier, and F. S. Pettit, “Mechanisms controlling the durability of thermal barrier coatings,” Prog. Mater. Sci., vol. 46, no. 5, pp. 505–553, 2001.
[66] E. P. Busso, J. Lin, S. Sakurai, and M. Nakayama, “A mechanistic study of oxidation-induced degradation in a plasma-sprayed thermal barrier coating system.: Part I: model formulation,” Acta Mater., vol. 49, no. 9, pp. 1515–1528, 2001.
[67] K. P. Jonnalagadda et al., “A study of damage evolution in high purity nano TBCs during thermal cycling: A fracture mechanics based modelling approach,” J. Eur. Ceram. Soc., vol. 37, no. 8, pp. 2889–2899, 2017.
[68] X. N. Li, L. H. Liang, J. J. Xie, L. Chen, and Y. G. Wei, “Thickness-dependent fracture characteristics of ceramic coatings bonded on the alloy substrates,” Surf. Coatings Technol., vol. 258, pp. 1039–1047, 2014.
[69] M. Khoshnejad, “Determination of mechanical properties of APS thermal barrier coatings under thermal loading by indentation test methode,” (under submission).
[70] B. Li, X. Fan, H. Okada, and T. Wang, “Mechanisms governing the failure modes of dense vertically cracked thermal barrier coatings,” Eng. Fract. Mech., vol. 189, pp. 451–480, 2018.
[71] H.-J. Jang, D.-H. Park, Y.-G. Jung, J.-C. Jang, S.-C. Choi, and U. Paik, “Mechanical characterization and thermal behavior of HVOF-sprayed bond coat in thermal barrier coatings (TBCs),” Surf. Coatings Technol., vol. 200, no. 14–15, pp. 4355–4362, 2006.
[72] Z. B. Chen, Z. G. Wang, and S. J. Zhu, “Tensile fracture behavior of thermal barrier coatings on superalloy,” Surf. coatings Technol., vol. 205, no. 15, pp. 3931–3938, 2011.
[73] P. Jiang, X. Fan, Y. Sun, D. Li, B. Li, and T. Wang, “Competition mechanism of interfacial cracks in thermal barrier coating system,” Mater. Des., vol. 132, pp. 559–566, 2017.
[74] T. C. Totemeier, W. F. Gale, and J. E. King, “Isothermal fatigue of an aluminide-coated single-crystal superalloy: Part II. effects of brittle precracking,” Metall. Mater. Trans. A, vol. 27, no. 2, pp. 363–369, 1996.
[75] E. Tzimas, H. Müllejans, S. D. Peteves, J. Bressers, and W. Stamm, “Failure of thermal barrier coating systems under cyclic thermomechanical loading,” Acta Mater., vol. 48, no. 18–19, pp. 4699–4707, 2000.
[76] B. Baufeld, E. Tzimas, H. Müllejans, S. Peteves, J. Bressers, and W. Stamm, “Thermal-mechanical fatigue of MAR-M 509 with a thermal barrier coating,” Mater. Sci. Eng. A, vol. 315, no. 1–2, pp. 231–239, 2001.
[77] Y. H. Zhang, P. J. Withers, M. D. Fox, and D. M. Knowles, “Damage mechanisms of coated systems under thermomechanical fatigue,” Mater. Sci. Technol., vol. 15, no. 9, pp. 1031–1036, 1999.
[78] P. K. Wright, “Influence of cyclic strain on life of a PVD TBC,” Mater. Sci. Eng. A, vol. 245, no. 2, pp. 191–200, 1998.
[79] J. Shi, A. M. Karlsson, B. Baufeld, and M. Bartsch, “Evolution of surface morphology of thermo-mechanically cycled NiCoCrAlY bond coats,” Mater. Sci. Eng. A, vol. 434, no. 1–2, pp. 39–52, 2006.
[80] A. Peichl, T. Beck, and O. Vöhringer, “Behaviour of an EB-PVD thermal barrier coating system under thermal–mechanical fatigue loading,” Surf. Coatings Technol., vol. 162, no. 2–3, pp. 113–118, 2003.
[81] B. Baufeld, E. Tzimas, P. Hähner, H. Müllejans, S. D. Peteves, and P. Moretto, “Phase-angle effects on damage mechanisms of thermal barrier coatings under thermomechanical fatigue,” Scr. Mater., vol. 45, no. 7, pp. 859–865, 2001.
[82] B. Baufeld, M. Bartsch, S. Dalkiliç, and M. Heinzelmann, “Defect evolution in thermal barrier coating systems under multi-axial thermomechanical loading,” Surf. Coatings Technol., vol. 200, no. 5–6, pp. 1282–1286, 2005.
[83] M. Bartsch, G. Marci, K. Mull, and C. Sick, “Fatigue testing of ceramic thermal barrier coatings for gas turbine blades,” Adv. Eng. Mater., vol. 1, no. 2, pp. 127–129, 1999.
[84] M. Bartsch, B. Baufeld, S. Dalkilic, L. Chernova, and M. Heinzelmann, “Fatigue cracks in a thermal barrier coating system on a superalloy in multiaxial thermomechanical testing,” Int. J. Fatigue, vol. 30, no. 2, pp. 211–218, 2008.
[85] Z. B. Chen, Z. G. Wang, and S. J. Zhu, “Thermomechanical fatigue behavior of an air plasma sprayed thermal barrier coating system,” Mater. Sci. Eng. A, vol. 528, no. 29–30, pp. 8396–8401, 2011.
[86] M. Bäker and J. Rösler, “Simulation of crack propagation in thermal barrier coatings with friction,” Comput. Mater. Sci., vol. 52, no. 1, pp. 236–239, 2012.
[87] J. Rösler, M. Bäker, and M. Volgmann, “Stress state and failure mechanisms of thermal barrier coatings: role of creep in thermally grown oxide,” Acta Mater., vol. 49, no. 18, pp. 3659–3670, 2001.
[88] K. P. Jonnalagadda, R. Eriksson, X.-H. Li, and R. L. Peng, “Fatigue life prediction of thermal barrier coatings using a simplified crack growth model,” J. Eur. Ceram. Soc., vol. 39, no. 5, pp. 1869–1876, 2019.
[89] S. Sjöström and H. Brodin, “Thermomechanical fatigue life of TBCs-experimental and modelling aspects,” in 34th International Conference on Advanced Ceramics and Composites, Daytona Beach, USA, 24th-29th January, 2010, 2010, vol. 31, pp. 23–39.
[90] H. Brodin, R. Eriksson, S. Johansson, and S. Sjöström, “Fracture mechanical modelling of a plasma sprayed TBC system,” in 33rd International Conference on Advanced Ceramics and Composites, Daytona Beach, FL, USA, January 18-23, 2009, 2009, vol. 30, no. 3, pp. 113–124.
[91] J. Aktaa, K. Sfar, and D. Munz, “Assessment of TBC systems failure mechanisms using a fracture mechanics approach,” Acta Mater., vol. 53, no. 16, pp. 4399–4413, 2005.
[92] L. Wang et al., “Influence of cracks in APS-TBCs on stress around TGO during thermal cycling: A numerical simulation study,” Surf. Coatings Technol., vol. 285, pp. 98–112, 2016.
[93] T. S. Hille, a. S. J. Suiker, and S. Turteltaub, “Microcrack nucleation in thermal barrier coating systems,” Eng. Fract. Mech., vol. 76, no. 6, pp. 813–825, 2009.
[94] M. Mohammadi, and E. Poursaeidi, “Finite Element Analysis of the Effect of Thermal Cycles and Ageing on the Interface Delamination of Plasma Sprayed Thermal Barrier Coatings,” Surf. Coatings Technol, (under rivision).
[95] J. Song, S. Li, X. Yang, H. Qi, and D. Shi, “Numerical investigation on the cracking behaviors of thermal barrier coating system under different thermal cycle loading waveforms,” Surf. Coatings Technol., 2018.
[96] S. T. Kyaw, I. A. Jones, and T. H. Hyde, “Simulation of failure of air plasma sprayed thermal barrier coating due to interfacial and bulk cracks using surface-based cohesive interaction and extended finite element method,” J. Strain Anal. Eng. Des., vol. 51, no. 2, pp. 132–143, 2016.
[97] J. Jiang, W. Wang, X. Zhao, Y. Liu, Z. Cao, and P. Xiao, “Numerical analyses of the residual stress and top coat cracking behavior in thermal barrier coatings under cyclic thermal loading,” Eng. Fract. Mech., vol. 196, pp. 191–205, 2018.
[98] J. Song, S. Li, X. Yang, D. Shi, and H. Qi, “Numerical study on the competitive cracking behavior in TC and interface for thermal barrier coatings under thermal cycle fatigue loading,” Surf. Coatings Technol., vol. 358, pp. 850–857, 2019.
[99] R. Xu, X. L. Fan, W. X. Zhang, Y. Song, and T. J. Wang, “Effects of geometrical and material parameters of top and bond coats on the interfacial fracture in thermal barrier coating system,” Mater. Des., vol. 47, pp. 566–574, 2013.
[100] R. Xu, X. Fan, and T. J. Wang, “Mechanisms governing the interfacial delamination of thermal barrier coating system with double ceramic layers,” Appl. Surf. Sci., vol. 370, pp. 394–402, 2016.
[101] W. Zhu, L. Yang, J. W. Guo, Y. C. Zhou, and C. Lu, “Numerical study on interaction of surface cracking and interfacial delamination in thermal barrier coatings under tension,” Appl. Surf. Sci., vol. 315, no. 1, pp. 292–298, 2014.
[102] X. Fan, W. Zhang, T. Wang, G. Liu, and J. Zhang, “Investigation on periodic cracking of elastic film/substrate system by the extended finite element method,” Appl. Surf. Sci., vol. 257, no. 15, pp. 6718–6724, 2011.
[103] حیدریان آ. و پورسعیدی ا.، بدست آوردن مقدار چقرمگی شکست بین‌‌لایه‌‌ای برای پوشش‌‌های سپر حرارتی تولید شده به روش APS، دومین کنفرانس ملی تحقیقات بین رشته‌‌ای در مهندسی کامپیوتر، برق، مکانیک و مکاترونیک، تهران، ایران، 1396.
[104] A. Heydarian, E. Poursaeidi, “Determination of interlayer fracture toughness for thermal barrier coatings with four point bending test and investigating the effect of ageing on its value,” (under submission).
[105] C. V. Di Leo, J. Luk-Cyr, H. Liu, K. Loeffel, K. Al-Athel, and L. Anand, “A new methodology for characterizing traction-separation relations for interfacial delamination of thermal barrier coatings,” Acta Mater., vol. 71, pp. 306–318, 2014.
[106] M. Eshraghi, “Design and construction of a four point two tone bending machine and doing a laboratory test with numerical simulation,” Zanjan University, 1396.
[107] Q. Zhu, W. He, J. Zhu, Y. Zhou, and L. Chen, “Investigation on interfacial fracture toughness of plasma-sprayed TBCs using a three-point bending method,” Surf. Coatings Technol., vol. 353, pp. 75–83, 2018.