Abstract
Failure due to interfacial oxidation is one of the most important factors in the failure of alloy systems at high temperatures. To analyze high-temperature interfacial oxidation in alloys under deformation, we develop a thermodynamically consistent continuum theory of alloy interfacial oxidation process considering diffusion, oxidation, expansion, viscoplasticity, and deformation processes. Balance equations of force, mass, and energy are presented at first, while the coupled constitutive laws and evolution equations are constructed according to energy dissipation inequality. The coupled kinetics reveals a new mechanism whereby deformation affects the oxidation reaction by changing the alloy’s critical oxygen concentration. External tensile loads decrease the critical oxygen concentration and promote oxidation of the alloy. Conversely, external compressive loads increase the critical oxygen concentration and suppress the oxidation of the alloy. Finally, this theory is applied to thermal barrier coatings (TBCs), exhibiting a good consistency with the high-temperature oxidation experiment of TBCs under external loads. The model successfully explains that the experimental phenomenon of external tensile load accelerates the growth of Al2O3−TGO (thermally grown oxides). Besides, external compressive loads slow down the growth of Al2O3−TGO at the interface and lead to internal oxidation of the bond coat. The presented framework has shown great potential for modeling high-temperature interfacial oxidation processes in alloy systems under deformation.
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Chen Y, Zhao X, Dang Y, et al. Characterization and understanding of residual stresses in a nicocraly bond coat for thermal barrier coating application. Acta Mater, 2015, 94: 1–14
Rabiei A, Evans A G. Failure mechanisms associated with the thermally grown oxide in plasma-sprayed thermal barrier coatings. Acta Mater, 2000, 48: 3963–3976
Xu T, Faulhaber S, Mercer C, et al. Observations and analyses of failure mechanisms in thermal barrier systems with two phase bond coats based on nicocraly. Acta Mater, 2004, 52: 1439–1450
Zhou Q Q, Yang L, Luo C, et al. Thermal barrier coatings failure mechanism during the interfacial oxidation process under the interaction between interface by cohesive zone model and brittle fracture by phase-field. Int J Solids Struct, 2021, 214–215: 18–34
Schlichting K W, Padture N P, Jordan E H, et al. Failure modes in plasma-sprayed thermal barrier coatings. Mater Sci Eng-A, 2003, 342: 120–130
Ma K, Schoenung J M. Isothermal oxidation behavior of cryomilled nicraly bond coat: Homogeneity and growth rate of tgo. Surf Coatings Tech, 2011, 205: 5178–5185
Evans A G, Mumm D R, Hutchinson J W, et al. Mechanisms controlling the durability of thermal barrier coatings. Prog Mater Sci, 2001, 46: 505–553
Zhou C H, Ma H T, Wang L. Comparative study of oxidation kinetics for pure nickel oxidized under tensile and compressive stress. Corrosion Sci, 2010, 52: 210–215
Seo D, Ogawa K, Nakao Y, et al. Influence of high-temperature creep stress on growth of thermally grown oxide in thermal barrier coatings. Surf Coatings Tech, 2009, 203: 1979–1983
Dong X L, Fang X F, Feng X, et al. Diffusion and stress coupling effect during oxidation at high temperature. J Am Ceram Soc, 2013, 96: 44–46
Chen Y, Fan X, Sun Y, et al. Effect of tensile load on high temperature oxidation of conicraly coating. Surf Coatings Tech, 2018, 352: 399–405
Clarke D R, Oechsner M, Padture N P. Thermal-barrier coatings for more efficient gas-turbine engines. MRS Bull, 2012, 37: 891–898
Schulz U, Leyens C, Fritscher K, et al. Some recent trends in research and technology of advanced thermal barrier coatings. Aerospace Sci Tech, 2003, 7: 73–80
Padture N P, Gell M, Jordan E H. Thermal barrier coatings for gas-turbine engine applications. Science, 2002, 296: 280–284
Zhang X, Zhou K, Xu W, et al. Reaction mechanism and thermal insulation property of Al-deposited 7YSZ thermal barrier coating. J Mater Sci Tech, 2015, 31: 1006–1010
Zhang X, Zhou K, Xu W, et al. In situ synthesis of α-alumina layer on thermal barrier coating for protection against CMAS (CaO−MgO−Al2O3−SiO2) corrosion. Surf Coatings Tech, 2015, 261: 54–59
Gheno T, Rio C, Ecochard M, et al. Alumina failure and post-failure oxidation in the nicocraly alloy system at high temperature. Oxid Met, 2021, 96: 487–517
Meng G H, Zhang B Y, Liu H, et al. Highly oxidation resistant and cost effective mcraly bond coats prepared by controlled atmosphere heat treatment. Surf Coatings Tech, 2018, 347: 54–65
Busso E P, Evans H E, Qian Z Q, et al. Effects of breakaway oxidation on local stresses in thermal barrier coatings. Acta Mater, 2010, 58: 1242–1251
Zhang X, Deng Z, Li H, et al. Al2O3-modified PS-PVD 7YSZ thermal barrier coatings for advanced gas-turbine engines. npj Mater Degrad, 2020, 4: 31
Evans A G, Clarke D R, Levi C G. The influence of oxides on the performance of advanced gas turbines. J Eur Ceramic Soc, 2008, 28: 1405–1419
Ammar K, Appolaire B, Cailletaud G, et al. Finite element formulation of a phase field model based on the concept of generalized stresses. Comput Mater Sci, 2009, 45: 800–805
Loeffel K, Anand L. A chemo-thermo-mechanically coupled theory for elastic-viscoplastic deformation, diffusion, and volumetric swelling due to a chemical reaction. Int J Plast, 2011, 27: 1409–1431
Loeffel K, Anand L, Gasem Z M. On modeling the oxidation of high-temperature alloys. Acta Mater, 2013, 61: 399–424
Zhang X, Zhong Z. A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction. J Mech Phys Solids, 2017, 107: 49–75
Hu S, Shen S. Non-equilibrium thermodynamics and variational principles for fully coupled thermal-mechanical-chemical processes. Acta Mech, 2013, 224: 2895–2910
Liu E, Lai Y, Wong H, et al. An elastoplastic model for saturated freezing soils based on thermo-poromechanics. Int J Plast, 2018, 107: 246–285
Suo Y, Shen S. Coupling diffusion-reaction-mechanics model for oxidation. Acta Mech, 2015, 226: 3375–3386
Suo Y, Shen S. General approach on chemistry and stress coupling effects during oxidation. J Appl Phys, 2013, 114: 164905
Attariani H, Levitas V I. Coupled large-strain mechanochemical theory for solid-state reaction with application to oxidation. Acta Mater, 2021, 220: 117284
Xu G N, Yang L, Zhou Y C, et al. A chemo-thermo-mechanically constitutive theory for thermal barrier coatings under cmas infiltration and corrosion. J Mech Phys Solids, 2019, 133: 103710
Anand L. 2014 drucker medal paper: A derivation of the theory of linear poroelasticity from chemoelasticity. J Appl Mech, 2015, 82: 111005
Zhou Q, Wei Y, Zhou Y, et al. A thermodynamically consistent phase-field regularized cohesive fracture model with strain gradient elasticity and surface stresses. Eng Fract Mech, 2022, 273: 108760
Zhu Y, Kang G, Kan Q, et al. Thermo-mechanically coupled cyclic elasto-viscoplastic constitutive model of metals: Theory and application. Int J Plast, 2016, 79: 111–152
Fox A C, Clyne T W. Oxygen transport by gas permeation through the zirconia layer in plasma sprayed thermal barrier coatings. Surf Coatings Tech, 2004, 184: 311–321
Karlsson A M, Hutchinson J W, Evans A G. The displacement of the thermally grown oxide in thermal barrier systems upon temperature cycling. Mater Sci Eng-A, 2003, 351: 244–257
Hille T S, Turteltaub S, Suiker A S J. Oxide growth and damage evolution in thermal barrier coatings. Eng Fract Mech, 2011, 78: 2139–2152
Ristinmaa M, Ottosen N S. Consequences of dynamic yield surface in viscoplasticity. Int J Solids Struct, 2000, 37: 4601–4622
Zhu H, Sun L. A viscoelastic-viscoplastic damage constitutive model for asphalt mixtures based on thermodynamics. Int J Plast, 2013, 40: 81–100
Levitas V I, Nesterenko V F, Meyers M A. Strain-induced structural changes and chemical reactions—I. Thermomechanical and kinetic models. Acta Mater, 1998, 46: 5929–5945
Liu Z Y, Yang L, Zhou Q Q, et al. Modeling stress evolution in porous ceramics subjected to molten silicate infiltration and corrosion. Corrosion Sci, 2021, 191: 109698
Yang Q S, Qin Q H, Ma L H, et al. A theoretical model and finite element formulation for coupled thermo-electro-chemo-mechanical media. Mech Mater, 2010, 42: 148–156
Levitas V I. Thermodynamically consistent phase field approach to phase transformations with interface stresses. Acta Mater, 2013, 61: 4305–4319
Ottosen N S, Ristinmaa M. The Mechanics of Constitutive Modeling. Lund: Elsevier, 2005
Rösler J, Bäker M, Volgmann M. Stress state and failure mechanisms of thermal barrier coatings: Role of creep in thermally grown oxide. Acta Mater, 2001, 49: 3659–3670
Shen Q, Li S Z, Yang L, et al. Coupled mechanical-oxidation modeling during oxidation of thermal barrier coatings. Comput Mater Sci, 2018, 154: 538–546
Zhu W, Zhang Z B, Yang L, et al. Spallation of thermal barrier coatings with real thermally grown oxide morphology under thermal stress. Mater Des, 2018, 146: 180–193
Bäker M. Finite element simulation of interface cracks in thermal barrier coatings. Comput Mater Sci, 2012, 64: 79–83
Yang L, Liu Q X, Zhou Y C, et al. Finite element simulation on thermal fatigue of a turbine blade with thermal barrier coatings. J Mater Sci Tech, 2014, 30: 371–380
Rösler J, Bäker M, Aufzug K. A parametric study of the stress state of thermal barrier coatings. Part I: Creep relaxation. Acta Mater, 2004, 52: 4809–4817
Siry C W, Wanzek H, Dau C P. Aspects of tbc service experience in aero engines. Mat-wiss u Werkstofftech, 2001, 32: 650–653
Pint B A, Wright I G, Lee W Y, et al. Substrate and bond coat compositions: Factors affecting alumina scale adhesion. Mater Sci Eng-A, 1998, 245: 201–211
Brindley W J, Miller R A. TBCs for better engine efficiency. Adv Mater Process, 1989, 136: 29–33
Kitazawa R, Kakisawa H, Kagawa Y. Anisotropic TGO morphology and stress distribution in EB-PVD Y2O3−ZrO2 thermal barrier coating after in-phase thermo-mechanical test. Surf Coatings Tech, 2014, 238: 68–74
Kageshima H, Shiraishi K. Relation between oxide growth direction and stress on silicon surfaces and at silicon-oxide/silicon interfaces. Surf Sci, 1999, 438: 102–106
Yata M. External stress-induced chemical reactivity of O2 on Si(001). Phys Rev B, 2010, 81: 205402
Chen W R, Wu X, Marple B R, et al. The growth and influence of thermally grown oxide in a thermal barrier coating. Surf Coatings Tech, 2006, 201: 1074–1079
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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11890684, 12032001, and 51590891), the Technology Innovation Leading Program of Shaanxi (Grant No. 2022TD-28), and the Hunan Provincial Natural Science Innovation Research Group Fund (Grant No. 2020JJ1005).
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Zhou, Q., Yang, L., Nie, M. et al. A chemo-thermo-mechanically constitutive theory of high-temperature interfacial oxidation in alloys under deformation. Sci. China Technol. Sci. 66, 1018–1037 (2023). https://doi.org/10.1007/s11431-022-2208-6
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DOI: https://doi.org/10.1007/s11431-022-2208-6