Skip to main content
Log in

A chemo-thermo-mechanically constitutive theory of high-temperature interfacial oxidation in alloys under deformation

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. 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

    Article  Google Scholar 

  2. 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

    Article  Google Scholar 

  3. 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

    Article  Google Scholar 

  4. 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

    Article  Google Scholar 

  5. 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

    Article  Google Scholar 

  6. 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

    Article  Google Scholar 

  7. 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

    Article  Google Scholar 

  8. 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

    Article  Google Scholar 

  9. 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

    Article  Google Scholar 

  10. 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

    Article  Google Scholar 

  11. 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

    Article  Google Scholar 

  12. Clarke D R, Oechsner M, Padture N P. Thermal-barrier coatings for more efficient gas-turbine engines. MRS Bull, 2012, 37: 891–898

    Article  Google Scholar 

  13. 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

    Article  Google Scholar 

  14. Padture N P, Gell M, Jordan E H. Thermal barrier coatings for gas-turbine engine applications. Science, 2002, 296: 280–284

    Article  Google Scholar 

  15. 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

    Article  Google Scholar 

  16. 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

    Article  Google Scholar 

  17. 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

    Article  Google Scholar 

  18. 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

    Article  Google Scholar 

  19. 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

    Article  Google Scholar 

  20. 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

    Article  Google Scholar 

  21. 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

    Article  Google Scholar 

  22. 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

    Article  Google Scholar 

  23. 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

    Article  MATH  Google Scholar 

  24. Loeffel K, Anand L, Gasem Z M. On modeling the oxidation of high-temperature alloys. Acta Mater, 2013, 61: 399–424

    Article  Google Scholar 

  25. 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

    Article  MathSciNet  Google Scholar 

  26. Hu S, Shen S. Non-equilibrium thermodynamics and variational principles for fully coupled thermal-mechanical-chemical processes. Acta Mech, 2013, 224: 2895–2910

    Article  MathSciNet  MATH  Google Scholar 

  27. 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

    Article  Google Scholar 

  28. Suo Y, Shen S. Coupling diffusion-reaction-mechanics model for oxidation. Acta Mech, 2015, 226: 3375–3386

    Article  MathSciNet  MATH  Google Scholar 

  29. Suo Y, Shen S. General approach on chemistry and stress coupling effects during oxidation. J Appl Phys, 2013, 114: 164905

    Article  Google Scholar 

  30. Attariani H, Levitas V I. Coupled large-strain mechanochemical theory for solid-state reaction with application to oxidation. Acta Mater, 2021, 220: 117284

    Article  Google Scholar 

  31. 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

    Article  MathSciNet  Google Scholar 

  32. Anand L. 2014 drucker medal paper: A derivation of the theory of linear poroelasticity from chemoelasticity. J Appl Mech, 2015, 82: 111005

    Article  Google Scholar 

  33. 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

    Article  Google Scholar 

  34. 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

    Article  Google Scholar 

  35. 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

    Article  Google Scholar 

  36. 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

    Article  Google Scholar 

  37. 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

    Article  Google Scholar 

  38. Ristinmaa M, Ottosen N S. Consequences of dynamic yield surface in viscoplasticity. Int J Solids Struct, 2000, 37: 4601–4622

    Article  MATH  Google Scholar 

  39. Zhu H, Sun L. A viscoelastic-viscoplastic damage constitutive model for asphalt mixtures based on thermodynamics. Int J Plast, 2013, 40: 81–100

    Article  Google Scholar 

  40. 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

    Article  Google Scholar 

  41. 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

    Article  Google Scholar 

  42. 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

    Article  Google Scholar 

  43. Levitas V I. Thermodynamically consistent phase field approach to phase transformations with interface stresses. Acta Mater, 2013, 61: 4305–4319

    Article  Google Scholar 

  44. Ottosen N S, Ristinmaa M. The Mechanics of Constitutive Modeling. Lund: Elsevier, 2005

    Google Scholar 

  45. 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

    Article  Google Scholar 

  46. 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

    Article  Google Scholar 

  47. 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

    Article  Google Scholar 

  48. Bäker M. Finite element simulation of interface cracks in thermal barrier coatings. Comput Mater Sci, 2012, 64: 79–83

    Article  Google Scholar 

  49. 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

    Article  Google Scholar 

  50. 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

    Google Scholar 

  51. Siry C W, Wanzek H, Dau C P. Aspects of tbc service experience in aero engines. Mat-wiss u Werkstofftech, 2001, 32: 650–653

    Article  Google Scholar 

  52. 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

    Article  Google Scholar 

  53. Brindley W J, Miller R A. TBCs for better engine efficiency. Adv Mater Process, 1989, 136: 29–33

    Google Scholar 

  54. 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

    Article  Google Scholar 

  55. 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

    Article  Google Scholar 

  56. Yata M. External stress-induced chemical reactivity of O2 on Si(001). Phys Rev B, 2010, 81: 205402

    Article  Google Scholar 

  57. 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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Li Yang or YueGuang Wei.

Additional information

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).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-022-2208-6

Navigation