Modelling and analysis of the oxide growth coupling behaviour of thermal barrier coatings

  • Xiaokang Wang
  • Xueling FanEmail author
  • Yongle Sun
  • Rong Xu
  • Peng Jiang
Computation and theory


A chemo-transport-mechanics model is developed to study the growth of thermally grown oxide (TGO) and its impact on deformation and stress in air plasma-sprayed thermal barrier coatings (TBCs). As the driving force for oxygen transport, the chemical potential consists of contributions from both species concentration and hydrostatic pressure. The model suggests that both the concentration boundary condition and the transport process of the oxygen are affected by hydrostatic stress. Since oxygen has smaller diffusion coefficient in TGO than in BC, the retarding effect of the formed TGO on oxygen transport is considered and clarified by the coupled model. The competition between geometrical imperfection (i.e. concave morphology) and the chemo-mechanics coupling to influence the transport of oxygen is also identified numerically. The geometrical imperfection can introduce additional oxygen transport at the margin of the concave imperfection due to the horizontal component of the gradient of the chemical potential of the oxygen, which plays a dominant role in the TGO growth kinetics for the studied TBCs. Consequently, there is a limited effect of the chemo-mechanics coupling on the growth kinetics of a concaved TGO. The amplitude change of the concave portion is found to be up to 0.36 µm after 600-h exposure at 1150 °C, which leads to large tensile stress above the concave portion potentially causing micro-cracks.

List of symbols


Hydrostatic stress


Stress component


Strain component


Stiffness matrix


Elastic strain


Plastic strain


Thermal strain


Growth strain


Chemical strain




Coefficient of thermal expansion (CTE)




Reference temperature


Pilling–Bedworth ratio


Oxide volume percentage


Oxygen concentration


Partial molar volume


Chemical potential


Reference chemical potential


Gas constant


Diffusion flux


Diffusion coefficient


Reference diffusion coefficient


Step function


Chemical reaction rate


Chemical reaction constant


Ratio of diffusion coefficient of oxygen in TGO to that in BC



This work is supported by NSFC (11472204 and 1171101165) and the Fundamental Research Funds for the Central Universities.

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.


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Authors and Affiliations

  1. 1.State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace EngineeringXi’an Jiaotong UniversityXi’anChina
  2. 2.School of Mechanical, Aerospace and Civil EngineeringThe University of ManchesterManchesterUK

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