Interface Delamination Analysis of Dissimilar Materials: Application to Thermal Barrier Coatings

  • Yutaka Kagawa
  • Makoto Tanaka
  • Makoto Hasegawa
Living reference work entry


Recent progress of gas turbine technologies requires protection of superalloy components from harsh use environments. To satisfy this requirement, surface protection coatings have been developed. The coatings allow protection of superalloy substrate from use environments, which includes temperature. Among the coatings, thermal barrier coatings (TBCs) have been developed to protect high temperature metal components. TBCs are usually composed of oxide ceramic topcoat layer, metal or intermetallic bond coat layer, and substrate. Currently, yttria stabilized zirconia (YSZ) is believed the best material for TBCs. YSZ-TBCs reduce temperature of a metal component because of its low thermal conductivity and cooling of metal substrate, and allows safety operation of superalloy components.

List of Abbreviations


Thickness of TBC layer


Thickness of substrate


Thickness of thermally grown oxide (TGO) layer

h1, h2:

Thickness of coating layer (1) and substrate (2) for analytical model


Young’s modulus of TBC layer


Young’s modulus of substrate


Young’s modulus of TGO layer


Shear modulus


Poisson’s ratio of TBC layer


Poisson’s ratio of substrate


Poisson’s ratio of TGO layer


Applied load


Applied stress


Stress of TBC layer


Stress of substrate


Stress of TGO layer

\( {\sigma}_{tbc}^T \):

Thermal expansion misfit stress of TBC layer

\( {\sigma}_s^T \):

Thermal expansion misfit stress of substrate

\( {\sigma}_{tgo}^T \):

Thermal expansion misfit stress of TGO layer


Normal stress component


Normal stress component


Shear stress component

x, y, z:





Phase angle at crack tip


Steady state phase angle at crack tip


Bi-material constant


In plane strain of TBC layer


In plane strain of substrate


In plane strain of TGO layer


Applied strain


Length of TBC layer


Length of substrate


Interface crack length


Crack length at buckling


Steady stare strain energy release rate (calculated value)


Strain energy release rate (calculated value)


Strain energy release rate at a ≅ 0


Steady stare strain energy release rate (measured value)


Critical strain energy release rate (measured value)


Thermal expansion coefficient of TBC layer


Thermal expansion coefficient of substrate


Thermal expansion coefficient of TGO layer


Temperature difference


Strain energy release rate (measured value)


Young’s modulus ratio Ω = Etbc/Es


Thickness ratio η = htbc/hs


Nondimensional shape factor


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Katayanagi Advanced Research LaboratoriesTokyo University of TechnologyTokyoJapan
  2. 2.Materials Research and Development LaboratoryJapan Fine Ceramics CenterNagoyaJapan
  3. 3.Division of Systems Research, Faculty of EngineeringYokohama National UniversityYokohamaJapan

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