Fig. 1. Schematic T-t curve during TBC service.

Fig. 2. Geometry relating to scale thickening by grain boundary diffusion with participation of vacancies and electrons.

Fig. 3. Dependence of scale thickness h on oxidation time t with varied grain size d.

Fig. 4. Dependence of normalized energy release rate g on oxidation time t (a) and dependence of service lifetime tcr on grain size d for interfacial delamination (b).

Fig. 5. Thermal cycle lifetime vs. TGO thickness h (data presented by Dong et al. (2014), DOI: 10.1111/jace.12868).

Fig. 6. Schematic tensile strain produced in Al2O3 scale for epitaxial lattice match.

Fig. 7. Schematic channel cracking in epitaxial film under the semi-infinite plane condition.

Fig. 8. Superposition procedure to calculate stress distribution in an elastic layer.

Fig. 9. Dependence of normalized strain εavg x/ε0 x on d/h with varied relief coefficient ξ (a) and on scale thickness h with varied grain size d (b).

Fig. 10. Dependence of normalized energy release rate g on scale thickness h with varied grain size d: (a) with large scale thickness range, (b) during the early growth of TGO, and (c) the critical thickness hcr at the peak of ERR under different grain sizes d.

Fig. 11. Dependence of normalized energy release rate g on oxidation time t with varied relief coefficient ξ during the whole service of TBCs (a) and during the early growth of Al2O3-TGO (b).

Fig. 12. Dependence of normalized energy release rate g on oxidation time t with varied ζ during the whole service of TBCs (a) and during the early growth of Al2O3-TGO (b).

Fig. 13. Dependence of normalized energy release rate g on oxidation time t with varied grain size d.

Fig. 14. Dependence of energy release rate G with large range (a) and small range (b) on oxidation time t.

Fig. 15. Surface morphologies of pre-oxidized bond coat with different Al2O3 scale grain sizes: (a) ～500 nm and (b) ～10 μm. Chanel cracking widely occurred in Al2O3 grains larger than ～4 μm.