**2.2 The origin and category of stress during service**

TBCs usually operate in harsh environments such as high temperatures, high pressures, and extreme mechanical loads. TBCs may undergo chemical changes such as oxidation and sintering, and withstand external loads such as particle erosion and CaO-MgO-Al2O3-SiO2 (CMAS) corrosion, as shown in **Figure 4**. The composition, microstructure and properties may change dynamically. The stress state may also evolve, and the internal crack may appear and propagate, leading to the failure behaviors such as fracture, delamination and even spalling [2, 22].

During service, the aluminum element in the bond coat may continuously diffuse to the interface between the bond coat and the TGO, and react with oxygen entering from the external environment to generate α-Al2O3. In this process, TGO gradually grows thicker. Due to the constraint of the upper ceramic top coat and the lower bond coat, the volume expansion caused by the thickening of TGO is limited. A large compressive growth stress in TGO thereby generates [23]. Besides, the thermal expansion coefficient mismatch of the various layers may also produce high residual compressive stresses in TGO during cooling from the service to room temperature. It is found that the compressive stress in TGO can reach 3-6GPa at room temperature [24]. TGO is subjected to large in-plane compression, and tends to undergo elongation or bending deformation in order to release stress. At high temperatures, the plasticity of the bond coat will increase, and creep even may occur. In addition, there are usually many defects at the interface between the ceramic top coat and TGO. During service, TGO may have an out-of-plane displacement into the bond coat at these defects. The compressive stress in TGO may release, resulting in redistribution of stress. The out-of-plane displacement may cause out-of-plane stress in TBCs, leading to crack initiation, crack propagation, and eventual delamination damage [2, 4, 25]. The stress evolution in TGO plays a crucial role in the TBCs failure, and is one of the most important incentives for delamination failure [26].

When TBCs operate in high temperature environments, the ceramic top coat material may sinter. The sintering may cause the voids between the sheet structures and the cracks in the sheet structures to heal, resulting in a significant increase in the stiffness of the ceramic top coat. The changes in the mechanical properties may

**Figure 4.** *The factors affecting the stress among APS-prepared TBCs during service.*

lead to the change in residual stress. Particularly, the thermal mismatch stress may increase with increasing the modulus, thereby promoting the occurrence of failure [27]. When the temperature is higher than 1200°C, the non-equilibrium metastable phase of 7YSZ may transform into tetragonal phase and monoclinic phase. Large volume deformation may occur in the process of transforming into monoclinic phase, leading to the change in the stress state of TBCs [2].

In some service areas, such as Middle East, silicon-containing debris may enter the engine and melt on the concave (hot side) of the blade. The main component of the melt is CaO-MgO-Al2O3-SiO2, which is called CMAS [2, 28]. When the surface temperature of TBCs exceeds the melting point of CMAS (1240°C), CMAS will infiltrate into the microcracks and voids in TBCs and chemically react with the ceramic top coat material. During the shutdown process of the engine, the ceramic top coat after CMAS infiltration will quickly solidify into a dense layer. The strain tolerance of the top coat will decrease, and the stiffness will increase, increasing the thermal mismatch stress in TBCs [28, 29].

Besides, solid particles in air may also enter the engine, impacting TBCs at high speed during service. The erosion of high speed particles may change the stress state in TBCs [30]. The erosion of the particles produces tensile stress in certain regions of TBCs. Defects such as sheet-like structural interfaces and microcracks in these regions may develop into macroscopic cracks under tensile stress. And macroscopic crack propagation will eventually lead to the spalling of TBCs [31].
