# Thermal Fatigue Life Prediction of Thermal Barrier Coat on Nozzle Guide Vane via Master-Slave Model
## 1 Introduction  
With the improvement of aero-engine performance with a high flow rate and high thrust-weight ratio, the temperature and pressure of gas at the outlet of the combustion chamber is rising. For instance, the temperature before the turbine for the new generation engines (e.g., F119, F120, EJ200, etc.) is over 1850 K. To meet the harsh working environment, a thermal barrier coat (TBC) is a key technology in protecting turbine blades (rotor blades and nozzle guide vanes (NGVs)) [1; 2; 3]. As the first stage NGV faces high combustion outlet temperatures, the TBC at the surface of the NGVs endures a high thermal cycle load, so its failure problems are particularly serious due to the thermal loads. Therefore, it is necessary to consider the thermal fatigue life (TFL) of the TBC to improve the design and machining of the first-stage NGV [4]. TBC life is seriously induced by four components as shown in Figure 1[5]: (i) Top coat (TC) layer: providing thermal insulation; (ii) Thermally grown oxide (TGO) layer: providing the bonding of TBC with bond coat (BC) to slow subsequent oxidation; (iii) BC layer: containing the source of elements to create TGO in oxidizing environment and provide oxidation protection; and (iv) superalloysubstrate: carrying mechanical loads. Through the oxidation of high-temperature gas, the aluminum in the BC is oxidized to produce an alumina layer (also called the TGO). With the increase in the TGO thickness, the material properties between the TC and BC are destroyed. The mixed layer TC/TGO is liable to crack and peel off under the combined effect of thermal stress and deformation in different layers, which eventually leads to the failure of the NGV [6]. Therefore, it is of some urgency to study the mechanical properties of a mixed layer TC/TGO with regard to a thermal shock environment. [PERSON] [7] presented a Thermo-Calc/Dictra-based approach for the life prediction of isothermally oxidized atmospheric plasma sprayed TBCs. The beta-phase depletion of the coating was predicted and compared to the life prediction criteria based on the TGO thickness and aluminum content in the coating. Based on the BC test results, the life of the TBC was predicted by [PERSON] [8], according to degradation and thermal fatigue. Many experiments indicated that the failure of the TBC systems under thermomechanical loading was complicated due to the influences of many factors such as thermal mismatch, oxidation, interface roughness, creep, sintering, and so forth [9; 10; 11]. Among the failure factors, the effect of TGO growth is particularly prominent, because volume expansion and compressive stress increase are correlative with the growth of TGO. When the NGV gets to the cooling state, the induced unbalanced temperature at the mixed layer TC/TGO leads to a high residual compressive stress, which varies directly with the strain energy. When the strain energy reaches the limit value, cracks occur. [PERSON] et al. [12; 13] tested an oxidation weight gain of the TBC at 1323 K and obtained the dynamic test curves for characterizing the TGO thickness. Based on this work, [PERSON] et al. [14] established a TFL model of a TBC regarding the phenomenological approach and low cycle fatigue theory. However, the working environment and micro-strain characteristics of the NGV were not discussed in detail. In the process of the thermal shock cycle, the flow, heat transfer, and structure interact with each other, thus it is difficult to separate the temperature field from thermal stress in the calculation of flow characteristics. Therefore, the TFL of a NGV is a typical fluid-thermo-structure (FTS) coupling problem. With the development of numerical simulation approaches, it is possible to calculate the thermal shock cyclic loads of a NGV by combining computational fluid dynamics (CFD) and finite element (FE) methods. [PERSON] et al.