PSI - Issue 13

Elena Fedorova et al. / Procedia Structural Integrity 13 (2018) 741–745 E.Fedorova et al./ Structural Integrity Procedia 00 (2018) 000 – 000

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Fig. 1. BSE SEM micrographs of: (a) representative TBC cross-section with TGO irregularity; (b) zoom in TGO irregularity.

Numerical analysis of stress state was carried out using a finite element model of a representative periodic segment shown on the Fig. 2. The interfaces TGO/BC and TGO/TC were modeled with a sinusoidal geometry having a constant value of wavelength L (50  m) and amplitude a of 10  m. A “defect” shape of the TGO layer, which represented a real irregularity observed during the microstructural analysis, was simulated (Fig. 2b).

Fig. 2. Finite element model of a representative periodic segment: (a) c alculation scheme, (b) “defect” shape of the TGO layer .

The model included more than 30000 second-order elements with the mesh refinement along the interfaces. The generalized plane strain conditions were applied. Thermomechanical properties of the TBC components and creep parameters have been extracted from Haynes, 2004; Hille, 2011; Munro, 1997. The following boundary conditions were imposed on the model: • symmetry for the nodes located on one edge of the segment (u x = 0); • displacement in the x direction of the nodes on the other edge are the same (periodicity conditions); • displacement in the y direction u y = 0 for the nodes located on the boundary of metallic substrate; • ideal contact on the interfaces; • temperature is the same for all elements at any time point. Five various cooling rates (1.5, 30, 145, 1000 and 2000 min -1 ) from the stress-free temperature (1100  С ) to room temperature were considered. For comparison, a cooling from 800  С at the rate of 1000 min -1 was also computed.

4. Results and discussion

The results of finite element calculation for the TBC system with the regular interface geometry (Fig. 2a) revealed that the cooling rate has an insignificant effect on the stress state of the TBO layer (Fig. 2). The maximum compressive stresses σ 3max of -1564 MPa are developed at the TGO/TC interface valley at the cooling rate of 30 °C/min. There is about 10 % difference with the stresses occurred in this region upon cooling at the rate of 2000 °C/min. At the TGO/BC interface the σ 3max value of -1497 MPa was calculated in the peak area when the cooling