PSI - Issue 42

Vera Petrova et al. / Procedia Structural Integrity 42 (2022) 1145–1152 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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4.2. Three edge cracks and an internal crack The presence of an internal crack can enhance or suppress the propagation of edge cracks. Fig. 5 presents critical loads p cr / p 0 and fracture angles ϕ as functions of gradation parameter λ and inclination angle β = β 1,2,3 ( d/a =2) for the geometry in Fig. 1d (for three edge cracks and one internal crack with ( x 4 0 , y 4 0 ) = ( d/a , -3) and β 4 = 0°). The influence of the internal crack with the center on the line of edge crack 2 is small, which can be seen from a comparison of the corresponding results in Fig. 5 with the results in Fig. 4c-e. However, the closer the crack is to the edge cracks, the stronger the influence. Besides, a crack with β 4 ≠ 0 (a non-zero angle of inclination to the surface) causes a greater effect on the fracture characteristics of edge cracks, see Table 2, where the relative difference (RD) for k I and p cr / p cr 0 is calculated by the formula RD f = ( f edg – f edg+int )/ f edg ×100% and is presented for cracks 1 and 2 with β 1,2 =90°. The “edge” index means the geometry with only edge cracks (Fig. 1c), and the “edge+int” index – the geometry in Fig. 1d. The propagation of crack 2 is restrained by the internal crack (negative RD k I and positive RD p cr / p cr 0 ), while the propagation of outer cracks 1 and 3 is enhanced by this internal crack (positive RD k I and negative RD p cr / p cr 0 ), as seen in Table 2.

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d Fig. 5. Critical loads (a, b) and fracture angles (c, d) as functions of β = β 1,2,3 and λ , d =4, β 4 = 0; (a, c) for crack 1, (b, d) for crack 2, for Fig. 3d. Table 2. Influence of an internal crack on edge cracks; relative difference (RD) for k I and p cr / p cr 0 . λ β 4 RD k I (1) % RD p cr, 1 / p cr 0 % RD k I (2) % RD p cr, 2 / p cr 0 % 0.2 0° +7 – 6 – 22 +18 45° +18 – 25 – 66 +40 3 0° +2 – 3 – 7 +7 45° +15 – 21 – 59 +38 4.3. Remark In TBC systems, ceramics, due to their low thermal conductivity, prevent overheating of the base metal. The appearance of metals degrades the insulation performance; therefore, it is important to have a certain limit on the ceramic content in the FGC in order to still have fully functional and stable coatings. The calculations provide the critical loads for different grading parameters, but what percentage of material content is required from an optimization point of view (balance of the content of ceramics and metal) needs to be determined in future studies, both theoretical and experimental. The proposed model provides a sound basis to optimize FGCs in order to improve the fracture resistance of FGC/H structures.