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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cracks in ceramic coatings; this mechanism is due to the shielding effect in these crack systems. A system of a finite number of edge cracks is a good candidate for investigating the effects of crack interaction, in particular crack shielding, i.e. the possibility of increasing fracture resistance. At the same time, additional defects, such as internal cracks can disrupt this shielding effect. As illustrating examples, two crack geometries are studied: a system of three edge cracks (Fig. 1c) and edge cracks with one internal crack (Fig. 1d). The results were obtained using functions based on the RoM (Eq. 2) to evaluate the FGM properties. In the following, the results for crack 1 and for middle crack 2 are presented. The behavior of fracture characteristics for crack 3 is similar to that of crack 1 and is not shown in the figures. The following parameters are used in the calculations: d/a = 2.0-10.0 (in the figures, d/a is denoted by d ), h/a = 4.0, 2 a – crack size, 2 a = 2; Δ T = 300 °C. Material parameters are listed in Table 1. Table 1. Material parameters Material property Top coat (ceramic) PSZ Bottom coat (metal) Steel Young’s modulus [GPa] (20 -1100) °C 48.0 207.0 Fracture toughness [MPa m 1/2 ] (20°C) 7.0 50.0 Thermal exp. coeff. [10 -6 K -1 ] (20 °C) 9.0 15.0 4.1. Three edge cracks Fig. 2 shows the normalized critical loads p cr / p 0 as functions of inclination angle β = β 1,2,3 for three FGM models, exponential, linear and RoM, Petrova and Schmauder (2018). Fig. 2a refers to crack 1 and Fig. 2b - for the middle crack 2 (see geometry in Fig 1c). The weakest crack is crack 1 (and crack 3) since p cr ,2 / p 0 > p cr ,1 / p 0 , and a shielding effect is observed for crack 2. The lowest p cr / p 0 value is for the RoM model. Different values of the critical load for different material models, but for the same crack, show a difference in the fracture toughness values determined by these models, which in turn shows a different concentration of ceramics (metal) near the crack tip.

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b Fig. 2. Critical loads as a function of β for three FG models, (a) for crack 1and (b) for the middle crack 2.

Figs. 3a and b present normalized SIFs k I and critical loads p cr / p 0 as functions of inclination angle β and distances d for the RoM for FGM ( λ =3). The shapes of 3D plots for k I (1) and k I(2) are similar, as well as for p cr, 1 / p 0 and p cr, 2 / p 0 . But the values of k I (1) and k I (2) are different and of p cr, 1 / p 0 and p cr, 2 / p 0 are different. The relative difference for k I (1) and k I (2) is 11% for β =60 ⁰ and 19% for 90⁰ , and for p cr, 1 / p 0 and p cr, 2 / p 0 is 19% and 25% for β =60 ⁰ and 90 ⁰ respectively, d/a =4 and λ =3 (| f 1 - f 2 |/ f 1 ×100% – f 1 and f 2 are the corresponding fracture parameters for cracks 1 and 2). The results in Fig. 3 demonstrate the shielding effect for crack 2, that is, the k I (2) are smaller than k I (1) , and the p cr, 2 / p 0 are greater than p cr, 1 / p 0 . As the distance d decreases, the k I values decrease and the p cr / p 0 values increase. Outer cracks 1 and 3 suppress the propagation of crack 2. This means that outer cracks 1 and 3 will start to propagate first. The influence of β on k I is more pronounced than on p cr / p 0 . Fig. 4 shows normalized SIFs k I , critical loads p cr / p 0 and fracture angles ϕ as functions of grading parameter λ and inclination angle β for distance d/a =2. The results show that the grading parameter λ has a dominant effect on these fracture characteristics. As the grading parameter λ increases, both k I and p cr / p 0 are increased, Figs. 4a-d. The dependence of ϕ on λ is more complicated, Fig. 4e and f. A higher grading parameter corresponds to a higher metal content and a lower ceramic content in the FGC.