PSI - Issue 28

Vera Petrova et al. / Procedia Structural Integrity 28 (2020) 608–618 Author name / Structural Integrity Procedia 00 (2019) 000–000

616

9

a 1 = 1 mm , a n = 2 a 1 (Fig. 4a) and a n = 0.5 mm (Fig. 4b). The midpoint coordinates of the internal cracks are ( x + i y )/ a = (– ih , d – ih , 2 d – ih )/ a (Figs. 4a and b). In Fig. 5, the non-dimensional distances d/a are denoted by d . In Figs. 6 and 7, the results for critical loads are obtained for d/a = 2. 4.1. Stress intensity factors Fig. 5 shows SIFs as functions of inclination angles β for edge cracks and for different distances d/a between the edge cracks for the geometry in Fig. 4a. Both k I and k II are non-zero, thus, the mixed–mode fracture conditions are realized. For most of the parameters β and d/a , the shielding effect is observed, because the values for k I for edge interacting cracks do not exceed the value 1.58 for a single edge crack. A strong dependence of SIFs on the angle β is observed, especially for k II . The effect of the distance d / a on the SIFs of the strongly interacting cracks 1 and 4 is negligible. The maximum effect of d/a is observed on SIFs k I for edge cracks 2 and 3. If the weakest crack is to be defined, and if this definition is based on the maximum SIF k I , then edge crack 1 has the highest k I value for β = 90° and d/a = 6. That is, it looks like the large edge crack 1 would start to propagate first. In the next section, the critical loads are defined and the identification of the weakest cracks is discussed.

a

b

c

d

Fig. 5. SIFs k I and k II as functions of edge crack angles β ( β n = β , n=1,2,3) and for different distances d between the edge cracks; (a) for edge crack 1 with half-length a 1 ; (b) and (c) for edge cracks 2 and 3 with half-length a 2 = a 3 =0.5 a 1 ; (d) for right tip of internal crack 4 with half-length a 4 =0.5 a 1 . 4.2. Critical loads Figs. 6 and 7 represent the results for critical loads as functions of inclination angle β and for distance d/a = 2, Fig. 6 is for the geometry in Fig. 4a and Fig. 7 for the geometry in Fig. 4b (for cracks of equal length). As mentioned above, the calculations are performed for the inhomogeneity parameters ε h = –0.5, ω h = –1.5, γ h = –2.3. These values correspond to material parameters that increase from the ceramic top to the metal substrate. Eq. (20) is used for dimensionless critical load, and Eq. (15) for fracture angles in Eq. (20).