Issue 36

V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02 13 Two arbitrary inclined cracks Figs. 2, 5 and 8 show the SIFs k I,II , Figs. 3, 6 and 9 – the fracture angles, and Figs. 4, 7 and 10 – the critical loads as functions of inclination angles of the two edge cracks to the surface and for different distances d . It is observed that for all angles β SIF k I increases with increasing the distance d between the cracks and k I tends to the value for a single edge crack, e.g., to k I = 1.12 and k II = 0 at β = 90°. Besides, for all parameters of the problem the values of k I are smaller than the values of k I for a single crack (Figs. 2, 5 and 8). That is, the shielding effect is observed, which is known for parallel cracks under tensile load normal to the crack lines. Figs. 2–4 present results for two equal edge cracks inclined arbitrarily to the surface with the same angle β=β n ( n =1, 2). Stress intensity factors k I and k II as functions of the inclination angle β are presented for the angles 60°≤ β ≤120° in Figs. 2 a, b and for 15°≤ β ≤90° in Figs. 2 c, d and for different distances d between the cracks. In the interval 60°≤ β ≤120° a small variation of the magnitude of k I with β is observed (Fig. 2 a, b), but in the interval 15°≤ β ≤60° for the small inclinations angles this variation is significant (Figs. 2 b, c). k I is increased from 0.2 to 0.99 for 15°≤ β ≤90° (for d =2) and then decreased for 90°≤ β ≤120°. SIFs k II are mostly nonzero, the absolute values of k II are greater than k I , and k II is monotonically decreased for 60°≤ β ≤120° (Fig. 2 a, b) and increased for 15°≤ β ≤45° (Figs. 2 b, c). (a) (b) (c) (d) Figure 3 : Fracture angles ϕ 1) and ϕ (2) as functions of the inclination angle β=β n of the edge cracks to the surface for different distances d between the cracks: (a) for crack 1 (60° ≤ β ≤ 120°), (b) for crack 2 (60° ≤ β ≤ 120°), (c) for crack 1 (15° ≤ β ≤ 90°), (d) for crack 2 (15° ≤ β ≤ 90°). Two equal edge cracks. The fracture angles ϕ for two edge cracks are presented in Figs. 3, strong influence of the inclination angles β on the fracture angles ϕ is observed. For all β fracture angles ϕ are increased and changed the sign from negative to positive at β ≈103° (crack 1) and at β ≈77° (crack 2) for d =2, for larger distances d these points are shifted towards β ≈99° (crack 1) and β ≈81° (crack 2) for d =4 (Fig. 3 a, b). These changes of sign mean the changes of direction of the crack propagation. Fig. 4 shows results for the non-dimensional critical loads for crack 1 and for both cracks in Fig. 4 b (60°≤ β ≤120°) and 4 d (15°≤ β ≤90°). The larger the distance between the cracks – the less the p cr , i.e. the material becomes weaker with respect to fracture resistance. What crack starts to propagate first depends on the inclination angle, for 62°≤ β ≤90° p cr (1) < p cr (2) and the crack 1 propagates first and for 90°< β<118° the crack 2 will be starting first (Fig. 4 b). For small angles 15°≤