Issue 36

V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02

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 = 0 at β = 90°. Besides, for all parameters of the problem the values for a single crack (Figs. 2, 5 and 8). That is, the shielding effect is observed, which is tends to the = 1.12 and k II

value for a single edge crack, e.g., to k I are smaller than the values of k I of k I

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) 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°≤ and ϕ (2) as functions of the inclination angle β=β n

13