13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 3cos 1 cos 1 1 cos 16 1 1 sin 2cos 16 1 , cos 1 cos 16 1 22 12 11 − + + + − = − − = − + = ϕ ϕ ϕ κ κ ϕ ϕ ϕ κ ϕ G a G a G a (4) and, ϕ the angle related to the plane of the crack, G the shear modulus of the core material, ν κ 3 4 = − (plain strain). The minimum energy density possesses a stationary value which is derived from 0= ∂ ∂ ϕ S at which , 0 ϕ ϕ= (5) where 0ϕ is the crack propagation angle with respect to the plane of the crack with the minimum energy density. From the numerical calculations and the core material considered (Table 1), we have: 80 , 0 =± ϕ which is too high comparing with the kinking angle from the experimental investigation. Secondly the maximum hoop stress is used [15]. The tangential stress component at the vicinity of the crack tip is given by: ( ) ( ) ( ) − + = ϕ ϕ ϕ π σθθ sin 2 3 1 cos 2 1 2 cos 2 1 II I K K r (6) where r is the distance from the crack tip and θθ σ the tangential stress. According to the maximum hoop stress criterion the crack will propagate in the direction in which θθ σ obtains its maximum. The direction of max θθ σ can be found by the relations 0 0 , 2 < ∂ ∂ = ∂ ∂ ϕ σ ϕ σ θθ θθ (7) From the numerical calculations, the following kinking angle is derived
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