13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- accurate analysis of mode III higher order (non-singular) terms on the induced mode II is carried. 0 0.4 0.8 1.2 1.6 2 0 0.1 0.2 0.3 0.4 0.5 Normalized coordinate z/H KIII KII C Stress Intensity Factors K c II, KIII (MPa mm0.5) Fig. 4. Distribution of the stress intensity factors (mode III and the coupled mode) along the plate thickness, at a distance x = 0.05 mm from the crack tip. The out-of-plane displacement, w, beyond the area of 3D effects (this 3D area is confined within a cylinder with the axis of symmetry along the crack front and radius equal to half of the plate thickness) can be expressed as [29]: ⎟φ ⎠ ⎞ ⎜ ⎝ ⎛ − μ =∑ ∞ = + n 0 n 2 1 n n 2 1 C sin r w (5) with π = ∞ 2 C KIII 0 (6) The previous results are related to the case when C 0 0 ≠ or K 0 III ≠ and all other terms in the asymptotic expansion (5) are zero (C 0 n ≡ at = ∞ n 1,2... ). In Fe simulations the corresponding displacement boundary conditions far from the crack tip were applied to avoid effect of the finite boundaries of the FE model. In the following analysis the situation when a through-the-thickness crack loaded with C0 = KIII = 0 is considered. It will be demonstrated that such a loading of a through-the-thickness crack is capable of inducing the singular coupled singular mode, the same as for the leading term in the asymptotic expansion of the two-dimensional displacement/stress field. It suggests that this coupled singular mode has a potential to cause fracture. In contrast, the classical two-dimensional theory of brittle fracture states that fracture by crack propagation is impossible due to the absence of the energy release rate when KIII=0.
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