13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- λIII= 0.5. This value remains constant from the crack tip until the external radius is reached. It has been found that the in-plane shear stress components associated with the coupled mode change in a wider range from zero at the mid-plane as expected to values of the same order as the applied stress intensity factor. In contrast, the out-of-plane shear stresses associated with the applied KIII mode do not significantly change across the thickness and the maximum shear stresses take place at the mid-plane of the plate decreasing smoothly towards the free surfaces. As mentioned above, the results were obtained for the above specified conditions (applied stress intensity factor, material properties and plate thickness) and can be easily rescaled or represented in a dimensionless form if necessary. 3.2 Stress Intensity Factors The stress intensity factor of the coupled mode can be defined similar to mode II, or as ( ) ( ) II 1 xy x 0 C II z x K z 2 lim −λ → = π τ (4) In general there are many similarities between the coupled mode and mode II corresponding to the shear loading of a crack. However there are some essential differences between these two singular modes. The coupled mode is a local mode, which is concentrated in the vicinity of the plate free surfaces. It is generated due to the boundary conditions, which negate the out-of-plane shear stress components corresponding to the applied mode. For this coupled fracture mode the effect of Poisson’s ratio is rather small in comparison with the coupled mode generated by mode II loading [14]. The coupled modes rapidly decay with distance from the crack tip as it will be demonstrated later in this paper. The distributions of the local intensities of mode III, KIII(z) associated with the applied antisymmetric loading and ( ) K z C II , associated with the coupled mode are shown in Fig. 4. As it can be seen from this figure the coupled mode is localised in the close vicinity of the free surfaces and propagates into the thickness to the distance of approximately 0.2 H. There is a significant drop in the intensity of the applied mode in the precincts of the free surface. In the very close vicinity of the free surface the intensity of both modes is approaching to zero. As it was mentioned in the Introduction, at a point where a corner front (crack front) intersects a free surface the applied and coupled modes disappear and a new type of singularity, 3D corner singularity, develops instead. Consequently, the numerical results could be not very accurate in the vicinity of this location [10]. 4. Anti-plane Loading with KIII = 0 and Scale Effect 4.1 Coupled Mode due to Anti-plane Loading For an elastic plate with a crack, the possible contribution of higher order terms of the classical Williams’ solution [28] to the fracture initiation was discussed with reference to a plane elastic problem in [29-31]. As discussed in Ref. [30] in some cases of practical interest, the contribution of the higher order stress terms to the stress state in the vicinity of the crack tip (in addition to the stress intensity factors and the T-stress) is not negligible. A set of equations has been proposed for accurately describing the crack tip stress components particularly for those cases where the mode I and mode II stress intensity factors used in combination with the T-stress component, are unable to capture with satisfying precision the complete stress field ahead the crack tip. In this session an
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