13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- negligible effects of the coupled modes. One of these interesting features is a coupling of this mode with the non-singular terms at shear loading. It means, if a crack is loaded in shear with KII= 0, the intensity of the coupled K0- mode can be different from zero. At such loading the intensity of the out-of-plane mode is finite and capable of initiating brittle fracture [23, 24]. The latter result and other three-dimensional features are in contradiction with the classical two-dimensional view on fracture, which states that brittle fracture can only be initiated with non-zero stress intensities of primary fracture modes (conventional mode I, II and III). Important features of the out-of-plane singular mode were revealed in a careful three-dimensional numerical study of typical welded lap joint geometry [25] aimed to investigate the contribution of this mode to the overall stress state in the close vicinity of the slit/notch tip. The extension of the present study to sharp and blunt notches under mode II loading has been recently made by the present authors [26, 27]. In contrast to mode II loading, the coupled mode corresponding to mode III loading is much less investigated and there were no systematic studies focusing on the investigation of this mode except many remarks in literature on the coupled nature of modes II and III as well as the influence of this coupled mode on fracture appearance, crack path and crack initiation [19, 20]. The aim of this paper is to investigate this coupled mode using the Finite Element method and provide numerical estimates of the possible contribution of this mode to brittle fracture. In the beginning of the present paper, a numerical technique based on FE method is developed and validated for the investigation of the coupled mode associated with the anti-plane loading. Because this mode is localised in the close vicinity of the crack tip, a careful meshing is required in order to avoid large numerical errors in this region. Further, a systematically study of this mode is carried out focusing on the effect of Poisson’s ratio on the stress intensity of this mode, which also varies along the crack front. It is also demonstrated that similar to the K0-mode, a non-singular mode III loading (KIII=0) is capable of generating the coupled singular stress state along the crack front. In this case, a strong scale effect exists and the intensity of the coupled mode strongly depends on the thickness of the plate. 2. Approach 2.1 Geometry Because the coupled singular modes are local modes and spread to the distance of approximately half of the plate thickness as explained in the Introduction, the problem geometry is truncated to a disk with such dimensions which avoid the effect of the finite boundaries on the stress state of the coupled mode as well as the influence of bending stresses. The antisymmetric boundary conditions are utilised to further simplify the geometry. The final geometry is shown in Fig. 2 and appropriate displacement boundary conditions corresponding to anti-plane loading were applied on the cylindrical surface. The origin of the Cartesian coordinate system (x,y,z) is located at the crack tip, at the mid-surface where x direction was chosen to be the direction of the crack bisector.
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