13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 0 10 20 30 40 50 60 0 0.1 0.2 0.3 0.4 0.5 Normalized coordinate z/H Stress Intensity Factor K c II (MPa mm0.5) H-increasing Fig.5. Effect of the thickness on the intensity of the coupled mode at distance x/H= 0.02 (a); Consider the first non-singular term in the asymptotic expansion. Set its value C1=1 MPa/ m corresponding to n=1 in Eq. (5). Such loading produces no singularities corresponding to the applied antisymmetric loading, i.e. KIII = 0, which is also valid in the area of 3D effects (very close to the crack tip). The results of the FE calculations are presented in Fig.5, which reveals that a non-zero stress intensity of the coupled mode does exist at such loading. The latter effect has many implications for failure assessment. In particular, it indicates that brittle failure by crack propagation is possible even the intensity of the primary load (2D stress intensity factor) is close to zero( ) K 0 III ≈ . It is interesting that the non-singular loading reveals a strong scale effect of deterministic nature, which can be also found from dimensionless considerations. Indeed, due to the localised nature of the coupled mode, its intensity has to be a linear function of the applied intensity, or 1 C II K C≈ . 5. Conclusion Below the most important findings of this work will be summarised: a) Anti-plane loading of a through the thickness crack leads to generation of a singular stress state (or a coupled fracture mode), which has the similar singular behaviour as classical mode II. However there are some essential differences between these modes. The coupled mode is a local mode, which is concentrated in the vicinity of the plate free surfaces and is generated due to the Poisson’s effect and boundary conditions, which negate the out-of-plane shear stress components corresponding to the applied mode. The coupled mode rapidly decays with distance from the crack tip. The local nature of the coupled modes means that the obtained results for the truncated geometry are applicable to other finite geometries provided that there is no interaction between the boundary conditions and the area of 3D effects. b) The intensity of the primary (applied) anti-plane mode in the vicinity of the crack tip is moderately affected by Poisson’s ratio. In contrast, the intensity of the coupled mode is largely unaffected by Poisson’s ratio. c) The singular coupled mode can be induced by, so called, non-singular anti-plane loading with KIII = 0. In this case a strong thickness effect is found and confirmed by FE calculations. The
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