13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- intensity of the coupled mode decays (increases) with the decrease (increase) of the plate thickness as a power function. When several anti-plane non-singular terms are applied to the crack in an elastic plate the scale effect can be rather complicated. The influence of the higher terms on the stress intensity of the coupled mode depends on the number of the asymptotic mode, n, and this influence is more significant for the higher mode numbers. All these theoretical findings, specifically the effects of Poisson’s ratio and plate thickness on the stress intensities, have direct implications to the failure initiation conditions for cracks stressed in mode III. These findings demonstrate essential differences between classical two-dimensional considerations and 3D Fracture Mechanics. For example, the generation of the coupled singular mode at anti-plane loading with KIII = 0 indicates that contrary to the classical 2D theories, fracture under such loading conditions can be initiated due to the induced singular coupled modes. Such fracture is likely to take place close to free surfaces. It is also recognised that much work needs to be done to understand the contribution of the coupled modes to fracture initiation and fatigue. Finally, all Finite Element results of the current study can be re-scaled to make these available for assessment of comparative studies. The only reason as to why it has been used particular values was to provide some physical feeling for the results of our finite element study. References [1] R.J. Hartranft, and G.C. Sih, Effect of plate thickness on the bending stress distribution around through cracks, J. Math. Phys., 47 (1968) 276–291. [2] R.J. Hartranft, G.C. Sih, The use of eigenfunction expansions in the general solution of three-dimensional crack problems. J. Math. Mech., 19 (1969) 123–138. [3] R.J. Hartranft, G.C. Sih, An approximate three-dimensional theory of plates with application to crack problems, Int. J. Eng. Sci., 8 (1970) 711-729. [4] G.C. Sih, A review of the three-dimensional stress problem for a cracked plate, Int. J. Fract. Mech., 7 (1971) 39–61. [5] M.L. Williams, The Bending Stress Distribution at the base of a stationary crack, ASME J. Appl. Mech., 28 (1961) 78–82. [6] M.K. Kassir, and G.C. Sih. Application of Papkovich-Neuber potentials to a crack problem, Int. J. Solids Struct., 9 (1973) 643–654. [7] Y. Kawagishi, M. Shozu, Y. Hirose, Experimental evaluation of stress field around crack tip by caustic method, Mech. Mater., 33 (2001) 741-757. [8] J.P. Benthem, State of stress at the vertex of a quarter-infinite crack in a halfspace, Int. J. Solids Struct., 13 (1977) 479–92. [9] Z.P. Bazant, L.F. Estenssoro, Surface singularity and crack propagation, Int. J. Solids Struct., 15 (1979) 405–26. [10] L.P. Pook, A note on corner point singularities, Int. J. Fract., 53 (1992) R3–R8. [11] L.P. Pook Some implications of corner point singularities, Eng. Fract. Mech., 48 (1994) 367–378. [12] Z.H. Jin, R.C. Batra, A crack at the interface between a Kane-Mindlin plate and a rigid substrate, Eng. Fract. Mech., 57 (1997) 343-354. [13] C. She, W. Guo, The out-of-plane constraint of mixed-mode cracks in thin elastic plates, Int. J. Solids Struct., 44 (2007) 3021–3034.
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