13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Figure 2. Geometry of the plate and coordinate system with z=0 in the mid-plane 2.2 Boundary Conditions The displacement boundary conditions are applied to the outer cylindrical edge of the plate. In the beginning the out-of-plane displacement field corresponding to the first singular term in the asymptotic expansion of the stress field, which is valid far from the crack tip (model boundaries), was prescribed as follows: 2 sin 2 r 2K w u III z φ μ π = = u 0 x = u 0 y = (1) where μ is the shear modulus. It is linked to Young’s modulus by a well-known relationship: ( ) +ν μ= 21 E (2) In further numerical examples Young’s modulus was set at 200 9 10 × Pa. However, the numerical results to be presented in the following sections can be easily rescaled for other values of mechanical properties, loading or plate thickness. x y z a ρ = 0 mid plane free surface free surface R x y ux uy r θ Η
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