13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- factor and the reference crack face loadings are expressed in Eq. (5) and Eq. (6) with the following coefficients, respectively: ia : 3.4345, -6.9715, 14.5781, -19.9230, 16.9424, -8.5301, 2.3134, -0.2595. (a/r≤2.0) Sm : 3.0643, -6.6864, 13.1677, -16.9513, 13.7335, -6.6293, 1.7273, -0.1861. (x/r≤2.0) 3.1. Uniform remote tension The normalized stress intensity factor of a radial crack emanating from a semi-circular notch in a semi-infinite plate under uniform remote tension, fB,S, is given in Eq. (5), as: i i i B S r a f ( ) 7 0 , ∑ = = α (12) With the information of fB,S and m(a, x), the crack surface displacements can be easily calculated from Eq. (4). Figure 2 shows the normalized crack surface displacements of a radial crack emanating from a semi-circular notch in a semi-infinite plate under uniform remote tension for non-dimensional crack length a/r = 0.05 to 1. The circular symbols in Fig. 2~3 are obtained by the crack surface displacement analytical equations, which will be explained later. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 weight function method uB,S=uA,S ⋅(f B,S/fA,S )⋅M (u⋅ Ε')/(σ⋅r) x/a a/r=0.05 a/r=0.1 a/r=0.5 a/r=1 Figure.2 Non-dimensional crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate subjected to uniform remote tension. 3.2. Partial crack surfaces subject to Dugdale loading For partial crack surfaces subject to Dugdale loading (see Fig. 1(a), b2=a), the stress distribution is expressed in a simple form: σ σ = ( )x ) ( 1b x a ≤ ≤ (13) For partial crack surfaces subject to Dugdale loading, the normalized stress intensity factor of a radial crack emanating from a semi-circular notch in a semi-infinite plate is easily calculated by inserting Eq.(13) and Eq. (7) into Eq. (2), with
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