13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⋅ − − = ∑ − 4 1 2 1 1 , ) ( ) (1 (2 1) 1 2 i i B a b r a i f β π σ (14) With the above σ,Bf -expression and m(a, x), the crack surface displacements (Eq. (4)) for partial crack surfaces subject to Dugdale loading can be readily calculated from the following equation: ∫ ∑ ∑ ⋅ ⋅ ⋅ − − ⋅ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = = = a a ii i i i B s s x s r s b i s r s x s b E u 0 ( / ) (1- ) )d ) (1 2 1 ( / ) 11- ( 1 4 i 1 1 -1 4 1 2 1 1 ' , β β π σ σ (15) Figure 3 present the results, the normalized crack surface displacements of a radial crack emanating from a semi-circular notch in a semi-infinite plate with crack surfaces subject to Dugdale loading (b2=a，b1=d). The non-dimensional crack lengths in Fig. 3 are: a/r=0.05, 0.1, 0.5 and 1.0. 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.05 0.10 0.15 uB,σ=uA,σ ⋅(f B,σ/fA,σ )⋅M weight function method b 2/a=1 (u⋅ Ε')/(σ⋅r) d/a=0.9 d/a=0.5 d/a=0.1 d/a=0.01 x/a a/r=0.05 (a) 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 (u⋅ Ε')/(σ⋅r) uB,σ=uA,σ ⋅(f B,σ/fA,σ )⋅M weight function method b 2/a=1 d/a=0.9 d/a=0.5 d/a=0.1 d/a=0.01 x/a a/r=0.1 (b)
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