13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- M f f u u A B B A ⋅ ⋅ = (16) where the subscripts A and B represent the two load cases. Because the crack surface displacements of a center crack in an infinite plate (see Fig. 1(b)) have exact solutions, this case (see Fig. 1(b)) is selected as load case A, a radial crack emanating from a semi-circular notch in a semi-infinite plate is selected as load case B. For a center crack in an infinite plate under uniform remote tension, the exact crack surface displacement equation is [11] a x x a E S uA S ≤ − − = ) 2(1 2 2 2 . η (17) The normalized stress intensity factor is 1 , = A S f (18) For a center crack in an infinite with crack surfaces subject to Dugdale loading, the exact crack surface displacement equation is [11] u h x h x x a A = + − ≤ ( ) ( ) , σ (19a) d a d b a d a x ad x a dx d x E h x = = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − + − − − − = 1 ) arcsin( ) )arccosh( ( ) 2(1 ( ) 2 2 2 2 π σ η (19b) The normalized stress intensity factor is [11] d a d b A a d f = = − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 1 sin ( ) 2 1 , π σ (20) 4.1. Analytical crack surface displacement equation for uniform remote tension For a radial crack emanating from a semi-circular notch in a semi-infinite plate under uniform remote tension, the crack-surface displacement analytic equation can be expressed as B S A S B S B S A S M f f u u , , , , , ⋅ ⋅ = (21a) where B S f , ， A S f , and A S u , are given in Eq. (12), Eq. (18) and Eq. (17), respectively. The factor MB,S is determined by fitting the crack opening displacement results obtained from the weight function method. The fitted expression is
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