13th International Conference on Fracture June 16–21, 2013, Beijing, China 4 1 12 1 12 12 1 12 12 1 0 1 1 12 12 1 0 2( 1) 1 ( , , ) ( )cos[ ( )] ( )cos[ ( )] 4( 1) (1 ) 2( 1) 4 ( 1) cos[ ( )] ( ) sin[ ( )] , (1 ) 1 { } A c c A c A K x t p k k t x d k k t x d i t x d k k i t x d (17) 1 21 1 21 21 1 21 21 1 0 1 1 21 21 1 0 2 1 ( , , ) ( )cos[ ( )] ( )cos[ ( )] 4 (1 ) 2 4 ) cos[ ( )] ( ) sin[ ( )] , (1 ) 1 { } A c c A c A K x t p k k t x d k k t x d i t x d k k i t x d (18) 2 22 1 22 22 1 22 22 1 0 2 1 22 22 1 0 2 1 ( , , ) ( )cos[ ( )] ( )cos[ ( )] 4 (1 ) 2 cos[ ( )] ( ) sin[ ( )] , (1 ) { } A c c A c A K x t p k k t x d k k t x d t x d k k i t x d (19) 1 4 2 3 2 1 1 2 11 12 3 2 1 4 3 2 1 4 , , E J E J E J E J i i k k J J J J J J J J (20) 1 4 2 3 2 1 1 2 21 22 3 2 1 4 3 2 1 4 , , FJ F J F J FJ i i k k J J J J J J J J (21) 3 4 1 1 4 4 3 1 3 1 1 1 3 4 3 4 3 4 3 4 , GEF EF GEF FE J G E F FE E F FE (22) 4 3 2 3 2 3 4 2 2 4 2 2 3 4 3 4 3 4 3 4 , GEF FE GEF EF J G E F FE E F FE (23) 3 1 3 1 4 1 1 4 3 3 4 3 4 3 4 3 4 1 , E F FE E F EF J E F FE E F FE (24) 3 2 3 2 4 2 2 4 4 3 4 3 4 3 4 3 4 1 . E F FE E F E F J E F FE E F FE (25) and ( , 1,2) ijc k i j are the complex conjugates of . ij k The solutions of the singular integral equations Eq.(15) are [14] 2 2 1 1 2 2 ˆ ( , ) ( , ) / 1 , ( , ) ( , ) / 1 . g u p G u p u g u p G u p u (26) The stress intensity factors in Laplace domain can be defined as 1 1 1 1 0 1 1 2 2 ˆ ( , ) lim 2( ) ( ,0) ( ) / 2 ( 1, ), 1 a I y y x a e K a p a x x b a G p (27) 1 1 1 1 0 1 1 2 2 ˆ ( , ) lim 2( ) ( ,0) ( ) / 2 (1, ), 1 b I y y x b e K b p x b x b a G p (28) 1 1 1 1 0 1 1 1 2 ˆ ( , ) lim 2( ) ( ,0) ( ) / 2 ( 1, ), 1 a II x y x a e K a p a x x b a G p (29) 1 1 1 1 0 1 1 1 2 ˆ ( , ) lim 2( ) ( ,0) ( ) / 2 (1, ). 1 b II x y x b e K b p x b x b a G p (30)
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