7 . ) ) 2( (4 4 ( 1) ( 1) ) 2 ) ( (1 ) ) 2(1 )( ) 2( 1) 2 ( 1) ( )( 1) ( ( ) ( 1)( 1)( , ) ) 2( (4 4 ( 1) ( 1) ) 2 ) ( (1 ) 2( 1) )( ) ( ) 2( 1) 2 (1 )( 1) ( ( ) ( 1)( 1)( 1 1 2 1 1 2 1 1 1 2 4 1 1 1 2 6 3 1 4 2 1 2 1 2 1 1 1 3 2 2 1 2 1 2 1 1 1 3 2 2 1 2 1 3 2 1 2 2 2 1 1 2 1 1 2 1 1 1 2 4 1 1 1 2 6 3 1 4 2 1 2 1 2 1 1 1 3 2 2 1 2 1 2 1 1 1 3 2 2 1 2 1 3 1 1 2 2 1 R R R R R R R R R R R R A X R R R R R R R R R R R R A X (22) Furthermore it is deduced from Eqs. (2) and (13)1 that the mean stress is linearly distributed within the interphase layer as , ) ( 1)( ) 2( 1) )( 8( ) 2( 1) )( 8( , ) ( 1)( ) 2 ( 1) )( ( ( ) 2 1 2 1 1 2 2 2 1 2 1 2 1 1 1 1 1 2 1 2 1 1 1 2 2 1 2 1 1 2 2 1 2 1 2 1 1 1 2 R R R X y R R X x R R z R R R R R X X z yy xx 2 z S (23) By making use of Eqs. (16) and (17), 3( ) and 3( ) in Eqs. (14) and (15) can be re-expressed into , ) ( 1)( 1)( ) ( ) (4 4 ( 1) ( 1) (1 ) 2 ) 2 ( 1) )( ) ( ) 2 ( 1) 2 (1 )( 1) ( ( i ) ( ( ) 2 2 1 2 1 3 1 2 1 1 2 6 1 2 1 1 2 1 1 1 1 1 2 4 1 3 4 2 1 2 1 2 1 1 1 3 2 2 1 2 1 2 1 1 1 3 2 2 2 1 2 3 R R R X R X R R R R X X R R R X X R A A ) ( 2R (24) , ) ( 1)( 1)( ) ( ) (4 4 ( 1) ( 1) ) 2 ( ) 2 ( 1) )( ) ( 2 ( ) 2 ( 1) )( ) ( ( ) ( 1) ( 1)( 1)( 2 ) 2 ( i ) ( ( ) 2 2 1 2 1 3 1 2 1 1 2 6 1 2 1 1 2 1 1 1 1 1 2 4 1 3 3 1 2 1 2 1 1 1 3 3 2 2 1 2 1 2 1 1 1 3 2 3 4 2 2 2 2 1 2 1 3 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 3 R R R X R X R R R X X R R R X X R R R R R R R R B B ) ( 2R (25) where the two complex constants and are defined as ) 2 ( 1) . )( 1) ( ) 2 ( 1) ( )( 2 ( 1) ( ) ( ) (4 4 ( 1) ( 1) ( 1) 2 ) , ( ) (4 4 ( 1) ( 1) (1 ) 2 ) 2 ( 1) )( ) ( ) 2 ( 1) 2 (1 )( 1) ( ( 1 2 1 2 1 1 1 3 2 1 2 1 2 1 1 1 3 2 2 1 1 2 6 1 2 1 1 2 1 1 1 1 1 2 4 1 3 4 2 1 1 2 6 1 2 1 1 2 1 1 1 1 1 2 4 1 3 4 2 1 2 1 2 1 1 1 3 2 2 1 2 1 2 1 1 1 3 2 R R X X R R X X R R X R X R R R X R X R R R R X X R R R X X (26) It is found that 3( ) and 3( ) given by Eqs. (24) and (25) are analytic outside the circle R2 (in
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