Issue 48

T. Profant et alii, Frattura ed Integrità Strutturale, 48 (2019) 503-512; DOI: 10.3221/IGF-ESIS.48.48 507 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 ˆ ˆ ˆ 2 2 ˆ ˆ ; ; cos sin ; cos sin ; cos cos 2 ; cos sin ; cos sin ; cos 2 sin , XXX XYY XXY XXY YXX YYY YXY H X H H H H H H q q q q q q q q q q q q X =- + - - - + - X Ξ X Ξ X Ξ X Ξ X Ξ X Ξ (13) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 ˆ ˆ ˆ 2 2 ˆ ˆ ; ; cos sin ; cos sin ; cos 2 sin ; cos sin ; cos sin ; cos cos 2 , XXX XYY XXY YXY YXX YYY YXY H X H H H H H H q q q q q q q q q q q q X = - - + - + - X Ξ X Ξ X Ξ X Ξ X Ξ X Ξ (14) where 1 1 1 1 ˆ ˆ ˆ ˆ cos cos , sin sin , cos cos , sin sin R X R X R R a q a q a q a q é ù é ù = + + = +X +X ê ú ê ú ë û ë û X Ξ (15) and ( ) ( ) ( ) { ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n XXX n n n n n n n H n h k h k n h k p k g g g g ¥ - - - - - - = - - - - - - = Á Z - Z + + + Z - Z å X Ξ Z Z ZZ Z (16) ( ) ( ) ( ) { ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n XYY n n n n n n n H n h k h k p n h k p k g g g g ¥ - - - - - - = - - - - - - = Á Z - Z - - + Z + Z å X Ξ Z Z ZZ Z (17) ( ) ( ) ( ) { ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n XXY n n n n n n n H n h k h k n h k p k g g g g ¥ - - - - - - = - - - - - - = Â - Z + Z + + + Z - Z å X Ξ Z Z ZZ Z (18) ( ) ( ) ( ) { ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n YXX n n n n n n n H n h k h k n h k p k g g g g ¥ - - - - - - = - - - - - - = Â Z + Z + + + Z - Z å X Ξ Z Z ZZ Z (19) ( ) ( ) ( ) { ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n YYY n n n n n n n H n h k h k n h k p k g g g g ¥ - - - - - - = - - - - - - = Â Z + Z - - + Z + Z å X Ξ Z Z ZZ Z (20) ( ) ( ) ( ) { ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; . n n YXY n n n n n n n H n h k h k n h k p k g g g g ¥ - - - - - - = - - - - - - = Á Z + Z - - + Z + Z å X Ξ Z Z ZZ Z (21) The symbols { } . Â and { } . Á mean real and imaginary value of the complex expression. The dislocation is continuously distributed along the ˆ / x e -axis in the interval ( ) ˆ 0,1 X Î . This process is modelled by introducing the density of the Burgers vector ( ) ˆ ˆ Y B X and ( ) ˆ ˆ X B X , which is in relation with Burgers vector ( ) ˆ ˆ , X Y b b = b as follows ( ) ( ) ( ) ( ) ˆ ˆ ˆ ˆ ˆ ˆ d d ˆ ˆ , , ˆ ˆ d d Y X Y X b b B B X X X = X = X X (22)