Issue 44

V. Reut et alii, Frattura ed Integrità Strutturale, 44 (2018) 82-93; DOI: 10.3221/IGF-ESIS.44.07

  0,

 

  ,

  ,









y   

u y

v y

u a y

v a y

(1)

0, 0,

0,

0,

0,

0









( , ) x u x y u x y  , ,

( , ) y v x y u x y  are the displacements that satisfy the Lame’s equilibrium equations ,

here

2

2

2

 





   

   

u x y

u x y

v x y x y u x y x y

( , )

( , )

( , )

1 1 1 1

2







0

     

2

2



1   





x

y

(2)

2

2

2







v x y

v x y

( , )

( , )

2

( , )







0

2

2



1   





x

y

where   is the Muskchelishvili’s constant. Two cases of the boundary conditions on the short edge are considered. In the first case (Fig. 1) the semi-strip is loaded at the edge 1 0, 0 y x a      1 ( , 0) , ( , 0) 0, 0 y xy x p x x x a       (3) 3 4  

1 0, y a x a   

and conditions of the slide contact are executed at the segment

( , 0) 0, 

( , 0) 0, xy x  

a x a  

v x

(4)

1

Figure 1 : First case: geometry and coordinate system of the problem.

Figure 2 : Second case: geometry and coordinate system of the problem.

0, 0 y x a   

In the second case (Fig. 2) the semi-strip is loaded at the edge

 



( , 0) x p x 



( , 0) 0, x 

 

x a

(5)

,

0

y

xy

, c x c y B    the crack is situated

At the segment 0

1

     , u x B u x B v x B v x B     0 , , 0 , 

 0     0 

 u x B ,



  x







   

c

x c x c

0,

1

0

1

(6)

  x

 v x B ,









c

0,

2

0

1

84