PSI - Issue 72

Taras Dalyak et al. / Procedia Structural Integrity 72 (2025) 13–19

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0   in formulas (7), we obtain a solution to a similar problem

It is worth noting that by formal substitution

without taking into account the contact of the crack edges. The asymptotic expression for the contact reaction at closed crack edges is as following:

   

   

   

   ( 3 1 2 )(2

)

 16(1 ) 3 2   

4 1

 (1 ) | | m  

4 1

2

 32(1 )      2 0 0





  

  

  

4 

( ) 6 

 2

0 2

0

.

( , 0)

  1

t

O

N t y











1

h





3.2 Numerical Analysis The numerical solution of problem (5), (6) is constructed by the mechanical quadrature method (Savruk (1981b)). Fig.2 shows the graphical dependences of the intensity factors of forces ( | ), 1,2 (|    l i K hK m i i  ) and moments ( ), 3,4 (    K K m l i i i  ) on the parameter  , obtained for 0.3   . The solid curves indicate the numerical results, the dashed curves correspond to the asymptotic dependences (7).

Fig. 2. Dependencies of membrane forces and bending moment intensity factors on the relative position of defects

As can be seen from these graphs, the contact interaction of the crack edges leads to a significant decrease in the moment intensity factor 3 K and to the appearance of non-zero membrane force intensity factor 1 K . When the cracks get closer (with increasing  ), the stress concentration ( 1 3 , K K ) near their tips increases in the lack of the