PSI - Issue 81

Ivan Shatskyi et al. / Procedia Structural Integrity 81 (2026) 240–243

242

To investigate the effect of a flexible coating on the strength of a shell with a through crack, we used a cut model with hinged joined edges and the method of singular integral equations, as it was developed in the works of Shatskyi et al. (2018, 2019). Based on the small parameter method, approximate asymptotic formulas were obtained for estimating the strength of a cylindrical shell with a flexible coating in the vicinity of a defect according to two (for shell and for coating) strength criteria. In particular, for the case when the flexible coating is applied to the inner surface of the cylindrical shell, the expressions (3) determine the limit internal pressure of the restored pipe according to the crack resistance of its material. It means the pressure value when the crack starts to grow:

   

2

2

   

   

  

K

 3(1 ) 2(3 2 )   

  64 7 10

 96 5 37

 16 1 5

 R h l c

  

 



  

  

  

2

8 0

1

.

(3)

1

3(1

)

ln

p

  3













2

  3 2

Correspondingly, the expression (4) determines the limiting internal pressure of the restored pipe according to the coating strength criterion when the bandage starts to be destroyed:

2

   

   

  

h

0  

 3(1 ) 2(3 2 )   

 1 3(1 )   

 3 1 11

  

 



  

  

  

cov

.

(4)

[ ] 

1

 (2 ) 

(1 5 )ln 

p

  4





 

cov

2

16 48

8

R

  3 2

cov [ ]  – are the ultimate tensile strength for pipe and composite patch materials, respectively; c K 1

In formulas (1) – (4) [ ]  ,

2

) /( ) l Rh  2 2

, thus for fixed R , h ,  and variable l ,  is practically the

– is the critical stress intensity factor;

12(1   

ln 0  

... 0,5772

parameter of the crack length;  – is Poisson ’ s ratio,

– is Euler's constant.

3. Results and discussion We conducted the comparative strength analysis of intact, damaged, and restored pipelines with the following geometrical and mechanical parameters. For the structural steel pipe: 57 10 m 3    D , 5 10 m 3    h , ( )/2 25 10 m 3      R D h , [ ] 360 10 Pa 6    , 2 10 Pa 11   E , 0.3   , 6 1 100 10   c K Pa∙m 1/2 . For the bandage patch: 1 10 m 3 cov    h , [ ] 10 10 Pa 6 cov    . After carrying out the appropriate calculations using the above parameters, we constructed graphical dependencies of the limit values of internal pressure i p  , (i = 1, 2, 3, 4) on the defect length according to formulas (1) – (4), as shown in Fig. 2.

Fig. 2. Dependences of the limit values of internal pressure on the half-length of the defect: 1 – defect-free pipe, 2 – pipe with a crack, 3 , 4 – restored cracked pipe.

Here, the limit pressure for the pipe without defects is constant 76.6 *1  p MPa. As can be seen from the asymptotic lines 2 and 3, the critical pressures calculated using crack resistance criteria for unrepaired and repaired pipes decrease with increasing defect length, as expected. However, for longer defects ( 20  l mm), the small by assumption parameter  becomes quite large,