PSI - Issue 40

N.A. Makhutov et al. / Procedia Structural Integrity 40 (2022) 283–295

292 10

N.A. Makhutov at al. / Structural Integrity Procedia 00 (2022) 000 – 000

(13)

2/ (1 ) 

(1 )/ (1 ) for e e m m m m e    

K



 

e

n

n

y

2/ (1 ) for e e m     (14) The deformation concentration effect increases significantly ( ≤ ≤ 1,75 ) ) in the zone of increasing plastic deformation ( ≤ ≤ 20 ) for m values specified above. For pipelines with identified concentration of stresses the strength based on the local deformation criterion will be determined using expression similar to (1), (8), (9), (12), (13)-(15) where [ ] – permitted deformation; − deformation safety factor. In the pipeline strength verification calculations the safety margin n eu can be linked to regulatory strength margin in expression (1) using relation (11) 1/ m eu u n n  (16) As the nominal ( ) and local ( ) deformations increase in the identified concentration zone (for 1.1 ≤ ≤ 3) and margins of in 2.0 ÷ 2.2 range, the safety margins of are selected in 5 ÷ 10 range. If condition (16) is met, operation of the pipeline section being analyzed can be continued. For sections with identified non-penetrating cracks with dimensions ( ) and ( ) according to Fig. 3, it is recommended to conduct verification calculation based on criteria and equations of linear ( ) and non-linear ( ) fracture mechanics by Plyuvenazh (2019) ( ) ( ) ( ) ( ( )) / ( ) [ ] , IC Ie s n S s s s I k K K l f l K n             (17) e y K  max ( ) [ ] s e , u e eu e e n    (15)

K





ke P

( ) 

( ) S 

[ ] Ie K  

,

(18)

K

K



Iec

Ie s

I

n

ke where , – stress and deformation intensity factors for time τ S ; – nominal stresses in expressions (1) and (6); F( / ) − correction function, depending on , and а; [ ], [ ] – permitted stress and deformation intensity factors; , – safety margins for intensity and deformation factors; с, – critical stress and deformation intensity factors. Exponent of as material characteristic depends on level and is calculated using equation 2 0,5(1 )[1 / ] 1 n y ke m P m       

(19)

Expressions (18) and (19) in verification calculations are taken in the following intervals

(3 5)

(20)

u k ke n n n    