PSI - Issue 59

Roman Hrabovskyy et al. / Procedia Structural Integrity 59 (2024) 112–119 Roman Hrabovskyy et al. / Structural Integrity Procedia 00 (2024) 000 – 000

114

3

used to estimate the stress state and to determine the conditions of main gas pipelines fracture with the existing surface axial two-dimensional (crack-like) defects in the form of corrosion pit ( a / c =1/2.5) and corrosion furrows ( a / c =1/25). 3. Results and discussion Determination of the stress intensity factor value K I along the front of an axial semi-elliptical crack with the ratio of semi-axes a / c placed on the outer surface of a hollow cylinder under internal pressure was carried out using the dependence (Newman and Raju (1980)):

 2



2 2 а i  2 2 а i

  

   

R R R R

t

  a t

0.97

1 0.5   

1.07

I 1.1 0.35

×

;

(1)

K F

а    

a t

I с а K K 

a c



 

I

а

R

 

i

where σ are the tensile stresses; p is the internal gas pressure in the pipeline; t is the thickness of the pipe wall; R i = d /2 is the inner radius of the pipe; R a = R i + t – a is the distance from the pipe axis to the top of the semi-elliptical defect; a is the crack depth; 2 c is the length of the surface crack:

2

4

( ) M M a t 

( )

M a t

i pR t



1.65 1 1.464( ) Q a c   ;

1

2

3

F





;

;

Q

а с

1

0.89

 24

 14 1  

1 1.13 0.09  

M

0.5  

0.54  

M

a c

M

;

;

.

2

3

0.65

0.2

a c

a c





At that the known dependence is used (Rice (1968))

2

1

E 

2

,

(2)

J

K



1

1

where ν is Poisson ’ s ratio; E is the modulus of elasticity of the 1 st kind; the J-integral, which characterizes the plastic work of deformation and fracture, as well as the field of stresses and strains under elastic-plastic deformation in the vicinity of the crack tip (similarly to the stress intensity factor K I for elastic body) were determinate. The results are presented in Fig. 2. a b

Fig. 2. Calculated dependences of the fracture toughness J a changes at the tip of a semi-elliptical crack ( 1 – a / c =1/2.5; 2 – a / c =1/25) along the wall depth of gas pipes made of 17H1S (a) and 10H2BТ (b) steels.

In addition, the fracture toughness of the investigated 17H1S and 10H2BТ steels was determined experimentally. For this, five beam samples of rectangular cross-section (10 mm/t) (Table 1) with an edge crack with the length of l ≈ 0.5 t . The critical value of the J cr -integral was determined according to the method described in the Standard (GOST 25.506 – 85 (1985)) according to the scheme (Fig. 3) of the three-point bending.