PSI - Issue 59

Ihor Dmytrakh et al. / Procedia Structural Integrity 59 (2024) 74–81 Ihor Dmytrakh et al. / Structural Integrity Procedia 00 (2024) 000 – 000

79

6

2c

t

a

p

d

D

a

2c

Fig. 5. Model of crack-like defects in pipeline’s wall as semi -elliptical cracks with different a / c ratio.

Three different cases of defected pipes were considered, namely (see Table 2): the pipe with a longitudinal semi elliptical crack at outer surface (1), the pipe with a longitudinal semi-elliptical crack at inner surface (2), and the pipe with a circumferential semi-elliptical crack at inner surface (3). The corresponding relations for calculation of the stress intensity factors were taken from Dmytrakh et al. (2012). Based on the threshold Δ K th and critical Δ K fc stress intensity factors (Table 1) and using the formulae for calculation of stress intensity factors (Dmytrakh et al. (2012)), the corresponding values of threshold a th and critical a fc crack depth were calculated for these considered cases. Using the values of threshold a th and critical a fc crack depth in the formula (3), the residual durability N f of defected pipelines was calculated. These results are presented as the dependences of N f on the hydrogen concentration C H in metal for pipelines of both sizes which contain the different types of defects (Figs. 6 and 7). Table 2. Schemes of defected pipes. 1 2 3

Note: a is a crack length; 2 c is the crack width; R i is the internal radius of the pipe; t is the thickness of the pipe wall; p is the internal pressure. a b c

a/c=0,25 a/c=0,50 a/c=0,75

a/c=0,25 a/c=0,50 a/c=0,75

700000

120000

120000

a/c=0,25 a/c=0,50 a/c=0,75

Степенной (a/c=0,25) Степенной (a/c=0,50) Степенной (a/c=0,75)

600000

Степенной (a/c=0,25) Степенной (a/c=0,50) Степенной (a/c=0,75) 500000

100000

100000

Степенной Степенной Степенной

80000

80000

y = 31734x -0,3115 R 2 = 0,8568 y = 42322x -0,3131 R 2 = 0,86 200000 300000 400000

y = 29562x -0,3122 R 2 = 0,8582 60000

3

60000

3

y = 29386x -0 R 2 = 0,987 y = 65794x R 2 = 0,99

N f , cycles

N f , cycles

N f , cycles

2

2

y = 39356x -0,3134 R 2 = 0,8605 40000

40000

3

2

20000

20000

y = 57536x -0,3134 R 2 = 0,8605 100000

y = 53427x -0,3134 R 2 = 0,8604

1

y = 167745x R 2 = 0,98

1

1

0

0

0

0 1 2 3 4 5 6 C H , ppm

0 1 2 3 4 5 6 C H , ppm

0 1 2 3 4 5 6 C H , ppm

Fig. 6. Residual durability N f of pipeline ( D 1 =610 mm; t 1 =11 mm) versus hydrogen concentration C H in metal in the case of a longitudinal semi elliptical crack at the outer surface (a); a longitudinal semi-elliptical crack at the inner surface (b) and a circumferential semi-elliptical crack at the inner surface (c): 1 – a / c =0.25; 2 – a / c =0.50; 3 – a / c =0.75.