Issue 49

B. G. N. Muthanna et alii, Frattura ed Integrità Strutturale, 49 (2019) 463-477; DOI: 10.3221/IGF-ESIS.49.44

where  is the Poisson’s ratio. K eq , this indicates again that pure mode I is not obtained. Fig. 13 presents the equivalent stress intensity factor with the orientation  of semi-elliptical crack in different angular position  It shows that orientation of 90° has more efficiency for elbow pipeline. The influence of relative depth ratios (a/t) changing from 0.1 to 0.8 on stress intensity factors (K I , K II , K III ) is shown in Fig. 14 for a/t = 0.5. for crack orientation angle  = 90° is higher than K I

120

110

 = 90°  = 45°  = 0°

100

90

60 eq (MPa.m 0.5 ) 70 80

R

i = 298.45 mm

t = 12.7 mm  = 500 mm P = 7 MPa

K

50

40

30

0

20

40

60

80

100

angle crack orientation  (°)

Figure 13: Equivalent stress intensity factor versus relative crack orientation for different angular position (Elbow: internal radius Ri = 298.45 mm, wall thickness t = 12.7 mm, elbow radius  mm, P = 7 MPa, a/t =0.5). Due to the concentration of energy in the critical zones in the elbow, stress intensity factors in mode K I and K eq increase with relative crack depth ratios (a/t) as seen in Fig. 13 and 14.

100 110 120 130 140

I (MPa.m 0.5 )

a/t=0.1 a/t=0.2 a/t=0.3 a/t=0.4 a/t=0.5 a/t=0.6 a/t=0.7 a/t=0.8

30 40 50 60 70 80 90

Stress intensity factor K

0

20 40 60 80 100 120 140 160 180

crack-tip angle  (°)

Figure14: Stress intensity factor in mode KI versus angular position for different relative crack depth ratios (a/t)

The maximum equivalent stress intensity factor K eq is approximately negligible. Semi elliptical crack with different relative depths was examined at a critical position (  = 75°) and a critical crack angle (θ = 90°). A failure criterion for mixed mode of loading was used: was obtained for  = 90° while K II

2

2

2

I        IC    K K 

K K

K K

      

  





II

III



C

(3)

IIC

IIIC

472