Issue 49

B. G. N. Muthanna et alii, Frattura ed Integrità Strutturale, 49 (2019) 463-477; DOI: 10.3221/IGF-ESIS.49.44 472 where  is the Poisson’s ratio. K eq for crack orientation angle  = 90° is higher than K I , 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. 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. 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 was obtained for  = 90° while K II 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: 2 2 2 I II III IC IIC IIIC K K K C K K K                         (3) 0 20 40 60 80 100 30 40 50 60 70 80 90 100 110 120 R i = 298.45 mm t = 12.7 mm  = 500 mm P = 7 MPa K eq (MPa.m 0.5 ) angle crack orientation  (°)  = 90°  = 45°  = 0° 0 20 40 60 80 100 120 140 160 180 30 40 50 60 70 80 90 100 110 120 130 140 Stress intensity factor K I (MPa.m 0.5 ) crack-tip angle  (°) 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