Issue 49

B. G. N. Muthanna et alii, Frattura ed Integrità Strutturale, 49 (2019) 463-477; DOI: 10.3221/IGF-ESIS.49.44 474 L r =  θ θ,max /  0 (7) with  0 =  y +  ul /2 (8)   y is the yield stress,  ult the ultimate stress. In FAD, failure is given by the following condition; if the assessment point of coordinate * * [ , ] r r L k is under the failure curve given by the following equation , = ሺ , ) where the subscript c indicates critical condition , the structure is safe. If the assessment point is above the curve, failure occurs. Fig. 16 represents the Failure Assessment Diagram for elbow and straight pipe for different value of relative depth crack ratio (a/t) in the range 0.1 - 0.8. Values of fracture toughness take into account the constraint effect [29, 37]. Constraint is defined by T stress [38] and determined by the Stress Difference Method [39, 40]. Material Failure Master Curve (MFMC) expressed the dependence of fracture toughness with effective critical constrain , . For pipe steel, MFMC has been determined by Eqn. 9 where it obeys a linear relationship , ,0 IC ef C IC k aT K   (9) where a is equal to -0.069√m and K IC,0 is the reference fracture toughness for T ef,c =0 andK IC,0 =77.28 MPa√m. For a straight pipe, a value of K IC =116.6Mpa√m was obtained and corresponds to a low constrain which has generally encountered in a pipe submitted to internal pressure. For elbow, the value of fracture toughness was reduced to K IC,0 =95 Mpa√m due to a higher constrain. Evolutions of assessment points for different relative crack depth ratios are reported in FAD for straight pipe and elbow with same pressure, diameter and thickness in Fig. 16. It is noted that due to stress amplification and higher constrain, the assessment points for the same defect size is located with higher ordinates. Critical defect sizes are defined when evolution curves cross the failure curve. For elbow, the relative critical defect depth is (a⁄t=0.28), which is higher for a straight pipe (a⁄t=0.66). Assessment points for elbow and below failure are located in the brittle zone of the FAD. This is proving the use of a linear behavior for computing SIF. This assumption is not valid for a straight pipe but it is given here for comparison. Figure 16: Failure Assessment Diagram for straight pipe and elbow Evolution of assessment points with relative crack depth (a/t=0.1 – 0.8) and (K IC =95 and 116.6 Mpa.m 0.5 )