Issue 49

B. G. N. Muthanna et alii, Frattura ed Integrità Strutturale, 49 (2019) 463-477; DOI: 10.3221/IGF-ESIS.49.44 473 Failure condition is given by C=1, K I  , K II  and K III  are applied in elbow at critical zone for mode I, II and III K IC , K IIC and K IIIC are the fracture toughness of three modes equal to 116.6, 116.6 and 67.27 MPa √ m respectively for API X52 pipe steel. In steel; K IC = K IIC (4) And where the equation of calculation K IIIC is given by as follow C IIIC IIC C k K    (5) where  c and  c are critical shear and normal stresses. Fig. 15 gives an evolution of fracture condition C for different crack orientations under the same internal pressure and for a relative crack depth a/t =0.5. Figure 15: Evaluation of fracture condition equation with crack orientation C=f(θ) Fracture condition is fulfilled for crack orientation in the value range of θ from 32.52° to87.66° for semi-elliptical crack front position (  P ARTICULAR F AILURE A SSESSMENT D IAGRAM (FAD) USE FOR E LBOW CRACK DEFECT n order to analyze the behavior of elbows failure the task of Failure Assessment Diagram was focused on the determination of stress intensity factors which was examined depending the critical crack depth ratios at a critical position and a critical angle. In the case that the stress intensity factors was not enough to show the critical zones along the propagation of the cracks in the elbow, the FAD becomes a necessary step to predict the crack zones depending on three zones: the security zone, the safety zone, and the failure zone. The assessment of elbow defect harmfulness is made using Failure Assessment Diagram (FAD). FAD presents defect loading conditions in a graph where the non-dimensional crack driving force k r is plotted versus non-dimensional applied stress L r . Due to a mixed mode loading, the non-dimensional crack driving force k r is defined as the ratio of maximum equivalent stress intensity factor, K eq,max , to the fracture toughness of material in mode K IC . k r =K eq /K Ic (6) Here in this particular FAD Non-dimensional load L r is defined as the ratio of maximum circumferential stress   max and flow stress  o : 0 10 20 30 40 50 60 70 80 90 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4  =87.66°  =32.52°   K IC =116.6 MPa.m 0.5 K IIC =116.6 MPa.m 0.5 K IIIC =67.27 MPa.m 0.5 C=1 C=(K I /K IC ) 2 +(K II /K IIC ) 2 +(K III /K IIIC ) 2 Crack orientation  (°) a/t=0.5  =75°  =90° I