Issue 49

D. E. Belhadri et alii, Frattura ed Integrità Strutturale, 49 (2019) 599-613; DOI: 10.3221/IGF-ESIS.49.55 603 specimen; (ii) general static ‘STEP’-option was used for analysis with ABAQUS; (iii) Automatic increment of steps was used with maximum increments number of 100. Minimum increment size was 10 −5 and maximum increment size was 1. Nevertheless, the ABAQUS solver code could override matrix solver choice according to the ‘STEP’-option. The Von Mises yield criterion is used to predict plastic deformation. Incremental plasticity theory is introduced to model the material nonlinearity. The FE simulations are carried out using the static general procedure to analyze this problem. R ESULTS AND DISCUSSION A) Evaluation of the failure mode: In this part, we will focus on the crack failure. Fig. 4 presents the variation of the stress intensity factors in mode I, II, and III as a function of normalized line of the crack front for an unrepaired cracked pipe. We note that the behavior of the SIF is non-linear and that there are three areas. Zone 1 is influenced by shear mode II, which gives importance to circumferential stresses; in zone II, K1 has larger values than K2 and K3 until the end of the crack comes the appearance of mode III but of low intensity. We conclude that 75% of the crack front is controlled by mode II, 20% by mode I and only 5% of the crack front for mode III. -10 0 10 20 30 40 50 60 70 80 90 100 110 -5 0 5 10 15 20 25 30 35 Normalized distance from the crack front K ( MPa.mm 0,5 ) zone 1 zone 2 zone 3 K I K II K III Figure 4: Variation of the SIF along the front of the elliptical crack for an unrepaired pipe (c = 60mm, a = 5mm). In Fig. 4, composite repair does not change the configuration. Fig. 5 shows the variation of the SIF along the crack front for a repaired pipe fig 3, indeed the Zone 1 is still controlled by K II but with more or less variable reductions for the three modes. To verify this reduction, each mode has been traced separately to quantify the rates of improvement knowing that these rates change from one crack to another. In what follows we will use the variables * K i (SIF*), which will represent the improvement provided by the repair where: * , , unrep rep i i i unrep i K K K i I II III K    (6) Fig. 6 (A) shows the distribution of the Mode I stress intensity factor along the crack front for a repaired and unrepaired pipe. There is a net reduction of the K I in the crack tip with a maximum of 46%, this fall of the SIF decreases as the front touches the edge of the pipe. In Fig. 6 (B) is shown the effectiveness of the repair expressed by K*, the latter confirms the Fig. (A) since it is clear that the efficiency decreases towards the edge of the crack. Crack front