Issue 50

M. Belhamiani et alii, Frattura ed Integrità Strutturale, 50 (2019) 623-637; DOI: 10.3221/IGF-ESIS.50.53 632 The FE limit results for plane strain pipe with extended inner axial crack Fig .1(a) are compared with Chell and Carter’s solutions Fig. 9. To avoid mesh problems associated with incompressibility, reduced integration elements within ABAQUS (element type CPE8R) were used in this case. To take into consideration the effect of the crack face, 50% of the internal pressure was applied in this case. In the same scope our results reach agreement with two models and it is more conservative than Chell’s model because the consideration of the internal pressure applied on the crack face. For a/t greater than 50% our results converge to Carter’s model. Figure 9 : Comparison of the FE limit results for plane strain pipe with extended inner axial crack with Chell’s and Carter’s solutions. Carter’s and Chell’s model are considered a plane strain analysis, another popular work which is Folias’s [30] and Erdogan’s [31] models investigate three dimensional problems. The dimensions and geometry for axial through-wall cracked pipes (Fig.1d) where Folias’s and Erdogan’s model was respectively given by Eqn. (11, 12): L m 2 y P R 1 = σ t 1+1.05σ (11)   1 0.614 0.87542 0.386exp 2.275 L m y P R t        (12) where: m c R t   (13) For the axial through-wall cracked pipes (Fig. 10) compares FEA solution with Folias’s and Erdogan’s models. this shows that this solution is more conservative than Folias’s solution if ρ<1,5 where it converges to Folia’s solution if ρ>1,5. Also, this figure validates our FEA model. for this we plot Fig. 11 which will present PLP* (equ. 6) with (c/t) to evaluate the efficiency of the repaired system toward the plastic collapse pressure. It is visible that the repaired system gives a high beneficial effect on the plastic collapse increasing the plastic limit load up to 220% for a crack length c/t=18. We can complement that in Fig. 11 the PLP* shows an exponential behaviour with crack geometry. To illustrate the efficiency of this repair system, Fig. 12 compares the plastic limit load for cracked pipes for the three models with a repaired pipe.