Issue 50

I. G. F. Silva et alii, Frattura ed Integrità Strutturale, 50 (2019) 46-53; DOI: 10.3221/IGF-ESIS.50.06 50 Figure 1 : Leakage rate curves versus crack size. Elastic-plastic J-integral analysis After defining the leakage crack size (L Q ), the elastic-plastic J-integral analysis was applied to verify the stability of the crack. Initially, this check consisted of the calculation of applied J-Integral according to Eq. 1 [16]. When it is smaller than J IC , the crack growth does not occur, but if it is equal to or greater than J IC , the tearing is initiated. n 1 2 2 b 0 0 1 3 2 0 f M θ M J  ασ ε πR 1 H π M R t E                 (1) Two applications of the elastic-plastic J-integral analysis were performed for each of the evaluated materials, called Case 1 and Case 2, defined according to the LBB application methodology. In Case 1, the verification considered the crack size of 2L Q and normal operation loading plus SSE. In Case 2, the verification considered the crack size of L Q and excessive loading. Tabs. 5 and 6 present the details of the calculation for Case 1 and 2, respectively. Material θ [rad] t [m] R [m] M [Nm] M 0 [Nm] f b H 1 J 1 [J/m 2 ] SA-508 Cl. 3 1.6871 0.02857 0.12224 55942 117760 3.4603 0.6792 38672 SA-106 Gr. B 1.6948 0.02857 0.12224 55942 61148 3.7450 1.0480 57352 SA-376-TP304 1.2256 0.02857 0.12224 55942 77742 1.5553 1.4880 65616 Table 5 : Details of the calculation of applied J-Integral for Case 1. Material θ [rad] t [m] R [m] M [Nm] M 0 [Nm] f b H 1 J 2 [J/m 2 ] SA-508 Cl. 3 0.8435 0.02857 0.12224 79102 377275 0.6041 0.6500 13486 SA-106 Gr. B 0.8474 0.02857 0.12224 79102 197998 0.6465 0.9410 14308 SA-376-TP304 0.6128 0.02857 0.12224 79102 148949 0.3647 1.0560 24803 Table 6 : Details of the calculation of applied J-Integral for Case 2. The safety margin was defined as the ratio between J IC and applied J-Integral, where M 1 corresponds to the safety margin for Case 1, and M 2 corresponds to the safety margin for Case 2. The performance evaluation of materials for elastic-plastic J-integral analysis was based on the values of these safety margins. Figs. 2 and 3 present the safety margin M 1 and M 2 , respectively, for each of the evaluated materials.