atw - International Journal for Nuclear Power | 04.2019

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atw Vol. 64 (2019) | Issue 4 ı April OPERATION AND NEW BUILD 218 | | Fig. 7. Allowable size for axial crack. 4.1.2 Circumferential cracks Fracture mechanics analysis (brittle failure): The circumferential cracks in all the risers of the jet pumps are under tension and bending. Both loading conditions have to be evaluated. Tension: The allowable length of a through thickness circumferential crack was evaluated with equation 1.1, vol. 1, pag 1-1 [16]. All the evaluation was carried on with Matlab code. The stress intensity factor was evaluated with the following equation. (12) This relation is valid when 0 < ≤ 0.55, 10 ≤ ≤ 20 and . The geo metrical factor is (13) (14) K I is the stress intensity factor. σ is the axial stress and depends on the mean radius R. P is the axial load, t is the thickness and θ is the mean angle of the crack. For the case of bending, (15) This relation is valid when 0 < ≤ 0.55, 10 ≤ ≤ 20 and (16) (17) K I is the mode I stress intensity factor, σ b is the bending stress and it depends on the mean radius, M is the bending moment and t is the thickness. θ is the mean angle of the crack and F b is a geometric factor. | | Fig. 8. Allowable size for axial crack, limit load of collapse. The maximum length of a circumferential crack was evaluated with loading conditions for the range of operation considered. Two analyses were carried out. In the first one, the two circuits (normal operation) of the Reactor Recirculation Core System were operating. In the second, only one of them was in operation (single loop operation). The results are summarized in the Figure 9. Again, Matlab coupled with Excel are applied to make the iterations. The results showed that the allowable crack length is reduced as the core flow core is augmented. This happens because of the hydraulic forces exacerbate the vibration of the riser and the jet pumps. As a result, fatigue should be considered. Limit load analysis (ductile failure): In this case, the cross section of the riser is under plastic collapse, the allowable length of a through wall crack is evaluated with the equation 1.2, Vol. 1, pag. 1-4 [16]. All the iterations were done with Matlab coupled with Excel. (18) (19) This equation is valid when ≤ 0.1 (20) M is the limit moment for plastic collapse, σ f is the flow stress, R is the mean radius, t is the thickness and θ is the mean angle of the crack. α is a geometrical factor. The results are summarized in Figure 10. In this case, the maximum allowable length of a circumferential crack was evaluated with an analysis of limit load under collapse conditions. These evaluations were carried out for a range of operations, which is between 95 % and 107 % of the output power. These evaluations considered the operation of either, one or two circuits of the Reactor Recirculation Core system. | | Fig. 9. Allowable size for circumferential crack, LEFM. | | Fig. 10. Allowable size for circumferential crack, limit load of collapse. It can be observed that the allowable circumferential crack length decreases as the flow of water increases. Under these conditions, the hydraulic loads generate more vibrations and fatigue. 5 Failure Assessment Diagram R6 This is a methodology that is widely used to evaluate the elasto-plastic failures in structural components. In general terms, the failure is determined by the interaction between ductile and brittle behavior of a material. The first versions were based on the “Strip-Yield” model. The Stress Intensity Factor for an infinite plate with a central crack through thickness is a methodology that is widely used to evaluate the elasto-plastic failures in structural components. In general terms, the failure is determined by the interaction between ductile and brittle behavior of a material. The first versions were based on the “ Strip-Yield” model. The Stress Intensity Factor for an infinite plate with a central crack through thickness is (21) This equation is asymptotic with respect to the yield strength of the material; thus, it has to be modified. It should be considered the flow stress, instead the yield stress, and the effective stress intensity factor has to be obtained. An adimensional relation is proposed for this purpose. The new relation is divided by the Stress Intensity Factor in mode I. Operation and New Build Failure Analysis of the Jet Pumps Riser in a Boiling Water Reactor-5 ı Pablo Ruiz-López, Luis Héctor Hernández-Gómez, Juan Cruz-Castro, Gilberto Soto-Mendoza, Juan Alfonso Beltrán-Fernánde and Guillermo Manuel Urriolagoitia-Calderón
atw Vol. 64 (2019) | Issue 4 ı April (22) In this equation, the square root of the semi-length is eliminated. In this way, it is independent of the geometry, as the strip model. In order to use an adimesional form, the following parameters have to be established. and The new equation is (23) This curve is the boundary between the safe and unsafe zones (Fig. 9). Fracture would take place when the Effective Stress Intensity Factor is bigger than the Fracture Toughness, K r > 1 On the other hand, ductile failure is expected if S r > 1. Also, it is important to observe that in the elastoplastic analysis, fracture and collapse are in interaction. The points defined by K r and S r have to be localized in the failure diagram so as to determine if they are in the safe or unsafe zones. The material hardening has not been considered in the “Strip-Yield” model. Therefore, this situation can be included in an elastoplastic analysis with the J-integral. The equation proposed by the British Standard BS 7910 is (24) The Failure Diagram shown in Figure 11 compares different failure curves. This was used in the evaluations, which were carried out in this paper. 6 Cases of analyses The allowable horizontal and vertical projections of a helicoidal crack in the riser were determined in the previous section. In this section, some cases have been postulated, as an example, in order to show the application of the evaluation of the structural integrity of the riser. 6.1 Circumferential cracks As an example, a circumferential crack at the weld of the riser was postulated. Its length was 4 inches. The reactor is in operation with the two loops of recirculation and 107 % | | Fig. 11. Diagram of evaluation of failure by plastic deformation. | | Fig. 12. Postulated case circumferential length of crack. | | Fig. 13. Failure Diagram R6. of the flow of the water flowing through the core. Initially, the evaluation was done in accordance with linear elastic fracture mechanics. The allowable crack length is 4.9 inches (Figure 9). The length of the actual crack is lower than this limit. So, this crack is acceptable. After this, the evaluation was done under the scope of the Collapse Limit Load analysis (Figure 10). The allowable crack length is 16.36 inches. The length of the actual crack is lower. Therefore, it can be accepted. This evaluation was complemented with the Failure Assessment Diagram. The following parameters were calculated: and . As this point is located within the safe zone. It is considered safe. However, this point is located close to the vertical axis in the zone in which a brittle failure can take place. So, this is the dominant failure mechanism, it is recommended to increase the inspection and to determine the remaining life because a brittle failure is undesirable (Figure 11 and 12). | | Fig. 14. Failure diagram, postulated case circumferential projection of crack. | | Fig. 15. Failure Assessment Diagram, Postulated case axial projection of crack. | | Fig. 16. Failure Assessment Diagram, Postulated case circumferential projection of crack. 6.2 Safe helical crack In this case, a helical crack close to the weld of the riser brace is postulated. Its length is 4 inches. Its projections along the circumferential and the axial axis are 3.5 inches and 1.94 inches, respectively. The output power of the reactor is 100 % and the two circuits of the RRC system have been in operation. Initially, the axial projection of the crack was evaluated. In accordance with Linear Elastic Fracture Mechanics, brittle fracture is developed, when the allowable crack length is greater than 11.689 inches (Figure 7). Regarding the ductile failure, the evaluation was done with the Collapse Limit Load analysis. The allowable crack length is 11.11 inches (Figure 8). It is greater than the axial pro jection of the crack. These results were evaluated with the Failure Diagram R6. The following parameters were calculated too. and , then they are localized in the diagram, Figure 13. In the case of the circumferential projection of the helical crack, it was evaluated against the brittle fracture with linear elastic fracture mechanics OPERATION AND NEW BUILD 219 Operation and New Build Failure Analysis of the Jet Pumps Riser in a Boiling Water Reactor-5 ı Pablo Ruiz-López, Luis Héctor Hernández-Gómez, Juan Cruz-Castro, Gilberto Soto-Mendoza, Juan Alfonso Beltrán-Fernánde and Guillermo Manuel Urriolagoitia-Calderón
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