PSI - Issue 28

L.A. Igumnov et al. / Procedia Structural Integrity 28 (2020) 2086–2098 L.A. Igumnov, I.A. Volkov/ Structural Integrity Procedia 00 (2019) 000–000

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As a result of the numerical analysis it was found that, in all the versions of the analyses conducted, the second stage (holding), accompanied by intensively developing creep strains and growing defects, proved to be the most important one from the viewpoint of long-term strength. In particular, it was found that, for p 2 ≤ 1.3 MPa (in the version of the temperature field shown in Fig. 7a) and p 2 ≤ 0.6 MPa in the version of the temperature field (Fig. 7b), at time t > 5 hour in the first version of the analyses and t > 57 hour for the second one, the creep strain rate in the zone of maximal loading of the reactor vessel, located in the zone of the apex of the elliptical bottom, proved to be close to zero. For pressures p 2 ≥ 1.3 MPa in the first version of the analyses and p 2 = 0.6 MPa in the second one, deformation of the reactor vessel under a loading effect was accompanied by an intensive change of form due to progressive creep of the material in the central part of the elliptical bottom. Figure 11 depicts stress intensity distribution over the cross-section of the reactor vessel for p 2 = 1.5 MPa at different times for the temperature field version (Fig. 7a), whereas Fig. 7 shows the same for p 2 = 1 MPa for the temperature field version presented in Fig. 7b. Numerical analysis of the stress field of the facility reveals the fact that the zone of maximal loading, from the viewpoint of stress intensity values, displaces with time, and at T = 111.5 min (for the first version of the analysis) and at T = 126.4 min (for the second one), when the growth of creep strains in the central part of the elliptical bottom leads to the loss of carrying capacity of the vessel (nucleation of a macrocrack), it is localized on the external surface in the vicinity of the region where the cylindrical sidewall transfers to the elliptical bottom of the reactor vessel. Figure 13 presents the inelastic strain intensity distribution over the cross section of the vessel at different times for p 2 = 1.5 MPa and the temperature field (Fig. 7a), and Fig. 14 illustrates the same for p 2 = 1 MPa and temperature field (Fig. 7b). It is evident that, in contrast to the results presented in Figs. 11 and 12, the most “critical” zone (that with the highest level of creep strain intensity) is located in the central part of the elliptical bottom of the reactor vessel, where damage accumulation processes are the most intensive. The damage degree distribution over the reactor vessel cross section at the time of nucleation of a macrocrack for the first version of the analysis is shown in Fig. 15, and for the second one in Fig. 16. It can be seen that a macroscopic crack for both versions of the analysis nucleates in the central part of the elliptical bottom in the vicinity of the median surface of the structural element (in Figs. 15 and 16, the part of the zone where a macrocrack nucleates is shown separately). Analysis of the obtained numerical results reveals the following characteristic laws of the deformation process of the NPP reactor vessel:  for the version of the temperature field depicted in Fig. 7a, the limiting value of pressure p 2 , not resulting in the nucleation of a macrocrack according to the long-term strength mechanism must not exceed p 2 = 1.3 MPa, whereas for the temperature field in Fig. 7b this value is p 2 = 0.6 MPa;  the numerical results of determining limiting values of pressure, obtained in the present work, agree with those published in (Semishkin V.P. et al. (2007)). Thus, the present numerical analyses and their comparison with the available experimental data make it possible to conclude that the developed defining relations of MDM adequately accounts for the degradation of structural materials according to the long-term strength mechanism and can be effectively used for evaluating long-term strength of materials and structures. In general, when analyzing the obtained numerical results, it can be noted that the developed model of MDM qualitatively and quantitatively describes the main effects observed in nonstationary creep of structural materials (metals and their alloys) and the degradation of initial strength properties of materials according to the long-term strength degradation mechanism. 4. Conclusion A mathematical model of MDM has been developed, that describes processes of complex viscoplastic deformation and damage accumulation in structural alloys affected by fatigue and creep. The model developed makes it possible to account for.