PSI - Issue 33

D.D. Okulova et al. / Procedia Structural Integrity 33 (2021) 1055–1064 Author name / Structural Integrity Procedia 00 (2019) 000–000

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For more detailed analysis of the observed feature, geometries of the sphere with only two notches were built. We considered the values of the distance between these two defects’ centres in the range containing average d : between 4 mm and 13 mm. Maximum relative principal stress and von Mises stress were calculated depending on the distance between defects observed in geometries with two notches (Fig. 7) . As seen from Figure 7, as the distance between defects’ centres increases, the stresses change non-monotonically. Firstly, when the distance between two notches’ centres is small enough (4–5 mm), the maximum relative principal stress is close to its value observed in the presence of only one defect ( 0 K = 36.6). This is explained by the fact that for these geometries, the notches strongly overlap and do not form a sharp edge; the maximum stresses, in this case, are observed at the bottom of them. Then, as the centres of the notches move away from each other (up to a certain distance), the edge between them becomes sharper and the stresses increase up to a certain value. In these cases, the stresses reach their maximum values on the edge between the defects. After reaching the maximum, the stresses K drop sharply and then tend to the stress value corresponding to a single notch. Maximum relative stress in the shell with two defects was observed at a distance about 10.1 mm between the centres of the defects. The analysis shows that for randomly distributed defects the average distances d between the centres of the defects where the maximum stress value was observed (Fig. 5) are very close to the “critical” distance between adjacent uniformly arranged defects (Fig. 6) as well as to the distance providing the maximum stress in the vessel with two defects (Fig. 7).

Fig. 7. The maximum relative principal stress and the maximum relative von Mises stress depending on the distance between defects at n = 2. Linearly elastic model

5. Conclusion The paper presents an analysis of stress concentration caused by multiple nearly hemispherical defects located randomly on the outer surface of a spherical vessel along its equator, under internal pressure. Finite element analysis of the stress state in the vicinity of defects in the framework of pure elastic and elastic-plastic models is carried out. The analysis allows to formulate the following conclusions: