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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4.2. Effect of the distance between the neighbouring defects (Linearly elastic model) As noted above, the maximum stresses in all the considered geometries occurred between certain notches that almost touched or slightly overlapped. To investigate the effect of the distance between neighbouring defects, we considered the distances between the centres of the adjacent defects where the stress reached its maximal value, using the linearly elastic model. Here, the centre of a defect is the centre of the corresponding spherical surface (point A in Fig. 1). The distances between these notches were calculated for each geometrical model. The average distances calculated for each number n of defects (average over five geometries for each n ) are denoted by d . The global average value over them is average d  9.6 mm. For all the considered defects (where the maximum stress was observed), the distance to the nearest notches (between their centres) was close to average d . Average distances d between the centres of the defects with maximum stress value are demonstrated in Fig. 5 for different numbers of n . The red points mark the distances averaged over five geometries used for each n ; the black line shows the global average distance average d between defects where the maximum stress appeared. At the same time, the maximum stress was not always observed when the distance to adjacent defects was close to average d . There were situations, when the distance between two defects was very close to average d , nevertheless the maximum stress was observed in a different location of the same geometrical model. That is, there is no reliable causation between the distances between two adjacent notches and the stress increase. Thus, we can see that the distance between the defects is important, though not the only factor affecting the stress concentration in a vessel. The mutual arrangement of all the defects on the surface must be taken into account. It could be concluded that the stresses depend on the entire distribution of notches over the surface. In most cases, maximum stresses generally occur on the edge between adjacent defects. Geometries with notches uniformly (or periodically) located along the equator of the sphere were also built. In this case, the distances between all the centres of all the defects were equal and depended on the number of the defects and geometric parameters of the sphere and notches. Figure 6 shows the dependence between the maximum relative stress K and the distance d between adjacent uniformly located notches. Maximum relative stress occurred in the vessel for geometry with the distance between the centres of neighbouring defects d = 10 mm. This distance corresponds to n = 222 defects.

Fig. 6. The maximum relative stress K depending on the distance d between adjacent defects. Uniform arrangement. Linearly elastic model