PSI - Issue 47

Sergei Kabrits et al. / Procedia Structural Integrity 47 (2023) 513–520 S. Kabrits and E. Kolpak / Structural Integrity Procedia 00 (2019) 000 – 000

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Figure 2 on the right shows the stress distribution along the shell meridian at time t 2 when the thickness of the shell at its thinnest point is halved. Here, sig1 and sig2 denote the meridional and the circumferential stresses, correspondingly. Lettering "plus" refers to the stresses on the outer surface and the "minus" to the inner surface; σ * is a maximum allowable stress. For given corrosion kinetics constants, time t 2 = 72.69 years. Figure 3 on the left shows the graphs of the relative maximum stresses at the initial time, t = 0, (dashed lines) and at t = t 2 (solid line). On the right, thickness of the shell at t = 0, (dashed lines) and at t = t 2 (solid line) is plotted.

Fig. 3 The maximum relative stresses (left) and the thickness (right) at the initial ( t=0 ) and final ( t 2 ) time along the meridian.

As we can see, the stress concentration near the junction of the spherical and cylindrical elements of the same radii and thicknesses is relatively low and does not lead to a noticeable mechanochemical effect, at least at considered geometrical parameters – for thin shells. Therefore, the lifetime of such compound shells may be estimated by the analytical solutions for cylindrical shells of Pronina et al. (2015, 2018), especially when the criterion of the minimal allowable thickness is used. Add that the last solution also holds true for cases when both internal and external pressures are applied and, in contrast to the thin shell theory, it takes into account the pressure values themselves, but not only their difference. Our calculations revealed that in cases when the cylindrical and spherical shells have different radii, the maximum stress near the junction may rocket up to the strength limit, other conditions being the same. Therefore, the wall of the shell in the vicinity of junction should be thickened or the toroidal element should be used to smooth the junction. The second considered example is the calculation of the shell consisting of three fragments: a spherical part of radius R sph , a fragment of a torus of radius R tor which provides a smooth transition to a cylinder of radius R cyl (Figure 4). Here, R sph = 2 R cyl , R tor = 0.5 R cyl , h 0 =0.02 R cyl . Figure 4 on the right shows the stress distribution along the shell meridian at time t 2 when the thickness of the shell at its thinnest point is halved. The notations are the same as in Figure 2. Figure 5 on the left shows the graphs of the relative maximum stresses at the initial time, t = 0, (dashed lines) and at t = t 2 (solid line). On the right, thickness of the shell at t = 0, (dashed lines) and at t = t 2 (solid line) is plotted. As we can see, despite the smooth junction of the elements of different shapes, the stresses in the vicinity of junction fluctuate significantly. Nevertheless, the total mechanochemical effect in this case of double-sided corrosion is not very strong: the time t 2 in both the considered problems are close, in this case t 2 = 69.38 years. This is because of the fact that increase of the stress on the external surface is accompanied by the decrease of the stress on the internal one. In cases of one-sided corrosion, the situation may be different. Non-uniformity of the stress state may lead to local corrosion such as pittings. Interaction of multiple corrosion pittings is considered in the work of Okulova et al. (2023).