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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elements (see, for example, Dolinskii (1967), Gutman (1994), Pronina (2011, 2013), Elishakoff et al. (2012), Gutman et al.(2016), Sedova and Pronina (2015, 2016)). However, there are some works dealing with non-uniform corrosion. For example, Gutman et al.(2005), Pronina (2017), and Zhao and Pronina (2019) considered 2-D problems with some deviations from cylindrical symmetry; Awrejcewicz et al. (2020) investigated problems of corrosion of shallow shells and plates under complex loading. Sedova and Pronina (2022) made a comparative analysis of the service life of cylindrical and spherical vessels of different radii and thicknesses under the same pressures, in the frame-work of linear elasticity and without taking into account edge effects. However, junction of shells of different shapes causes strong non-uniformity of the stress state in the vicinity of junction, when internal and external pressures are not equal to one another. This may lead to acceleration of corrosion in places with high stresses and, thus, dramatically reduce the service life of the shell. Such problems should be investigated by the use of geometrically nonlinear shell theory. In this paper we consider the geometrically nonlinear problem of corrosion of compound shells consisting of cylindrical and spherical parts. In cases when their radii are not equal to one another, a part of a toroidal shell is used to connect them and provide the continuity of the curvature at the junction of the elements of different shapes.

Nomenclature Z

axis of revolution

initial mid- radius of the spherical element initial mid-radius of the curvature of the torus element initial mid-radius of the cylindrical element

R sph R tor R cyl

thickness of the shell meridian arc length

h s σ

maximum normal stress at a corresponding point of the shell

maximum allowable stress

σ* h*

minimum allowable thickness of the shell

time when the thickness of the shell at its thinnest point is halved

t 2

time

t

corrosion kinetics constants

a, m

2. Problem statement Consider a thin-walled shell of revolution, consisting of spherical, toroidal, and cylindrical shell elements (Figure 1), subjected to constant internal pressure p . Setting the radii of the sphere, torus, and cylinder, as well as the length of the cylinder, uniquely determines the geometry of the compound shell, provided that the angle between the normal to the median surface and the axis of revolution Z is continuous. The shell material is supposed to be linearly elastic. Geometrically nonlinear equations of axisymmetric deformation of shells of revolution are used to calculate the stress-strain state. The shell is subjected to double-sided mechanochemical corrosion defined as a general dissolution of the shell wall. According to Dolinskii (1967) and Pronina and Sedova (2021), the rate of mechanochemical corrosion, ν , may often be described by the following relations ( , ) ( ( , , ) ( ), , ) ( ), , ( , ) i o i i i i o o o o s dh s t dh s t s t a t s m s t a m d dt t t     = − = + = − = + (1) were a and m are constants determined from the experiments; ( , ) s t  is the maximum principal stress at a point s on the corresponding surface at time t ; sign m = sign  ; ( , ) dh s t − is a decrement of the shell thickness for time dt ; indices i and o refer to the inner and outer surfaces, correspondingly.