PSI - Issue 47

Alexander Ilyin et al. / Procedia Structural Integrity 47 (2023) 290–295 A. Ilyin and Y. Pronina / Structural Integrity Procedia 00 (2019) 000–000

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considered by Anguiano et al. (2022), Argatov and Chai (2020, 2022), Butusova et al. (2020), Javadi et al. (2020), Javanbakht and Ghaedi (2020), Kazemian et al. (2022), Kostyrko et al. (2019, 2020), Mróz et al. (2018), Shuvalov and Kostyrko (2021), Song (2020), Wee et al. (2022), Xia et al. (2021)). Most of the works devoted to mechanochemical corrosion of pressurized shells are focused on the study of pipes and spherical vessels (Gutman (1994), Gutman et al. (2016), Pronina et al. (2018), Sedova and Pronina (2022)). Unlike a circular cylinder under plane strain conditions, a toroidal shell under pressure has a non-uniform distribution of the circumferential stresses along the surface. It was first discussed by Dean (1939). Analytical solution for the membrane stress distribution in toroidal shell were presented by Audoly and Pomeau (2010), Rossettos and Sanders (1965), and Sanders and Liepins (1963). This work is devoted to assessment of the service life of a toroidal shell subjected to general non-uniform stress-assisted corrosion under internal pressure, without accepting the hypotheses of the theory of thin shells.

Nomenclature A

axis of revolution

distance parameter of the torus

R r i r o

initial inner radius of the torus cross-section

initial outer radius of the torus cross-section h(s, t) thickness of the shell at position s of the torus cross-section at time t p internal pressure σ 1 maximum normal stress at a corresponding point of the torus cross-section σ* maximum allowable stress h* minimum allowable thickness of the shell t* service life of the shell t time

2. Description of the problem Consider a linearly elastic isotropic thick-walled toroidal shell with constant outer radius r o (Figure 1), subjected to constant internal pressure p . Distance parameter R is the distance between the torus center (axis of revolution A) and the tube center.

Fig. 1. The geometry of toroidal shell

The torus is subjected to internal mechanochemical corrosion defined as a general dissolution of the material with a rate ν proportional to the maximum normal stress σ 1 at a corresponding point of the inner surface (1) (see Dolinskii (1967) and Pronina and Sedova (2021)). Here, a and m are empirically determined constants of the corrosion kinetics; ( , ) dh s t is an increment of the depth of the material dissolution in the radial direction during a time interval dt at a position s on the inner surface at time t . Here we consider moderately non-uniform wear when we can neglect the change in the normal to the corroding surface. 1 σ ( , ) s t ( , ) dh s t dt a m s t = + ( , ) ν =−