PSI - Issue 33

I.A. Evstafeva et al. / Procedia Structural Integrity 33 (2021) 933–941 Author name / Structural Integrity Procedia 00 (2019) 000–000

934 2

addressed by Butusova et al. (2020), Mróz et al. (2018), Poluektov et al. (2018), Shuvalov and Kostyrko (2021)). According to a number of experimental observations, the rate of mechanochemical corrosion is often proportional to mechanical stress (Dolinskii (1967), Pavlov et al. (1987), Petrov et al. (1987)) and is exponentially dependent on temperature (Naumova and Ovchinnikov (2000)). Linear dependence of corrosion rate on stress may also be considered as an approximation of the exponential dependence proposed by Gutman (1994) – see Elishakoff et al. (2012). In general case, durability of pressure vessels under mechanochemical corrosion conditions is mostly assessed using numerical calculations (Naumova and Ovchinnikov (2000), Awrejcewicz et al. (2020)). However, several closed-form solutions have been obtained for the corrosion problems of thin-walled elastic shells under internal or external pressures, e.g. by Karpunin et al. (1975), Petrov et al. (1987), and Gutman et al. (1984, 2005). Being derived on the basis of the Laplace law for thin shells, these solutions do not reflect the difference in the elastic stresses through the shell thickness and the effect of the internal and external pressures (but only the difference between them). As shown by Pronina et al. (2015), this may lead to an essential under- or overestimation of the life of the shell. Pronina et al. (2018) proposed a closed-form solution – free of the mentioned drawback – for an elastic thin spherical shell under pressure without temperature taken into account. Solutions to corrosion problems for thick walled cylindrical and spherical vessels under pressure and different temperatures at the internal and external surfaces were obtained by Pronina (2011), Pronina and Sedova (2021), but in a rather cumbersome form. In the present paper, we propose new solution for a thin-walled pipe subjected to internal and external pressures of different media at different temperatures. This solution reflects the effect of the internal and external pressures (but not only their difference) and, at the same time, has a form as simple as the solutions for thin shells under pressures only, based on the Laplace formulas, only the constants being different.

Nomenclature 0 r

initial inner radius of the pipe initial outer radius of the pipe initial thickness of the pipe

0 R 0 h

r R ,

instantaneous inner and outer radii of the pipe, correspondingly

h

instantaneous thickness of the pipe

c R

middle radius of the pipe assumed to be constant

t

time

r p R p p 

internal pressure external pressure

r R p p  

r T R T

temperature of the internal environment temperature of the external environment

R r T T  

T  r a R a r m R m

corrosion rates of the unstressed material in the internal environment corrosion rates of the unstressed material in the external environment coefficient of mechanical activation of corrosion in the internal environment coefficient of mechanical activation of corrosion in the external environment

r  , R  coefficients of temperature activation of corrosion th r T threshold temperature for the internal environment th R T threshold temperature for the external environment ( ) r  circumferential stress at the internal surface of the pipe ( ) R  circumferential stress at the external surface of the pipe E  elastic stress component T  thermal stress component E Young’s modulus  Poison’s ratio  coefficient of thermal expansion