PSI - Issue 59

Oksana Hembara et al. / Procedia Structural Integrity 59 (2024) 190–197 Oksana Hembara et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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4

D 1 =610 mm and a thickness of t 1 =11 mm. On the inner surface of the pipe, the existence of a crack-like defect with initial dimensions is allowed: a depth of “ a ” and a length of 2 c (Fig. 1a). In this study, five types of crack-like defects on the inner surface of the pipe were considered: a semi-circle crack ( a / c =1), semi-elliptical cracks ( a / c =0.25; a / c =0.5; a / c =0.75), which simulate corrosion damage of the pitting, and a crack-like defect in the form of a corrosive pitting ( a / c =0.1). Considering that pipelines in hydrogen energy systems must withstand high internal pressures, six levels of maximum load were selected. Therefore, calculations were performed for internal pressures of 7, 10, 20, and 30 MPa. Since pipelines are subjected to long-time operation under the internal pressure of the transported hydrogen containing product, a steady-state distribution of hydrogen is established over time, depending on the internal pressure. Therefore, our interest lies in the concentration of hydrogen in the equilibrium steady state. To determine accurately the hydrostatic stress distribution and hydrogen concentration around crack-like defects, a linear section of the pipe with a defect was considered. The calculations were performed using the ANSYS 2022R1 software. Taking into account the symmetry of the structural element and the applied load, the pipe was constrained by two planes passing through the pipe’s diameter, forming a 30° angle in the cross -section. Therefore, considering the symmetry conditions with relative to the planes formed, a computati onal model was adopted for a pipe fragment with a 30° sector, at the center of which a crack is located. It was divided into 76,601 finite tetrahedral elements, using 123,245 nodal points (Fig. 1b). To determine accurately the distribution of hydrostatic stress under conditions of plasticity, true stress-strain diagrams according to Dutkiewicz et. al. (2022, 2023) for steel AISI 1020 were used as material characteristics. a b

Fig. 1. Schematic representation of the geometry of a pipe with a crack (a), and its breakdown into finite elements (b).

For the analysis of hydrogen diffusion, we considered boundary conditions on the defect surface in the form of a specified value of hydrogen concentration C B , which can be determined using the volatility of gaseous hydrogen (Takayama et. al. (2011))

exp B z C k p p   





(8)

1

2         T z

where z 1 and z 2 are constants, T is the absolute temperature, and k is the solubility, which follows the Arrhenius formula: 0 exp( / ) s k k H RT   (9) where k 0 represents the pre- exponential factor of solubility, Δ H s is the enthalpy of solution. To determine the hydrogen concentration in the equilibrium steady-state, similar to Takayama et. al. (2011), we neglected the dependence on the history of plastic deformation (the fourth term) in equation (2). We obtained the following steady-state hydrogen diffusion equation:

DCV

  

  





(10)

D C

h 



  

L L H

L L

RT

By integrating equation (10), we obtained   ln H h L B V RT C C const   

(11)