PSI - Issue 50

I.G. Emel’yanov et al. / Procedia Structural Integrity 50 (2023) 57–64 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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possible to give a refined quantitative assessment of the structure resource depending on the number of cycles and loading history. 4. An example of determining the service life of a shell lying on a support According to the proposed method, the problem of estimating the resource of a fragment of a gas pipe lying on a lodgement-type support is solved. A pipe loaded with external static loads in the form of a transverse force P ex and pulsating gas pressure p (Fig. 1). In the calculation, the length of the shell was assumed to be sufficiently large L =200 cm, and the contact of the shell in the meridional direction was studied far from the boundary conditions in the cross-section s =100 cm. It was assumed in the calculation that the steel shell of radius cm, thickness h= 0.74 cm, modulus of elasticity E =2 ×10 5 MPa and Poisson's ratio  =0.3 interact with a rigid base. Between the shell and the support there is a gasket with a compliance coefficient c p =10 8 N/m 3 . The lodgment coverage angle is equal to  2 130   , the breakdown of the contact area was made by central angles equal to  =5  , the value of the external load P ex =40 kN, the internal pressure is p 0 =5 MPa, and the pressure amplitude is p 1 =0.1 p 0 , the technical frequency of pressure change is f =20 Hz, the logarithmic decrement of oscillations is assumed to be one percent. The oscillation period of the pulsations T =2 × π/ω was divided into sixteen parts. Half the length of the contact area is approximated by thirteen contact elements. After solving the contact problem (1), contact pressures were determined depending on various parameters of the problem, Vasilenko and Emelyanov (1995), Vasilenko and Emelyanov (2002). Fig. 3 shows the distribution of the contact pressure q along the circumferential coordinate  in half of the contact area. Curves 1, 2, 3 correspond to the contact pressure distribution for time points equal to t =0, t = T /4, t =3 T /4. The presence of an elastic gasket ensures a smooth distribution of q along the entire length of the lodgment for all characteristic time point.

3 q  10, Н/м -5

3

2

2

1

1

0





0

20

40

60







Fig. 3 Distribution of contact pressure q on half of the contact area

For the problem of determining the service life of the shell, the maximum possible average contact stress acting on the shell was σ =50 MPa, with an amplitude from average stresses of 5 MPa. The tensile strength for pipe steel is 470 MPa. The index of fatigue curve for steels with tensile strength σ B ≤ 550 MPa can be taken as α=4, endurance limit on the base number of cycles N 0 = 2·10 6 equals σ -1 = 43 MPa. The calculation was carried out according to the hypothesis of linear summation (3) and according to the model of cyclic degradation of the material (6), (7), for different exponents m of the curve S B ( σ M , n ). Previously, it was experimentally established, Emelianov and Mironov (2012), that the kinetic coefficient of the falling curve of the ultimate strength of the material for most structural steels is close to 2. But at higher values of the kinetic coefficient m , certain steels are characterized by a longer retention of the initial tensile strength in the process of operating time. For a given material of a shell made of pipe steel, we take the value of the kinetic coefficient m equal to 2 (curve 2).