PSI - Issue 28

Vasilii Gorokhov et al. / Procedia Structural Integrity 28 (2020) 1416–1425 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The resulting picture of the distribution of damage measure ω by the end time-delay on the inner surface of the bellows is shown in Fig. 3.

Fig. 3. The distribution of damage measure by the end time-delay on the inner surface of the bellows

In the third problem, the results of numerical modeling of the process of deformation and failure of a spherical shell are presented, illustrating the influence of brittle fracture of the material under irradiation as a result of creep strain development. The process of deformation of a spherical shell, loaded with an internal pressure of intensity p , symmetric with respect to the axis of symmetry X with uniform heating to a temperature melt T T 0.607  followed by exposure time at a given neutron flux for some time to failure is considered. Relative thickness of the sphere is ) 100% 2% ) ( 2( 2 1 2 1     R R R R . The calculation was carried out for the symmetrical 1 4 part of the sphere. The shell loading diagram is shown in Fig. 4. Along the symmetry plane of the sphere fragment (along AD direction), X displacements were taken equal to zero ( 0  u ), and on the axis of symmetry (line BC), Z displacements were also taken equal to zero ( 0  w ).The internal pressure varied linearly along the axial coordinate from the value т 0.0095σ  p (at 0  Х ) to Y p 0.0143σ  (at 1 R Х  at the point B ). The calculations were based on quadratic isoparametric finite elements of an axisymmetric body with a uniform breakdown of the fragment along the thickness (4 FE) and along the meridian (20 FE). Loading was carried out in 2 steps: heating up to temperature melt T T 0.607  and increasing pressure (step 1); exposure to irradiation until destruction (step 2). The second step was divided into sub-steps with a time step 1 60   t hour. As a result of the calculation, it was found that from the beginning of exposure, creep deformations began to develop over the entire volume of the shell, the maximum rate of which was observed in the region of the sphere pole (point B). Until   t t 0.1873 the creep process was accompanied by a corresponding increase in material damage without any manifestation of brittle fracture effects. At   t t 0.1873 , in the point С of the sphere where the values of the main tensile stresses turned out to be the highest (the measure values of creep strains here are also close to maximum), the process of brittle fracture began, sequentially taking over the nearest points of the sphere due to the redistribution of stresses.