PSI - Issue 16

Yaroslav Ivanytskyi et al. / Procedia Structural Integrity 16 (2019) 126–133 Yaroslav Ivanytskyi et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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At the first stage of solving the three-dimensional problem of elastic-plastic deformation, the initial distribution of stresses and deformations was determined. Then, at each moment of time t i+1 = t i + ∆ t (i = 0,1,2,…) the distribution of hydrogen concentration from the diffusion equation (10) and the creep deformation (6) was calculated. To do this, corresponding software modules in FORTRAN programming language were developed and compiled n MSC Marc Mentat.

Table 2. Constants of kinetic equations of creep and long-term strength for steel 0.5Cr0.5Mo0.25V A, MPa / n s  B, MPa / m s  n m χ ɸ β a 2. 027·10 -16 1.085·10 -14 6.23 0 5.8383 3.0937 0.3 7.19

The step increment was set on time based on the minimum allowable error. Calculations on new time steps with new values of coefficients were repeated until the parameter of damage to the limit value in any finite element of the structure was reached. At the same time, the data obtained in the previous step was used as the initial stress state for the next step of the load. This makes possible to determine the distribution of the equivalent stresses (Fig. 4) and the creep deformations (Fig. 5), depending on time in each section of the partition.

Fig 4. Distribution of equivalent stresses (MPa) at different time : (а) 160 h; (b) 800 h; (c) 1550 h.

Fig 5. Distribution of creep deformation (%) at different time : (а) 160 h; (b) 1550 h.

To determine the redistribution of hydrogen concentration in the sample during loading, the following characteristics were used: -10 D=10 m 2 /s, R = 8.31 J/(mol· К ), H V =1,96 cm 3 /mol, Т =640 °C . In Fig. 6a change in hydrogen concentration at different time at an initial hydrogen concentration of 3.4 ppm is shown. Comparing the obtained results it can be seen that the distribution of the fields of hydrogen concentration and deformation in the sample volume was changed. Over time, the maximum values of these parameters were shifted to the external surface of the sample near the concentrator. The parameter of damage was calculated using two approaches: the kinetic equation of Kachanov-Rabotnov- Lokoschenko (7) and the energy approach (8). The calculated creep curves (Fig. 7a) and the deformation energy (Fig. 7b) were compared with that obtained experimentally in air and in hydrogen. A satisfactory correlation between estimated and experimental data was observed. The kinetics of the change in the damage parameter calculated by two approaches were also defined (Fig. 7c).