PSI - Issue 59

Oleksandr Andreykiv et al. / Procedia Structural Integrity 59 (2024) 182–189 O. Andreykiv et al. / Structural Integrity Procedia 00 (2023) 000 – 000

188

7

Now let us examine another specific case where there is no neutron irradiation, but the plate is saturated with a concentration of hydrogen C 0 , that is formed during the dissociation of hydrogen on the metal surfaces of equipment. In this case Ф 0 = 0, and the equation (28) will be reduced to the following form

( A K K

)

dt dl

1 2

m



4

( ) K E C  1 2

,    1 2 0





2

t

I

IC

0 I

t

1

K K



2 2 

I (32) By integrating equation (32) with the initial and boundary conditions (29) to determine the subcritical crack growth period in a plate under high-temperature creep, we obtain the formula: IC

  l

(1

 dl p lK 2 2 ) 



t



  IC E C K p lK 2 2 1 1 (1    

m A p l K 2 ( ) 

4

)





2

2

m





.

(33)

2

1 2

0

t

IC

t

IC

IC

l

0

Let us apply formula (33) to determine the dependence of the period * t t  of subcritical crack growth in high temperature creep on the initial crack size 0 l for the case when the plate is made of steel 15Kh2MFА (Babii et al. (2008)). In this case, the following loading parameters and characteristics of 15 Kh2MFА steel are considered: 0.9ppm 0  C , 100MPa  p , T C 0 450  , 3.56 10 m/h 3 2    t A MPa, 2.13 , 1670   m t  , m K IC   210MPa (Lokoshchenko et al. (2008)). Based on this data, dependencies 0 ~ t l  were plotted in Fig. 1b, taking into account the effect of hydrogen (solid curve 1) and without considering the effect of hydrogen (dashed curve 2). As seen in Fig. 1b, the hydrogen environment reduces the period of subcritical crack growth in plates made of 15 Kh2MFА steel (residual life of thin-walled structural elements). This is because high-temperature creep in 15 Kh2MFА steel occurs through the mechanism of vacancy diffusion and condensation, as well as the growth of pores, which is stimulated by diffusively mobile hydrogen. Therefore, in the case of 15Kh2MFА steel, hydrogen increases the rate of high-temperature creep crack propagation and, thus, reduces the residual life of the plate. 4. Conclusions Based on the energy approach, a mathematical model has been developed to determine the residual life of thin walled metal elements with cracks under long-term static loading, high temperature, neutron irradiation, and the action of hydrogen-containing environments. The model was tested in a problem of long-term stretching of a plate with a through crack at high temperature, irradiation, and the action of hydrogen-containing environments. Specific cases of the effect on a plate with a crack under high-temperature creep and neutron irradiation or high-temperature creep and the action of hydrogen-containing environments were studied. For the case of neutron irradiation, the residual life of a plate made of 304 steel was calculated, and for hydrogen-containing environments, 15Kh2MFA steel was investigated. In the first case, graphical dependencies of the residual life of plate on the load magnitude were constructed, and in the second case, on the initial crack length. It was shown that the residual life of a plate irradiated with a neutron flux is lower than that of a non-irradiated plate. It was established that with an increase in load, the effect of neutron irradiation on the residual life decreases. This can be explained by the reduction of the irradiation dose, as the irradiation time of the plate before failure also decreases. In the second case, it was shown that a hydrogen-containing environment accelerates the propagation of high-temperature creep cracks. References Andreikiv, O.E., Dolins'ka, I.Y., Yavors'ka, N.V., 2012. Growth of creep cracks in structural elements under long-term loading. Materials Science 48, no. 3, 266 – 273. Andreikiv, O.E., Dolins’ka, I.Y. , Dobrovol’s’ka, L.N. , Yavors’ka, N.V. , 2015. influence of hydrogen on the initiation of creep-fatigue cracks in plates near stress concentrators. Materials Science 50, no. 4, 507 – 515. Andreikiv, O.E., Dolinska, I.Y., Zviahin, N.S., Liubchak, M.O., 2023. Acoustic-emission method for determining residual life of power equipment with creep cracks under static load. Materials Science 59, 103 – 111.