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

187

6

2 I ( )  K E t

1   , 

In the case when the crack is macroscopic, and the equalities are satisfied

,

K K

 

1  

2 2 

It

It Ic

I

IC

m * t t  of subcritical crack growth in high-temperature creep in a plate in the presence of a hydrogen-containing environment and neutron irradiation will take the following form I IC t A K K ( 1 2 2 0 ) (0) 2   , mathematical model (26), (27) for determining of the period It   

( A K K

)

dt dl

1 2

m



4

( ) ( 1 

),    

2 K E

C





 

2

t

I

IC

0 I

1 2 0

0

t

1



K K



2 2 

(28)

I

IC

 

  , , l 

0, 0 l

, l t t l t

IC K   ( ) .

t

I K l



 

(29)

0

*

*

*

Here A m t , 2 are the characteristics of high-temperature creep of the material. 3. Partial cases of the final problem

Let us consider the problem of long-term tension of a plate with a through-thickness crack of high-temperature creep (analogous to Griffith's problem). Suppose the plate is only subjected to neutron irradiation, and there is no hydrogen embrittlement. In this case K p l I   . In this case, the equation (28) can be reduced to the form

1 p l K A p l K m t    2 2 2 2 2 2

dt dl

2

m

4    0

( ) E   

2 p l



IC

0

t

.

(30)

IC

By integrating equation (30) under the conditions (29), we get:

 * l

    2 2 2 (1 4 ) (1 p l K dl  

t



2 IC K p l K E  2 )

  

*

2 A lp K  ) ( m

2

 (31) To validate the solution of the problem, let us consider a plate made of 304 stainless steel containing a crack with a length of 10  l mm. The data for the calculations are taken from the papers (Chopra et al. (2006, 2008), Kurata et al. (2000)): 5 10 m/h 6 2    t A , 1.1  m , 0.1 0   , 1.5 10 cm /n 2 19      , 213MPa m irr  IC K , 454MPa m unirr  IC K , 175GPa  E , 178MPa unirr  t  , 787MPa irr  t  , flux density h) 10 n/(cm 2 17 0    . According to equation (31), the dependencies of the residual life of the plate on the load change are plotted in Fig. 1a. As seen in Fig. 1a, the residual life of the plate irradiated by neutron flux (curve 1) is lower than that of the non-irradiated plate. It is observed (Fig. 1a) that with increasing load, the influence of neutron irradiation on the residual life decreases. This can be explained by the reduction in the radiation dose, as the time of irradiation of the plate before failure also decreases. 0 0 0 2 l t IC IC IC t .

Fig. 1. (a) Griffith’s problem analogue plate residual life-time: 1 – unirradiated, 2 – irradiated; (b) Dependence of the residual life of the plate on the initial size of the crack: 1 – under the action of hydrogen, 2 – without hydrogen.