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

186

5

As the results of experimental research show (see, for example, (Babii et al. (2008), Lokoshchenko et al. (2008))), for low and moderate hydrogen concentrations ( ) C t H the rate ( ) 0 C t   of deformation can be represented as a linear relationship ( )) ( ) (0)(1 1 0 C t C H t t        . (19) Based on the results of Andreikiv et al. (2007), the change by time t in hydrogen concentration ( ) C t H in the pre fracture zone for small times can also be represented as a linear relationship C t C t H 2 0 ( )   . Based on (18), (19), the relationship (9) can be expressed as follows:



( , , ) x t C

( ,0) x

(0) [1 t

]

C t













1 2 0 

.

(20)

0

It

It

It

  ( , ) 0

2 W t C pl

:

Let us substitute the relationship (18) into (13), and we obtain the formula for determining



 2

 

  2 W t C pl



( , )

(0,0,0)

0 (1 t

)

C t



 







1 2 0 

0 (21) Analyzing the results from (13) – (21), we can consider that the primary mechanism of crack propagation is high temperature creep, and neutron irradiation and hydrogen influence only intensify this process independently. In this case, the approximate relationships (9) and (11) can be written as follows: 0 It It t .



( , , ) 0 0 t C

(0,0,0)

(0)[1 ( t

)]   C

t



 







  

,

(22)

0

1 2 0

It

It

It





0 0 ( , , ) C

[ (0,0,0)  

(0)[1 (

2   ) ]] C t

(2) W t pl

t

 





  

.

(23)

0

0

1 2 0

t

It

It



In equations (6) and (12), included the duration c t t  of the incubation period for the elementary crack jump in high-temperature creep is involved. We will determine this quantity as follows. We assume that the crack will start to propagate when the maximum opening in the pre-fracture zone ( , , ) 0 0  t C It  reaches a critical value Ic  , which means based on the relationship (18), we obtain the following equation:



(0,0,0)

(0) [1 ( t 

) ] c t    0

C



 





 

.

(24)

Ic

1 2 0

It

It

c

By solving equation (24) for the value c t at small value

, we get:

0 1 2 0    C

 

  

( 1

)   

c t



.

(25)

It

Ic

t

Substituting the relationships (22) – (25) into equation (12) to determine the period * t t  of critical crack growth in high-temperature creep considering the effects of hydrogen and neutron irradiation, we obtain the following kinetic equation:

  It 

2

(0)

dt dl

4

(

)    

C





 

0

0

1 2 0

0

Ic

1

(0,0,0)





  It

1



(26)

Ic

with initial and boundary conditions     , , , 0, 0 * * * 0 l l t t l t l t    

Ic   ( ) . 

It l



(27)