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

185

4

[ (0,0,0) [ ( )       



0 0 ( , , ) C

0 C t ( )] ]

(2) W t pl



 

2



 

,

,

.

(11)

(0,0,0) t It  



0

0

t

It

It

It

f

t Ic

t

By substituting (11) into (6) – (8), to determine the period * t t  of subcritical crack growth period in high temperature creep in a plate, taking into account the influence of radioactive neutron irradiation and hydrogen saturation, we obtain the following mathematical model:   t t C C      ( ) / ] ( ) ( ) 2 [ ( )             ( ) * . Let us consider the case when only neutron irradiation is present. High-temperature creep of materials subjected to neutron irradiation is accelerated due to defect formation and the phenomenon of radiation swelling of the metal (Holt (2008)). Therefore, based on the results of Iskhakov et al. (2013), in a wide range of stresses, we can express the steady-state creep rate using the following linear approximation: ( )) ( ( ) (0) 1 t t            , (13) where    is the neutron damage rate, t t 0 ( )   is the fluence value, 0  is the neutron flux density or flux (measured in s) n/(m 2  ). According to (Andreikiv et al. (2012)), the following relationship is valid: Ic It It It C It It dt dl   (0,0,0) 1 0 0 0 0 0   (12) * * * 0 , ( ) , 0, (0) l l t t l t  l t    , Ic It l  

   It

( )        ( ) 1

1



.

(14)

Ic

c

Then, we can write the following:





) ( ) (0)(1     



 

.

(15)

It

It

The crack opening in the pre-fracture zone (9), taking into account (15), can be rewritten as follows:



t ( , )

It 0     (0)

(0)(1

t t )  



  

.

(16)

0

It

It

Substituting (16) into (11), we rewrite the mathematical expression for (2) pl W as:   2 0 0 0 (2) ) (0) (0)(1 ( , ) t t W t It It t pl            . (17) Let us consider the case when a hydrogen-containing environment is present, and neutron irradiation is absent. In formulas (8) – (12) included value ( ) 0 C It   crack tip opening rate due to high-temperature creep of the material in the pre-fracture zone under the influence of hydrogen is involved. This quantity is proportional to the rate ( ) 0 C t   of deformation in the steady-state creep region (Andreikiv et al. (2015)), and there is a relationship between them:



( ) 0 C

( ) 0 C     t





1



.

(18)

It

Ic c