PSI - Issue 68

Oleksii Milenin et al. / Procedia Structural Integrity 68 (2025) 1010–1016 Oleksii Milenin et al./ Structural Integrity Procedia 00 (2025) 000–000

1012

3

be described by the non-stationary heat conduction equation. Heat dissipation into the surrounding environment, including both the technological equipment and the atmosphere, is accounted for by imposing boundary conditions based on the Newton-Richmann and Stefan-Boltzmann laws.

Fig. 1. Finite element scheme in cylindrical coordinates.

Relation between austenitic, bainitic and martensitic phases in pipe steel depends on temperature as follows (Makhnenko et al., 1999):

(

)

(

)

(

)

( (A )'(A )'(A )' ' ' ( BA* ' ' + + ( + ( , ! ! ! + + $ % &  & ( ) = *  * & & ( ) + , $ % .  / = *   * ) ( ) !" #$! !" #$! % % % % % % % % % '( '( & ) & ) & *+, ! " # AB& # # # # AB& &'

&

" # # # # # - # # # # # 4

=

(1)

( ( +

) ) ,

0 2

1 3

#

#

# # &' B "   /

+ + + +

$ ( +

% ) ) ,

. 0 2

( ) ( + ( = "

AB&

& *+, * (   * ,

&'

1 3

"

" " &' B 

+ +

Parameters of (1) are determined based on CCT-diagram for specific steel. The algorithms for numerical predicting the progression of diffusion processes are proposed by Makhnenko at al (2002) and are based on solving the following equation:

( D()" % * % H ! "# $ = ! ) ( !

( )

)

(2)

# $ " & !

,

"#$ % & D()" " " %

"#

'

(

where Π is a concentration potential, K is solubility coefficient of diffusible hydrogen, H = K Π is a concentration of diffusible hydrogen, V is convective transfer velocity vector, D is diffusion coefficient, Q H is losses per unit time and unit volume of diffusion hydrogen associated with reversible and irreversible traps and chemical reactions,

# ( *

$ ) +

!

"##

!$%

#

%

&

(3)

,

$

µ = '

!

'

'

'

!

#&"

!'%

%

"&'

(

%

+

"

"

To account for variations in hydrogen diffusion parameters within a spatially heterogeneous material, such as steel undergoing phase transformations in a non-stationary temperature field, the lever rule is applied as follows: