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

1013

4

#

#

( ) # $ ! ! = " # !

( )

( )

! " " # $ % % # $ = " = "

!

(4)

,

!

!

!

!

!

!

!

!

Within the framework of the problem of stresses and strains kinetics, the increments of strain tensor can be expressed as follows:

(

)

! & & & & & ! ! ! " ! # = + + $ + "

(5)

,

#$

#$

#$

#$

%

where , , dφ are the components of the increment in the strain tensor caused by the elastic deformation mechanism, plastic strains, linear temperature expansion, and phase transformations, respectively. The dependence of strains on stresses is determined by Hooke's law and the associated law of plastic flow, based on the following relationship (Velikoivanenko et al., 2014): ! "# $ ! ! "# $ ! ! " ! ,

!

(

)

(

) ( % +

(

)

)

%

(6)

"

$

$

& = ( # ) (

!" !

" # "

+ (

# ! $ ( + & + & ) (

# " # ) (

(

#

!"

!"

!"

#

!"

!"

#

%

(

where δ ij is the Kronecker symbol, σ is the mean stresses, K is the volume compression modulus, E is Young's modulus, ν is Poisson's ratio, G is the shear modulus, the symbol "*" indicates that the corresponding variable belongs to the previous step tracing, Ψ is a function of the state of the material, which determines the condition of plastic flow according to the Von Mises criterion:

!

" #$

"

" =

  <

!

"

%

#

#

!

(7)

" #$

"

  =

" >

!

"

%

#

#

&'(')

#&*#+(,-#&&#./)0

  >

!

"

where σ Y is the yield stress of material. The interdisciplinary problem involving temperature kinetics, phase composition, hydrogen diffusion, and the stress-strain state was addressed using finite element analysis, implemented through the integration of specialized modules within the Weld Predictions software package (Velikoivanenko et al., 2014). 2.2. Probabilistic criteria of susceptibility to cold cracking. The complexity of the physical phenomena influencing the susceptibility of weld metal to cold cracking presents significant challenges in defining a precise quantitative criterion for fracture. In this context, a probabilistic criterion based on the principles of Weibull's statistical mechanics is considered the most appropriate for numerical evaluation. The probability of cold crack initiation, as a function of diffusible hydrogen content V H (ml/100 g) and mechanical stresses within the material, can be quantitatively assessed using the following expression:

# ( ( /

$ ) ) 0



( ) !

" #

" & %

 , .

1

( ) !

( ) !

(8)

! "#$ = % %

%

A #

#

" #

*

>

"

+ -

!

B

The coefficients A , B , η for the three-parameter distribution is determined experimentally and has been reported, for instance, in the work of Makhnenko et al. (2009).