PSI - Issue 68

Yu.G. Matvienko et al. / Procedia Structural Integrity 68 (2025) 641–645 Matvienko, Pokrovskii / Structural Integrity Procedia 00 (2025) 000–000

643

3

"

(3)

" #

! =

= !

!

!

$

#

"

!

! !

where is the local strength of the material, r c is the size of the fracture process zone. For each point along the crack front, a local coordinate system is considered and oriented as follows: the х and z axes lie in the crack plane perpendicular and parallel to the crack front, respectively, and the у axis is directed perpendicular to the crack plane. The fracture criterion is based on the maximum tangential stress which should be equal to the local strength in the fracture process zone ahead of the crack tip front. The size of the fracture process zone and the local strength are determined taking into account the stress intensity factor K I , the nonsingular stresses ( T xx and T zz ) and employing the Tresca–Saint-Venant criterion and the Huber–Mises plasticity criterion, respectively. As a result, the following equation can be written for the local strength of the material and the size of the fracture process zone as it was given by Pokrovskii and Matvienko (2023a, 2023b)

!

! $ # #

! " " " " + ! !! "" !! ""

! ! ! # !! !$% ! & # µ ""

! ! ! # !! !$% ! & # µ ""

! % '

" & (

,

(4)

$ = #

+

+

"

#

!

$% ! & # µ

!

! $

" % )

!

$% ! & ! # µ

"

.

(5)

#

=

" !

!

"

# & ' + (

!!

Substituting the local strength (4) and the size of the fracture process zone r c (5) into the criterion equation (3), the following useful relation can be written

!

! $ # #

! # # # # + ! !! "" !! ""

! " " # !! !%' ! & # µ ""

! " " # !! !%' ! & # µ ""

%

&

! % (

" & )

# #

" #

$ +

.

=

= #

+

+

"

#

#

"

""

!

%' ! & # µ

%' ! & # µ

!

$

'

#$

!

Then, the basic equation for the fracture criterion takes the following form

#$

! " " " " ! ! ! + + " + # # % # !! !

.

(6)

#

#

=

"

" !

(

)

(

)

#

# + ! " " &

# ! ! " ""

!

!!

""

!!

"" !!

""

!!

The yield stress is denoted in these equations as σ Y . The proposed criterion allow taking into account two-dimensional constraint in the vicinity of the crack front in the transverse and longitudinal directions. To simplify this expression, the following parameters expressing the ratios of T-stresses to the yield strength are introduced. Taking the left-hand side of the equation (6) as the effective stress intensity factor, the following expression has been written ! ! " !! "" ! " # # ! = ! = " "

"#$ % + !

%

.

(7)

!""

%

=

!

#

!

" " % &#$ +

" $

" #

#

%

"

! " !

"! "! + ! ! "! + !

$

#

$ #

$

#

3. Results and verification of the proposed fracture criterion To verify the proposed fracture criterion, the experimental data of the center cracked specimen with a height of 2 H , a width of 2 W and a thickness of 2 t with a coaxial transverse crack of length 2 l under uniaxial tension has been