PSI - Issue 68

4

I. Shatskyi et al. / Structural Integrity Procedia 00 (2025) 000–000

Ivan Shatskyi et al. / Procedia Structural Integrity 68 (2025) 9–15

12

For the configuration shown in Fig. 2c: ,

! $ "# " ! " ! # # ± ± = " ! # ! ± !

.

where are known functions (Isida, 1966; Savruk and Datsyshin, 1974) obtained by solving the integral equation of the problem for a half-plane with an internal section, the “+” sign corresponds to the furthest and the "–" sign to the crack tip closer to the edge. For small ones, there is an approximation (Isida, 1966; Savruk and Datsyshin, 1974; Savruk, 1981): . For (Atkinson, 1975; Atkinson and Javaherian, 1980; Savruk, 1981): ! " ! #'#$%& #'#($% #'#%)& #'&*+) " ! & #'+, #'&+, ) % $ , - * + & ! ! ! ! ! ! ! ! ! " + + + = + ± ! ! ! ! ! "

( ) ! ! " # ! ! " # ! #$ " (

$ $ % &

( ) ! ! " # ! #$ " '

$ $ % &

$ $ % &

"

"

"

'

+

& % )

"

,

,

& % " (

"

!

"

!

=

+ +

= + +

"

"

#$

#$

(

'

#$ ( (

where . The limit load in the case of healing near the edge of the half-plane will be: #" ! #" ! " ! ! + # =

%! ! & '

. !" ! # $

(

&

#

#

&

'

'

%

%

(4)

$%&

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

.

$

=

)

(

"

'

'

By comparing expressions (4) and (1), we finally got the formula for the healing efficiency:

! ! % ! ! & '

! ! " ! ! # $

&

!

0

(5)

.

.

= ) " ( !"!&!' 1/ 0

#$%

"

!

.

/

! !

! !

++ , -

(( ) *

++ , -

(( ) *

+ .

+ .

/ /

/ /

.

+

!

!

!

!

2.3. Periodic series of surface cracks Now, as a starting configuration, consider a half-plane with a periodic system of surface cracks located perpendicular to the edge. As before, we consider mode I. Let is the length of unhealed cracks, and is the distance between them (period). The stress intensity factor and ultimate load for this problem depend on the dimensionless parameter : ! ! !

" ! ! " = !

!

!

% $ # #

"

$

"

"

!

(6)

#

" # % $ ! $ "# " ! =

&

,

.

.

$

%

=

=

!

$

#

! !

% $

#

! # !

"

!

"

!

The behavior of is described in detail in Ejike (1973), Sie (1973) and Savruk (1981). For a periodic system of cracks healed near the vertices, in formula (6) it is necessary to make substitutions for the length of the cracks and the characteristics of the crack resistance of the material: " ! # ! !

'

'

$ # " %

!

$ ! # % %

"

"

'

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

E

#

(7)

,

.

.

&

=

=

#

$ ! #

! !

$ # "

! !

!

!