PSI - Issue 68

3

Ivan Shatskyi et al. / Procedia Structural Integrity 68 (2025) 9–15 I. Shatskyi et al. / Structural Integrity Procedia 00 (2025) 000–000

11

b)

c)

a)

h

h

l 2

l 0

l 0

l 0

p

p

Fig. 2. Scheme of crack healing near the edge of the half-plane. As a result of the healing of the crack near the top, instead of the starting configuration (Fig. 1a), we get a new configuration (Fig. 1b). By assumption, the elastic properties of the materials of the filler and the main body do not differ from each other, so we take a half-plane with a shortened surface crack in length as the calculated model of the healed defective body (Fig. 1c). The length of the treated area is , so the degree of crack filling is the parameter . Let's find the limit loads for the configurations shown in Fig. 1a and Fig. 1c using known expressions for the stress intensity factors in a half-plane with an edge section (Isida, 1966; Savruk and Datsyshin, 1974; Atkinson, 1975; Atkinson and Javaherian, 1980; Savruk, 1981). In the initial configuration . Following the Griffiths criterion: , we obtain the ultimate load for a half-plane with an edge crack: ! ! ! ! ! %$#"! ! & $ $ " ! = ! ! ! # ! " "%"#"$ " ! # ! = ! ! " " # ! = = " # " ! $

!

!

#

#

"%"#"$ "

"%"#"$ "

"

"

!

"

(1)

%

.

#

$

=

=

#

! !

! !

!

!

Here

is the Young's modulus of the material.

!

!$!"!# ! =

#

" ! !

For a shortened crack

and accordingly

%

%

"$"!"# "

"$"!"# "

!

#

"

"

%

"

&

#

(2)

.

.

$

=

=

#

! !

! !

We define the desired healing efficiency for a single crack as the ratio of limit loads (2) and (1):

= = % % % ! ! "

"

#! " $ # "

(3)

.

.

!

$

!

!

As a result of the healing of the defect near the edge of the half-plane to the depth , instead of the starting configuration (Fig. 2a), we get a different configuration (Fig. 2b). In this case, we take a half-plane with an internal crack of length , located on the segment , as the calculation model (Fig. 2c). The following relations are obvious: , . The location of the internal crack relative to the edge of the half-plane will be characterized by a dimensionless parameter, which is the ratio of the half-length of the section to the depth of its center: . ! ! # " ! $ " ! " " ! ! = ! " %$#"! $ ! = " ! " %$#"! ! = = $

" "

+ " ! !

# #

+ "