PSI - Issue 68

Oleh Yashiy et al. / Procedia Structural Integrity 68 (2025) 126–131 O. Yashiy et al. / Structural Integrity Procedia 00 (2025) 000–000

128

3

The overall internal stresses (both thermal and mechanical) within the inhomogeneity are associated with the influence function (2) as follows (Pasternak et al., 2022):

#

#

#

( ) ! !

( ) ! !

( ) ! !

( ) ! $ " ! !

( ) ! !

( ) ! $ # ! ! !

$ ! "

$

,

(3)

! $

"

=

=

"

=

!

"

!

#

!!

!

!

" #$

" #$

" #$

! !

where is a tangent vector to the curve at the point , and ! !

! $ %& = ! ! ! "

( ) ! !

( ) ( ) ! !

.

(4)

" #

!

One can associate the brittle fracture of an inhomogeneity with the maximum normal stress. Therefore, the internal fracture criterion for the inclusion can be expressed as follows:

"

! ! ! ! + + !

!

(5)

.

$

!

"

!

#

$%

! "#

In the analysis, one should also account for the point , where the critical stress is exceeded and fracture of the inhomogeneity is initiated. 3. Fracture of the interface We will assume that the failure of the composite begins at the interface between the inclusion and the matrix, specifically at the point where the contact stresses reach critical levels. The modeling of thread-like inhomogeneities is based on the principle of coupling continua of different dimensions using a linear representation of the inclusion (Pasternak et al., 2022). Given the specific singularity (Pasternak et al., 2022) of the stress field at the vertices of the inclusion, directly applying this criterion is not feasible. However, since the influence function of the inclusion, as described in (2), represents the integral of contact stresses along the perimeter normal to the cross-section of the inhomogeneity, we can associate the failure at the body-inclusion interface with the attainment of certain critical values by these influence functions in specific regions, particularly near the ends of the thread-like inhomogeneity. Furthermore, because inclusions typically delaminate through a shear mechanism (Murakami, 2002), the failure criterion for a body with a thread-like inclusion can be expressed as follows: ! ! where is the parametric coordinate of the vertex of the thread-like inclusion, is a small neighborhood around the vertex, and is the critical value of shear forces at which the bonds between the inclusion and the surrounding medium fail. The magnitude of depends on many factors, including surface properties, adhesion forces, manufacturing technology, and so on. It should be determined experimentally for problems with the simplest geometry and then extended to more complex cases. In calculations, it is suggested to select the parameter within the range of , where is the regularization parameter in the thread-like inclusion model (Pasternak et al., 2022). 4. Fracture initiation near the inhomogeneity According to Pasternak et al. (2022), the stress field in the vicinity of the tip of a thread-like inhomogeneity is singular. This singularity arises from the assumptions made during its modeling as a spatial curve, rather than as an ! ! ( ) !" ! ! " ( ) !" ! ! " ! ! " # < $ ! ( ) ( ) # $! % ! ! " $ ! ! ( ! " ) ( ) ( ) !" " ! " # % , (6)