PSI - Issue 68

M. Perelmuter et al. / Procedia Structural Integrity 68 (2025) 219–224 M. Perelmuter / Structural Integrity Procedia 00 (2025) 000–000

222

4

! !"# $ $ =

"#

subregions (

under external tension. A circular interface bridged crack is placed at the materials interface and for material parameters are shown in Fig. 2. The bonds stiffness in the radial direction was taken to be equal to zero ( !

between subregions. Results for different width of the bridged layer

! µ

" = = = ! ! #$ ! !

%&'

" µ

! ! " " =

! ! =

). Relative bonds stiffness in the axial direction is defined for

as (see relation (3))

! $ $ % % $ % &

(4) Variation in the relative bond stiffness was performed by changing the parameter . The SIF module reduction effect can be used as a criterion of cracks healing efficiency. From the results shown in Fig. 2 it follows that the efficiency of the SIF reduction at ( in this case of the crack surface is filled with bonds) varies insignificantly. Thus, sufficient efficiency of crack healing is achieved already at . Distributions of the normal stresses in bonds over the interface crack bridged zone of width for various relative bond stiffness are shown in Fig. 3 for the problem above considered. It is observed the significant increasing of bonds stresses if the stiffness of bonds became bigger. The maximum stress value for linearly elastic bonds is observed at the trailing edge of the crack bridged zone. The crack openings over its radius ( ) for the bridged zone of width and the same bonds stiffness values together with the crack opening without bonds are shown in Fig. 4, where is the opening at the crack center of length between materials with the same properties in bonds absence, for plane strain case (England, 1965). These dependencies show that the increasing in bonds stiffness with corresponding increase of bonds stresses in the crack bridged zone leads to decreasing of the crack opening, i.e. its partial healing. When using the SIF module as the criterion of cracks healing effectiveness, it is evident from Fig. 2 that at the SIF module decreasing is exhausted, although the crack is not completely closed. ! ! " # $ # " # $ !# " # $ % ! " " # & % & & $D D ! ! " # " # " = = = = = ' ( ) * ! ! "#$ ! " ! !"#$ ! "#$ ! " ! ! "#$ ! " = ! ! " < ! ! "#$ ! " = ! ! ! ! ! "#$ ! " =

Fig. 3. Normal bonds stresses over the bridged zone, variation of bonds stiffness.

! "#$ ! " =

Fig. 4. Crack opening over its radius,

, variation of bonds

stiffness.

Next, we consider the stress distribution near the spherical cavity in the infinite region under uniform external tension . The problem has the axial symmetry, its analytical solution is given in Timoshenko and Goodier (1970). Axial stress distribution in the plane is (5) ! ! ! ! = ! " $ " % !! ! " # # # $ = + + =

" #

&

'

(

)

(

)

( ) " $

( ) " $

# !

"

"

where is radius of the spherical cavity, is the distance from the rotation axis. The BIE calculation was performed for the model taking into account the problem symmetry (the thin shaded zone in ! !