PSI - Issue 68

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

223

5

the Fig. 5a shows the area of the boundary conditions for displacements along the symmetry plane, this notation is only in the figure, it is not the computation model part), for the cases of the ideal contact along the symmetry plane (zero normal displacements) or damaged zone (weak interface) along the symmetry plane (see relation (3)). Number of nodes at the boundary of the region is 52, the material Poisson ratio is . The BIE calculation with the ideal contact boundary conditions gives the maximum axial stress at the cavity edge as , analytical solution (see (5) for and ) gives value . The axial stresses in the plane for different types of the boundary conditions obtained in the calculation and the comparison with the analytical solution with the ideal contact condition are given Fig. 5b where the effect of damaged zone stiffness variation is clearly observed. !"# ! = ! " #$!% !! ! ! = ! ! = !"# ! = ! " #$!%& !! ! ! " ! ! =

!

! " ! " =

Fig.5. (a) BIE computational model, (b) normal stress over symmetry plane

- the external radius of the cylindrical region,

;

! ! =

, ideal contact and damaged zone boundary conditions.

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

Below are also presented the computation results for a hollow circular cylinder of inner radius

, outer radius around its

! !"#$ ! " =

, height

and with a semi-circular external groove of radius

!"#$ ! " =

!"# ! =

circumference at the mid-height of the cylinder, the material Poisson ratio is

. The cylinder faces subjected to

! !

a uniform normal stress . The BIE model of the cylinder half is presented in Fig. 6a (shaded zone has the sense as in Fig 5a). As in the previous example the cases of the ideal contact along the symmetry plane and the damaged zone (weak interface) along this plane were considered. The stress concentration factor (the axial stress at the groove edge, ) for the ideal contact case was obtained in our computation as 3.49. The same problem also was analyzed by the BIE in (Bakr (1983)), where the result is presented. For the damaged zone case along the symmetry plane the stress concentration factor for different values of relative bonds stiffness (stiffness variation was performed as in the previous sample, see relation (4)) is shown in Fig. 6b. This parameter increases rather rapidly for small bonds stiffness and tends asymptotically to the case of ideal contact as bonds stiffness tends to infinity. 4. Summary The computation of the bridged stresses and the SIF module analysis is the first step in bridged cracks and damaged zones growth modeling. Analysis of bridged cracks growth can be considered in the frame of the nonlocal criterion of bridged cracks growth (Perelmuter (2007)) which can be easily incorporated into the developed boundary element code. The bridged crack and damaged zone models can be used also to modeling cracks or flaws self-healing assuming that the self-healing process is the result of the crack bridged zone formation or strengthening of the damaged zone ! " !! ! ! ! " #$%& !! ! ! =