PSI - Issue 77

Victor Rizov et al. / Procedia Structural Integrity 77 (2026) 389–396 Author name / Structural Integrity Procedia 00 (2026) 000–000

393 5

i

i

i

=

=

=

δ

λ

λ

(

)

∑∫∫ U a u dA * 0 1 2 * = L L

∑∫∫

∑∫∫ 1 ( ) = i A

L L u dA * 0 2 3

L L * 0 3 4

dA

l a 1

l

u

+ −

+

.

(21)

2

A 1 ( )

1

i

i

=

=

A ( )

i

i

i

* 0 1 2 L L u ,

* 0 2 3 L L u and

* 0 3 4 L L u are the complementary strain energy densities in the internal

In formula (22),

delamination arm and portions, 2 3 L L and 3 4 L L , of the member, respectively. The SERR found by (20) is verified by analyzing the energy balance via

π 2 1

  

   ,

a U

∂

∂

T ϕ

a ϕ

∂

G

T

M

=

+

−

M

∂ (22) where U is the strain energy in the member, T is the torsion moment at the free end of the internal delamination arm, M is the bending moment in section, 3 L . 3. Numerical results Calculations of the SERR are carried-out in order to explore the effects of the velocities of the angles twist and bending on the behaviour of the delamination crack. ∂ ∂ a R B

/ T G G α β 1

0.5

/ T G G α β 1

1.0

/ T G G α β 1

2.0

T v ϕ curves (1 – for

1 = T

1 = T

1 = T

Fig. 2. The SERR -

, 2 – for

and 3 – for

).

0.010 = D R m,

0.006 = B R m,

3 = δ ,

The following numerical data are used in these calculations: The following numerical data are used in these calculations:

0.010 = D R m,

0.006 = B R m,

3 = δ ,

5 = λ ,

0.400

0.300

0.5 = Gi b ,

0.5 = Hi b ,

0.7 = Ei b ,

0.5 = Si b ,

0.002 ∆= m, 0.7 = Qi b and

0.200 = a m,

2 = l

1 = l

m,

m,

0.7 = Pi b . The effects of the change of material properties along the layer thickness on the SERR are explored too. The results obtained are used to draw the curves shown in Figs. 2, 3, 4 and 5. The curves in Fig. 2 indicate how the SERR (in non-dimensional form) changes when the velocity of the angle of twist increases. This change is investigated at three 1 1 / T T G G α β ratios (this ratio is a measure for the variation of 1 T G along the layer thickness). It is obvious that both the velocity of the angle of twist and 1 1 / T T G G α β ratio have significant influence of the SERR.