PSI - Issue 77

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

395

7

The effects of the velocity of bending and variation of material properties involved in (4) along the layer thickness on the SERR are shown in Fig. 4 and Fig. 5.

1 1 / β α P P curves (1 – for

/ β α Q Q 1 1

0.5

/ β α Q Q 1 1

2.0

/ β α Q Q 1 1

1.0

=

=

=

Fig. 5. The SERR -

, 2 – for

and 3 – for

).

4. Conclusions The SERR for a delamination crack in a planar multilayered structural member of circular cross-section is derived. The member has horizontal and vertical portions. The member is subjected to torsion and bending. The free end of the horizontal portion is under angle of twist, while the section in which the horizontal and the vertical portions are connected is under angle of bending (both angles increase with time at constant velocities). These velocities are taken into account when deriving the SERR (this is the main contribution of the present paper). For this purpose, non-linear stress-strain constitutive laws for torsion and bending which include terms with the first derivatives of the strains are applied. Curves indicating the effects of the velocities of the angles of twist and bending and the change of material properties along the layer thickness on the SERR are shown. A significant rise of the SERR is detected at increase of velocities, T v ϕ and T v ϕ . It is observed that the SEER can be reduced by increasing of 0.5 / 1 1 = T T G G α β and 1 1 / β α E E ratios. Growth of 1 1 / α β H H , 1 1 / β α S S , 1 1 / β α P P and 1 1 / β α Q Q ratios, however, leads to rise of the SERR. The approach presented in this paper can be applied in analyses of safety and integrity of planar structures under bending and twisting with considering the influence of loading velocity on delamination. Acknowledgements The author expresses his gratitude to the Research and Design Center (CNIP) of UACEG for the financial support of this study under grant BN-326/25.