PSI - Issue 68

Victor Rizov et al. / Procedia Structural Integrity 68 (2025) 146–152 V. Rizov / Structural Integrity Procedia 00 (2025) 000–000

147

2

(Dolgov, 2005; Dolgov, 2016; Yu et al., 2003; Rizov, 2019; Sy-Ngoc Nguyen et al., 2015; Sy-Ngoc Nguyen et al., 2020). The fracture properties strongly influence the behaviour of the multilayered materials. In particular, delamination fracture is responsible for many uncertainties in structural applications of multilayered engineering materials (Freund, 1995; Kim et al., 1999; Markov and Dinev, 2005; Mušálek et al., 2010; Tokova et al., 2017). For instance, delamination puts on risk integrity, stability and life of components of various structures and mechanisms made of multilayered materials (Hutchinson and Suo, 1992; Rizov, 2021; Rizov, 2022). The primary aim of this paper is to analyze the SERR in a fixed-ended multilayered beam structure under support twisting. The layers are longitudinally inhomogeneous. There is an inner delamination crack in the beam. The support twisting induces torsion moment in the beam since the latter is statically undermined. Because there is a notch in the upper delamination arm, the latter is stress free. The lower delamination arm is loaded in torsion as a result of support twisting. Solutions of the SERR are derived. Using these solutions, the change of the SERR caused by variation of different parameters is analyzed. The results of the analysis are reported in form of various graphs. 2. Theoretical analysis The paper studies the fixed-ended multilayered beam structure with a delamination crack as shown in Fig. 1.

Fig. 1. Fixed-ended beam under twisted support.

The right end of the beam is twisted at angle,

. This is the only influence on the beam. Since the layers are

! ! !

! "

inhomogeneous along the beam length, the shear modulus,

, changes smoothly. This change is defined by

formula 1.

! "

#

$% $ $ ' ' & =

,

(1)

where

, " ! ! ! ! " $"#"!!!!" =

(2)

!

.

(3)

The quantities , and ! !

!

!" #

! "

! "

are defined in Fig. 1. The quantities

and

represent the value of

at the left

end of the beam and the parameter of the change of the modulus of elasticity, respectively.