PSI - Issue 51

Victor Rizov et al. / Procedia Structural Integrity 51 (2023) 206–212 V. Rizov / Structural Integrity Procedia 00 (2022) 000–000

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the integrity, reliability and durability of multilayered structures (Dolgov (2005, 2016)). Therefore, the safety of multilayered members depends on their delamination fracture behaviour. The aim of this paper is to study analytically the effects of relaxation on delamination of a multilayered inhomogeneous viscoelastic beam configuration whose moduli of elasticity are time-dependent. Previous papers (Rizov (2021a, 2021b)) have been focussed on analysis of delamination of multilayered inhomogeneous beams without considering the variation of the moduli of elasticity with time. The multilayered beam under consideration here consists of vertical layers. Each layer is continuously inhomogeneous along its width. A solution to the TDSERR that accounts for the relaxation and the change of the moduli of elasticity with time is found by considering the TDSE. A TDSERR is derived also by considering the compliance. The results are identical (this is a verification of the analysis). 2. Solution of the TDSERR with taking into account the relaxation A multilayered viscoelastic cantilever beam with vertical layers is depicted in Fig. 1.

Fig. 1. Multilayered beam with a delamination.

The width, height and length of the beam are b , h and l , respectively. The length of delamination is a . The widths of delamination arms are 1 b and 2 b . Relaxation conditions are induced in the beam. The angles of rotations of the delamination arms are 1  and 2  (Fig. 1). These angles do not change with time. The relaxation is analyzed by the model in Fig. 2. The moduli of elasticity of the springs are i D E and i H E . The dashpot has coefficient of viscosity i  . The modulus of elasticity, i D E , varies continuously with time, t :