PSI - Issue 68

Victor Rizov et al. / Procedia Structural Integrity 68 (2025) 139–145 V. Rizov / Structural Integrity Procedia 00 (2025) 000–000

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conventional structural materials (metals, alloys, fibre reinforced composites) in numerous applications in aeronautics, aerospace, car industry, nuclear power plants, etc. (Mahamood and Akinlabi, 2017; Yan et al., 2020). It is important to carry-out research aiming to clarify and improve longitudinal fracture behaviour of various structural members made of functionally graded materials since longitudinal cracks may significantly degrade the stiffness and the load-resisting capacity of structures. The functionally graded structural members used in the current engineering practice may have a great variety of geometrical shapes and properties. Besides, they may be subjected to various loading conditions. However, the engineering structures whose longitudinal fracture is analyzed in the scientific literature mainly represent straight beams having linear-elastic behaviour (Dowling, 2007). This work is confined to longitudinal fracture analysis of an L-shaped functionally graded shaft located in the vertical plane. The shaft has non-linear viscoelastic behaviour. The vertical member of the shaft is under angle of twist that grows non-linearly with time. Therefore, the horizontal member of the shaft is under time-dependent bending around its vertical axis. Besides the clamping in the right-hand end of the horizontal member, the shaft is supported also in its vertical member by a rotational spring support located in the horizontal plane (the purpose is to examine the effect of the spring support on longitudinal fracture). Solution of the SERR problem in the L-shaped shaft is derived. It is ascertained that the SERR is highly sensitive with respect to the rigidity of the spring support and the geometry of the shaft. The effects of loading and variation of material properties along the cross-section radius are also examined. 2. Theoretical model and analysis The load-carrying shaft that is treated in this work is L-shaped (Fig. 1).

Fig. 1. L-shaped shaft with longitudinal crack.