PSI - Issue 83

Victor Rizov et al. / Procedia Structural Integrity 83 (2026) 85–94

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for generating revenue and increasing economic efficiency. The benefits of using additive manufacturing include design freedom (this is mainly the result of the application of digital models), creating lightweight components, reducing costs, reducing production time, and more (Frazier (2014)). Furthermore, additive manufacturing technologies are excellent for environmentally friendly production. The rapid development of additive manufacturing technologies contributes to the widespread use of advanced structural materials, such as functionally graded materials, in various fields of modern engineering (Bohidar et al. (2014), El-Galy et al. (2019), Gururaja Udupa et al. (2014)). As known, functionally graded materials represent a class of highly efficient materials with continuously changing properties (Shrikantha and Gangadharan (2014)). These materials offer significant advantages in such high-tech areas as aeronautics, automotive, and biomedicine. The quick growth of the application of functionally graded materials requires constant improvement in various aspects of their characteristics (Toudehdehghan et al. (2017)). For instance, because additively manufactured functionally graded materials are built up layer by layer, they are prone to longitudinal fracture (Mahamood and Akinlabi et al. (2017), Rizov (2019), Rizov and Altenbach (2020)). Appearance and growth of longitudinal cracks is one of the basic weaknesses of these materials. Longitudinal cracks pose a serious threat to structural integrity and reliability, as they can lead to a sharp reduction in load-bearing capacity, increased deformations, and deterioration of stability. Furthermore, these cracks can cause component destruction, which compromises the performance of the entire structure or facility. Therefore, studying longitudinal fracture is an up-to-date problem of significant importance for the structural integrity and safety of functionally graded materials and structural components manufactured by additive technologies. This paper has for its main goal to analyze longitudinal fracture in a moving functionally graded beam structure under creep conditions. Such analysis is important because functionally graded components manufactured through additive technologies can be used in engineering applications in various mechanisms and devices where they perform different types of motion. Here we are focused on elucidating the effects of non-linear creep on longitudinal fracture in a beam rotating about a vertical axis that is moving vertically. The laws of beam rotation and the vertical axis motion are known. The inertia loads in the beam structure are constant with time. This induces creep behavior which affects the longitudinal fracture of the moving beam. The solution of SERR derived here accounts for the change of material parameters across the beam thickness. The J integral is used for verification. It is investigated how SERR under creep conditions is affected by the geometry of the beam and its acceleration due to rotation and motion of the vertical axis. The results of the investigation are illustrated with various plots showing the change in the SERR – time curve. 2. Theoretical analysis The horizontal beam structure, 1 3 LL , sketched in Fig. 1 rotates around vertical axis, s . The law of rotation is defined in Eq. (1). t    , (1) where  is the angle of rotation shown in Fig. 1,  is a parameter, t is time. Simultaneously with the rotation, the beam moves upward along axis, s , according to the law in Eq. (2).

2   , t

OL

(2)

3

where  is a parameter. Point, O , is the origin of s (Fig. 1). The beam treated in this paper is under conditions of non-linear creep. Equation (3) defines the creep behaviour (Dowling (2007)).



  

H t



E  

,

(3)