PSI - Issue 83

Victor Rizov et al. / Procedia Structural Integrity 83 (2026) 95–104

96

unique properties and advantages (Gururaja Udupa et al. (2014), Nezhadfar et al. (2021)). The functionally graded materials are composites having in most of the cases two components (Dowling (2007), Toudehdehghan et al. (2017)). The ratio of these components changes continuously so that the transition from one component to another is smooth. These new materials have characteristics that make them successfully used to manufacture key components in high-performance engineering applications. The contribution of functionally graded materials for the progress in aeronautics, nuclear reactors, automotive industry, biomedicine, microelectronics and other important sectors is essential. This is due mainly to the fact that the properties of functionally graded materials change continuously along predefined directions in the structural component. In this way, the material and mechanical characteristics can be improved in certain (subject to more severe impacts) parts of the structural component. The quick progress in technologies for additive manufacturing in recent years has made it possible to produce functionally graded components of various structures, mechanisms, and devices with complex geometric shapes (Frazier (2014), Reichardt et al. (2020)). The intensive use of additively manufactured functionally graded components in engineering applications, where they perform different motions, requires studying their strength and fracture behavior under dynamic loading conditions (Sha et al. (2023), Yan Li et al. (2020)). Because additively manufactured functionally graded components are built up layer by layer, there is a high probability of lengthwise cracks occurring (Mahamood and Akinlabi (2017), Rizov and Altenbach (2019), Rizov and Altenbach (2020)). This type of crack not only poses a high risk to the reliable functioning of structural components, but also threatens the integrity and safety of the entire facility and can lead to its collapse with serious consequences, including human casualties. In addition to this, it should be noted that lengthwise cracks are difficult to detect, which makes them even more dangerous. All this highlights the strong need to conduct research in the field of longitudinal failure of additively manufactured functionally graded components. In this paper, our attention is focused on the analysis of longitudinal fracture in moving planar components with complex geometric shapes. In particular, a component made by three rigidly connected functionally graded bars is considered. The component moves according to a certain law. One of the bars hosts a lengthwise crack. The SERR in the moving component under inertia load is solved. This takes into account the non-linear elastic behavior of the component. The solution is checked by applying the J -integral approach. One of basic aims of the analysis is to examine how the SERR is affected by the complex geometric shape of the moving component. In this regard, the change of SERR when changing several geometric parameters is shown using various graphs. The effect of changing parameters of the non-linear stress-strain law along the thickness of bars on the SERR is also examined. 2. Theoretical model 1 2 4 5 DD D D , sketched in Fig. 1, consists of three rigidly connected bars, 1 2 DD , 2 4 D D and 4 5 D D , which have different lengths denoted by 1 l , 2 l and 3 l , respectively. The angle between bars, 1 2 DD and 2 4 D D , is  . The bars, 2 4 D D and 4 5 D D , are perpendicular. The component moves in vertical plane. The motion law is The frame-like planar component,

2

5 x D  z D  5

ft

, ,

(1) (2)

2

nt

rt   .

(3)

5 D x and

5 D z - coordinates of point, 5 D , in the coordinate

In Eqs. (1), (2) and (3) the following notations are used:

system, Oxz ; t - time;  - angle of rotation (shown in Fig. 1); f , n and r - parameters. The acceleration, 5 D a  , of 5 D can be obtained in the conventional manner, i.e.

D D x D z a a a 5 5 5      ,

(4)