PSI - Issue 79

Victor Rizov et al. / Procedia Structural Integrity 79 (2026) 109–116

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1. Introduction A continuously inhomogeneous structural material can be defined as a composite material created as a result of mixing of two or more heterogeneous phases (El-Galy et al. (2019), Kou et al. (2012), Rizov and Altenbach (2020)). The new material obtained in this way possesses characteristics that the starting components do not have (Saiyathibrahim et al. (2016), Rizov (2017)). At the time being, as a result of intensive research work in the field of material science in many countries around the world different continuously inhomogeneous composite materials have been developed and applied in modern technology (Mahamood and Akinlabi (2017), Yan et al. (2020)). Among them an important place is occupied by the functionally graded structural materials which form an entirely new branch in material science that strongly attracts the attention of the scientists and engineers (Bohidar et al. (2014), Kieback et al. (2003)). One of the important features of the continuously inhomogeneous (functionally graded) materials is the smooth change of their properties along particular directions in a solid (Nemat-Allal et al. (2011), Reichardt et al. (2020)). Due to the significant advance in the technologies for manufacturing of functionally graded materials that has been made in the recent decades, the change of material properties in a solid can be tailored with purpose of achieving of certain goals (for example, strengthening of parts of a structural member that are loaded more heavy, reducing the weight of the structure, improving the fracture performance, etc.). Strength, safety, reliability and durability of various engineering structures, mechanisms and devices manufactured by continuously inhomogeneous structural materials depend in a high extent on their fracture behavior. It is known that one of the common reasons for structural failure is the appearance of cracks. This fact indicates that studying the problems of fracture mechanics of continuously inhomogeneous materials and structures is a very topical task given the accelerated use of these materials and structures in a variety of applications in different areas of current engineering. This paper is concerned with analyzing the effects of normal and tangential accelerations on the longitudinal fracture in continuously inhomogeneous structure rotating around a motionless horizontal axis. The analyzed problem represents a significant interest since continuously inhomogeneous materials are widely used for manufacturing of members of various mechanisms and devices which perform different motions. The structure considered here consists of a horizontal and a vertical member which exhibit continuous material inhomogeneity along the length. The behavior of the structure is non-linear viscoelastic. The inertia loads induced by the normal and tangential accelerations are determined. The strain energy release rate (SERR) in the structure under the inertia loads is solved. The obtained solution is confirmed by results from the scientific literature. The influences of the normal and tangential accelerations and the parameters of the model on the SERR are studied. 2. Theoretical model The structure depicted in Fig. 1 has a horizontal and a vertical member denoted by 1 3 LL and 3 4 L L , respectively. This structure rotates around a motionless horizontal axis, 1 n . The law of rotation is given in Eq. (1). ( 1) = − t e    , (1)

where  is the angle of rotation, t is time,  and  are parameters. The angular velocity,  , of the structure is obtained by Eq. (2). t e dt d     = = . Equation (3) is applied for deriving the angular acceleration,  , of the structure. t e dt d     2 = = .

(2)

(3)

The angular velocity and the angular acceleration of the structure are shown around axis, 1 n , in Fig. 1. The normal and tangential accelerations of an arbitrary point, D , of the structure horizontal member are denoted