PSI - Issue 83

Victor Rizov et al. / Procedia Structural Integrity 83 (2026) 105–114

106

various structures, machines, devices and apparatuses in different sectors of modern engineering (Bourell et al. (2017), Yan et al (2020)). As is known, functionally graded materials are a special category of relatively new highly advanced composites that have been the subject of intensive research in recent decades in many countries around the world (Toudehdehghan et al. (2017), Naebe and Shorvanimoghaddam (2026)). These materials are formed from two or more phases in order to obtain specific properties that cannot be realized with just one of the phases. The properties and behavior of functionally graded materials are strongly influenced by material composition and microstructure. The variation of material properties within a functionally graded structural component can be designed to achieve the desired distribution, with the aim of improving the performance in specific locations of the component. Physically, the property variation can be realized by adjusting the composition and microstructure of functionally graded materials. These materials are known also with their attractive mechanical, thermal and electrical properties, and high wear resistance. Due to their important advantages, functionally graded materials have positioned themselves as vital engineering materials, contributing greatly to the advancement of various industries, including aircraft construction, aerospace technology, nuclear power, automobile manufacturing, etc. Thanks to up-to-date digital technologies, additive manufacturing enables also precise control over the production process of functionally graded materials (Mishra et al. (2023), Yadav et al. (2024)). Other benefits of additive manufacturing are the unprecedented freedom in design, significant reduction of the component weight, and production of multifunctional components with complex shapes (Nezhadfar et al. (2021), Reichardt et al. (2020), Gururaja Udupa et al. (2014)). On the other hand, use of additively manufactured functionally graded components in such responsible engineering industrial applications as mechanisms and machines places high demands with respect to the fracture and failure behavior of these components under dynamic loads. In this paper we deal with delamination in stepwise functionally graded beam components performing translational motion. One of the basic features of the stepwise functionally graded materials is their discontinuous structure of distinct layers. There is a sharp difference between the properties of the layers. Therefore, one of the frequently encountered degradation mechanisms in stepwise functionally graded beam components after putting them in service is the delamination fracture (Gururaja Udupa et al. (2014), Naebe and Shorvanimoghaddam (2026), Rizov (2017), Rizov (2018)). In order to avoid failure of these components by delamination it is important analyze a broad specter of problems associated with delamination fracture. In this regard, the purpose of the present paper is to analyze dynamic delamination in a stepwise functionally graded beam component by using the integral J . The stepwise functionally graded beam component is treated as a multilayered beam hosting a delamintion. The law of translational motion of the beam is known. The beam has non-linear viscoelastic behavior. The SERR is derived for control of the solution of the integral J . The effects of different parameters of the moving beam structure on the J integral are investigated. 2. Analysis of stepwise functionally graded beam with delamination The beam component, 1 3 RR , shown in Fig. 1 performs translational motion in vertical plane, Oxz . The motion law is

3   ,   . t t 3

x R z R

(1) (2)

1

1

1 R x and

1 R z - coordinates of point, 1 R , on the horizontal and

The notations used in the above equations are:

vertical axis; t - time;  and  - parameters. Since the beam moves translationally, its inclination angle,  , remains constant during the motion process (Fig. 1). The acceleration of point, 1 R , in the beam is a a i a k R z R x R    1 1 1   , (3)