PSI - Issue 72

Victor Rizov / Procedia Structural Integrity 72 (2025) 128–134

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inhomogeneous materials (Ariga et al. (2012), Hsueh (2002)). These materials have attractive mechanical properties which explain the significant interest towards them in the engineering community (Lloyd and Molina-Aldareguia (2003), Wang et al. (2019)). However, there are various issues (especially in the area of safety, reliability and durability) related to the wide-range industrial use of these materials. One of the issues that remain subject of intensive studies and debate in the research circles throughout the world is the delamination behaviour (Dolgov (2005), Dowling (2007), Narisawa (1997), Rizov (2019), Rizov (2020)). The objective of the current article is delamination under harmonic load. The interest to the harmonic load may be explained by the fact that this kind of loading is frequently encountered in the modern engineering. In particular, a beam-like multilayered inhomogeneous structural component that is symmetrically delaminated in its ends is analysed. The harmonic load is in the mid-span. Besides, the component analysed is placed on two springs in its ends. This allows us to explore the combined influence of two factors (harmonic load and springs) on delamination. The integral J is used in the analysis. The extreme values of J under harmonic load are determined. The extremals of the SERR are deduced from the energy balance in the conditions of harmonic load for check-up of J extremals. The evolution of J with spring constants and harmonic load is explored. 2. Model of delaminated beam-like structural component The geometry of the beam-like structural component studied in the current article is reported in Fig. 1.

Fig. 1. Beam-like structural component with two symmetrical delaminations in its two ends.

This structural component is subjected to a harmonic load, F . The maximum value of the load is F n . The harmonic load is generated by a motor of mass, m p . The motor weight, P , is P m g P  (1) where g is the acceleration of gravity. The beam-like structural component is symmetrically delaminated by two delaminations as reported in Fig. 1. Because of symmetrical character of the delamination, only part, H 3 H 4 H 5 , of the component is treated in the analysis by the J -integral (Fig. 1) (Broek (1986)). The total value (for both delaminations) of J under static load, P , is J st and can be estimated by   J J P st 2  (2)

where J ( P ) is the value for one delamination. Equation (3) estimates J ( P ), i.e.   3 2 1 stD stD stD J J J P J    ,

(3)