PSI - Issue 54

Victor Rizov et al. / Procedia Structural Integrity 54 (2024) 475–481 Victor Rizov/ Structural Integrity Procedia 00 (2019) 000 – 000

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belong to the class of composites (Kim et al. (1999), Markov and Dinev (2005), Tokova et al. (2017)). A typical multilayered system represents a composition of layers of different materials (Freund (1995), Dolgov (2005), Dolgov (2016)). The layers may have different thickness. A wide variety of combinations of layers can be realized in order to meet specific requirements with respect to strength, stiffness, temperature resistance, stability, ductility, weight, corrosion resistance, durability and other properties of the engineering structures (Sy-Ngoc Nguyen et al. (2015), Sy-Ngoc Nguyen et al. (2020)). Layers can be made also of inhomogeneous materials like, for instance, functionally graded materials (Ariga et al. (2012)). As known, the functionally graded materials are one of up-to-day engineering materials which are subject of intense studies (Mahamood and Akinlabi (2017), Reichardt et al. (2020)). The integrity and safety of multilayered structural systems are strongly influenced by their delamination behaviour. In many cases, delamination is the basic cause for failure of multilayered load-bearing structures. In day-to-day work, the practicing engineers frequently have to deal with design of various multilayered non linear viscoelastic inhomogeneous structures and structural components subjected to mobile external loading. On account of this, it is especially important to develop delamination analyses which account for the loading mobility. Therefore, this paper aims to analyze delamination of a multilayered beam structure loaded by an external force that movies slowly along the upper beam surface at a constant velocity. The beam layers are continuously inhomogeneous in longitudinal direction. The strain energy release rate (SERR) is obtained for the case of non linear viscoelastic behaviour. An examination of the SERR is done by the J -integral. Numerical results for the ascendency of the mobile loading parameters over the SERR are obtained. The principal novelty of this paper is that a mobile loading applied on a non-linear viscoelastic beam is considered (the previous publications are concerned with analyses of delamination in viscoelastic layered beam structures under a motionless loading (Hutchinson and Suo (1992), Rizov (2019), Rizov (2021), Rizov (2022)). The research significance of the present paper is that the SERR is found with considering of two important factors (the mobility of the load and non-linearity of the viscoelastic behaviour of the delaminated multilayered inhomogeneous beam). 2. Analysis The multilayered viscoelastic beam structure considered in this paper is supported in its two ends as displayed in Fig. 1. A delamination of length, a , is situated in the beam so that the upper and lower crack arms have different thicknesses denoted by 1 h and 2 h , respectively.

Fig. 1. Multilayered beam with a delamination crack loaded by a mobile force, F . The loading represents a force, F , that moves along the upper surface of the beam from point, 1 B , towards point, 2 B , at a constant velocity, F v . Thus, the distance, s , between the force and point, 1 B , varies linearly with time, t s v t F  , (1) where s l l a     1 0 , 1 0 t t   . The value of time at which the force reaches to 2 B is found as

F v l l a   1

t



.

(2)

1