PSI - Issue 25

Victor Rizov / Procedia Structural Integrity 25 (2020) 88–100

89

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

2

significantly deteriorates the operational performance of the multilayered structures and reduces their load-bearing capacity. One of the main reasons for disintegration of multilayered structures that may lead to catastrophic failure is the delamination fracture. Therefore, the analysis of delamination fracture behaviour of multilayered materials and structures is an important topic for researchers and engineers (Cantwell et al. (1999), Davidson and Sundararaman (1996), Ducept et al. (1999), Guadette et al. (2001), Jiao et al. (1998), Kevin O’Brien (1998), Narin (2006), Rizov (2017), Rizov (2018), Rizov (2019), Suo Guo et al. ( 2005), Szekrenyes (2010), Szekrenyes and Vicente (2012), Yeung et al. (2000), Yokozeki et al. (2007)). Delamination fracture behaviour of layered beams has been analyzed by using linear-elastic fracture mechanics in (Suo Guo et al. ( 2005)). The effects of residual stresses have been evaluated. The fracture has been studied in terms of the strain energy release rate. The contributions of the mechanical and thermal stresses to the strain energy release rate have been investigated and discussed in detail. Analyses of delamination fracture in various layered beam configurations have been developed in (Yokozeki et al. (2007)). For this purpose, solutions to the strain energy release rate have been obtained by using a laminated beam model. Methods of linear-elastic fracture mechanics have been applied. Effects of residual thermal stresses on the delamination fracture behaviour of some frequently used layered beam structures have been evaluated and discussed. Delamination fracture behaviour of layered beam specimens subjected to four-point bending has been invtstigated in (Yeung et al. (2000)). The fracture properties have been analyzed by using methods of linear-elastic fracture mechanics. The fracture has been studied in terms of the strain energy release rate by using analytical expressions. The main goal of the present paper is to develop an analytical investigation of the influence of the viscoelastic material behaviour on the delamination of multilayered beams subjected to creep. The delamination fracture is studied in terms of the strain energy release rate by considering the balance of the energy. The viscoelastic behaviour is treated by using four linear rheological models for a constant applied stress. The strain energy release rate is obtained also by differentiating the strain energy with respect to the delamination crack area for verification. The influences of the coefficients of viscosity and the moduli of elasticity of the beam layers on the delamination fracture behaviour of a multilayered cantilever beam configuration loaded in bending are evaluated. 2. Analysis of the strain energy release rate in multilayered beams with viscoeleastic behaviour Delamination fracture in multilayered beam structures made of adhesively bonded horizontal layers which exhibit viscoelastic material behaviour is under consideration in the present paper. The number of layers in the beams is arbitrary. Each layer has individual thickness and material properties. A delamination crack of length, a , is located arbitrary between layers. The beams are loaded by an arbitrary system of forces and moments. The delamination fracture behaviour is studied in terms of the strain energy release rate, G . The balance of the energy is analyzed in order to derive the strain energy release rate. For this purpose, a small increase, a  , of the crack length is assumed. The balance of the energy is written as

a F w M U Mi i i m i Fi i     

i n        1 1 i

a Gb a   

,

(1)

where n and m are, respectively, the numbers of external forces and bending moments applied on the beam, Fi w  and Mi  are, respectively, the increase of the projection of the displacement of the application point of the force, i F , on the direction of the force and the increase of the angle of rotation of the beam cross-section in which the bending moment, i M , is applied, U is the strain energy cumulated in the beam structure, b is the width of the beam. From (1), the strain energy release rate is derived as