Antiplane–inplane shear mode delamination between two second-order shear deformable composite plates

2020

Arch Appl Mech

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This work deals w ith the development and extension of higher-order models for delaminated doubly curved composite shells with constant radii of curvatures. The mechanical model is based on the method of four equivalent single layers and the system of exact kinematic conditions. A remarkable addition of this work compared to some previous ones, is a modified and improved continuity condition between the delaminated and undelaminated parts of the shell. Using the principle of virtual work, the equilibrium equations of the shell systems are brought to the stage and solved by using the classical Lévy plate formulation under simply supported conditions. Four different scenarios of elliptic and hyperbolic delaminated shells are investigated providing the solutions for the mechanical fields as well as for the J-integral. The analytical results are compared to 3D finite element calculations, and excellent agreement was obtained for the displacement components and normal stresses. On the contrary, it was found that the transverse shear stresses are captured quite differently by the proposed method and the finite element models. Although the role of shear stresses should not be underrated, they seem to be marginal because the distributions of the J-integral components are in very good agreement with the numerically determined energy release rates.

Section: Introductionmentioning

confidence: 99%

Higher-order semi-layerwise models for doubly curved delaminated composite shells

2020

Arch Appl Mech

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“…Similarly to the theory of laminated and composite beams [83][84][85][86][87][88][89][90] the literature is very rich in the different theories to model laminated composite plates and shells. Thin flat plates can be modeled by the classical or Kirchhoff plate theory, 91,92 while for relatively thick plates the first-order shear deformation theory (FSDT or Mindlin), [93][94][95][96][97][98][99][100] second-order shear deformation theory (SSDT), [101][102][103][104][105] general third-order theory (TSDT), [106][107][108] Reddy third-order theory, [109][110][111][112] other higher-order shear deformation theories (HSDT), [113][114][115] layerwise theories, [116][117][118][119][120][121] and the 3D elasticity solutions 122,123 are developed. These theories have been utilized to model curved shells [124][125][126] and delaminated and cracked laminates …”

Section: Department Of Applied Mechanics Budapest University Of Techmentioning

confidence: 99%

Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

Journal of Composite Materials

2015

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This paper revisits the problem of free vibration of delaminated composite plates with Lévy type boundary conditions. The governing equations are derived for laminated Kirchhoff plates including through-width delamination. The plate is divided into two subplates in the plane of the delamination. The kinematic continuity of the undelaminated part is established by using the system of exact kinematic conditions. The free vibration analysis of orthotropic simply supported Lévy plates reveals that the delaminated parts are subjected to periodic normal and in-plane shear forces. This effect induces parametric excitation leading to the susceptibility of the plates to dynamic delamination buckling during the vibration. An important aspect is that depending on the vibration mode the internal forces have a two-dimensional distribution in the plane of the delamination. To solve the dynamic stability problem the finite element matrices of the delaminated parts are developed. The distribution of the internal forces in the direction of the delamination front was considered. The mode shapes including a half-wave along the width of the plate accompanied by delamination buckling are shown based on the subsequent superimposition of the buckling eigenshapes. The analysis reveals that the vibration phenomenon is amplitude dependent. Also, the phase plane portraits are created for some chosen cases showing some special trajectories. KeywordsDelamination, free vibration, laminated plate theory, dynamic stability, parametric excitation, harmonic balance, finite element method IntroductionDelaminations are typical defects in composite and sandwich structures induced by indentations (e.g. local loading by spherical indentors), 1,2 low-velocity impact and free edge effects (normal and shear stress concentration between layers at free edges), 3-6 finally by fabrication defects. 7,8 The cracks and delaminations reduce significantly the strength and stiffness of composite laminates.9-11 The material defects also influence the dynamic behavior of the structures.12-20 One of the widely known dynamic phenomena is parametric excitation, which takes place in machine tools, 21 [73][74][75][76][77][78] and sandwich beams. 79In Burlayenko and Sadowski, 80 the foam/core debonding in sandwich plates was investigated during free vibration. However, the existence of the parametric excitation was not revealed in any of the former papers.To the best of the author's knowledge, the existence of the parametric excitation in the course of free vibration of delaminated composite beams was first revealed in Szekre´nyes 81 and was solved effectively by the FE and harmonic balance methods in Szekre´nyes.82 It was also shown that the delamination buckling takes place only if the free vibration amplitude exceeds the so-called critical amplitude at a specified point of the beam. The existence of the critical amplitude was also proved experimentally. The parametric excitation in delaminated plates is possible to appear, as well. 9,10,[127][128][129] subseq...

“…In the following, to analyse a delaminated composite beam under mixed-mode I/II fracture conditions, the basic idea of higher-order beam theories is utilised with the semi-layerwise approach [51]. The concept of the proposed description can be seen in Fig.…”

mentioning

confidence: 99%

Fracture and mode mixity analysis of shear deformable composite beams

Kiss

2019

Arch Appl Mech

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To analyse delaminated composite beams with high accuracy under mixed-mode I/II fracture conditions first-, second-, third-and Reddy's third-order shear deformable theories are discussed in this paper. The developed models are based on the concept of two equivalent single layers and the system of exact kinematic conditions. To deduce the equilibrium equations of the linearly elastic system, the principle of virtual work is utilised. As an example, a built-in configuration with different delamination position and external loads are investigated. The mechanical fields at the delamination tip are provided and compared to finite element results. To carry out the fracture mechanical investigation, the J -integral with zero-area path is introduced. Moreover, by taking the advantage of the J -integral, a partitioning method is proposed to determine the ratio of mode-I and mode-II in-plane fracture modes. Finally, in terms of the mode mixity, the results of the presented evaluation techniques are compared to numerical solutions and previously published models in the literature.Keywords Delamination · Energy release rate · Mixed-mode I/II fracture · J -integral · Higher-order beam theories IntroductionAs the composite materials play important role in the industrial applications [11], the strong adhesion between the laminated layers is essential and must remain reliable even at high strains and high stresses [15]. Presence and propagation of a delamination in lightweight composite materials [35,38] can significantly decrease the load bearing capability of the structure [7,26,28], modify the dynamic properties [6,20,27,39,40], and furthermore, they can easily lead to sudden and catastrophic failure of the brittle mechanical system. Thus, the description [22,36] and the avoidance [10,59] of an interlaminar failure, which may take place because of low-velocity impact [5,24], blast loading [32,37], manufacturing defects [16][17][18] and free edge effects [13], are inevitable from engineering point of view.The application of the linear elastic fracture mechanics is one possibility to characterise the interlaminar fracture resistance of conventional high performance composites with inherent brittleness [8,9]. The critical value of the energy release rate G c , which can be considered as a material property, is suitable to characterise the strength of an interface layer between two elastic plies [19]. Like any other material parameters, mechanical tests must be carried out to be determined. In the case of fracture mechanical investigation, as linear elastic fracture mechanics works only if the location, size andshape of the crack are known, the experiments must be B. Kiss (B) · A. Szekrényes