The use of ECT and 6PBP tests to evaluate fracture behavior of adhesively bonded steel/epoxy joints under Mode-III and Mixed Mode III/II

2020

Arch Appl Mech

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: Discussionmentioning

confidence: 99%

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

2020

Arch Appl Mech

“…The details of the FE models are presented in a recent paper (Szekr enyes, 2014d). The delamination tip elements and the global mesh resolution were chosen in accordance with recommendations of the literature (Raju et al, 1988;Mehrabadi, 2014) The position of the delamination was varied in the through thickness direction, these were assigned as cases I, II, III and IV (Szekr enyes, 2014d). The problems are solved for some selected cases and different boundary conditions.…”

Section: Resultsmentioning

confidence: 99%

“…The resistance against the delamination is characterized by mode-I (Jumel et al, 2011a,b;Salem et al, 2013;Kim et al, 2011;Peng et al, 2011;Gracia et al, 2015) mode-II (Arrese et al, 2010;Argüelles et al, 2011;Yoshihara and Satoh, 2009;Rizov and Mladensky, 2012) mode-III (Rizov et al, 2006;Szekr enyes, 2009aSzekr enyes, , 2011aRodríguez-Gonz alez et al, 2014;Khoshravan and Moslemi, 2014;L opez-Men endez et al, 2014;Marat-Mendes and Freitas, 2009;Mehrabadi and Khosravan, 2013;Yoshihara, 2006) mixed-mode I/II (de Baere et al, 2012;Davidson et al, 2009;Fern andez et al, 2013;Islam and Kapania, 2014;Peng et al, 2012;Kenane et al, 2010;Marat-Mendes and Freitas, 2010;Nikbakht et al, 2010;Nikbakht and Choupani, 2008;Plain and Tong, 2011;Liu et al, 2015;Pereira et al, 2014) mixedmode II/III (Szekr enyes, 2007;Kondo et al, 2011Kondo et al, , 2010Mladensky and Rizov, 2013;Kotousov et al, 2013Kotousov et al, , 2012Szekr enyes, 2012;Mehrabadi, 2013Mehrabadi, , 2014Miura et al, 2012;Takeda et a...…”

Section: Introductionmentioning

confidence: 99%

“…It has also to be mentioned that coupled multilayer/interface models have already been introduced in the literature, which are able to provide accurate energy release rate (ERR) calculations compared to FE models using solid type elements (Bruno and Greco, 2001;Bruno et al, 2003Bruno et al, , 2005). An important aspect of these formulations is that it avoids the complications arising from the oscillatory singularities for a delamination between different materials.The delaminations may take place because of low-velocity impact (Ganapathy and Rao, 1998; Rizov et al Peng et al, 2012;Kenane et al, 2010;Marat-Mendes and Freitas, 2010;Nikbakht et al, 2010;Nikbakht and Choupani, 2008;Plain and Tong, 2011;Liu et al, 2015;Pereira et al, 2014) mixedmode II/III (Szekr enyes, 2007;Kondo et al, 2011Kondo et al, , 2010Mladensky and Rizov, 2013;Kotousov et al, 2013Kotousov et al, , 2012Szekr enyes, 2012;Mehrabadi, 2013Mehrabadi, , 2014Miura et al, 2012;Takeda et al, 2013;Suemasu et al, 2010) The previous developments e that this paper is based on e are summarized as follows: In some recent papers the so-called interface constraints were applied to model delaminated composite plates by CLPT, FSDT, SSDT and TSDT with midplane cracks and symmetric lay-up (Szekr enyes, 2014a(Szekr enyes, ,c,e, 2013a. Later, the models were generalized to asymmetrically delaminated plates and the socalled system of exact kinematic conditions (SEKC) was proposed for the FSDT (Szekr enyes, 2013b), SSDT (Szekr enyes, 2014b) and Reddy third-order theory (Szekr enyes, 2014d).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Nonsingular crack modelling in orthotropic plates by four equivalent single layers

European Journal of Mechanics - A/Solids

2016

Keywords:Delamination Mixed mode II/III fracture Energy release rate Second-order plate theory Theoreom of autocontinuity Q3 a b s t r a c tIn this work the second-and third-order laminated plate theories are applied to model delaminated composite plates with material orthotropy. The method of four equivalent single layers is proposed and a general third-order displacement field is utilized in each layer. The kinematic continuity between the layers is established by the system of exact kinematic conditions. Apart from the continuity of the inplane displacements between the interfaces of the layers even the continuity of shear strains, their derivatives and curvatures is imposed. As a novelty a so-called shear strain control condition is introduced, which means that the shear strains at two or more points located along the thickness are imposed to be the same. Using the proposed conditions the equilibrium equations are derived for the delaminated and undelaminated regions of the plate. Plates with different boundary conditions are solved as examples and the theorem of autocontinuity is introduced, which is essentially related to the continuity conditions between the delaminated and undelaminated parts. The stress and displacement fields as well as the J-integral are determined in the examples and compared to finite element calculations. The results indicate that the control condition works very well in the case of the second-order plate theory, in contrast it is rather a disadvantage in the case of the third-order approximation.© 2015 Published by Elsevier Masson SAS. IntroductionAnisotropic composites (Chaudhuri and Balaraman, 2007; Czig any and De ak, 2012; M esz aros et al., 2013) are often utilized in air-, spacecraft (Smojver and Ivan cevi c, 2010;Ivan cevi c and Smojver, 2011; Ivan cevi c, 2011, 2012;Langdon et al., 2014) and sport industry (Jiang, 2014;Li and Jing, 2014;Su, 2014;Zhang, 2014;Tang, 2014), composite panels are also applied in cars and vehicles (Norhidayah et al., 2014;Wennberg and Stichel, 2014;Khan et al., 2014), ships (Chirica et al., 2011;Chirica, 2013), pressure vessels (Gheshlaghi et al., 2006 and many other engineering applications (Goch et al., 2012). The mechanical behavior of laminated composite plates and shells can be described by different theories. The classical laminated plate theory (CLPT) is based on the Kirchhoff assumption and so, it does not take the shear deformation into account (Radosavljevi c and Dra zi c, 2010;Eftekhari and Jafari, 2012;Hajheidari and Mirdamadi, 2013). The first-order shear deformation (FSDT or Mindlin) theory assumes constant shear strain distribution over the thickness of the plate (Kreja and Schmidt, 2006;Endo and Kimura, 2007;Assie et al., 2012;Batista, 2012;Nanda and Sahu, 2012;Sabik and Kreja, 2013;Endo, 2015). As a next step, the second-order plate theory (SSDT) proposes that the in-plane displacements are captured by quadratic functions in terms of the through-thickness coordinate (Baddour, 2011;Izadi and Tahani, 2010;Shahrjerdi et al., 2011...

“…in plates subjected to inplane loads. Apart from that in the last years several plate bending specimens have been developed for the characterization of mode-III [137] and II/ III [138] interlaminar fracture of laminated composite materials. These specimens are created with straight delamination front, i.e.…”

Section: Example: a Simply Supported Delaminated Platementioning

confidence: 99%

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

Mathematics and Mechanics of Solids

2016

The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton's principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.