Analysis of Mode II Crack in Bilayered Composite Beam

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...

Section: Introductionmentioning

confidence: 99%

Nonsingular crack modelling in orthotropic plates by four equivalent single layers

European Journal of Mechanics - A/Solids

2016

“…[14,15]) and changes the dynamic properties significantly, and therefore has a major influence on the lifetime of the structure. The delamination behavior of composite materials is characterized by different specimens for mode-I [16][17][18][19][20][21][22][23], mode-II [24][25][26], mixed-mode I/II [27][28][29][30][31][32][33][34][35][36][37], mode-III [38][39][40][41][42][43][44][45][46][47][48], mixed-mode I/III [49] mixed-mode II/III [42,[50][51][52][53][54][55][56][57][58][59] and mixed-mode I/II/III [60][61]…”

Section: Introductionmentioning

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.

Semi-layerwise analysis of laminated plates with nonsingular delamination—The theorem of autocontinuity

Applied Mathematical Modelling

2016

Available online xxxKeywords: Delamination Mixed mode II/III fracture Energy release rate Third-order plate theory Theoreom of autocontinuity a b s t r a c tThe proposed semi-layerwise approach captures the mechanical behavior of delaminated composite plates using four equivalent single layers independently of the lay-up. Two equivalent single layers are applied for both the top and bottom parts of a delaminated plate. The updated version of the system of exact kinematic conditions formulates the continuity of the in-plane displacements between the neighboring layers, the location of the global reference plane of the plate and -as important additions compared to previous papers -the continuity of shear strains, their derivatives and curvatures, respectively. The method is demonstrated using the first-, second-and third-order plate theories. As examples, simply supported delaminated plates are considered.The continuity between the delaminated and undelaminated plate regions is established through the theorem of autocontinuity. The J-integral is calculated along the straight delamination front and compared to the results of the virtual crack closure technique. The results indicate that the the first-and third-order plate theories provide the best solutions, and give good approximation even in those cases when the previous models failed, i.e., when the delamination is asymmetrically placed between two layers and it is close to the free surface of the plate.