Beam on elastic foundation with anticlastic curvature: Application to analysis of mode I fracture tests

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.

mentioning

confidence: 91%

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

Applied Mathematical Modelling

2016

“…The DCB specimen is a very well known, common specimen [11][12][13][14][15][16], schematically shown in Fig. 2.…”

Section: Example 1 -Mode-i Double-cantilever Beammentioning

confidence: 99%

“…In this paper some basic problems are analyzed, which are in fact simple, but -to telling the truthnot available in the literature and could be useful for those who face to the J-integral application for the first time. Four examples are considered here: the mode-I double-cantilever beam (DCB) [8][9][10][11][12][13][14][15][16], the mode-II end-notched flexure (ENF) specimen [14,15,17,18] and the mixed-mode I/II single-leg bending (SLB) system [14,15,17,18]. Finally, a simply-supported delaminated elastic plate subjected to a point force is analyzed.…”

Section: Introductionmentioning

confidence: 99%

J-integral for delaminated beam and plate models

2012

Per. Pol. Mech. Eng.

In this work the J-integral is applied to calculate the energy release rate in simple beam and plate models. Four examples are considered: the mode-I double-cantilever beam, the mode-II end-notched flexure, the mixed-mode I/II single-leg bending specimens and a delaminated plate with simply-supported edges, respectively. In each example the details of calculation are given, in the latter case the distribution of the energy release rate along the crack front is calculated. While for delaminated beams the literature presents the energy release rates in numerous studies, the J-integral calculation is not trivial in theses cases. Moreover for delaminated bent plates the application of the J-integral is not documented. It is shown that considering the classical plate theory there are serious limitations to calculate representative energy release rates.Keywords composite · J-integral · beam theory · plate theory · energy release rate distribution Acknowledgement

“…[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.