Energy release rate and phase angle of delamination in sandwich beams and symmetric adhesively bonded joints

Wang, Jialai; Zhang, Chao

doi:10.1016/j.ijsolstr.2009.09.003

Cited by 23 publications

(10 citation statements)

References 38 publications

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“…The influence of shear forces will be neglected in this study. The effect of shear deformation can be formally considered for shear composite beams as considered by Qiao and Wang (2004), Wang and Qiao (2006), Hamey (2007), or Wang and Zhang (2009). The centroid of the fully composite section is given by y cg;∞ ¼ E 2 A 2 h 0 =EA 0 ) where E 2 A 2 is the axial stiffness of Subelement 2 and EA 0 ¼ E 1 A 1 þ E 2 A 2 is the total axial stiffness of the composite member.…”

Section: Basic Assumptions and Notationsmentioning

confidence: 99%

Boundary-Layer Effect in Composite Beams with Interlayer Slip

Challamel

Girhammar

2011

J. Aerosp. Eng.

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An apparent analytical peculiarity or paradox in the bending behavior of elastic-composite beams with interlayer slip, sandwich beams, or other similar problems subjected to boundary moments exists. For a fully composite beam subjected to such end moments, the partial composite model will render a nonvanishing uniform value for the normal force in the individual subelement. This is from a formal mathematical point of view in apparent contradiction with the boundary conditions, in which the normal force in the individual subelement usually is assumed to vanish at the extremity of the beam. This mathematical paradox can be explained with the concept of boundary layer. The bending of the partially composite beam expressed in dimensionless form depends only on one structural parameter related to the stiffness of the connection between the two subelements. An asymptotic method is used to characterize the normal force and the bending moment in the individual subelement to this dimensionless connection parameter. The outer expansion that is valid away from the boundary and the inner expansion valid within the layer adjacent to the boundary (beam extremity) are analytically given. The inner and outer expansions are matched by using Prandtl's matching condition over a region located at the edge of the boundary layer. The thickness of the boundary layer is the inverse of the dimensionless connection parameter. Finite-element results confirm the analytical results and the sensitivity of the bending solution to the mesh density, especially in the edge zone with stress gradient. Finally, composite beams with interlayer slip can be treated in the same manner as nonlocal elastic beams. The fundamental differential equation appearing in the constitutive law associated with the partial-composite action in a nonlocal elasticity framework is discussed. Such an integral formulation of the constitutive equation encompassing the behavior of the whole of the beam allows the investigation of the mechanical problem with the boundary-element method.

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Section: Basic Assumptions and Notationsmentioning

confidence: 99%

Boundary-Layer Effect in Composite Beams with Interlayer Slip

Challamel

Girhammar

2011

J. Aerosp. Eng.

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“…In order to study the mechanics of delaminating 10–17 growth under cyclic loading, constant amplitude cyclic loading was conducted to establish the delamination growth rate da / dN as function of the total strain energy release rate Δ G T through the Paris power law , where the material constants d and B are depending of the mode ratio .…”

Section: Introductionmentioning

confidence: 99%

Fracture and fatigue study of unidirectional glass/epoxy laminate under different mode of loading

Kenane¹,

Benmedakhene²,

Azari³

2010

Fatigue Fract Eng Mat Struct

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A B S T R A C TInterlaminar fracture is the dominant failure mechanism in most advanced composite materials. The delaminating behaviour of materials is quantified in terms of the strain energy release rate G. In this paper, the experimental measurements of the fatigue delaminating growth for some combinations of energy release rate mode ratio have been carried out on unidirectional glass/epoxy laminates. On this base the constants in the Paris equation have been determined for each G II /G T considered modal ratio. The fatigue threshold strain energy release rate G Tth , below which delaminating doesn't occur, were measured. Three type specimens were tested, namely: double cantilever beam (DCB), end-loaded split (ELS) and mixed-mode bending (MMB) under mode I, mode II and mixed-mode (I + II) loading, respectively. Scanning electron microscopy techniques were used to identify the fatigue delamination growth mechanisms and to define the differences between the various modes of fracture.Keywords composite; fatigue; fatigue threshold strain energy release rate; mixed mode fracture; strain energy release rate; unidirectional glass/epoxy laminates. I N T R O D U C T I O NA considerable amount of current research is devoted to the study of failure mechanisms in laminated composite materials. The interlaminar damage is the most common one and can cause major reductions in the stiffness or strength of a structure. Delaminating grow between laminates as a consequence of the presence of unidirectional fibres above and below a ply interface. 1,2 It results generally from different loading arrangements labelled 'modes'. Mode I is tensile (opening) loading, mode II (in-plane) shear loading, and mixed-mode (I + II) conditions are also of interest. 3 Several test configurations have been proposed for studying delaminating fracture behaviour under various kinds of loading as summarized in a recent study. 4 Double cantilever beam (DCB) for mode I, endloaded split (ELS) for mode II and mixed-mode bending (MMB) for mixed mode (I + II) specimens are used in these experiments. Several studies have shown that the MMB specimen is the unique test which presents some advantages, including the possibility of working a wide range of mixed mode ratios. 4-6 Correspondence: M. Kenane.The total fracture strain energy release rate, G TC (G TC = G IC + G IIC ) describe the resistance of a material against delaminating growth under the applied static load. Both can be determined for different mode ratios considered. In previous study, 7 these experimental results have permitted us to propose a semi-empirical criterion through the plotting of the G TC versus the GII GT modal ratio. We note that this semi-empirical criterion was verified for several materials 8,9 and it was found to accurately predict the critical delamination length.In order to study the mechanics of delaminating 10-17 growth under cyclic loading, constant amplitude cyclic loading was conducted to establish the delamination growth rate da/dN as function of the total strain energy r...

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“…Smith and Shivakumar [96] used the total energy release rate G T to analyze their Cracked Sandwich Beam specimen to avoid issues with respect to mode separation that could occur when using VCCT. Wang and Zhang [97] presented a new analytical solution for the energy release rate and the phase angle at an interface crack in a sandwich based on interface fracture mechanics solutions and composite beam theory. A promising method for the prediction of disbond propagation at the sandwich face sheet/core interface was suggested by Berggreen et al [98,99].…”

Section: Crack Surface Displacement Extrapolation (Csde) Methodsmentioning

confidence: 99%

Fracture Mechanics Analyses for Interface Crack Problems - A Review

Krueger

Shivakumar

Raju

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Recent developments in fracture mechanics analyses of the interfacial crack problem are reviewed. The intent of the review is to renew the awareness of the oscillatory singularity at the crack tip of a bimaterial interface and the problems that occur when calculating mode mixity using numerical methods such as the finite element method in conjunction with the virtual crack closure technique. Established approaches to overcome the nonconvergence issue of the individual mode strain energy release rates are reviewed. In the recent literature many attempts to overcome the nonconvergence issue have been developed. Among the many approaches found only a few methods hold the promise of providing practical solutions. These are the resin interlayer method, the method that chooses the crack tip element size greater than the oscillation zone, the crack tip element method that is based on plate theory and the crack surface displacement extrapolation method. Each of the methods is validated on a very limited set of simple interface crack problems. However, their utility for a wide range of interfacial crack problems is yet to be established.

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Energy release rate and phase angle of delamination in sandwich beams and symmetric adhesively bonded joints

Cited by 23 publications

References 38 publications

Boundary-Layer Effect in Composite Beams with Interlayer Slip

Boundary-Layer Effect in Composite Beams with Interlayer Slip

Fracture and fatigue study of unidirectional glass/epoxy laminate under different mode of loading

Fracture Mechanics Analyses for Interface Crack Problems - A Review

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