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REVIEW ARTICLES

Free-Edge Effects in Composite Laminates

[+] Author and Article Information
Christian Mittelstedt1

 AIRBUS Deutschland GmbH, Kreetslag 10, D-21129 Hamburg, Germanychristian.mittelstedt@airbus.com

Wilfried Becker

Fachbereich Maschinenbau, Fachgebiet Strukturmechanik, Technische Universität Darmstadt, Hochschulstraße 1, D-64289 Darmstadt, Germanybecker@mechanik.tu-darmstadt.de

1

Corresponding author.

Appl. Mech. Rev 60(5), 217-245 (Sep 01, 2007) (29 pages) doi:10.1115/1.2777169 History:

There are many technical applications in the field of lightweight construction as, for example, in aerospace engineering, where stress concentration phenomena play an important role in the design of layered structural elements (so-called laminates) consisting of plies of fiber reinforced plastics or other materials. A well known stress concentration problem rich in research tradition is the so-called free-edge effect. Mainly explained by the mismatch of the elastic material properties between two adjacent dissimilar laminate layers, the free-edge effect is characterized by the concentrated occurrence of three-dimensional and singular stress fields at the free edges in the interfaces between two layers of composite laminates. In the present contribution, a survey on relevant literature from more than three decades of scientific research on free-edge effects is given. The cited references date back to 1967 and deal with approximate closed-form analyses, as well as numerical investigations by the finite element method, the finite difference method, and several other numerical techniques. The progress in research on the stress singularities which arise is also reviewed, and references on experimental investigations are cited. Related problems are also briefly addressed. The paper closes with concluding remarks and an outlook on future investigations. In all, 292 references are included.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Symmetric four-ply laminate under uniaxial extension, allocation of coordinate axes

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Figure 5

Computational model and stress distributions according to Puppo and Evensen (17)

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Figure 6

Bilinear approximation of the interlaminar normal stress σ33 according to Pagano and Pipes (19)

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Figure 8

Stress distributions in an angle-ply laminate along the in-plane coordinate x2, Tang and Levy (55)

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Figure 9

Distributions of interlaminar stresses through the thickness of angle-ply laminates, Tang and Levy (55)

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Figure 10

General bimaterial notch with a plane interface between two dissimilar layers (k) and (k+1) with arbitrary notch opening angles (left), special case of a free laminate edge with right notch opening angles (right), and allocation of coordinate systems

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Figure 11

Order λ of the stress singularity at the free edge of a (±θ) interface, according to Wang and Choi (87)

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Figure 12

Finite element discretization employing sectorial elements around the singular point of a layered notch geometry according to Pageau (115), and sectorial element and natural coordinates

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Figure 13

Finite element discretization around the singular point of a layered notch geometry according to Yosibash and Szabo (119), and p version of the finite element method with variable polynomial degree of approximation within a single row of finite elements

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Figure 14

Finite element mesh of one laminate quadrant of a symmetric four-layer laminate according to Raju and Crews (131); upper portion: coarse, medium, and fine rectangular meshes; lower portion: mesh refinement in the free-edge region, and width coordinate x2 measured from the laminate center point

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Figure 15

Numerical results of Pipes and Pagano (10), stresses in the interface between the +θ and the −θ layer in (±θ)S angle-ply laminates under uniaxial extension; left portion: scaled stresses along the normalized width coordinate x2∕l2 measured from the laminate center point for θ=45°; right portion: normalized interlaminar free-edge stresses σ13 for varying θ

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Figure 16

Finite element discretization of one quadrant of a symmetric four-layer laminate, as employed by Wang and Crossman (161), and width coordinate x2 measured from the laminate center point

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Figure 20

Numerical results of Rohwer (165-167) for the stress field at the free edge of a (90°∕0°)S laminate

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Figure 21

Numerical results of Rohwer (165-167) for the stress field at the free edge of a (±45°)S laminate

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Figure 22

Finite element mesh of one laminate quadrant of a symmetric four-layer laminate according to Frick and Klamser (173); upper portion: medium mesh; lower portion: fine mesh and employed element types

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Figure 23

Finite element mesh of one laminate quadrant of a symmetric four-layer laminate according to Wang and Yuan (193-194), application of a hybrid singular edge element, and width coordinate x2 measured from the laminate center point

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Figure 24

Principle of scalability and discretization of a three-dimensional interface corner according to the SBFEM, and origin of coordinates placed at the corner tip

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Figure 25

Exemplary discretization of a symmetric four-ply laminate under uniaxial extension according to the SBFEM

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Figure 26

Laminate under thermomechanical load with circular hole through the thickness

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Figure 2

The free-edge effect in a cross-ply laminate (0°∕90°)S under uniaxial extension

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Figure 3

The free-edge effect in an angle-ply laminate (±45°)S under uniaxial extension

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Figure 4

Symmetric laminate coupon with four layers under uniaxial extension (upper portion), investigation of a central piece (lower left portion), and consideration of one quarterpiece (lower right portion) due to symmetry properties of the resultant displacement field

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Figure 7

Distribution of the scaled interlaminar normal stress σ33 in the middle plane of a (0°∕90°)S laminate under uniaxial extension according to Pagano (24)

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Figure 19

Finite element mesh of one laminate layer according to Rohwer (165-167)

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Figure 17

Numerical results of Wang and Crossman (161) for the interlaminar normal stress σ33 in (0°∕90°)S and (90°∕0°)S cross-ply laminates under uniaxial extension, scaled stresses along the normalized dimensionless width coordinate x2∕l2 measured from the laminate center point; left portion: σ33 in the laminate middle plane x3=0; right portion: σ33 in the interface at x3=d∕4

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Figure 18

Numerical results of Wang and Crossman (161) for the scaled interlaminar normal stress σ33 in the interfaces of a (90°∕0°∕−45°∕+45°)S laminate along the normalized dimensionless width coordinate x2∕l2 measured from the laminate center point (left portion); scaled interlaminar stresses σ33 and σ13 through the thickness of the same laminate (right portion)

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