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Research Papers

Interlaminar Stresses in Composite Laminates Subjected to Anticlastic Bending Deformation

[+] Author and Article Information
Oleksandr Kravchenko

School of Aeronautics and Astronautics,
Purdue University,
701 W. Stadium Ave.,
Armstrong Hall of Engineering,
West Lafayette, IN 47907

R. Byron Pipes

School of Aeronautics and Astronautics,
Schools of Materials Engineering and Chemical Engineering,
Purdue University,
701 W. Stadium Ave.,
Armstrong Hall of Engineering,
West Lafayette, IN 47907

Manuscript received August 7, 2012; final manuscript received October 17, 2012; accepted manuscript posted October 30, 2012; published online May 16, 2013. Assoc. Editor: Anthony Waas.

J. Appl. Mech 80(4), 041020 (May 16, 2013) (7 pages) Paper No: JAM-12-1378; doi: 10.1115/1.4007969 History: Received August 07, 2012; Revised October 17, 2012; Accepted October 30, 2012

Approximate elasticity solutions for prediction of the displacement, stress, and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension and uniform temperature change were developed earlier by the authors. In the present paper, the authors have extended these solutions to treat bending deformation. Bending and torsion moments are combined to yield a deformation state without twisting curvature and with transverse curvature due only to the laminate Poisson effect. This state of deformation is termed anticlastic bending. The approximate elasticity solution for this bending deformation is shown to recover laminated plate theory predictions at interior regions of the laminate and thereby illustrates the boundary layer character of this interlaminar phenomenon. The results exhibit the anticipated response in congruence with the solutions for uniform axial extension and uniform temperature change, where divergence of the interlaminar shearing stress is seen to occur at the intersection of the free edge and planes between lamina of +θ and –θ orientation. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem and thereby provide an efficient and compact solution available for parametric studies of the influence of geometry and material properties. Finally, the solution was exercised to determine the dimensions of the boundary layer in bending for very large numbers of layers.

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Figures

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Fig. 1

(a) Laminate geometry; (b) boundary value problem

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Fig. 2

U,y at the free edge for four-ply laminate

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Fig. 3

In-plane and interlaminar shearing stress approaching the free edge for four-ply laminate

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Fig. 4

Interlaminar shearing stress at the free edge for four-ply laminate

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Fig. 5

U across the top surface, z = 2h0, for four-ply laminate

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Fig. 6

U at the free edge for four-ply laminate

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Fig. 7

Interlaminar shearing stress at free edge for eight-ply laminate

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Fig. 8

U at free edge for eight-ply laminate

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Fig. 9

U at free edge for 32 -, 64 -, and 128-ply laminates

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Fig. 10

Dependence of U on lamina fiber orientation

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Fig. 11

U approaching free edge for 4 -, 8 -, and 16-ply laminates illustrating boundary layer phenomenon

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Fig. 12

Dependence of boundary layer width on lamina fiber orientation

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Fig. 13

Dependence of boundary layer importance on lamina fiber orientation

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