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Research Papers

Local Delamination Buckling of a Laminated Beam due to Three-Point Bending

[+] Author and Article Information
M. Toya1

Department of Mechanical Engineering, Graduate School of Science and Engineering, Kagoshima University, 1-21-40, Korimoto, Kagoshima 890-0065, Japantoyamasa@mech.kagoshima-u.ac.jp

K. Fukagawa

Department of Technology Education, Faculty of Education, Kagoshima University, 1-20-6, Korimoto, Kagoshima 890-0065, Japan

M. Aritomi, M. Oda, T. Miyauchi

Department of Mechanical Engineering, Graduate School of Science and Engineering, Kagoshima University, 1-21-40, Korimoto, Kagoshima 890-0065, Japan

1

Corresponding author.

J. Eng. Mater. Technol 132(3), 031007 (Jun 16, 2010) (9 pages) doi:10.1115/1.4001444 History: Received November 30, 2009; Revised March 12, 2010; Published June 16, 2010; Online June 16, 2010

Asymmetric three-point bending of a layered beam containing an interior interface crack is analyzed on the basis of the classical beam theory. Axial compressive and tensile forces are induced by bending in the parts of the beam above and below the delamination, and they are determined by modeling the cracked part as two lapped beams jointed together at the corners of both beams. When the magnitude of the applied load is small, the beam deflects, retaining the mutual contact of whole crack faces, but as the applied load reaches a critical value, local delamination buckling of the compressed part occurs. The relation between the magnitude of the applied load and the deflection at the point of load application is found to be nearly bilinear. The validity of this prediction is confirmed by experiments. It is also shown that once the delamination buckling occurs, the energy release rate generally becomes larger as compared with the case of a perfect contact of delaminated surfaces.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Three-point bending of a laminated beam containing an interface crack

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Figure 2

Analytical model for the delaminated part (free-body diagrams for the interval BD)

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Figure 3

Plots of F(Z) for several values of the applied force: (a) P=1.0 N, (b) P=2.3 N, and (c) P=3.5 N

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Figure 4

Deflection curves corresponding to the solution Z(1), Z(2), and Z(3) of F(Z)=0 for P=3.5 N: (a) Z(1), (b) Z(2), and (c) Z(3). Delamination lies between 0.11 m≤x≤0.35 m and loading point is at x=0.15 m.

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Figure 5

Relation between the applied load P and the deflection at the point of load application δ: (a) c=240 mm(d≥aL); (b) c=160 mm(d≤aL)

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Figure 6

Critical buckling load Pcr plotted for the crack length c/L

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Figure 7

Split-beam element with unit width under general loading condition (η is the distance of the neutral axis of the bonded beam from the top surface)

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Figure 8

Energy release rates: (a) left-hand tip; (b) right-hand tip

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Figure 9

Comparison of the compliances Φ between the theory and experiments. Dashed and solid line curves represent the theoretical values for post- and pre-bucklings, respectively. Triangles and circles represent the experimental results for post- and pre-bucklings, respectively.

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