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TECHNICAL PAPERS

Energy Release Rates for an Edge Delamination of a Laminated Beam Subjected to Thermal Gradient

[+] Author and Article Information
M. Toya

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

M. Oda, A. Kado, T. Saitoh

ULSI Device Development Division,  NEC Corporation, Kanagawa 229-1198, Japan

J. Appl. Mech 72(5), 658-665 (Nov 04, 2004) (8 pages) doi:10.1115/1.1978917 History: Received June 28, 2001; Revised November 04, 2004

Energy release rates for an edge delamination of a laminated beam subjected to through-thickness temperature gradient are analyzed on the basis of the classical beam theory. The decomposition of the energy release rate into mode I and mode II components is made by combining the analyses of the energy release rates by Toya (1992) and the two-dimensional elasticity solutions for a split-beam element by Suo and Hutchinson (1990). The energy release rate is a quadratic function of the temperatures of the top and bottom surfaces of the beam. The transition of the type of crack growth between pure mode II and mixed mode type occurs at the temperature difference corresponding to the minimum energy release rate. Numerical analyses based on finite-element method are also carried out, which show that the theory agrees well with numerical results when temperature jump across the delaminated surfaces is relatively small as compared with the temperature difference between the top and bottom surfaces of the layered beam.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Model of a laminated beam with an edge delamination subject to temperature gradient

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Figure 2

Cut and paste procedure for analyzing thermal stress of a cracked laminate. (y¯ is the distance of the neutral axis of the bonded part from the top surface.)

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Figure 3

Schematic diagram of the mesh division

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Figure 4

Variation of energy release rate and its components with temperature difference for the case of T2=0°C and Bc=∞. (a) Alumina (upper layer)∕titanium alloy (lower layer), h1=h2=4mm; (b) alumina∕Pyrex glass, h1=h2=2mm.

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Figure 5

Variation of energy release rate and its components with temperature difference for the case of T2=500°C and Bc=∞. (a) Alumina (upper layer)∕titanium alloy (lower layer), h1=h2=4mm; (b) alumina∕Pyrex glass, h1=h2=2mm; (c) titanium alloy∕alumina, h1=h2=4mm.

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Figure 6

Effect of Bio number on the relation between energy release rate and temperature difference for alumina (upper layer)∕Pyrex glass (lower layer) laminate of h1=h2=2mm. (a) T2=0°C; (b) T2=500°C.

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Figure 7

Variation of energy release rate with thickness ratio for alumina (upper layer)∕carbon steel (lower layer) laminate (Bc=∞,T2=0°C)

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Figure 8

Variation of energy release rate with the length of delamination for alumina (upper layer)∕Pyrex glass (lower layer) laminate (Bc=∞,T1=250°C,T2=0°C,h1=h2=4mm)

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