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RESEARCH PAPERS

Size Effect on Strength of Laminate-Foam Sandwich Plates

[+] Author and Article Information
Zdeněk P. Bažant

Department of Civil and Environmental Engineering,  Northwestern University, 2145 Sheridan Road, CEE∕A135, Evanston, IL 60208z-bazant@northwestern.edu

Yong Zhou1

Department of Civil and Environmental Engineering,  Northwestern University, Evanston, IL 60208

Isaac M. Daniel

Department of Civil and Environmental Engineering,  Northwestern University, 2145 Sheridan Road, CEE∕A135, Evanston, IL 60208imdaniel@northwestern.edu

Ferhun C. Caner2

 Northwestern University, Evanston, IL 60208

Qiang Yu

Department of Civil and Environmental Engineering,  Northwestern University, Evanston, IL 60208

1

Currently Assistant Professor, Department of Building Engineering, Tongji University, Siping Road 1239, Shanghai, China; e-mail: yongzhou@mail.tongji.edu.cn

2

Ramón y Cajal Researcher and Lecturer on leave from UPC (ETSECCPB, Campus Nord), Jordi Girona 1-3, Edif. D2, E-08034 Barcelona, Spain; e-mail: ferhun.caner@upc.edu

J. Eng. Mater. Technol 128(3), 366-374 (Dec 29, 2005) (9 pages) doi:10.1115/1.2194557 History: Received September 28, 2004; Revised December 29, 2005

Experiments on size effect on the failure loads of sandwich beams with PVC foam core and skins made of fiber-polymer composite are reported. Two test series use beams with notches at the ends cut in the foam near the top or bottom interface, and the third series uses beams without notches. The results demonstrate that there is a significant nonstatistical (energetic) size effect on the nominal strength of the beams, whether notched or unnotched. The observed size effect shows that the failure loads can be realistically predicted on the basis of neither the material strength concept nor linear elastic fracture mechanics (LEFM). It follows that nonlinear cohesive (quasi-brittle) fracture mechanics, or its approximation by equivalent LEFM, must be used to predict failure realistically. Based on analogy with the previous asymptotic analysis of energetic size effect in other quasibrittle materials, approximate formulas for the nominal strength of notched or unnotched sandwich beams are derived using the approximation by equivalent LEFM. Different formulas apply to beams with notches simulating pre-existing stress-free (fatigued) cracks, and to unnotched beams failing at crack initiation. Knowledge of these formulas makes it possible to identify from size effect experiments both the fracture energy and the effective size of the fracture process zone.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Dimensions of test beams with notches on top

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Figure 2

(a) Photo of top-notched test beams of all three sizes and (b) photo of top-notched beam of medium size during the test

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Figure 3

(a) Load-deflection diagrams measured on top-notched beams of three sizes and (b) nominal strength values of these beams compared to the classical energetic size effect law

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Figure 4

Dimensions of test beams with notches at bottom

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Figure 5

(a) Photo of bottom-notched test beams of all three sizes; and (b, c, d) photos of typical failure modes of bottom-notched beams for each of three sizes

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Figure 6

(a) Load-deflection diagrams measured on bottom-notched beams of three sizes and (b) nominal strength values measured on these beams of three sizes, compared to the classical energetic size effect law

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Figure 7

Dimensions of test beams with no notches

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Figure 8

(a) Photo of unnotched test beams of all three sizes; (b), (c), and (d) photo of typical failure modes for each of three beam sizes

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Figure 9

(a) Load-deflection diagrams measured on unnotched beams of three sizes and (b) nominal strength values measured on these beams, compared to the size effect law for failure at crack initiation

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Figure 10

Softening cohesive stress-slip curve for shear crack and its initial linear approximation

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Figure 11

Illustrations for beam-type analysis of fracture in the Appendix

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Figure 12

Fits of the numerical values of g(α) for the test series I and test series II

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