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Research Papers

# The Damage Tolerance of a Sandwich Panel Containing a Cracked Honeycomb Core

[+] Author and Article Information
I. Quintana Alonso

Department of Engineering, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UK

N. A. Fleck1

Department of Engineering, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UKnaf1@cam.ac.uk

1

Corresponding author.

J. Appl. Mech 76(6), 061003 (Jul 21, 2009) (8 pages) doi:10.1115/1.2912995 History: Received July 30, 2007; Revised October 23, 2007; Published July 21, 2009

## Abstract

The tensile fracture strength of a sandwich panel, with a center-cracked core made from an elastic-brittle diamond-celled honeycomb, is explored by analytical models and finite element simulations. The crack is on the midplane of the core and loading is normal to the faces of the sandwich panel. Both the analytical models and finite element simulations indicate that linear elastic fracture mechanics applies when a $K$-field exists on a scale larger than the cell size. However, there is a regime of geometries for which no $K$-field exists; in this regime, the stress concentration at the crack tip is negligible and the net strength of the cracked specimen is comparable to the unnotched strength. A fracture map is developed for the sandwich panel with axes given by the sandwich geometry. The effect of a statistical variation in the cell-wall strength is explored using Weibull theory, and the consequences of a stochastic strength upon the fracture map are outlined.

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Copyright © 2009 by American Society of Mechanical Engineers
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## Figures

Figure 10

Dependence of K¯ on the Weibull modulus. The dotted lines denote the analytical estimate of Eq. 33 for large m.

Figure 8

FE model used to assess the fracture toughness of the lattice

Figure 9

Maximum principal stress distribution for a typical strut in the lattice

Figure 11

Fracture map for a honeycomb core sandwich panel where the statistical variability of the cell-wall strength is included

Figure 1

Center-cracked sandwich plate made from a diamond-celled honeycomb and subjected to uniaxial tension

Figure 2

Crack morphology

Figure 3

(a) Regime I: uniform stress with practically no stress concentration at the crack tip. (b) Regime II: K-field exists. Strength is independent of crack length. (c) Regime III: K-field exists. Strength scales with crack length as a−1∕2. In all three regimes, the effective stress far ahead of the crack tip is equibiaxial, and of magnitude t¯σa upon neglecting the contribution from beam bending.

Figure 4

Fracture map for a panel containing a center crack and subjected to prescribed displacements. The sample geometries P1, P2, and P3 are explored in detail in Sec. 3 to illustrate the response within each regime.

Figure 5

Normalized net strength as a function of crack size. The width of the sandwich panel is much larger than its height (W∕H=20), and its height is much larger than the cell size (H∕ℓ=702). The solid lines denote analytic predictions.

Figure 6

Net strength as a function of relative density for a sandwich panel made from a lattice, which contains a central crack of length a∕ℓ=32. The panel has aspect ratios W∕H=20 and H∕ℓ=702.

Figure 7

Normal tractions directly ahead of the crack tip. The geometries are specified by P1:t¯=5×10−5, a∕ℓ=32; P2:t¯=0.15, a∕ℓ=3502, and P3:t¯=0.15, a∕ℓ=32.

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