Size Effect of Cohesive Delamination Fracture Triggered by Sandwich Skin Wrinkling

[+] Author and Article Information
Zdeněk Bažant

 Northwestern University, CEE, 2145 Sheridan Road, Evanston, IL 60208

Peter Grassl1

 University of Glasgow, Glasgow, United Kingdom


Formerly of Northwestern University, Evanston, IL.

J. Appl. Mech 74(6), 1134-1141 (Jan 24, 2007) (8 pages) doi:10.1115/1.2722778 History: Received May 16, 2006; Revised January 24, 2007

Because the observed size effect follows neither the strength theory nor the linear elastic fracture mechanics, the delamination fracture of laminate-foam sandwiches under uniform bending moment is treated by the cohesive crack model. Both two-dimensional geometrically nonlinear finite element analysis and one-dimensional representation of skin (or facesheet) as a beam on elastic-softening foundation are used. The use of the latter is made possible by realizing that the effective elastic foundation stiffness depends on the ratio of the critical wavelength of periodic skin wrinkles to the foam core thickness, and a simple description of the transition from shortwave to longwave wrinkling is obtained by asymptotic matching. Good agreement between both approaches is achieved. Skin imperfections (considered proportional to the the first eigenmode of wrinkling), are shown to lead to strong size dependence of the nominal strength. For large imperfections, the strength reduction due to size effect can reach 50%. Dents from impact, though not the same as imperfections, might be expected to cause as a similar size effect. Using proper dimensionless variables, numerical simulations of cohesive delamination fracture covering the entire practical range are performed. Their fitting, heeding the shortwave and longwave asymptotics, leads to an approximate imperfection-dependent size effect law of asymptotic matching type. Strong size effect on postpeak energy absorption, important for impact analysis, is also demonstrated. Finally, discrepancies among various existing formulas for critical stress at periodic elastic wrinkling are explained by their applicability to different special cases in the shortwave-longwave transition.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 6

Initial stress envelope represented in the principal stress space obtained with the damage loading function

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Figure 8

Deflection of the upper skin for the postpeak regime for imperfection δ=0.1 and for the sizes: (a) ξ=0.05 and (b) ξ=1 obtained from the softening foundation model

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Figure 1

(a) The geometry of a typical sandwich beam subjected to pure bending and (b) the beam subjected to an axial compression force P supported by a softening foundation

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Figure 2

Force-displacement relation of the softening foundation

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Figure 3

(a) The deflection of the top skin, (b) equilibriated stress acting on the foam, (c) equivalent height for shortwave, and (d) longwave wrinkling

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Figure 4

Evolution of the equivalent height heq for the transition from shortwave to longwave wrinkling

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Figure 5

Finite element mesh

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Figure 7

Load λ versus the midpoint displacement wa obtained with the softening foundation model and the finite element model for the imperfections: (a) δ=0.1, (b) δ=0.5, and (c) δ=1 for two sizes (ξ=1 and ξ=0.05)

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Figure 9

Load λ versus the blister length (mid beam region in which w>1) of the upper skin for the imperfections: (a) δ=0.1, (b) δ=1, and (c) δ=4 and for the sizes ξ=1, ξ=0.5, and ξ=0.1 obtained from the softening foundation model

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Figure 10

Comparison of the size effect law in Eq. 26 with the nominal strength-size curves obtained from the softening foundation model for different imperfections




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