Metal Foams: A Design Guide

120 Metal Foams: A Design Guide
F
Mode
A
F = F A
Mode A Mode B
H t
Overhang, H
Mode B
F = F B
Figure 10.5 The competition between collapse modes A and B for core
shear
In order to gage the practical significance of the overhang, let us take some
representative values for a typical sandwich panel comprising aluminum skins
c and a metallic foam core, with c/ℓ D 0.1, t/c D 0.1, y / f y D 0.005. Then,
the transition overhang length, Ht, isgivenbyHtD0.1ℓ: that is, an overhang
of length 10% that of the sandwich panel span ℓ is sufficient to switch the
collapse mode from mode A to mode B. Furthermore, the enhancement in
collapse load due to plastic bending of the face sheets above the load required
to shear the core is about 20% for a small overhang, H − Ht, and is about
40% for H>Ht. In much of the current literature on sandwich panels, a gross
approximation is made by neglecting the contribution of the face sheets to the
collapse load.
Parallel expressions can be derived for the collapse of a sandwich beam in
four-point bending by core shear. The collapse load for mode A becomes
FA D 2bt2 f
y
ℓ s
C 2bc c �
y 1 C 2H
�
⊲10.20⊳
ℓ s
and that for mode B is
FB D 4bt2
ℓ s
f
y C 2bc c y
⊲10.21⊳
The transition length of overhang at which the expected collapse mode
switches from mode A to mode B is given by the same expression (10.19) as
for a beam in three-point bending.
10.3 Collapse mechanism maps for sandwich panels
It is assumed that the operative collapse mechanism for a sandwich beam is the
one associated with the lowest collapse load. This can be shown graphically