Metal Foams: A Design Guide

116 Metal Foams: A Design Guide
10.2 The strength of sandwich beams
In the design of sandwich beams, the strength is important as well as the stiffness.
Consider again the sandwich beams under four-point bending and under
three-point bending, as sketched in Figure 10.2. Simple analytical formulae
can be derived by idealizing the foam core and solid face-sheets by rigid,
ideally plastic solids of uniaxial strength f y and c y , respectively.
Face yield
When the skins of a sandwich panel or beam are made from a material of
low yield strength, face yield determines the limit load Ffy. The simplest
approach is to assume that plastic collapse occurs when the face sheets attain
while the core yields simultaneously at a stress level of
the yield strength f y
c
y
. For both three- and four-point bending, the collapse load is determined
by equating the maximum bending moment within the sandwich panel to the
plastic collapse moment of the section, giving
Ffy D
4bt⊲c C t⊳
ℓ
f
y
C bc2
ℓ
for three-point bending, and
Ffy D
4bt⊲c C t⊳
ℓ s
f
y
c
y
C bc2
ℓ s
c
y
⊲10.9⊳
⊲10.10⊳
for four-point bending.
These relations can be simplified by neglecting the contribution of the core
to the plastic collapse moment, given by the second term on the right-hand
sides of equations (10.9) and (10.10). On labeling this simplified estimate of
the collapse load by Ffy we find that
Ffy
Ffy
D 1 C t c
C
c 4t
c
y
f
y
⊲10.11⊳
for both three- and four-point bending. The error incurred by taking Ffy
instead of Ffy is small for typical sandwich panels with a metallic foam core.
For example, upon taking the representative values t/c D 0.1 and c y / f y D
0.02, we obtain an error of 15% according to equation (10.11). It is safer to
design on Ffy than on Ffy because a low-ductility core will fracture almost
as soon as it yields, causing catastrophic failure.