Metal Foams: A Design Guide

Indentation
Sandwich structures 117
The indentation mode of collapse involves the formation of four plastic hinges
within the top face sheet adjacent to each indenter, with compressive yield of
the underlying core, as sketched in Figure 10.3. Early studies on the indentation
of polymer foams (for example, Wilsea et al., 1975) and more recently
on metal foams (Andrews et al., 1999) reveal that the indentation pressure is
only slightly greater than the uniaxial compressive strength. The underlying
cause of this behavior is the feature that foams compress with little transverse
expansion (see Chapter 7 and Gibson and Ashby, 1997).
Plastic hinge
F/2
F
a ;;
λ ;; q
;;
;;
s C Y
M p
Figure 10.3 Indentation mode of collapse for a three-point bend
configuration
F/2
Consider first the case of three-point bending. Then the collapse load F on
the upper indenter can be derived by a simple upper bound calculation. Two
segments of the upper face, of wavelength , are rotated through a small angle
. The resulting collapse load is given by
F D 4Mp C ⊲a C ⊳ b c y ⊲10.12⊳
where Mp D bt2 /4 is the full plastic moment of the face-sheet section. Minimization
of this upper bound solution for F with respect to the free parameter
gives an indentation load FI of
FI D 2bt
� cy
and a wavelength
�
�
�
D t�
f y
c
y
f
y C ab c y
⊲10.13⊳
⊲10.14⊳
We note in passing that the same expression for FI and as given by
equations (10.13) and (10.14) are obtained by a lower bound calculation, by