Metal Foams: A Design Guide

160 Metal Foams: A Design Guide
That for the foam is
�
W Foam
w
D C1
s
� 1/2
ys
s
ε Foam
D
⊲11.14⊳
giving the same ratio as before – equation (11.12) – and with the same
conclusions.
More detailed calculations and measurements bear out the conclusions
reached here. Figure 11.10 shows the calculated energy per unit mass
absorbed by tubes plotted against the upper-bound collapse stress (the plateau
stress) compared with measured values for foams. Axially compressed tubes
outperform foams by a small but significant margin. Foams retain the
advantage that they are isotropic, absorbing energy equally well for any
direction of impact. Tubes hit obliquely are less good.
Energy absorbed/Unit mass (J/g)
20
10
8
6
4
2
1
0.8
0.6
0.083
0.155
d t /R = 0.01
0.168
Tubes
upper bound
0.02
0.276
0.3
0.345
0.05
0.646
Box
column
simulation
0.7
0.1
1.1
0.645
1
Alporas
Cymat
Alulight
Fraunhofer
0.1 0.5 1 5 10 50
Plateau stress, σ pl (MPa)
Figure 11.10 The energy absorbed per unit mass by tubes (full line) and by
metal foams, plotted against plateau stress, pl. The data for tubes derive
from an upper bound calculation of the collapse stress. Each foam is labeled
with its density in Mg/m 3
Foam-filled sections
A gain in efficiency is made possible by filling tubes with metal foam. The
effect is demonstrated in Figure 11.9 in which the sum of the individual loads