Metal Foams: A Design Guide

Energy management: packaging and blast protection 161
carried by a tube and a foam, at a given displacement, is compared with
the measured result when the foam is inserted in the tube. This synergistic
enhancement is described by
Filled tube
Wv D W Tube
v
C WFoam v C W Int.
v
⊲11.15⊳
where the additional energy absorbed, W Int.
v , arises from the interaction
between the tube and the foam. This is because the foam provides internal
support for the tube wall, shortening the wavelength of the buckles and thus
creating more plastic folds per unit length (Abramowicz and Wierzbicki, 1988;
Hanssen et al., 1999) A similar gain in energy-absorbing efficiency is found
in the bending of filled tubes (Santosa et al., 1999).
The presence of the foam within the tube reduces the stroke υ before the
folds in the tube lock up, but, provided the density of the foam is properly
chosen, the increase in the collapse load, Fm, is such that the energy Fmυ
increasesbyupto30%(Seitzbergeret al., 1999).
11.4 Effect of strain rate on plateau stress
Impact velocities above about 1 m/s (3.6 km/h) lead to strain rates which can
be large: a 10 m/s impact on a 100 mm absorber gives a nominal strain rate of
100/s. It is then important to ask whether the foam properties shown here and
in Figures 4.6–4.11 of Section 4, based on measurements made at low strain
rates (typically 10 2 /s⊳, are still relevant.
Tests on aluminum-based foams show that the dependence of plateau stress
on strain rate is not strong (Kenny, 1996; Lankford and Danneman, 1998;
Deshpande and Fleck, 2000). Data are shown in Figures 11.11 and 11.12 for
an Alporas closed-cell foam and an ERG Duocel (Al-6101-T6) open-cell foam.
They suggests that the plateau stress, pl, increases with strain rate Pε by, at
most, 30%, over the range
3.6 ð 10 3 /s < Pε