Metal Foams: A Design Guide

Energy management: packaging and blast protection 153
If the area of contact between the foam and packaged object is A, thefoam
will crush when
F D plA ⊲11.2⊳
Assembling these, we find the foam which will just protect the packaged
object from a deceleration a Ł is that with a plateau stress
Ł maŁ
pl �
A
⊲11.3⊳
The best choice of foam is therefore that with a plateau stress at or below this
value which absorbs the most energy.
If packaging of minimum volume is required, we seek the foams that satisfy
equation (11.3) and at the same time have the greatest values of the energy
per unit volume Wv absorbed by the foam up to densification:
Wv D plεD ⊲11.4a⊳
If packaging of minimum mass is the goal, we seek foams with the greatest
value of energy per unit weight, Ww, absorbed by the foam up to densification:
Ww D plεD
⊲11.4b⊳
where is the foam density. And if packaging of minimum cost is sought, we
want the foams with the greatest values of energy per unit cost, Wc, absorbed
by the foam up to densification:
Wc D plεD
Cm
⊲11.4c⊳
where Cm is the cost per unit mass of the foam. Figures 11.3, 11.4 and 11.5
show plots of energy per unit volume, mass and cost, plotted against plateau
stress, pl, for metal foams. These figures guide the choice of foam, as detailed
below.
It remains to decide how thick the package must be. The thickness of foam
is chosen such that all the kinetic energy of the object is absorbed at the
instant when the foam crushes to the end of the plateau. The kinetic energy
of the object, mv 2 /2, must be absorbed by the foam without causing total
compaction, when the force rises sharply. Equating the kinetic energy to the
energy absorbed by thickness h of foam when crushed to its densification
strain εD gives
plεDAh D 1
2 mv2
⊲11.5⊳