Metal Foams: A Design Guide

Energy management: packaging and blast protection 169
the thickness hblast of foam required to absorb the blast is
J 2 i
hblast D
2 bbWvol
⊲11.33⊳
The efficiency of absorption is maximized by using a heavy buffer plate ⊲ bb⊳
and choosing the foam with the greatest Wvol for a given pl.
An alternative strategy might be to minimize the combined mass per unit
area, mt of the buffer plate and the foam. The mass per unit area of the buffer
plate is mb D bb, and the mass per unit area of the foam is mf D hblast.
Substitution for hblast from equation (11.33) into the expression for mf gives
J 2 i
mt D mb C mf D bb C
2 bbWvol
and minimization of mt with respect to the buffer plate mass mb D bb gives
mb D mf, and
�
2
mt D 2mf D Ji
Wvol
The thickness of the buffer plate is related to that of the foam simply by
b D hblast/ b.
An example
A charge of 1 kg of TNT in air produces a pressure pulse p D 5MPa (50
atmospheres), generating an impulse Ji D 600 Ns/m 2 at a distance 1m from the
charge. A steel buffer plate ( b D 7900 kg/m 3 ) 5 mm thick acquires a velocity
v D 15.2 m/s and a kinetic energy Ui D 4.6kJ/m 2 . The structure can support
a pressure of 0.3 MPa (3 atmospheres). The selection chart of Figure 11.3
indicates that a Cymat aluminum foam of density 0.155 Mg/m 3 has a plateau
stress just below this, and absorbs Wvol D 200 kJ/m 3 . From equation (11.33)
the required thickness of foam is 25 mm.
References
Abramowicz, W. and Wierzbicki, T. (1988) Axial crushing of foam-filled columns. Int. J. Mech.
Sci. 30(3/4), 263–271.
Andrews, K.R.F., England, G.L. and Ghani, E. (1983) Classification of the axial collapse of
cylindrical tubes. Int. J. Mech. Sci. 25, 687–696
Deshpande, V. and Fleck, N.A. (2000) High strain rate compressive behavior of aluminum alloy
foams. Int. J. Impact Engng. 24, 277–298.
Hanssen, A.G., Langseth, M. and Hopperstad, O.S. (1999) Static crushing of square aluminum
extrusions with aluminum foam filler. Int. J. Mech. Sci. 41, 967–993.