Metal Foams: A Design Guide

Energy management: packaging and blast protection 163
11.5 Propagation of shock waves in metal foams
When a metal foam is impacted at a sufficiently high velocity, made precise
below, a plastic shock wave passes through it and the plateau stress rises.
Consider the idealized nominal compressive stress–strain curve for a metallic
foam, shown in Figure 11.13. It has an initial elastic modulus, E, and a plateau
stress, pl, before compaction occurs at a nominal densification strain, εD.
When such a foam is impacted an elastic wave propagates through it; and if the
stress rises above pl, this is followed by a plastic shock wave. In the simplified
one-dimensional case sketched in Figure 11.14(a) it is imagined that the bar
is initially stationary and stress-free. At a time t D 0, the left-hand end of the
bar is subjected to a constant velocity, V. In response, an elastic wave travels
σ
σ pl
U
ε
ε D
D
Figure 11.13 A schematic compressive stress–strain curve for a metal
foam; the stress jumps from the plateau level pl at U to the value D at D
Mass
M
Plastic wave front
Stress = σD Stress = σpl Velocity = VD Velocity = 0
Density = ρ/(1 - εD) Density = ρ
c pl
(a)
Plastic wave front
Stress = σD Stress = σpl Velocity = VD Velocity = 0
Density = ρ/(1 - εD ) Density = ρ
c pl
(b)
Figure 11.14 (a) The stress, velocity on either side of the plastic shock-wave
front for an impacted foam (b) The stress, velocity on either side of the plastic
shock wave front for an impacted foam carrying a buffer plate of mass M