Metal Foams: A Design Guide

152 Metal Foams: A Design Guide
Force F
δ D
Energy
W
F m
Stress σ
Displacement, δ Strain ε
(a) (b)
E
ε D
Energy W v
Figure 11.1 (a) A load-deflection curve and (b) a stress–strain curve for an
energy absorber. The area under the flat part (‘plateau’) of the curves is the
useful energy, W, or energy per unit volume, Wv, which can be absorbed.
Here F is the force, υ the displacement, the stress and ε the strain
Velocity
v
Packaging
Packaged
object,
mass m
Thickness h
Figure 11.2 A packaged object. The object is surrounded by a thickness, h,
of foam
nominal strain, εD. Energy absorbers for packaging and protection are chosen
so that the plateau stress is just below that which will cause damage to
the packaged object; the best choice is then the one which has the longest
plateau, and therefore absorbs the most energy before reaching εD. Thearea
under the curve, roughly plεD, measures the energy the foam can absorb,
per unit initial volume, up to the end of the plateau. Foams which have
a stress–strain curve like that shown in Figure 11.1 perform well in this
function.
Consider the package shown in Figure 11.2, made from a foam with a
plateau stress pl and a densification strain εD. The packaged object, of mass
m, can survive deceleration up to a critical value a Ł . From Newton’s law the
maximum allowable force is
F D ma Ł
σ P l
⊲11.1⊳