Metal Foams: A Design Guide

156 Metal Foams: A Design Guide
from which
h D 1 mv
2
2
plεDA
or using equation (11.3):
v 2
⊲11.6⊳
h D 1
2 a Ł ⊲11.7⊳
εD
with εD D 0.8 1.75⊲ / s⊳ (a best fit to recent data for metal foams). Manufacturers’
data sheets for the foams give pl and εD, allowing h to be calculated
for a given m, v and aŁ . Figure 11.6 shows a plot of equation (11.7). The use of
equations (11.6) and (11.7) to design packaging is summarized in Table 11.3.
Table 11.3 Summary of the steps in initial scoping to select a foam for
packaging
(1) Tabulate
ž The mass of the product, m
ž The limiting g-factor for the product (Table 11.1), aŁ ž The impact velocity (Table 11.2), v
ž The area of contact between the product and the package, A
ž The design objective: minimum volume, or mass, or cost
(2) Calculate the foam crush-stress (the plateau stress) which will just cause
the limiting deceleration from equation (11.3).
(3) Plot this as a vertical line on Figures 11.3, 11.4 or 11.5, depending on
the objective:
ž Minimum volume: Figure 11.3
ž Minimum mass: Figure 11.4
ž Minimum cost: Figure 11.5
Only foams to the left of the line are candidates; those to the right have
plateau stresses which will cause damaging decelerations. Select one or
more foams that lie just to the left of the line and as high as possible on
the energy scale. Note that the choice depends on the objective.
(4) Use these and the mass and velocity to calculate the required thickness
of foam h to absorb all the kinetic energy without reaching the
densification strain, using the plateau stress and densification strain
which can be read from the data sheet of the chosen foam.
(5) Apply sensible safety factors throughout to allow for margins of error on
mass, velocity and foam density.