Metal Foams: A Design Guide

212 Metal Foams: A Design Guide
16.5 Applications
Two examples of the method follow, each exploring the viability of metal
foams in a particular application. In the first, metal foams prove to be nonviable.
In the second, despite their present high cost, they prove to be viable.
The examples are deliberately simplified to bring out the method. The principles
remain the same when further detail is added.
Simple trade-off between two performance indices
Consider selection of a material for a design in which it is desired, for reasons
of vibration control, to maximize the specific modulus E/ (E is Young’s
modulus and is the density) and the damping, measured by the loss coefficient
. We identify two performance metrics, P1 and P2, defined such that
minima are sought for both:
and
P1 D E
P2 D 1
⊲16.10a⊳
⊲16.10b⊳
Figure 16.9 shows the trade-off plot. Each bubble on the figure describes
a material; the dimensions of the bubble show the ranges spanned by these
property groups for each material. Materials with high values of P1 have
low values of P2, and vice versa, so a compromise must be sought. The
optimum trade-off surface, suggested by the shaded band, identifies a subset
of materials with good values of both performance metrics. If high E/ (low
P1) is of predominant importance, then aluminum and titanium alloys are a
good choice; if greater damping (lower P2) is required, magnesium alloys or
cast irons are a better choice; and if high damping is the over-riding concern,
tin or lead alloys and a range of polymers become attractive candidates. It is
sometimes possible to use judgement to identify the best position on the tradeoff
surface (strategy 1, above). Alternatively (strategy 2) a limit can be set for
one metric, allowing an optimum for the other to be read off. Setting a limit of
>0.1, meaning P2 < 10, immediately identifies pure lead and polyethylenes
as the best choices in Figure 16.9. Finally, and preferably (strategy 3), a value
function can be determined:
1
V D ˛1P1 C ˛2P2 D ˛1 C ˛2
⊲16.11⊳
E
seeking materials which minimize V. Contours of constant V, likethoseof
Figure 16.7, have slope
� �
∂P2
D
∂P1
˛1
⊲16.12⊳
˛2
V