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Materials 63
Figure 2–15

Young’s modulus E for various materials. (Figure courtesy of Prof. Mike Ashby, Granta Design, Cambridge, U.K.)

1000
Tungsten carbides
Nickel alloys
Cast iron, gray
Low-alloy steel Titanium alloys
100
GFRP, epoxy matrix (isotropic)
Copper alloys
Soda-lime glass
10
Polyester
Wood, typical along grain
Wood, typical across grain
Young's modulus, GPa 0.1 1 Acrylonitrile butadiene styrene (ABS) Rigid polymer foam (MD)

0.01 Cork

Polyurethane
1e-3
Butyl rubber

Flexible polymer foam (VLD)
1e-4

in Fig. 2–15. Each vertical line represents the range of values of E for a particular
material. Only some of the materials are labeled. Now, more material information
can be displayed if the x axis represents another material property, say density.
Figure 2–16, called a “bubble” chart, represents Young’s modulus E plotted against
density ρ. The line ranges for each material property plotted two-dimensionally now
form ellipses, or bubbles. Groups of bubbles outlined according to the material families
of Table 2–4 are also shown. This plot is more useful than the two separate bar charts
of each property. Now, we also see how stiffness/weight for various materials relate.
The ratio of Young’s modulus to density, E r, is known as the specific modulus, or
specific stiffness. This ratio is of particular interest when it is desired to minimize
weight where the primary design limitation is deflection, stiffness, or natural frequency,
rather than strength. Machine parts made from materials with higher specific modulus
will exhibit lower deflection, higher stiffness, and higher natural frequency.
In the lower right corner of the chart in Figure 2–16, dotted lines indicate ratios of
b
E r. Several parallel dotted lines are shown for b = 1 that represent different values of
the specific modulus E r. This allows simple comparison of the specific modulus
between materials. It can be seen, for example, that some woods and aluminum alloys have
about the same specific modulus as steels. Different values of b allow comparisons for