Page 91 - Shigley's Mechanical Engineering Design

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66 Mechanical Engineering Design
Figure 2–17 1000 3 1
Modulus–density Ceramics 0.3
A schematic E versus ρ chart Metals
showing a grid of lines for Search Composites
100 region
various values the material 0.1
index M = E 1/2 /ρ. (From Increasing values
Young's modulus E, GPa Woods E /
1/2
M. F. Ashby, Materials Selection of index E /
in Mechanical Design, 3rd ed., 10
Elsevier Butterworth- 1/2
1/2
Heinemann, Oxford, 2005.) 1 (GPa) /(Mg/m) 3

0.1 Foams Polymers

Elastomers
MFA 04
0.01
0.1 1 10 100
Density, Mg/m 3
Figure 2–18 1000
Modulus–density Ceramics
The search region of Fig. 2–16 Metals
further reduced by restricting Search Composites
100 region
E ≥ 50 GPa, (From M. F.
Ashby, Materials Selection in
Young's modulus E, GPa 1 E 50 GPa
Index
Mechanical Design, 3rd ed., E / 3
1/2
Elsevier Butterworth- 10
Heinemann, Oxford, 2005.) Woods Modulus

0.1 Polymers

Foams
Elastomers
0.01 MFA 04
0.1 1 10 100
Density, Mg/m 3

50 GPa. Figure 2–18 shows how this further restricts the search region. This eliminates
woods as a possible material.
Another commonly useful chart, shown in Fig. 2–19, represents strength versus
density for the material families. The ratio of strength to density is known as specific
strength, and is particularly useful when it is desired to minimize weight where the pri-
mary design limitation is strength, rather than deflection. The guidelines in the lower
right corner represent different relationships between strength and density, in the form
b
of S r. Following an approach similar to that used before, it can be shown that for
axial loading, b = 1, and for bending loading, b = 2 3.
Certainly, in a given design exercise, there will be other considerations such as
environment, cost, availability, and machinability, and other charts may be necessary to
investigate. Also, we have not brought in the material process selection part of the pic-
ture. If done properly, material selection can result in a good deal of bookkeeping. This
is where software packages such as CES Edupack become very effective.