Page 108 - Mechanical Behavior of Materials

Section 3.8 Materials Selection for Engineering Components 109

Table E3.1
ρ C m ρ
Rank for Radius Rank for
2/3 2/3
Material σ c Min. Mass r, mm σ c Min. Cost
Structural steel 0.194 8 5.81 0.194 2
Low-alloy steel 0.0740 6 3.59 0.222 3
Aluminum alloy 0.0447 5 4.77 0.268 4
Titanium alloy 0.0402 4 3.50 1.81 7
Polymer 0.0766 7 9.37 0.383 6
Wood 0.0258 2 8.33 0.0387 1
Glass–epoxy 0.0381 3 5.12 0.381 5
Graphite–epoxy 0.0168 1 3.80 3.36 8

3
Notes: Units are g/cm for ρ and MPa for σ c . The strength σ c is the
yield strength for metals, and the ultimate strength for wood, glass, and
composites. Ranks are 1 = best, etc., for minimum mass or cost.

where the second form has been manipulated to obtain the desired separate f 1 and f 2 , as set off
by brackets.
Since all of the quantities in f 1 have fixed values, the mass will be minimized if the f 2
expression is minimized. For example, for AISI 1020 steel,
ρ 7.9g/cm 3
f 2 = = = 0.194
2/3 2/3
σ c (260 MPa)
The similarly calculated values for the other materials are listed in the first column of
Table E3.1.
The ranking of materials as to mass (1 = best, etc.) is given in the second column. On this
basis, the graphite–epoxy composite is the best choice and wood the second best.
(b) Values of the required beam radius r may be calculated from the equation just developed
with the given values of P, L, and X, along with σ c for each material. For AISI 1020 steel, this
gives
1/3 1/3

4PL X 4(200 N)(100 mm)(2)
r = = 2 = 5.81 mm
πσ c π(260 N/mm )
The similarly calculated values for the other materials are listed in the third column of
Table E3.1.

3.8.2 Discussion

In selecting a material, there may be additional requirements or more than one quantity that needs
to be maximized or minimized. For example, for the preceding beam example, there might be a