Page 109 - Mechanical Behavior of Materials

110 Chapter 3 A Survey of Engineering Materials

maximum permissible deflection. Application of the selection procedure to this situation gives a
new f 2 = f 2 (ρ, E) and a different ranking of materials. Hence, a compromise choice that considers
both sets of rankings may be needed.
Cost is almost always an important consideration, and the foregoing selection procedure can
be applied, with Q being the cost. Since costs of materials vary with time and market conditions,
current information from materials suppliers is needed for an exact comparison of costs. Some rough
values of relative cost are listed for the materials in Table 3.13. These relative costs are obtained by
rationing the cost to that of ordinary low-carbon structural steel (mild steel). Values are given in
terms of relative cost per unit mass, C m . The material ranking in terms of cost will seldom agree
with that based on performance, so compromise is usually required in making the final selection.
Other factors besides stiffness, strength, weight, and cost usually also affect the selection
of a material. Examples include the cost and practicality of manufacturing the component from
the material, space requirements that limit the permissible values of the geometry variable, and
sensitivity to hostile chemical and thermal environments. Concerning the latter, particular materials
are subject to degradation in particular environments, and these combinations should be avoided.
Information on environmental sensitivity is included in materials handbooks, such as those listed at
the end of this chapter.
In addition to deflections due to elastic strain, there are situations in which it is important
to consider deflections, or even collapse, due to plastic strain or creep strain. Also, fracture may
occur by means other than the stress simply exceeding the materials yield or ultimate strength. For
example, flaws may cause brittle fracture, or cyclic loading may lead to fatigue cracking at relatively
low stresses. Materials selection must consider such additional possible causes of component failure.
Note that plasticity, creep, fracture, and fatigue are covered in later chapters in this book, starting
with Chapter 8.
The general type of systematic materials selection procedure considered in this section is
developed in detail in the book by Ashby (2011), and it is also employed in the CES Selector 2009
materials database.

Example 3.2
For the beam problem of Ex. 3.1, extend the analysis to a consideration of cost.
Solution This can be accomplished by minimizing the quantity

Q = C m m
where C m is the relative cost per unit mass from Table 3.13. Using the expression obtained for
mass m near the end of Ex. 3.1, we find that this Q is

C m ρ
Q = [ f 1 (L, P, X)]
2/3
σ c
where f 1 is the same as before, and the quantity to be minimized is the expression in the second
brackets. Values of this new f 2 are added to Table E3.1, along with a new ranking.