An engineering component, such as a beam, shaft, tension member, column, or machine part, must not deform excessively or fail by fracture or collapse. At the same time, the cost and often the weight must not be excessive. The most basic consideration in avoiding excessive deformation is to limit the deflection due to elastic strain.
For a given component geometry and applied load, the resistance to elastic deflection—that is, the stiffness—is determined by the elastic modulus E of the material. As to strength, the most basic requirement is to avoid having the stress exceed the failure strength of the material, such as the yield strength σo from a tension test.
Material Selection for Engineering Components
Consider the general situation in which an engineering component must meet one or more requirements related to its performance, such as a maximum permissible deflection and/or a given safety factor against yielding in the material.
Further, assume that any of several candidate materials may be chosen. It is often possible in such situations to perform a systematic analysis that will provide a ranking of materials for each performance requirement, thus providing an organized framework for making the final choice. Such methodology will be introduced in this section.
The elastic modulus E is specifically a measure of the stiffness of the material under axial loading. For shear stress and strain, which are important for torsional loading, it is replaced by the similarly defined shear modulus G.
The yield strength σo is mainly relevant to ductile materials, where this stress characterizes the beginning of relatively easy further deformation. For brittle materials, there is no clear yielding behavior, and the most important strength property is the ultimate tensile strength σu.
In addition, we will need to employ some results from elementary mechanics of materials, specifically equations for stresses and deflections for simple component geometries.
A few representative structural engineering materials from various classes and some of their properties are listed in Table 1. We will use this list in examples and problems related to materials selection. There are, of course, many thousands of engineering materials or variations of a given material.
Hence, selections from this list should be regarded only as a rough indication of what class or classes of material might be considered in more detail for a given situation.
Consider the case of a cantilever beam having a circular cross section and a load at the end, as in Fig. 1. Assume that the function of the beam requires that it have a particular length L and be capable of carrying a particular load P.
Further, let it be required that the maximum stress be below the failure strength of the material, σc = σo or σu, by a safety factor X, which might be on the order of 2 or 3. Weight is critical, so the mass m of the beam must be minimized.
Finally, the diameter, d = 2r, of the cross section may be varied to allow the material chosen to meet the various requirements just noted.
A systematic procedure can be followed that allows the optimum material to be chosen in this and other analogous cases. To start, classify the variables that enter the problem into categories as follows:
(1) requirements, (2) geometry that may vary, (3) materials properties, and (4) quantity to be minimized or maximized. For the beam example, with ρ being the mass density, these are
- Requirements: L, P, X
- Geometry variable: r
- Material properties: ρ, σc
- Quantity to minimize: m
Next, express the quantity Q to be minimized or maximized as a mathematical function of the requirements and the material properties, in which the geometry variable does not appear:
Q = f1 (Requirements) f2 (Material)
For the beam example, Q is the mass m, so that the functional dependencies needed are
m = f1(L, P, X) f2(ρ , σc)
with the beam radius r not appearing. Note that all the quantities in f1 are constants for a given design, whereas those in f2 vary with material.
For the procedure to work, the equation for Q must be expressed as the product of two separate functions f1 and f2, as indicated. Fortunately, this is usually possible. The geometry variable cannot appear, as its different values for each material are not known at this stage of the procedure.
However, it can be calculated later for any desired values of the requirements. Once the desired Q = f1 f2 is obtained, it may be applied to each candidate material, and the one with smallest or largest value of Q chosen, depending on the situation.
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 maximum permissible deflection.
Application of the selection procedure to this situation gives a new f2 = f2(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 1.
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, Cm. 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.
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.
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.