Principles of materials selection

Selecting materials involves seeking the best match between design require­ments and the properties of the materials that might be used to make the

Selecting a material for a portable bike shed. The requirements are expressed as constraints and objectives (objectives in blue). Records containing data for materials are screened using the constraints and ranked by the objectives to find the most attractive candidates. These are then explored further by examining documentation.

product. Figure 8.3 shows the strategy of the last section applied to select­ing materials for a portable bike shed. On the left is the list of requirements that the material must meet, expressed as constraints and objectives. The constraints: ability to be molded, weather resistance, adequate stiffness, and strength. The objectives: as light and as cheap as possible. On the right is the database of material attributes, drawn from suppliers’ data sheets, hand­books, Web-based sources, or software specifically designed for materi als selection. The selection "engine" applies the constraints on the left to the materials on the right and ranks the survivors using an objective, delivering a short list of viable candidates, just as we did with cars. If both objectives are active, tradeoff methods like that of Figure 8.2 resolve the conflict.

There is, however, a complication. The requirements for the car were straightforward—doors, fuel type, power—all explicitly listed by the man­ufacturer. The design requirements for a component of a product specify what it should do but not what properties its materials should have. So the first step is one of translation: converting the design requirements into con­straints and objectives that can be applied to the materials database (see Figure 8.4). The next task is that of screening—as with cars, eliminating

FIGURE 8.4

the materials that cannot meet the constraints. This is followed by the ranking step, ordering the survivors by their ability to meet a criterion of excellence, such as that of minimizing cost, embodied energy, or carbon footprint. The final task is to explore the most promising candidates in depth, examining how they are used at present, case histories of failures, and how best to design with them, the step we called documentation. Now a closer look at each step.

Translation. Any engineering component has one or more functions: to support a load, to contain a pressure, to transmit heat, and so forth. This must be achieved subject to constraints: that certain dimensions are fixed, that the component must carry the design loads without failure, must insu­late against or conduct heat or electricity, must function safely in a cer­tain range of temperature and in a given environment, and many more.

Table 8.1 Function,

constraints, objectives, and free variables

Function

What does the component do?

Constraints

What nonnegotiable conditions must be met?

Objective

What is to be maximized or minimized?

Free variables

What parameters of the problem is the designer free to change?

In designing the component, the designer has one or more objectives: to make it as cheap as possible, perhaps, or as light, or as environmentally benign, or some combination of these. Certain parameters can be adjusted to optimize the objective; the designer is free to vary dimensions that are not constrained by design requirements and, most important, free to choose the material for the component. We call these free variables. Constraints, objectives, and free variables (see Table 8.1) define the boundary conditions for selecting a material and, in the case of load-bearing components, the choice of shape for its cross-section.

It is important to be clear about the distinction between constraints and objectives. A constraint is an essential condition that must be met, usu­ally expressed as an upper or lower limit on a material property. An object­ive is a quantity for which an extreme value (a maximum or minimum) is sought, frequently the minimization of cost, mass, volume, or—of particu­lar relevance here—environmental impact (see Table 8.2).

The outcome of the translation step is a list of the design-limiting prop­erties and the constraints they must meet. The first step in relating design requirements to material properties is therefore a clear statement of func­tion, constraints, objectives, and free variables.

Screening. Constraints are gates: meet the constraint and you pass through the gate, fail to meet it and you are shut out. Screening (Figure 8.4) does just that: it eliminates candidates that cannot do the job at all because one or more of their attributes lies outside the limits set by the constraints. As exam­ples, the requirement that "the component must function in boiling water" or that "the component must be nontoxic" imposes obvious limits on the attri­butes of maximum service temperature and toxicity that successful candi­dates must meet. The left column of Table 8.2 lists common constraints.

Ranking: material indices. To rank the materials that survive the screen­ing step we need criteria of excellence—what we have called objectives. The right column of Table 8.2 lists common objectives. Performance is some­times limited by a single property, sometimes by a combination of them.

Table 8.2 Examples of common constraints and objectives*

Common constraints

Common objectives

Must be:

Minimize:

Electrically conducting

Cost

Optically transparent

Mass

Corrosion resistant

Volume

Nontoxic

Thermal losses

Nonrestricted substance

Electrical losses

Able to be recycled

Resource depletion

Energy consumption

Must meet a target value of:

Carbon emissions

Stiffness

Waste

Strength

Environmental impact

Fracture toughness

Thermal conductivity

Service temperature

*Environment-related constraints and objectives are italicized.

Thus the best materials to minimize thermal losses (an objective) are the ones with the smallest values of the thermal conductivity, A; those to mini­mize DC electrical losses (another objective) are those with the lowest electrical resistivity pe—provided, of course, that they also meet all other constraints imposed by the design. Here the objective is met by minimizing a single property. Often, though, it is not one but a group of properties that are relevant. Thus the best materials for a light stiff tie-rod are those with the smallest value of the group, p/E, where p is the density and E is Young’s modulus. Those for a strong beam of lowest embodied energy are those with the lowest value of Hmp /а2/3, where Hm is the embodied energy of the material and ay is its yield strength. The property or property-group that maximizes performance for a given design is called its material index.

Table 8.3 lists indices for stiffness and strength-limited design for three generic components—a tie-rod, a beam, and a panel—for each of four object­ives. The first three relate to design for the environment. Selecting mater­ials with the objective of minimizing volume uses as little materials as possible, conserving resources. Selection with the objective of minimizing mass is central to the ecodesign of transport systems (or indeed of anything that moves) because fuel consumption for transport scales with weight. Selection with the objective of minimizing embodied energy is important when large quantities of material are used, as they are in construction of

Table 8.3 Indices for stiffness and strength-limited design

Configuration and

Configuration

Minimum

Minimum

Minimum

Minimum

objective

volume:

mass:

embodied

material cost:

minimize

minimize

energy: minimize

minimize

Stiffness-Limited Design

Tie

1/E

p/E

Hmp/E

Cmp/E

Beam

1/E1/2

p/E1/2

Hmp/E1/2

Cmp/E1/2

Panel

1/E1/3

p/E1/3

Hmp/E1/3

Cmp/E1/3

Strength-Limited Design

Tie

1/&y

p /&y

Hmp/lJy

Cmp&y

Beam

1 / &2/3

1/ & y

p /&2/3

Hm p /&2/3

Cm p / & 2/3

Panel

1/2 1/&y

p /&1/2

Hm p / &y12

1/2

Cm p / & y

Table 8.4

Indices for thermal design

Objective

Minimum steady-state heat loss: minimize

Minimum thermal inertia: minimize

Minimum heat loss in a thermal cycle: minimize

A

Cpp

(ACpp)1/2

Density, p (kg/m3)

Elastic (Young’s) modulus, E (GPa) Thermal conductivity A (W/m. K) Thermal diffusivity, a = >JCpp (m2/s)

Price, Cm ($/kg)

Yield strength, &y (MPa)

Specific heat, Cp (J/kg. K)

Embodied energy/kg of material, Hm (MJ/kg)

buildings, bridges, roads, and other infrastructure. The fourth column, selection with the objective of minimizing cost, is always with us.

Table 8.4 lists indices for thermal design. The first is a single property, the thermal conductivity A; materials with the lowest values of A minimize heat loss at steady state, that is, when the temperature gradient is constant. The other two guide material choice when the temperature fluctuates. The symbols are defined below Table 8.4.

There are many such indices, each associated with maximizing some aspect of performance. They provide criteria of excellence that allow ranking of materials by their ability to perform well in the given application. Their derivation is described more fully in the appendix to this chapter and in Chapter 9. All can be plotted on material property charts to identify the best candidates. The charts for the indices of Tables 8.3 and 8.4 appear later in this chapter (Section 8.6).

To summarize, then: screening uses constraints to isolate candidates that are capable of doing the job; ranking uses an objective to identify the candidates that can do the job best.

Documentation. The outcome of the steps so far is a ranked shortlist of candidates that meet the constraints and are ranked most highly by the objective. You could just choose the top-ranked candidate, but what hid­den weaknesses might it have? What is its reputation? Has it a good track record? To proceed further we seek a detailed profile of each: its documenta­tion (Figure 8.4, bottom).

What form does documentation take? Typically, it is descriptive, graphical, or pictorial: case studies of previous uses of the material, details of its corrosion behavior in particular environments, of its availability and pricing, warnings of its environmental impact or toxicity, or descriptions of how it is recycled. Such information is found in handbooks, suppliers ‘ data sheets, Websites of environmental agencies, and other high-quality Websites. Documentation helps narrow the shortlist to a final choice, allowing a defin­itive match to be made between design requirements and material choice.

Why are all these steps necessary? Without screening and ranking, the candidate pool is enormous and the volume of documentation is over­whelming. Dipping into it, hoping to stumble on a good material, gets you nowhere. But once a small number of potential candidates have been iden­tified by the screening-ranking steps, you can seek detailed documentation for these few alone, and the task becomes viable.