Materials selection

Why it matters

There are tens of thousands of engineering materials. Picking one by habit ("we always use steel") or by a single property ("it's the strongest") often gives heavy, expensive or failure-prone designs. Michael Ashby's method, taught in engineering schools worldwide, makes selection systematic: translate the design into requirements, turn those into a performance index, and compare materials on charts that plot one property against another. This lesson walks through the method so you can apply it with a calculator and paper.

Step 1: translate the design

Write down four things:

• Function: what does the part do? (Carry a bending load, hold pressure, conduct heat.)
• Constraints: non-negotiable requirements. (Must not yield; must not deflect more than 5 mm; must survive 80 °C; must cost less than a set amount.)
• Objective: what to minimise or maximise. (Minimise mass, minimise cost.)
• Free variables: what you are allowed to change. (Usually the material, and often one dimension such as thickness.)

Step 2: derive a performance index

Combine the objective with the constraint, and eliminate the free dimension. The material properties that remain form the index.

Example: a light, stiff tie (a rod in tension, fixed length L, must not stretch more than a set amount; free variable: its area A). Stiffness is E·A/L, so the required area is A = k·L/E, and mass is m = A·L·ρ = k·L²·(ρ/E). To minimise mass, maximise E/ρ.

Example: a light, stiff beam (fixed length, square section of free size, must not deflect more than a set amount). Working through the bending stiffness, which depends on E·I with I proportional to the section size to the fourth power, gives an index of E^(1/2)/ρ.

Common indices to minimise mass:

Here σf is the failure strength (usually yield strength for metals). For minimum cost instead of mass, replace ρ with the cost per unit volume.

Step 3: compare materials

Worked example: a light, stiff beam. Approximate properties (E in GPa, ρ in Mg/m³, which is the same number as g/cm³):

For a stiff tie, steel, aluminium and titanium are almost identical (E/ρ ≈ 25). For a stiff beam, the square root changes everything: low-density materials win, and wood and carbon-fibre composite beat steel by a factor of more than three. That is why light aircraft wing spars, bicycle frames and racing car chassis have moved from steel to aluminium, then to composites, and why wood has been used for so long in bending members.

Ashby charts

An Ashby chart plots two properties on log-log axes, for example Young's modulus against density, with every material family appearing as a bubble. On such a chart, a performance index becomes a straight line: for E^(1/2)/ρ the lines have slope 2. Slide a line of the right slope across the chart; materials above the line are better than those below. Constraints (such as a maximum cost or a minimum service temperature) are drawn as boxes that remove candidates. Free and commercial software (for example Ansys Granta EduPack, used in many universities) contains these charts and databases.

Step 4: screen, rank, then check the details

The index gives a short list, not a final answer. Finally consider what it cannot capture:

• cost and availability;
• manufacturing: can it be shaped, joined and finished in the quantities needed?
• environment: corrosion, UV, temperature, moisture (wood and some composites change with humidity);
• failure modes: toughness, fatigue, fire behaviour;
• sustainability: embodied energy and CO₂, recyclability;
• codes and standards that limit which materials may be used.

For any part that carries safety-critical loads, the chosen material and its design values must come from certified data and the governing standard, and the design must be reviewed by a qualified engineer (a licensed professional engineer where required).

Common mistakes

• Comparing raw properties instead of an index. Steel's high E looks impressive until you divide by its density.
• Using the wrong index. A tie and a beam reward different properties.
• Ignoring units. Use the same units for every candidate; the absolute value of an index matters less than the ranking.

Recap

• Function, constraints, objective, free variables.
• Eliminate the free variable to get a performance index.
• E/ρ for stiff ties, E^(1/2)/ρ for stiff beams, E^(1/3)/ρ for stiff panels.
• Ashby charts turn indices into lines; then check cost, processing and environment.

Try it

On the Do tab, select a material for a simple household part on paper, using an index and a hand-sketched Ashby-style chart.