Property charts

Engineers compare hundreds of materials at once with a property chart, often called an Ashby chart after the engineer Michael Ashby, who developed the idea. Each material becomes a blob on a map. A classic one has density on the horizontal axis and Young’s modulus (stiffness, introduced in World 2) on the vertical axis.

Both axes are logarithmic. On a log axis each equal step means “times 10” rather than “plus 10”. That is the only way to fit foam (very light and very floppy) and steel (heavy and stiff) on one page, because their values differ by factors of thousands.

Look at where things fall. Materials of the same family cluster together: polymers sit low in stiffness, metals sit in a heavy, stiff group, ceramics and glasses are stiff, woods and foams are light. Typical rough ranges:

• Foams: density about 10 to 100 kg/m³, stiffness well below 1 GPa.
• Woods (along the grain): about 300 to 1,000 kg/m³, roughly 5 to 20 GPa.
• Aluminium alloys: about 2,700 kg/m³, roughly 70 GPa.
• Steels: about 7,800 kg/m³, roughly 200 GPa.
• Carbon-fibre composites (along the fibres): about 1,500 to 1,600 kg/m³, roughly 100 to 200 GPa.

The top-left corner (light and stiff) is the most wanted, and it is where carbon fibre and wood sit.

The chart also has guidelines for design. Suppose you need a light, stiff beam that bends as little as possible for its weight. Theory says the best materials are the ones with the largest value of E^½ ÷ ρ (the square root of the modulus divided by the density). On a log-log chart this is a straight line with slope 2, so you can slide a line across the map and see which materials lie above it.

Worked example with typical values, in units of GPa^½ per (Mg/m³): steel 14 ÷ 7.85 is about 1.8; aluminium 8.3 ÷ 2.7 is about 3.1; oak along the grain 3.5 ÷ 0.7 is about 5; carbon fibre composite 11.8 ÷ 1.55 is about 7.6. For a beam of the same stiffness, carbon fibre and wood are lighter than aluminium, and aluminium is lighter than steel.