Two numbers for a pull
Hang a weight from a wire and it stretches a little. Hang twice the weight and it stretches twice as much. A thicker wire stretches less, and a longer wire stretches more, so engineers compare materials with two numbers that cancel out the size of the sample. Stress is the force divided by the cross-section, in megapascals (newtons per square millimetre). Strain is the stretch divided by the original length, given here as a percentage.
A testing machine pulls a specimen slowly and records both. Plotted against each other they give a material’s stress–strain curve, which tells you almost everything about how it behaves when loaded. The steeper the first straight part, the stiffer the material: that slope is its Young’s modulus. The highest point is its tensile strength. How far the curve runs to the right is how much it stretches before it breaks.
Metals: springy, then plastic
At first a steel bar behaves like a very stiff spring. The atoms in its crystals are pulled slightly apart and, if you let go, they snap back. Pull harder and the bar yields: whole planes of atoms start to slide over each other inside the crystal grains. That slip is permanent. Let go now and the bar comes back only by its small springy part and stays longer.
Slipping is also what makes metals tough. Each grain that slips gets a little harder to slip further, so the bar carries more load as it stretches, until one spot starts to thin faster than the rest. That neck carries less and less, tiny voids open inside it and join up, and the bar tears in two. Mild steel stretches by more than a quarter of its length before that happens, which is plenty of warning.
Composites: strong fibres in light glue
A thin glass or carbon fibre is astonishingly strong along its length, because it is too fine to contain the flaws that weaken a thick piece. On its own, though, a bundle of fibres is as floppy as hair. Set them in a plastic resin such as epoxy and the resin shares the load between them and holds them in line. The result is a composite.
Composites do not yield. Their stress–strain line runs straight until the weakest fibres snap, the load jumps to their neighbours, and the whole specimen fails in a moment, leaving a brush of broken fibres.
Strength per kilogram
Carbon fibre composite is about three and a half times as strong as mild steel here, yet it weighs a fifth as much. Divide the tensile strength by the density and you get its specific strength: about 940 kilonewton-metres per kilogram for carbon fibre against 55 for mild steel, seventeen times more. That is why aircraft wings, racing bicycles and fishing rods are made of it, even though it gives no warning before it breaks and must be designed with a wide margin.
Try it: choose NiTi for Material, set Stretch to 5% and press Let go. The bar springs back to its own length. Do the same with Mild steel and it stays almost 5% longer.
A metal that springs back
Nickel–titanium, a shape-memory alloy, seems to break the rules. At room temperature its crystals are in a cubic arrangement called austenite. Pull on it and, at about 450 megapascals, rows of the crystal switch one after another into a longer, sheared arrangement called martensite. The bar stretches by about six percent with hardly any extra force: the flat plateau on its curve. Let go and the crystals switch back, so the bar returns to its own length. This superelasticity is used in glasses frames that survive being sat on, orthodontic wires and the stents that hold arteries open.
What this model leaves out
Each curve is a typical value; real ones vary with the alloy, its heat treatment, temperature and how fast it is pulled. Stress is the force divided by the original cross-section, so the curve falls as a metal necks even though the steel in the neck is carrying more stress than ever. A composite is far weaker across its fibres than along them, so real parts stack layers in several directions and end up less strong than the figure here. Nickel–titanium’s plateau stress rises with temperature, and its memory of shape when warmed is not shown. Repeated loading, which causes most real failures through fatigue, is left out.