On 16th January 1943 in Portland, Oregon, USA, the air was split by a crack so loud that it could be heard over a mile away. It was the sound of the tanker SS Schenectady breaking in two. The Wikipedia page with a rather impressive picture of the snapped-in-two tanker is here. It is believed that the hull just fractured – it was unusually cold that day and low temperatures can make metal brittle. The hull was found to be made of poor quality steel.

Clearly, ships breaking in two is upsetting. Worse is airliner fuselage fracturing, in the early days of jet airliners in the 1950s, the fuselages of a couple of Comets (one of the first commercial airliners) fractured, causing them to crash.

This forced people to ask the basic question: Why do things break? Can we predict how much force a material will bear before it breaks? Airplanes are a classic case where we need to be able answer the second question. For planes, weight is at absolute premium so we can’t just make fuselages thicker and thicker to make them stronger, as then they will be so heavy the plane won’t take off. But on the other hand the materials must be as reliable as possible, a fuselage failure when a passenger jet is 20 km up is likely to prove fatal for hundreds of passengers and crew.

The answer as to why things fracture was more-or-less discovered by an aerospace engineer called A.A. Griffiths, during the first world war. The reason is cracks.

If materials like steel and glass were internally perfect they would be almost unbreakable. But they aren’t perfect, and when say a piece of glass is bent or pulled, it can cause microscopic cracks (too small to be seen by the naked eye) to grow. These growing cracks then grow right across the glass and then the glass has cracked into two.

When you pull on say a metal or glass object, it will stretch elastically a little bit. For something like glass or steel the stretching is usually too small to be noticed, but it is there. And like with an elastic band where the stretching is much larger and so more noticeable, the stretching stores energy in the material.

Opening a crack can release some of this elastic energy. In fact for a crack of length l, opening it releases an energy of around s²l³/E, where s is the force you are applying (per unit area of material), and E is what is called the elastic modulus, it is a measure of how stiff the material is. Anyway, so the stored elastic energy around a crack of length l, scales as cube of length l, i.e., as a volume.

When a crack spreads new glass or metal surface is created, and work must be done to do this, this amount of work scales as an area,  i.e., it increases as l². This is an area.

So the elastic energy released when a crack of length l opens up increases as l³, while the energy cost of forming it increases as l². The cube of a number increases faster than the square. This means two things. The first is that small cracks stay closed unless a very large force is applied, which means that small cracks are not dangerous – they won’t open up if a small force is applied.

The second is that once a crack opens up it tends to keep going as the bigger it gets the larger is the imbalance between the elastic energy released, and the energy needed to create the new surface. So once large cracks start to open up it is a runaway process. The crack zooms up in size from too small to be seen to crossing the whole width of a ship.