What you Need
What to do
This experiment involves flames and very hot metal, which may stay hot for longer than you expect. Please make sure the experiment is done by a responsible person, and you take sensible precautions.
What may happen
You should find:
Why does it happen?
Metals, particularly iron based alloys such as steel, are much more complicated than you might expect. There are two different processes going on in this experiment to change how hard the paperclip is to bend.
Firstly, bending the paper clip back and forth produces an effect on the metal known as work hardening. As you do more work on the metal, it becomes harder and more brittle. Eventually, it will become so brittle that it will snap, and this is why you can snap a cheap spoon simply by bending it back and forth.
To understand why this happens, we will need to consider how a metal bends in the first place. A good place to start is the Naked Scientists Scrapbook: What is an alloy?, which explains not just what we mean by an "alloy" but also why the atomic structure of a metal is so important for it's properties.
In order to bend a metal, we must rearrange it's atomic structure. Metals form as crystals, meaning their atoms are arranged in repeating patterns. It would take a very large force to move a whole row of atoms along, so the bending actually occurs at tiny defects in the crystal called dislocations. These are where the lines of atoms don't quite meet up properly. Applying a small force can cause dislocations to move within the metal, allowing the metal itself to bend.
However if two dislocations which are oriented at different angles within the structure of the metal, come together, they can't move past each other. This means that the more you bend a metal, the more dislocations you create, and these block each other, making the material harder and harder to bend.
Heating up the steel gives the atoms in the steel lots and lots of energy. This allows any dislocations to move past each other, freeing them up, so when the steel is cooled it is once again very easy to bend. In fact, in this experiment it is actually easier to bend than it was to start with, as the very process of making a paper clip involves a lot of deformations. This means your original paper clip was already very work hardened.
The final process, heating followed by rapid cooling, is rather different, and is based on a very unusual property of iron. Iron has two different stable crystal structures and it switches between them at about 700°C. If you cool the metal slowly, there is plenty of time for the metal to change from one to the other, but if the metal is cooled very rapidly by dipping it in cold water, known as quenching, the atoms don't have time to reorganise themselves and the metal will form a third structure called martensite. This is very hard and very brittle, which makes the paperclip very stiff.