芯の折れないシャーペンって英語でなんて言うの？

The no-break mechanical pencil allows the lead to flex under pressure without breaking. It is an innovative product and has relatively recently come on the market to buy. They are not easy to find and purchase in UK shops, however they are available at some online stores.

Explanation: A mechanical pencil uses liquid graphite to produce a continuous stream of pencil as it is used.
Example sentence:
"I prefer writing with a liquid graphite pencil as it seems neater than pen."

A mechanical pencil is a pencil that can be extended when the lead runs out to have 'unbreakable lead' means that the lead end will not break and keep going
A liquid pencil has liquid grpahite so it is smooth and constantly writes

This mechanical pencil's lead does not break. - just informing the person that the lead of the mechanical pencil does not break.
My mechanical pencil's lead never breaks on me. - a slightly more personal response that informs the other person that your pencil is reliable.

a mechanic is the term used to descbribe someone who works with things such as a mechanical pencil and other mechanical things, such as cars and motors.
unbreakable, something that is unable to break.

These are other names for a mechanical pencil.