Just so you know, your ID does not contain an RFID chip.

As for the crack, there's no hard and fast rule as to what damages are accepted - rather it depends on the judgment of border officers in other countries. The fact that the machine-readable code is intact means it would probably be fine at Swiss land borders and other internal Schengen borders. At real border crossings, however, such as in the UK, you would probably be delayed as your identity is examined, while in non-EU/EFTA countries such as Turkey or Tunisia, it's unlikely you'd be let in.

I would get a new ID if I were you, at least if planning to venture outside of the EU/EFTA.

Just so you know, your ID does not contain an RFID chip.

As for the crack, there's no hard and fast rule as to what damages are accepted - rather it depends on the judgment of border officers in other countries. The fact that the machine-readable code is intact means it would probably be fine at Swiss land borders and other internal Schengen borders (if a check is performed that is, which is common when entering Switzerland by bus). 

At real border crossings, however, such as in the UK, you would probably be delayed as your identity is examined, while in non-EU/EFTA countries such as Turkey or Tunisia, it's unlikely you'd be let in.

I would get a new ID if I were you, at least if planning to venture outside of the EU/EFTA.