AC Current, Generators and Conductors

<...do conductors' life shortens because of the current flowing on it?...>

It depends upon how close to its melting point the applied current makes its temperature. Where terminals and other fittings are present, one might find local hot-spots. A loose terminal screw, for example, will seriously affect the condition of the conductor in the terminal, and local heating may be severe enough to destroy the conductor and the terminal. That is why BS7671 requires terminals to be accessible for maintenance.

<...can we say they have unlimited service life?...>

Say it, maybe, though it isn't necessarily true, as above.

no i dont mean the heat effect, i just mean the flow of a current on a conductor. Just "flow" does it cause any physical effect ?(is there any special deterioration we need to know? )

1. When a synchronous generator is excited with AC supply, the relative motion between the field and the stator conductor becomes zero. The induced emf will be zero as per Faraday's law and hence, the generator terminal voltage will be zero.

2. A conductor's life does not get shortened because of the current flowing in it. Of course, they can have unlimited service life with no physical deterioration as long as the conductor is carrying current well within its declared ampacity.