Is a relay stressed by a partial activation of the trigger?
I'm using a relay like the one in the picture, controlled by an Arduino. 


They are designed to receive  


5 V power on the Vcc pin, 
0 V or GND on the GND pin,
the module in your picture explains that an input of between 0 and 1.2 V will turn the relay on (and implies that any voltage above 1.2 V will turn it off) meaning that it is "active low".


The module is intended to be driven by a digital output off/on, low/high, 0V/5V. It is not intended to be used on an analogue output.


  I basically use it for turning mechanically on/off a circuit, when i have 0 as constant output from a series of values that describe a sinewave.


The Arduino doesn't have an analog out other than PWM which is fast digital pulse-width modulation which is either fully on or off. The PWM signals are much faster than the relay can respond. The Arduino outputs cannot switch negative so it is not possible to generate a sinewave from it.

Where is your sinewave coming from?


  The system does what i expect, ...


What do you expect?


  ... but every time that the sinewave cross the 0, it gives an input to the relay.


If you really are feeding it a sinewave then this is to be expected.


  The input is so short that it doesn't trigger its status... this is perfect for what i want, but i don't know if this stress applied to the relay might brake it in the long run.


The relay might be moving the contacts to the point where the spring pressure is lowered enough to give poor contact and this might cause problems - particularly on high current.

Your question needs a lot more details to be answered properly.