Can we change the volume of a wire by applying force on it in order to stretch it, if yes is there any way to calculate it ??
The volume will change while tension force is still being applied. You can calculate the change using Poisson's ratio for the material.
But when you release the tension the wire will return to its original volume, even if you applied enough force to permanently increase its length.
While the diameter may be reduced when increasing the length of the wire, the volume should remain unchanged. The only way the volume could change that I am aware of is if somehow stretching the wire changed the density of the wire material.
As far as determining whether or not there is an actual change in volume, I suppose you could make direct measurements before and after stretching. Length shouldn't be problem, but the change in diameter may not be uniform, particularly at or near the areas where the wire is grasped during stretching (e.g., the jaws of a tensile tester). Perhaps you could use some sort of displacement method, such as measuring the volume of water displaced with the wire submerged before and after stretching.
Hope this helps.