During tensile test, why does the specimen's(let's say mild steel) volume changes during elastic deformation and does not change during plastic deformation?
In short, elastic deformation of crystalline structures (like steel) happen on an atomic scale, where the bonds of the atoms in the lattice are stretched. This allows for a change in how close the individual atoms are packed together.
If you remove the load, the energy stored within these bonds can be reversed (comparable to a spring), therefore it's only elastic.
On the other hand, plastic deformation happens along gliding planes, for example between individual crystals (inter-crystalline) or within the crystal itself (intra-crystalline). During plastic deformation crystals "slide" along that plane, they perform a translation which is permanent, therefore plastic. The crystalline structure itself remains more or less unaffected during that translation, therefore no volumetric change occurs.