In general, there really isn't much true volumetric shrinking resulting from stress relief. But relieving internal stress can easily cause significant dimensional changes. The residual stress from a casting process can be very high and non-uniform. Think how far you can deflect a sheet of steel yet have it spring back without taking a permanent set. This gives you an idea of how much deformation can occur by relieving residual stress. Residual stress is all balanced by "elastic" or recoverable deformation within the part.
The crystalline microstructure does not really "pack closer", although a change in a crystalline phase can cause some volumetric change. Recrystallization is an extreme way to relieve stress and is not typical. It's more common to just use heat to accelerate "creep" or relaxation by dislocation movement within the microstructure.
For "shrinking", a torch will obviously heat the sheet metal much hotter than a disc. The mechanism is still the same - thermal expansion causes the heated region to deform because it is constrained by the surrounding cooler metal that does not expand. The "shrinking" still happens when the sheet cools and the thermal expansion relaxes and creates tensile stress that flattens the sheet.
The heat of the torch is high enough to cause a significant reduction in yield stress which increases the effect because the deformation is more pronounced.
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