Generally, the radius is controlled by the radius of the punch, rather than the die width, but the die width is an important factor. Not only does it affect tonnage, but by using larger die widths, the radius is increased. At one company we used 8 times the material thickness to find the die opening, and at another company we used 6 times the material thickness (different company standards). Using the same radius punch, the smaller die opening produced a tighter radius.
IT IS possible however to use one nose radius to achieve different inside bend radii if you do not have the correct tooling for a project. By adding a "cap" or "wrap" to the punch, you can increase the radii, however the thickness of the cap should generally be equal to or thicker than the material being formed.
Note: by a cap, I mean forming a piece of sheet metal into a "V" shape to fit snuggly over the punch, with the flanges having a bend in them to grip the punch by friction, and also a little bit of duct tape to hold it on.
We have used this on lighter gauges, up to 10 gauge.
For example, you have a 1/8" punch, and you are forming 16 ga. mild steel and you need an inside radius of 1/4". By making a cap of 11 ga. mild steel and put it on the 1/8" punch, you now have a punch that will form an inside radius of 1/4" to 5/32". (.125 + .120 = .245)
The bottom die width will have to be increased accordingly.
Flores