Steve, in the figure I´ve tried to illustrate a piece of material which has sprung back after having been tightly bent around the mandrel. The next time you bend something you should note down the spring back ratio k=R/r of the material. This, in my experience, is a material constant. So thereafter you can easily calculate which D you need for the R you really want as:
D=2R/k-t
where, obviously, t is the material thickness.
Stefan