Plastic deformation of rings

[brewnog]

I am designing a machine called a Ring Expander. Simply put, it's a machine used in metal forging operations to stretch metal rings (15 x 15cm cross section, 30cm inside diameter, 60cm outside diameter) by about 20mm on the diameter. It does this by forcing a cone through a set of jaws, which expand as the cone passes though them, the workpiece having been positioned around the jaws.

What I need to know is how to calculate the force required to expand these rings! Approximate dimensions are given above, materials include stainless steel and titanium, but also 718 alloy (which I believe has a yield stress below 600MPa at the temperatures I'm looking at). I played around with looking at the force required to cause yield at a single cross section, but as these rings are circular I suspect that my assumptions were too simple.

Any help would be appreciated! My engineering knowledge only goes as far as elastic behaviour of rings.

Thanks!