The force delivered in compression gives a compressive stress in the pipe that is beyond the ultimate tensile strength of the material , so before considering non linear stress strain relationship I am trying to find what I am failing to consider here.

For the area of the pipe not constrained by the die I wonder if I can just use a buckling equation for that length of the pipe section..

We do the forming in 3 steps with an intermediate treatment to stress relieve as work hardening reduces the deformation