aluminium bar cold forming calculation

glasvegas

I'm working on a problem that involves calculating force required to form a component. The problem is as follows (diagram attached):

A round aluminium bar, with the initial diameter d0 = 36 mm, has to be cold formed into the component shown in using a combined forward/backward extrusion process. Calculate the force required to form this component. Assume that friction accounts for 55% of the total force and that equation of the work hardening curve for aluminium is σ = 519(0.001 + ε)0.27 MPa.

d1=40 mm
h1 = 90
d2 = 26
h2 = 40
d3 = 31
h3 = 40
α = 45°

I know how to work out ε and then realize that I should integrate σ to get unit plastic work but can't perform this integral. Am a missing some trick or easy way of doing this?

Any help appreciated.

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