Question:
A cylindrical rod of annealed carbon steel is cold extruded from an initial diameter of 100 mm to a final diameter of 50 mm. The dependence of hardness (H) on strain for this steel is described by:
H = 3000ε0.2MPa for ε ≤ 1 and
H = 2400 + 600ε MPa for ε >I
When hardness measurements are made on the extruded rod, it is found that a very small region at the outer surface (- 50 μm along the radius) of the rod has a hardness of 4800 MPa, while the remainder of the rod has a hardness of 4200 MPa.
Assume that the yield stress σ(ε) = H(ε)/3. Use suitable engineering approximations as appropriate.
a) Estimate the level of redundant strain in the small outer region of the rod and the remainder of the bulk of the rod.
b) Assuming that the effects of friction are also included in the redundant straining, estimate the extrusion pressure for this forming operation.