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The figure below shows a symmetric plane-strain upsetting process. The process may also be thought of as a form of side extrusion. Observations show that the deformation is confined to two shear planes, each one being analogous to that seen in plane-strain cutting. You may assume that there is no friction between the work material and the tool/die walls; the uniaxial yield strength of the material is σy and is independent of strain rate and temperature, and the material behaves as a rigid plastic solid.
a) Calculate the pressure (p) required for the upsetting process in terms of σy.
b) If friction existed at the die walls and the frictional work (energy) dissipation was 30% of the energy required for shape change alone (part (a) above), then what would be the pressure (p)?
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