Question

A commercially pure copper rod is extruded from an initial diameter of 25 mm to a final diameter of 12.5 mm through a die of apex angle 60 degrees. When Vickers hardness measurements are made on the extruded rod, it is found that the outermost 50 micrometer surface layer has a hardness of 300 kg/mm2 , while the remainder of the rod (bulk) has a hardness of 270 kg/mm2 . Hardness measurements made on similar commercially pure copper samples compressed to different strains showed the hardness H (kg/mm2 ) to be equal to 60 + 120

Answer 1

$\textsf{initial diameter}= 25mm\\ \textsf{final diameter} = 12.5mm\\ \theta = 60°\\ \textsf{outermost layer hardness} =300kg/mm²\\ \textsf{normal hardness} = 200kg/mm²$

$Force = (300kg/mm² × 50×10^{-3}mm) ×9.8m/s²= 15\ kg× 9.8m/s² = 147\ N$

Force needed = 147/cos 60 = 294N$.$