Question $1$

A long, copper strip, $500$ mm wide, $3$ mm thick, was found to have $450$ MPa yield stress. The strip is required to be rolled in order to reduce its thickness. It was required to determine the appropriate capacity of the press needed for the process.

In the rolling process, the width remains practically unchanged while the rolls apply pressure in the thickness direction. An additional tension of $150$ kN is applied in the longitudinal direction to assist the forming process. Ignoring the change in the width and any friction effects, determine what roll pressure would just cause deformation:

i$.$ according to the Von Mises yield criterion

ii$.$ according to the Tresca yield criterion.

Based on the obtained results, which yield criterion would you adopt in making the decision about the press capacity. Explain the reason for your answer.

Material properties in the elastic range: $E=75$GPa,

$u($Poisson$\text{'}$s ratio$)=0\mathrm{.}4.$

$(18$ marks$)$