Calculate and plot the force vs$.$ reduction $(\%)$ in height curve in the open$-$die forging

of a cylindrical, annealed Ti$-6$Al$-4$V specimen that is $60$ mm high and $40$ mm in

diameter, up to a reduction of $50\%($height $=30mm),$ for the cases of $($a$)$ cold working $-$

$20$ degree C with friction coefficient $=0\mathrm{.}1,($b$)$ warm working $-$ a workpiece preheated

to a temperature of $200$ degree C with friction coefficient $=0\mathrm{.}2,($c$)$ hot working $-$ a

workpiece preheated to a temperature of $800$ degree C with friction coefficient $=0\mathrm{.}4.$

You can use Excel or Matlab to calculate and plot but show an equation for each

calculation step. Use the following table for $K$ and $n$ values.