$\backslash$table$[[$Material$,$K$($MPa$),$n$],[$Aluminum$,,],[1100-$O$,180,0\mathrm{.}20],[2024-$T$4,690,0\mathrm{.}16],[5052-$O$,202,0\mathrm{.}13],[6061-$O$,205,0\mathrm{.}20],[6061-$T$6,410,0\mathrm{.}05],[7075-$O$,400,0\mathrm{.}17],[$Brass$,,],[70-30,$ annealed,$900,0\mathrm{.}49],[85-15,$ cold$-$rolled,$580,0\mathrm{.}34],[$Cobalt$-$base alloy, heat$-$treated,$2070,0\mathrm{.}50],[$Copper$,$ annealed,$315,0\mathrm{.}54],[$Steel$,,],[$Low$-$C$,$ annealed,$530,0\mathrm{.}26],[1020,$ annealed,$745,0\mathrm{.}20],[4135,$ annealed,$1015,0\mathrm{.}17],[4135,$ cold$-$rolled,$1100,0\mathrm{.}14],[4340,$ annealed,$640,0\mathrm{.}15],[304$ stainless, annealed,$1275,0\mathrm{.}45],[410$ stainless, annealed,$960,0\mathrm{.}10],[$Titanium$,,],[$Ti$-6$Al$-4$V$,$ annealed, $20\backslash$deg C$,1400,0\mathrm{.}015],[$Ti$-6$Al$-4$V$,$ annealed, $200\backslash$deg C$,1040,0\mathrm{.}026],[$Ti$-6$Al$-4$V$,$ annealed, $600\backslash$deg C$,650,0\mathrm{.}064],[$Ti$-6$Al$-4$V$,$ annealed, $800\backslash$deg C$,350,0\mathrm{.}146]]$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.