An existing $2$ component die assembly has an insert radius of X mm and a ring outer radius of Y mm$.$ An existing $2$ component die assembly has an insert radius of $xmm$ and a ring outer radius of Y mm $.$

The insert and the ring were pre$-$stressed by interference fit resulting in a contact pressure, $P_k$ at the

interference diameter. The die working pressure of this $2-$component assembly was $1000$ MPa when

the extrusion process was carried out. Answer the following questions making use of a graph paper.

$($a$)$ Find the value of the interference diameter.

$($b$)$ Find the value of $P_k$

$($c$)$ Calculate the equivalent stress.

$($d$)$ Choose suitable materials for the dies, and explain the basis of your selection

X and $Y$ values depended on the last digit of your Student ID as follow:

Student ID ended with $0,1,2,$ or $3$:$x=15,Y=60$ Student

ID ended with $4,5,$ or $6$:$,x=20,Y=80$

Student ID ended with $7,8,9$ or $x$:$x=12\mathrm{.}5,Y=40\mathrm{.}5$

The insert and the ring were pre$-$stressed by interference fit resulting in a contact pressure, Pk at the

interference diameter. The die working pressure of this $2-$component assembly was $1000$ MPa when

the extrusion process was carried out. Answer the following questions making use of a graph paper.

$($a$)$ Find the value of the interference diameter.

$($b$)$ Find the value of Pk

$($c$)$ Calculate the equivalent stress.

$($d$)$ Choose suitable materials for the dies, and explain the basis of your selection

$*$X and Y values depended on the last digit of your Student ID as follow:

Student ID ended with $0,1,2,$ or $3$: X$=15,$ Y$=60$ Student

ID ended with $4,5,$ or $6$: X$=20,$ Y$=80$

Student ID ended with $7,8,9$ or X: X$=12\mathrm{.}5,$ Y$=40\mathrm{.}5$