$2.$A linear strain hardening material with a constitutive law: $=5000+30000$e$\backslash$sigma $=5000+30000$e$=5000+30000$e psi is being drawn into a wire. The initial diameter of the material is $0\mathrm{.}4$ in$.$ Assume that the friction loss is $30\%$ and the loss to redundant work is $25\%$ of the ideal deformation work.

a$.$ What is the minimum possible diameter of the wire at the exit of the die?

b$.$ What is the drawing force for the deformation of part a$?$

$3.$Repeat problem $2($parts a and b$)$ for a thin sheet. The sheet has a width of www$,$ so the conditions are plane strain.

a$.$ What is the minimum possible thickness of the sheet at the exit of the die?

b$.$ What is the drawing force for the deformation of part a$?$ Write your answer in terms of the width www$.$

Answer

$2.$

a$.$ Df$=0\mathrm{.}226$in

b$.$ FD$=1573\mathrm{.}6$lb

$3.$

a$.$ hf$=0\mathrm{.}1484$in

b$.$ FD$=5839\mathrm{.}4$w