Drawing of rods, wires and tubes

Since the yield condition for plane strain is σσσσ x + p = σσσσ ’ o and
B = µµµµ cot αααα, the differential equation for strip drawing is
dσ
x
=
'
σ B − σ ( 1+
B)
x
o
If B and σσσσ ’ o are both constant, Eq.4 can be integrated directly
to give the draw stress σσσσ xa .
σ
xa
Suranaree University of Technology Tapany Udomphol
Jan-Mar 2007
dh
h
B
' 1+ B ⎡ ⎛ ha
⎞ ⎤
' 1+
B
= σ o ⎢1
− ⎥ = o
B ⎜
⎢ h ⎟ σ
b ⎥ B
⎣ ⎝ ⎠ ⎦
For wiredrawing conducted with conical dies,
1+
B ⎡ ⎛ D
= σ ⎢ −
⎜
o 1
B ⎢⎣
⎝ D
⎞
⎟
⎠
2B
⎤
⎥
⎥⎦
[ ] B
1−
( 1−
r)
…Eq.4
σ xa
a
b
…Eq.5