Forging

We can evaluate C by looking at the boundary conditions. At the edge of the
workpiece where x = a, σ x = 0 and from the yield criterion σ y - σ x = σ ‘ o , so
so
⎛
C exp⎜
−
⎝
σ y = σ ‘ o and therefore: '
2µ
a
h
⎞
⎟
⎠
= σ
o
….Eq. 17
' ⎛ 2µ
a ⎞
σ
o
exp⎜
⎟
⎝ h ⎠
Friction hill
σ y
σ
'
o
⎡2µ
exp
⎢
⎣ h
⎤
( a − x) ⎥⎦
C
'
= σ
o
⎛
exp⎜
⎝
2µ
a
h
⎞
⎟
⎠
….Eq. 18
-a
a
σ‘ o
X
σ o
X
Using this in Eq.16, we find
σ
y
⎡2µ
= σ
o
exp⎢
x
⎣ h
⎤
( a − ) ⎥⎦
'
….Eq. 19
x = -a
x = 0
x = a
Suranaree University of Technology Tapany Udomphol
Jan-Mar 2007