Forging Reduction Ratio - Upset Before Reducing Area

[jmec87]

I know that forging reduction ratio is defined as the ratio of the original to the final cross-sectional area. However, I've recently encountered the suggestion that if an ingot is upset to increase the cross-sectional area before being forged to reduce the cross-sectional area, the reduction ratio is the ratio of the upset cross-sectional area to the final cross-sectional area. Is this reasonable? Can anyone recommend any references (such as standards or ASM handbooks) that would clearly allow or disallow determining the reduction ratio this way?

Example:
Ingot size: 20" diameter
Ingot upset to size: 24" diameter (for the whole length of the forging)
Final Forging size: 10" diameter

In this case, would the reduction ratio be (20^2)/(10^2) or (24^2)/(10^2)?

 

[MagBen]

why not (24²/10²) x (24²/20²) that is the real deformed ratio?

 

[cbunte]

For calculate the reduction ratio you can use the following criteria:

The constant-volume relationship in a cubic solid is expressed by:

V1 = h1 . w1 . l1
V0 = h0 . w0 . l0
1 = h1/h0 . w1/w0 . l1/l0

applying ln

0 = ε1 + ε2 + ε3 = 0

ε1 = ln (h1/h0)
ε2 = ln (w1/w0)
ε3 = ln (l1/l0)

ε = Real deformation
h = height
w = width
l = length

in case of height
h1 = Initial height
h0 = Final height

In compression the signal of ε1 is negative.
If you adopt as positive the compression stress (usual sign convention) because of forging, you should write as:

ε1 = - ln (h0/h1)

For rounded bar:

V = h0 . A0

you can use to calculate reduction rate and real deformation as:

r (reduction) = (A0 - A1)/ A0 = 1 - A1/A0 = 1 - L0/L1

ε (real deformation) = ln ( 1 / (1-r)) (X)

The real deformations (ε) can be sumed because of the logarithms. Reduction rate (r) is not possible to sum them to calculte the total reduction.
Finally you can calculate separately the firs reduction (upset) (20" to 24") and then the second foprging from 24" to 10". Sum the real deformation (ε) and get the reduction rate (r) from the equation (X).
Good luck...!

 

[cbunte]

r (reduction) = (A0 - A1)/ A0 = 1 - A1/A0 = 1 - h0/h1