# How can I calculate backward extrusion force

I am interested in finding a way to calculate the force necessary to do a backwards extrusion. Typically these would be for forgings 0.5 to 3" in diameter (or square) of different kinds of steel. The diagram below shows a typical type of forging I might want to do:

This would be die formed in A2 steel by backwards extrusion using a hex-shaped punch. The forging would be done with the work piece at its forging temperature.

I want a way to calculate the force (forging load) necessary do such extrusions.

You can find formulas for Backward extrusion in Groover's Principles of Modern Manufacturing 4th edition section 17.5.2. I summarized required formula but if you need more info ask or check the book. Also you can check these lecture notes I googled.

Reduction ratio: $r_x=\frac{A_0}{A_f}$

$A_0$ and $A_f$ are initial and final area in mm respectively.

In bacwards extrusion, effect of friction can be ignored so true strain is $\varepsilon = ln r_x$

Average flow stress is $\overline{Y_f}=\frac{K\varepsilon^n}{1+n}$

K is strength coefficient and n is strain hardening exponent. There are a few examples on wikipedia but you'll probably get A2 steel's info from datasheet or materials books. (K is in MPa so $\overline{Y_f}$ is in MPa)

Pressure required for indirect extrusion is $p=\overline{Y_f}\varepsilon_x$

Force required is $F=pA_0$

We could model your problem this way: the equipment creates shear stresses along the shapes of the extrusion, hence the extrusion will be created for a force which exceeds your materials' sheer resistance. Denote this resistance by T. Hence it follows that F = T*A = T*6*d*l, where d is the depth of the extrusion, and l is the length of the hexagon side. So, you only need to look up the steel shear resistance T and you can solve this.