A summary is furnished of Air Force Materials Laboratory efforts in the application of analytical and experimental methods for the determination of forces required for extrusion of metals and alloys. The analyses yield mathematical equations correlating extrusion pressures with process variables such as friction, die geometry, and materials resistance to deformation under processing conditions. The following two equations are used for extrusion force studies:
$Pt=Pd+4kL/Dand$

$Pd=Y(a+blnR)$

$+ScotαlnR$
where Pt = total pressure, Pd = die pressure, L = billet length in container, D = container diameter, Y = material flow strength at processing temperature and strain rate, R = reduction ratio, α = half die angle, a and b = constants for each die angle, and S and k = interface friction sheer stress in die and liner, respectively. These formulas plus an instrumented high speed extrusion press are utilized for quantitative evaluation of the effectiveness of lubrication systems in reducing total extrusion forces.
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