Analysis of Wire Drawing and Extrusion Through Conical Dies of Large Cone Angle

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Abstract
This work is a direct extension of reference [3]. There the problem was treated with the assumption that the cone angle was small. Here this limitation exists no more. The operations of wire drawing and extrusion through conical dies are treated on the assumption that “Mises” material is formed. An upper-bound solution is obtained for the drawing stress in wire drawing and for the pushing stress in extrusion. The effect of each of the process variables on these forces is presented graphically. The process variables are: the cone half-angle (α), initial (Ri) and final (Rf) wire radius, material yield limit (σ0) under uniaxial load, back pull (σxb) and front pull (σxf), coefficient of friction (μ) or shear factor (m), die land (L), exit velocity (vf), and entrance velocity (vi). On the assumption that the maximum front tension cannot exceed the yield limit of the material under uniaxial tension, a solution is obtained for maximum possible reduction in wire drawing. An analogous assumption, i.e., that the absolute value of the pushing stress also cannot exceed the yield value, gives a criterion for maximum possible reduction in extrusion.

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