Upper-bound analysis for backward extrusion of generally non-axisymmetric hollow shapes

A kinematically admissible velocity field suitable for backward extrusion of generally non-axisymmetric hollow shapes is proposed. By using the proposed velocity field, the upper-bound extrusion load and average extruded height for internally elliptic-shaped tubes from rectangular-shaped billets, internally regular polygonal-shape tubes from the similar shaped billets and internally trochoidal gear-shaded tubes from the similar shaped billets, are determined with respect to chosen parameters. Experiments were carried out with commercial pure aluminum and aluminum alloy billets at room temperature using various shaped punches. Both the extrusion load and average extruded height between the theory and experiment are shown to agree well for validating the proposed velocity field.