A numerical application of the upper-bound technique for round-to-hexagon extrusion through linearly converging dies

Abstract The growing interest in the modelling of metal forming processes in recent years has brought about the development of different analytical and/or numerical techniques. The SERR technique is eminently suitable for analyzing extrusion of sections having re-entrant corners. However, in its present form, it can not be used to analyse forming processes where the deformation zone has curved boundaries, since the elementary regions will no longer remain rigid. The present study is an endeavor to remodel this technique so that it can handle round billets. The circular cross-section of the round billet is approximated by a regular polygon of equal area and the number of sides of the polygon is increased progressively until convergence of the extrusion pressure is achieved. As a test, the extrusion of hexagon-section bars from round billets through linearly converging dies is analyzed.