3D upper-bound modeling for round-to-triangle section extrusion using the SERR technique

The spatial elementary rigid region (SERR) technique is eminently suitable for analyzing extrusion of section having re-entrant corners. However, in its present form, it cannot be used to analyze 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 approximating polygon is progressively increased until convergence of the extrusion pressure is achieved. As a test, the extrusion of triangular section bars from round billets through linearly converging dies is analyzed.