Upper bound analysis of extrusion from square billets through circular and square/rectangular dies

Abstract

Upper bound elemental technique (UBET) for prediction of extrusion pressure in three-dimensional forward extrusion process is presented. Using square/rectangular billets, the study of the effect of die land length has been extended for the evaluations of extrusion pressures to extrude sections such as circular, square and rectangular shaped sections with power of deformation due to ironing effect at the die land taken into account. The extrusion pressure contributions due to the die land evaluated theoretically for these shaped sections considered are found to increase with die land lengths for any given percentage reduction and also increase with increasing percentage die reductions at any given die land length. The effect of die land lengths on the extrusion pressures increases with increasing complexity of die openings geometry with rectangular section giving the highest extrusion pressure followed by circular with square section die opening, giving the least extrusion pressure for any given die reduction at any given die land lengths. The proper choice of die land length is imperative if excessive pressure buildup at the emergent section is to be avoided so as to maintain good quality and metallurgical structure of the extrudates.

An Upper Bound Approach of Ring Compression Test Solutions

“…Upper Bound Theorem (UBT), as a solution not only provides the minimum load value which ensures its deformation, but allows to discriminate the parameters that is possible to introduce in the equations optimizing process conditions [1][2][3][4][5].…”

Optimization of a progressive microforming process and in-process material behavior

“…Although FE modeling provides a rather accurate and visual description of material flow, stress and strain distribution during the process, it requires a relatively considerable amount of computing time; in some complicated cases a few days to get an accurate result for just one specific case [141]. More importantly, FE modeling is unable to provide a so-called comprehensive solution, and it needs to be conducted for each specific condition on a case by case basis.…”

“…The material-die contact after this length has no or limited effect on the energy loss. In this work, based on [141], the normalized effective die land length is assumed as 1 The other important factor to be considered was friction. Becker et al [20] reported that using the coulomb friction model sometimes can lead to a better solution in metal forming modeling [72].…”