Three dimensional analysis of lateral extrusion of some complex forms

Abstract

An upper bound solution for lateral extrusion of square, hexagon, spline and tracoidal forms has been developed. A simple kinematically admissible velocity field with optimization parameter is proposed. From the proposed velocity field the upper bound solution on relative punch pressure and extrusion load are determined with respect to chosen process parameters. The results are compared with theoretical and experimental result from a reference to illustrate the validity of the proposed velocity fields. This is indicating that the analysis presented here renders better upper bound solution. Three-dimensional brick shaped elements are utilized in finite element analysis by ALGOR software with linear and non-linear metal applied to upset forging of L shaped blocks. The upper bound elemental technique also used to analyze the problem. Detailed formulations of models are presented. The predictions both in forging load and the deformed configuration are in good agreement with the experiment qualitatively under different lubrication conditions. The proposed velocity field gives higher load values than the values experimentally obtained within 25 percent. The velocity field proposed in the present investigation can be used conveniently with short computational time for the prediction of extrusion loads & deformations in heading of different shapes. A higher order polynomial velocity field can be tested to get better results for different section.