A finite element method for three-dimensional analysis of metal forming

The importance of metal forming by extrusion was reviewed. A Finite Element Approach was developed to analyze extrusion processes. A brick type linear element and the Upper Bound theorem were used to analyze the extrusion of a cylindrical billet into a square cross-section prism. A minimization technique for a non-linear functional with linear constraints was developed. Different types of boundary conditions were also formulated. A frictionless extrusion was simulated using the computer program developed. Velocity profiles at different sections of the deforming solid were obtained and an average extrusion pressure was predicted for a given area reduction ratio. Extrusions from a cylindrical billet into a square cross-section prism were performed for four different area reduction ratios: 1:2.26, 1:2.55, 1:2.97 and 1:3.34. A Beta Press manufactured by Pressure Technology Corporation of America was used. Billets were made from 6061 T 651 Aluminium. The effect of friction was investigated analytically. Also a brick type quadratic element (20 nodes) was tested successfully using the compression of a short cylinder as an example --Abstract, page iii