Finite-element modelling of cold forward extrusion

Simulating metal forming processes using an updated Lagrangian finite-eleme nt formulation is not ideal when steady-state material flow conditions prev ail. Firstly, repeated calculations of large non-linear finite element syst ems are needed for continuously updating the mesh, and secondly, remeshing operations must be undertaken to avoid excessive mesh distortion and to int roduce localised refinements in regions where large gradients are likely to occur. The combined Eulerian-Lagrangian formulation overcomes these diffic ulties by using a temporary incremental mesh to calculate the strain and st ress fields, coupled with a mathematical scheme to interpolate the updated mechanical state into a spatially fixed mesh. In this paper the cold forward extrusion of rods is analysed using both the updated Lagrangian and the combined Eulerian-Lagrangian finite-element for mulations. The theoretical background for both formulations is reviewed, an d the numerical results obtained with the two formulations are compared wit h experimental extrusion data. Excellent agreement is found for the flow pa ttern and for the distribution of strain within the plastically deformed re gion. In what concerns the extrusion load curve, the results demonstrate th at the latter can be predicted more accurately using a combined Eulerian-La grangian finite-element formulation. (C) 1999 Elsevier Science S.A. All rig hts reserved.