Finite-element modelling of cold forward extrusion

Abstract

Simulating metal forming processes using an updated Lagrangian finite-element formulation is not ideal when steady-state material flow conditions prevail. Firstly, repeated calculations of large non-linear finite element systems are needed for continuously updating the mesh, and secondly, remeshing operations must be undertaken to avoid excessive mesh distortion and to introduce localised refinements in regions where large gradients are likely to occur. The combined Eulerian–Lagrangian formulation overcomes these difficulties by using a temporary incremental mesh to calculate the strain and stress 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 formulations. The theoretical background for both formulations is reviewed, and the numerical results obtained with the two formulations are compared with experimental extrusion data. Excellent agreement is found for the flow pattern and for the distribution of strain within the plastically deformed region. In what concerns the extrusion load curve, the results demonstrate that the latter can be predicted more accurately using a combined Eulerian–Lagrangian finite-element formulation.