Steady-state finite-element analysis of cold forward extrusion

Abstract

Finite-element analysis of metal forming processes is treated predominantly by the Updated Lagrangian formulation in which the mesh moves and deforms in space, in accordance with the deformation history of the material. However, the steady-state deformation characteristics of some metal forming processes such as extrusion, drawing and rolling, can be analysed advantageously using an Eulerian formulation in which the finite-element mesh is fixed in space. Extension of the latter to include work hardening material response can be accomplished through the use of a combined Eulerian–Lagrangian formulation. Such extension is based on the utilisation of an Updated Lagrangian temporary mesh, to calculate the strain and stress fields, coupled with a mathematical scheme to interpolate the strain and stress tensors into the Eulerian mesh, in order to determine the new distributions at the fixed mesh positions. An example of steady-state cold forward rod extrusion is analysed using both the Updated Lagrangian and the combined Eulerian–Lagrangian formulations. Comparisons are made between the theoretical finite-element predictions and experimental data obtained through the utilisation of visioplasticity and micro-hardness techniques.