Numerical flow front tracking for aluminium extrusion of a tube and a comparison with experiments

Abstract

Insight in the aluminium extrusion process can be gained with numerical simulations. This paper gives an overview of the research done to model aluminium extrusion with the Arbitrary Lagrangian Eulerian (ALE) FEM code DiekA. The ALE formulation is used to avoid mesh distortion, which is a major problem in the simulation of extrusion. The goal of this research is to increase the lifetime of extrusion dies and to decrease the number of corrections necessary to these dies. To model the rate-dependent behaviour of hot aluminium, normally a viscoplastic material model is used. However in the bearing the material behaviour is mainly elastic. The pressure and friction in the bearing are dominant factors in the extrusion process and an accurate modelling of this area is crucial for the final results. In this paper an elasto-viscoplastic material model is derived. This models can be simplified to a very efficient model that is elasto-viscoplastic for small deformation increments and viscoplastic for large increments. With this model it is possible to model the extrusion process including the elastic behaviour in the bearing without sacrifising efficiency. As an example the extrusion of a tube is treated. To avoid unacceptable calculation times, the simulation is split into three parts. First a detailed 2D simulation of the bearing area is made. The results of this simulation are used in a complex 3D simulation of the aluminium flow true the die. From this simulation, the loads on the die are determined. These loads are used in a stress analysis of the die. The results of these simulations give insight in the processes that occur in the aluminium and in the die.

Reference map technique for finite-strain elasticity and fluid–solid interaction

“…Koopman et al [18] use an "original coordinate" function akin to our reference map in defining a pseudo-concentration method for flow fronts. In [29], the map was used in conjunction with a level-set function for enhanced processing of data along an interface.…”

A remeshed vortex method for mixed rigid/soft body fluid–structure interaction

“…We choose the second approach, and adopt the inverse map technique described below to compute F in a purely Eulerian fashion-for a detailed comparison between these approaches the reader is referred to [77]. This methodology has been (re)discovered many times across different communities [77,78,79,80,81,82] and is known by several names (inverse map [78], initial-point set [83], LSPC [79], original-coordinates [80], backwardcharacteristics [84], reference-map [77], reference-coordinates [82]). In the context of flow-structure interaction, it has found use in simulating elastic membranes submerged in incompressible flow [81,84], and recently it has been extended to incompressible two-dimensional solids, using the p-v formulation of the Navier-Stokes equation and finite volumes and differences [18,85].…”

An Eulerian approach to the simulation of deformable solids: Application to finite-strain elasticity

“…To these authors' knowledge, it has never been used for the purposes of solving solid deformation as described above. Koopman et al [8] use an "original coordinate" function akin to our reference map in defining a pseudo-concentration method for flow fronts. The inverse of χ at time t, which is indeed equivalent to the ξ field, is also discussed in Belytschko [2] for use in finite element analysis.…”