Thixoforming : Semi-solid Metal Processing

method to increase the accuracy of boundary conditions and the tracking of
interfaces. One refers to this implementation as TruVOF.
. MAGMASOFT, based on the finite difference method, is a numerical simulation
tool for castings. It features the full process from mould filling to solidification. In
addition to the filling behaviour, volume shrinkage, thermal stresses and also
distortions can be calculated. It allows an iterative design of different casting
processes such as high-pressure die casting, thixocasting, sand casting and chill
casting, whereas both geometry (cast, feeder, cores, etc.) and casting parameters
(temperature, velocity, etc.) can be easily varied. MAGMASOFT is the most
established casting-simulation software worldwide.
. PETERA numerical code is based on the Lagrange–Galerkin approach that uses a
special discretization of the Lagrangian material derivative along particle trajectories
with a Galerkin finite element method [36]. The numerical model uses an analytical
solution of rate equations along segments of particle trajectories in addition to
backward particle trajectories tracking in time. The thermal energy conservation
equation is coupled with the mass conservation equation for the solid phase and
solved simultaneously in the time stepping process of the numerical algorithm. The
equations are solved for the prime unknowns in the model equations: temperature,
enthalpy and solid fraction. The use of fS as an independent variable allows
additional complicated equations to describe temperature–enthalpy relations for
metals in the mushy state to be avoided. The calculated fS is used in the flow
equations of the bulk and liquid phases. The numerical algorithm is based on the
fixed-grid methods, in which the free surface is at an unknown position between the
nodes. The determination of the free surface position in time is based on a modified
pseudo-density approach. The procedure of activating/deactivating mesh elements
in the transient process of filling/emptying the elements makes the algorithm less
time consuming and more resistant to numerical diffusion.
. LARSTRAN/SHAPE is a specialized FEM code for the simulation of metal
forming. It is based on a Lagrange formulation and implicit time integration.
Both elastic–plastic and rigid–plastic material behaviour can be modelled, including
full thermomechanical coupling (dissipation and phase changes) and heat
transfer.
6.2.4
Numerical Examples
6.2 Numerical Modelling of Flow Behaviourj201
6.2.4.1 One-phase, Finite Difference, Based on Flow-3d
The selected example is a die filling of a steering axle using aluminium alloy A356. A
steering axle is tested in order to study the influence of different parameters on the die
filling. It was found that above a critical inlet velocity, the filling is no longer laminar.
In Figure 6.35, a comparison of the numerical simulation and the experiments
performed in terms of flow front development for two different inlet velocities
(v1 ¼ 250 mm s 1 and v2 ¼ 500 mm s 1 ) is shown. The results show good agreement