Thixoforming : Semi-solid Metal Processing

Figure 6.36 Experimental setup, T-shaped die.
6.2 Numerical Modelling of Flow Behaviourj203
Model Parameter Determination and Adjustment The model parameters m, n, t0, k
and C (see Equation 6.1) were determined on the basis of the step change shear rate
experiments and also shear rate ramp experiments at a reference solid content f S,ref. of
52% The rheological experiments led to reliable results for the yield stress t0, the flow
exponent n and the consistency coefficient k. These model parameters are related to
steady-state conditions. The determination of the isostructure flow exponent m and
the rate constant c (Equation 6.5), which describe the transient behaviour of the
material, suffers from a slight uncertainty.
Ordinary die filling processes do not last longer than approximately 0.5 s. During
this time, the semi-solid alloy undergoes a lot of shear rate changes and jumps. Hence
the time span for a shear rate jump is in the range of milliseconds. So far there is no
possibility of acquiring viscosity values at these time scales with conventional
rheometers. A further problem arises from the permeability coefficient kP used in
the two-phase model.
In order to overcome these problems, a special approach of parameter adjustment
has been developed (Figure 6.37). The aim is to achieve congruence between
numerical and experimental results. The filling experiments are carried out under
isothermal conditions. Varying the filling velocity and the initial solid fraction of the
metallic suspension leads to different filling pressures, flow patterns and spatial
distributions of solid content. The simulation starts with a set of parameters
determined on the basis of the rheological experiments performed and a first guess
of the permeability coefficient. As long as no congruence of the flow front contour, the
solid fraction distribution and the filling pressure is achieved, a new simulation with
modified flow exponent m, rate constant c and permeability coefficient k P is carried
out.
Two-phase Simulation Using the obtained set of material parameters, the T-shaped
die-filling experiment described above was simulated using the two-phase model
implemented into the solving algorithm PETERA. In order to show that the flow is
mainly influenced by segregation effects, one-phase simulations considering yield