Thixoforming : Semi-solid Metal Processing

6.3.1
Model Description
Three phases are involved in the cooling channel semi-solid process: the liquid melt,
the solidifying grains and air. The volume averaging approach is employed to
formulate the conservation equations of mass, momentum, species and enthalpy
for the three phases. More details can be found elsewhere [38]. The air has no mass
transfer with the other phases, therefore the source term for the mass and species
exchange with air was set to zero. The description of the transport equations and the
definitions of the corresponding source terms are available in detail in the literature
[39–41].
An undercooling-dependant grain-density model according to Thevoz and Rappaz
[42, 43] was adopted, where the grain density can be calculated using the
Gaussian distribution, according to the following equation:
dn
dðDTÞ ¼ nmax
2p
ð Þ 1 2DT s
e 1 2
ð Þ 2
DT DT N
DTs
ð6:25Þ
where the characteristic parameters DTN, DTs and nmax are the mean undercooling,
standard deviation of undercooling, and maximum grain density, respectively. The
parameters were determined experimentally as explained later. The under cooling
value, DT, is calculated for each control volume at each time step. If DTof the current
time step is greater than that of the preceding one, then nucleation is allowed and the
newly formed nuclei will be added to the source term.
The presence of air in this model increases its flexibility as it can substitute metal
shrinkage, heat and drag force exchange, which makes the model closer to the real
metal flow and solidification. On the other hand, including air increases the
computational time and requires a finer mesh to account for the distinct interface
topology. The densities of both solid and liquid phases are temperature dependent to
account for the thermal convection that takes place during solidification and
particularly in the container.
6.3.2
Determination of Grain Nucleation Parameters
6.3 Simulation of Cooling Channelj209
The aim of this part is to determine the characteristic parameters required for the
grain nucleation model implemented in MeSES and to investigate the other models
provided in the simulation code. An experimental setup was built according to
Refs [42, 44]. Pre-experiments coupled with casting simulation using MAGMASOFT
were conducted to optimize the construction of the experimental setup for the grain
refined aluminium alloy A356 with the average composition given in Table 6.2. The
liquidus temperature of A356 was 614.6 C after Scheil simulation using Thermo-
Calc. More details of the experimental description and results can be found
elsewhere [45].
From the cooling curves, which were recorded at different cooling rates, the
maximum undercooling DTmax corresponding to the recalescence temperature was