Thixoforming : Semi-solid Metal Processing

350j 9 Rheocasting of Aluminium Alloys and Thixocasting of Steels
Table 9.7 Diffusion coefficients, [46].
Element
Mg 1.49 · 10 5
Si 1.38 · 10 5
Ti 1.12 · 10 1
Solid aluminium Liquid aluminium
D0 (m 2 s 1 ) Q (kJ mol 1 ) D0 (m 2 s 1 ) Q (kJ mol 1 )
120.5 1.49 · 10 5
117.6 1.34 · 10 7
260.0 9.90 · 10 5
71.6 0.34
30.0 7.11
36.3 0.10
Content (%)
taken into account during the simulations, averaged over the simulation domain, as
described recently [48].
The grain density was evaluated from micrographs by image analysis. Samples
were taken from the edge and the middle of each billet, etched (Barker method) and
analysed metallographically. A total of 50 pictures (five per sample) were analysed in
respect of the number of globules, and an average grain density of 77 mm 2 was
found (SD ¼ 2.61 mm 2 ). The average spacing of the globules was 114 mm. This
globule density does not represent the seed density directly after pouring, because the
dissolution of small grains due to Oswald ripening was not considered. As a starting
parameter for the simulation, this was accurate enough, especially as in the
simulation only stable grains were considered.
The MICRESS simulations were carried out on a 500 500 mm calculation
domain. Twenty seeds are needed to achieve an average globulitic spacing as
determined from the experimental results.
In order to determine the boundaries of the globular–equiaxed transition from the
simulations, a series of simulations with varying heat flux rate and seed density were
carried out. The heat flux rate was varied from the experimentally determined
0.94–10.0 J s 1 and the grain density from 5 to 40 grains per calculation domain.
The seeds were set at random locations in the calculation domain.
To analyse the results, a shape factor (F) for the simulated grains was calculated by
the following equation [47]:
F ¼ U
ð9:1Þ
4pA
where U is the circumference and A the area of a grain.
For F ¼ 1 all grains are circular and for F > 1 the grains exhibit an increasingly
complex shape. Due to the influence on the viscosity, the shape factor should be