Thixoforming : Semi-solid Metal Processing

of an undercooled liquid can be calculated with the KTG (Kurz–Giovanola–Trivedi)
model [23]. The complete undercooling of the solid–liquid boundary surface DT is
given by the sum of the following contributions:
DT ¼ DT c þ DT t þ DT r þ DT k
3.2 Backgroundj53
ð3:3Þ
where DTc, DTt, DTr and DTk are the undercooling contributions concerning the
concentration, the local temperature, the curvature of the dendrite barb and the
attachment kinetics, respectively. The kinetic undercooling term, DTk, is only
relevant to very high cooling rates and can be neglected under the conditions of
rheo- and thixoforming [24]. In general, lower undercooling is advantageous for the
formation of globular structures, so that the Gibbs–Thomson fraction, DTr, gains
importance. It incorporates the decrease in the liquidus temperature due to the bent
boundary surface and counteracts the contributions resulting from the temperature
gradient and the difference in the chemical composition. For small globulite radii,
this leads to the dissolution of solid-phase protrusions which prevent the formation
of a dendrite and benefit further globular growth. This self-healing effect only occurs
if the Gibbs–Thomson fraction is high in comparison with the other two contributions.
With increasing growth of the globulites, protrusions with increased radii can
also be formed. These protrusions do not degenerate and can lead to the formation
of dendrites. With increasing solidification, the contributions |Tc þ Tt|, therefore,
become increasingly important, so that these have to be reduced by appropriate
means to allow further globular solidification. This can be achieved by forced convection
or by lower cooling rates. In conclusion, three conditions for the development
of a small-grained, globular microstructure during the cooling to the partial liquid
state result from these deliberations [25]:
1. existence of a sufficiently high number of nuclei;
2. boundaries around the nucleus intervals;
3. slow cooling of the cast.
A general overview of the numerical simulation of solidification processes concerning
the prediction of the microstructure can be found in [26–28].
Structural Development During the Heating Process Particularly, apart from the
liquid phase content, the grain size and the grain shape, also the steric arrangements
of the solid and liquid phases are of critical importance for a treatment in the partial
liquid state. During heating, these parameters are decided or rather adjustable
through the homogeneity or inhomogeneity of the element distribution. In steels,
the fusion behaviour and the distribution of the solid and liquid phase can be
controlled through the carbide distribution. The steric arrangement of the solidphase
particles can be described by the degree of carcass development, the contiguity
and the contiguity volume.
No universally valid boundary value for the grain size is currently given in the
literature because such a threshold can be dependent on the wall thickness of the
to-be-filled component segment. For conventional aluminium alloys, it could already
be shown that the grain coarsening mechanisms that occur during semi-solid