Thixoforming : Semi-solid Metal Processing

234j 7 A Physical and Micromechanical Model for Semi-solid Behaviour
structure thus remains the same and is behaving in a Newtonian manner. This
behaviour provides the strong increase in the load observed after the peak.
As expected, decreasing the solid fraction decreases the yield stress and more
generally the load level, except at the end of the experiments. In this last step, as
mentioned previously, the semi-solid behaves as a suspension and its response is
slightly less dependent on the solid fraction (in the range between 0.6 and 0.8) than
before. In reality, an increase in temperature not only decreases the solid fraction but
also changes the degree of agglomeration, the size and the morphology of the
particles, maybe the mechanical resistance of the solid bonds, and so on. The
modelling allows one to separate all these effects on the overall response and
consequently can help to achieve a better understanding.
7.4.3
Non-isothermal and Non-steady-state Behaviour
As discussed previously, semi-solid behaviour depends strongly on the initial volume
solid fraction within the material. In addition, this volume solid fraction may change
during thixoforming because of viscoplastic dissipation or/and thermal exchanges
between the dies and the slug. For example, in the case of steels, Cezard et al. [35, 36]
highlighted the key role of thermal exchanges on the flow behaviour and the load level
during thixoforming. Since it is very difficult to obtain isothermal conditions for
industrial thixoforming, accounting for thermal exchanges is of great importance for
simulations. This section analyses the effect of increasing overall solid fraction due to
temperature loss simulating thermal exchanges between the die and semi-solid. The
relationship between temperature and solid fraction is given by the Sheil equation
(here we deal with a semi-solid aluminium alloy to obtain calculated data consistent
with real experiments, but only qualitative results, that may extended to other alloys,
are discussed). The kinetics of the active solid fraction used for these simulations is
given by Equation 7.7, where a and b are taken, arbitrarily, as equal to 1. The other
material parameters are the same as used in Section 7.2 and are given in Table 7.2.
The initial overall solid fraction is 0,8. Compression tests having temperature losses
equal to 0, 50 and 80 C are simulated using a ram speed and slug size identical with
those used in Section 7.2. Figure 7.9 shows the load–displacement curves. Clearly,
increasing temperature loss leads to an increase in the load peak. This peak is delayed
to higher displacement. Here again, these results are related to the microstructure
evolution. Material variable analysis reveals that the increase in the overall solid
fraction (see Figure 7.10) leads to a reduction in the decrease of the active solid
fraction. The presence of a higher quantity of solid able to contribute to the
deformation leads to a decrease in the strain rate within the solid phase and in
particular within the solid bonds. As a result, the critical strain to bond rupture is
reached for higher displacement. It is worth noting that the kinetics of the active solid
fraction result from both agglomeration/solidification and deagglomeration. It
obviously depends on parameters used for Equation 7.7. In particular, a and b of
the agglomeration/solidification are here chosen arbitrarily and further accurate
investigations are required to improve the modelling of such a phenomenon.