Thixoforming : Semi-solid Metal Processing

232j 7 A Physical and Micromechanical Model for Semi-solid Behaviour
is found. These results demonstrate the interest in such a modelling for predicting
the behaviour for different solid fractions, at least in an intermediate solid fraction
range.
7.4.2
Isothermal Non-steady-state Behaviour
Industrial thixoforming is a rapid process and the steady state is actually not achieved
for such mechanical conditions. In this section, we simulate isothermal compression
tests. Now, the evolution of the active solid fraction is accounted for by means of
Equation 7.6 in order to capture the transient rheological response. The material
parameters are given in Table 7.2. Note that in this study, we just compare
qualitatively our calculated results with experimental values found in the literature.
Consequently, there is no need to identify the material parameters precisely. Their
values are just taken to be consistent with experiments. For the simulated compression
tests, the ram speed is constant and equal to 500 mm s –1 . The radius and the
height of the initial slug are 15 and 45 mm, respectively. The load–displacement
curves for different solid fractions are shown in Figure 7.7. Typically, the load–
displacement curve displays a peak followed by a strong increase in the load, as is
often observed experimentally (Loue et al., 1992; [4, 32, 33]). In addition, in good
agreement with Liu et al. s experiments [34], the model predicts that the height of the
peak falls with decreasing solid fraction (or increasing temperature) and the minimum
load before and beyond the peaks also decreases with decreasing solid fraction.
The presence of the peak is attributed to the breakdown of the solid skeleton. To
understand better the relation between local deformation mechanisms and the
overall response, we analyse the strain rate distribution within the semi-solid.
Figure 7.8 shows the evolution of the strain rate within the overall material, the
solid particles and the solid bonds. The evolution of the solid fraction in the active
zone is also given in order to highlight relations between the microstructure and the
deformation mechanisms. At the beginning of the processing, the solid network is
highly connected (f s
A;initial ¼ 0.7 in Table 7.2). The magnitudes of the strain rate within
the solid bonds and the solid particles are not far from each other although it is, as
expected, slightly higher in the active zone. This means that, in this step, the whole
solid phase carries the deformation. Since the solid bonds are less resistant and more
deformed than the solid particles, the strain within the bonds reaches the critical
Table 7.2 Set of parameters used for simulations of isothermal
and non-isothermal compression tests.
Solid Liquid
K s particles K s bonds m s particles ¼
m s bonds
K l
Morphological
pattern
f A f c f s
A;initial
Internal
variable
30 000 Pa 20 000 Pa 0.2 0.8 0.01 0.4 0.7 1
g c