Thixoforming : Semi-solid Metal Processing

230j 7 A Physical and Micromechanical Model for Semi-solid Behaviour
literature. These were obtained using isothermal conditions and were carried out on
parallel plate compression [29] at shear rates ranging from 10 5 to 10 s 1 or on a
concentric cylinder viscometer [16, 30] at shear rates ranging from 2 to 1000 s 1 .For
the following calculations, the viscosity of the liquid phase is taken as equal to
1.81 10 3 Pa s [31]. The critical volume fraction of solid f c is equal to 0.4. The
parameters to be identified are the consistency K s and the strain rate sensitivity
parameter m of the solid phase, the ratio K dg/K ag, the coefficient n in Equation 7.3 and
the fraction of the active zone fA, assumed to be constant during changes of strain
rates. The identification of all these parameters results from successive comparisons
between the experimental Sn–15wt%Pb alloy data corresponding to a solid fraction of
0.5 found in the literature [16, 29] and the numerical results. Good agreement
between the experimental and calculated data is obtained as for both low strain rates
and high shear rates (Figures 7.5 and 7.6) with the set of values given in Table 7.1. At
low shear rates (Figure 7.5), experimental viscosities in the region of 10 7 Pa s are
obtained. These viscosities are many orders of magnitude greater than those obtained
for the same initial spheroidal structure after vigorous agitation at high shear rates
(Figure 7.6). The present model is able to describe well this experimental shearthinning
behaviour at low and high shear rates with the same set of parameters. In
such a modelling, the overall properties are mainly controlled by the active zone
behaviour. At low shear rates (from 10 5 to 10 s 1 ), solid particles can aggregate
Semi-solid viscosity (10 7 Pa s)
25
20
15
10
5
0
0
0.002
Laxmana & Flemings (1980) ; f s = 0.5
Micro-macro modelling ; f s = 0.5
Laxmanan & Flemings (1980) ; f s = 0.45
Micro-marco modelling ; f s = 0.45
0.004
0.006
Shear rate (s -1 )
Figure 7.5 Evolution of the semi-solid viscosity as a function of the
shear rate at low shear rates for the Sn–15wt%Pb alloy.
Experimental data were obtained using parallel plate compression
tests.
0.008
0.01