Thixoforming : Semi-solid Metal Processing

here it can be assumed that the databases used are reasonably accurate, particularly at
the relatively high temperatures of interest here.
5.1.2
Equilibrium Calculations
Using standard equilibrium calculations is a quick and easy way to obtain an overview
of the phases expected to appear in a particular material, their amounts and
temperature range in which they are stable. It is also useful for calculating various
thermodynamic properties of the material provided that it does not deviate too much
from the equilibrium state. In connection with semi-solid processing, the partially
liquid state and the solidification behaviour are obviously of major interest. The actual
solidification path, in principle, never follows the equilibrium path, due to limited
diffusion in the solid phase(s). This results in microsegregation and possibly nonequilibrium
solid phases forming. The actual fraction of solid phases at a particular
temperature is (almost) always smaller than the equilibrium fraction. For steels, the
equilibrium solidification path is often a reasonable first approximation since C is a
fast-diffusing element. In thixoforming, where the material is heated from the solid
state into the semi-solid state, the melting behaviour of the material is also of
importance. However, the melting behaviour of alloys has been far less studied than
the solidification behaviour. From the point of view of equilibrium, there is no
difference between solidification and melting. In order to see a difference, it is
necessary to take diffusion into account and in the case of melting the microstructure
of the solid starting material will have a decisive influence on the melting behaviour.
5.1.3
Scheil–Gulliver Calculations
5.1 Methods and Objectivesj149
The diffusion in the liquid phase is much faster than in the solid phase(s) and it is
often a useful approximation to assume that there is no diffusion at all in the solid
phase(s) and infinitely fast diffusion in the liquid phase during solidification. This is
called Scheil–Gulliver solidification [12, 13]. In the rest of this chapter we will use the
shorthand Scheil to mean Scheil–Gulliver. Numerically, Scheil solidification can be
realized as a series of equilibrium calculations, starting with the liquid phase and
decreasing the temperature until the liquid has (almost) disappeared. During each
temperature step the solid phase(s) formed in that temperature step is simply
removed from the calculation. Due to its simplicity, it can be easily realized with
standard Calphad software. However, Scheil solidification in this simple form is not a
good approximation for steels, because C diffuses fairly fast also in the solid phase(s),
ferrite and austenite in this case. For steels it is a better approximation to assume that
C diffuses fast enough also in the solid phase(s) to reach global equilibrium. This
modified Scheil solidification can also be realized numerically as a series of
equilibrium calculations, although not as easily. It has, however, been implemented
in the more recent versions of Thermo-Calc. No information on diffusion rates or
characteristic length scales is needed for these calculations and consequently the