Thixoforming : Semi-solid Metal Processing

Based on the solid fraction of the metallic suspension, one can distinguish between
the two groups of slurries and of corresponding models. When the solid fraction in
the semi-solid slurry ranges from 20 to 90%, suspensions above 60% behave as nonlinear
viscoplastic solids and are used in forging processes, and metal slurries below a
solid fraction of 60% are used in casting processes and exhibit a non-Newtonian,
history-dependent flow behaviour that is referred to as pseudoplasticity and thixotropy.
Consequently, there are basically two groups of models to describe semi-solid
slurries: for highly concentrated suspensions behaving as solid bodies, models based
on solid body mechanics are used; and for slurries with solid content less than 60%
that behave like non-Newtonian suspensions, models based on computational fluid
dynamics (CFD) are use. The models based on solid body mechanics are explained in
Section 6.1.2.
Models based on CFD can be classified according to whether the modelling is onephase,
where the material is assumed to be continuum, or two-phase, where both
liquid phase and globular particles are taken into account. Furthermore, classification
can also be made based on discretization methods, that is, methods of approximating
the differential equations by a system of algebraic equations such as finite element
(FE), finite difference (FD) and finite volume (FV) models.
Another important issue when dealing with such flows is the proper determination
of the interface position in time. There are basically two methods for dealing with this
issue: moving mesh strategies and fixed mesh approaches. The first group uses some
form of the mesh moving strategy, such as Lagrangian or arbitrary Lagrangian–
Eulerian (ALE) techniques. Due to the possibility of mesh distortion, such strategies
often need to be complemented by a remeshing strategy. The second approach uses a
fixed fluid mesh, supplemented by an appropriate strategy for tracking the fluid–solid
(fluid–air) interfaces.
The main difficulty when modelling thixoforming processes is to take into account
all the complex phenomena occurring within the flow. Some of the models refer to
the thixotropic behaviour only, where metals are treated as homogeneous materials
[32]. The others take into account the two-phase flow, but neglect the thixotropy.
Other authors, while considering thixotropy, neglect the heat transfer during the
process. Alexandrou et al. [33] implemented the heat transfer and the phase change
together with thixotropy in a commercial simulation package, but did not take the
phase segregation into account.
The literature on numerical models of thixoforming was recently reviewed by
Atkinson [2].
6.2.2
Numerical Models Used
6.2 Numerical Modelling of Flow Behaviourj197
6.2.2.1 Material Models
The basic point of any numerical method is the mathematical model, that is, the set of
partial differential or integro-differential equations and boundary conditions (an
appropriate model for the target application, incompressible, inviscid, turbulent; two-