Thixoforming : Semi-solid Metal Processing

7
A Physical and Micromechanical Model for Semi-solid Behaviour
Veronique Favier, Regis Bigot, and Pierre Cezard
7.1
Introduction
Semi-solid metals exhibit time- and strain rate-dependent behaviour denoted thixotropy:
they behave like solids in the undisturbed state and like liquids during shearing
provided that the shear rate is high enough (see, e.g., [1]). Semi-solid metal forming,
called thixoforming, exploits this thixotropic and shear-thinning behaviour since the
semi-solid slug may be handleable but also flow easily in the die. This last feature
contributes to form near net-shaped products. The use of finite element method
(FEM) simulations to obtain the filling of the dies and to optimize the thixoforming
process is clearly of great interest. To carry this out properly, the semi-solid flow and
the heat transfer into the die have to be correctly described. In practice, various
constitutive equations are used since discrepancies appear between experimental
rheological data, even under isothermal and steady-state conditions reached after a
period as an equilibrium microstructure is established. In addition to the shearthinning
behaviour, constitutive equations have to describe peculiar phenomena
such as the presence or not of plastic threshold, and normal and abnormal behaviour,
namely hardening and softening stress–strain rate relationship [2–5]; (Koke and
Modigell, 2003); [6]. The objective of this chapter is to propose a new constitutive
equation accounting for the mechanical role of liquids and solids and of their spatial
distribution within the material on the overall behaviour of semi-solids. To do so,
we use micromechanics and homogenization techniques that naturally relate the
microstructure and the deformation mechanisms to the overall properties. In the first
section, basic concepts of the micromechanics of heterogeneous materials are
recalled. Then, we apply these concepts to semi-solids and explain the mathematical
equations used in the modelling. Finally, some results concerning the isothermal
steady-state and also transient and non-isothermal behaviour are given and compared
with experimental data.
A List of Symbols and Abbreviations can be
found at the end of this chapter.
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