Thixoforming : Semi-solid Metal Processing

236j 7 A Physical and Micromechanical Model for Semi-solid Behaviour
semi-solid materials. It is based on the application of the micromechanics concept of
coated inclusion to the semi-solid behaviour and the introduction of a bimodal
distribution of the liquid and solid phases. The representative morphological pattern
allows the deformation mechanisms involving in the non-entrapped liquid and solid
bonds gathered in the coating of the coated inclusion to be elucidated. The evolution
of the microstructure with the shear rate is captured via an internal variable that
modifies the liquid–solid bimodal distribution in the coating and in the inclusion.
This variable represents the degree of agglomeration of the solid skeleton. The
proposed rate equation of structure breakdown accounts for the time and temperature
dependency. The model succeeds in describing the isothermal steady-state viscosities
of semi-solid alloys at low and high shear rates. In addition, it provides results in good
qualitative agreement for isothermal and non-isothermal compression tests. It
demonstrates the key role of both the liquid and the solid phases and their distribution
in the overall response and emphasizes the relationship between microstructure and
deformation mechanisms. This 3D model provides a useful tool for a better understanding
of thermomechanical mechanisms occurring within the material during
thixoforming. It is also able to predict the semi-solid response under different
conditions of loading paths or thermal history (by accounting for material variables
such as the solid fraction, the degree of agglomeration and the resistance of the solid
bonds) and can be exploited for semi-solid material design. It has been implemented
in the finite element code FORGE2005 [33] to simulate die filling for industrial
thixoforming.
List of Symbols and Abbreviations
DR thickness of the coating
_EB strain rate tensors of the medium B
_Eeq macroscopic von Mises equivalent strain rate
s stress tensor
_eij deviatoric strain rate tensor
_g overall shear rate
SB overall stress of the medium B
m viscosity
a, b positive material parameters
D macroscopic length parameter
d microscopic length parameter
f c
critical volume fraction
FEM finite element method
f l
volume fraction (liquid)
f s
volume fraction (solid)
K consistency
Kag material parameter, describing the agglomeration mechanism
Kdg material parameter, describing the deagglomeration mechanism
m strain rate sensitivity parameter