Semi-solid constitutive modeling for the numerical simulation of thixoforming processes.

Semi-solid thixoforming processes rely on a material microstructure
made of globular solid grains more or less connected to each other,
thus developing a solid skeleton deforming into a liquid phase.
During processing, the material structure changes with the
processing history due to the agglomeration of the particles and the
breaking of the grains bonds. This particular evolutive
microstructure makes semi-solid materials behave as solids at rest
and as liquids during shearing, which causes a decrease of the
viscosity and of the resistance to
deformation while shearing.

Thixoforming of aluminum and magnesium alloys is state of the art
and a growing number of serial production lines are in operation all
over the world. But there are only few applications of semi-solid
processing of higher melting point alloys such as steel. This can
partly be attributed to the high forming temperature combined with
the intense high temperature corrosion that requires new technical
solutions. However the semi-solid forming of steels reveals high
potential to reduce material as well as energy consumption compared
to conventional process technologies, such as casting and forging.
Simulation techniques exhibit a great potential to acquire a good
understanding of the semi-solid material process. Therefore, this
work deals with the development of an appropriate constitutive model
for semi-solid thixoforming of
steel.

The constitutive law should be able to simulate the complex rheology
of semi-solid materials, under both steady-state and transient
conditions. For example, the peak of viscosity at start of a fast
loading should be reproduced. The use of a finite yield stress is
appropriate because a vertical billet does not collapse under its
own weight unless the liquid fraction is too high. Furthermore, this
choice along with a non-rigid solid formalism allows predicting the
residual stresses after cooling down
to room temperature.

Several one-phase material modeling have been proposed and are
compared. Thermo-mechanical modeling using a
thermo-elasto-viscoplastic constitutive law has been developed. The
basic idea is to extend the classical isotropic hardening and
viscosity laws to the non solid state by considering two non-dimensional internal parameters. The first internal
parameter is the liquid fraction and depends on the temperature
only. The second one is a structural parameter that characterizes
the degree of structural build up in the microstructure. Those
internal parameters can depend on each other. The internal
parameters act on the the viscosity law and on the yield surface
evolution law. Different formulations of viscosity and hardening
laws have been proposed and are compared to each other. In all
cases, the semi-solid state is treated as a particular case, and the
constitutive modeling remains valid over the whole range of
temperature, starting from room temperature to above the liquidus.
These models are tested and illustrated by mean of several
representative numerical applications.