Constitutive model and parameters used for the simulation of mushy state steel forming need to be determined or specified.
Therefore, an experimental program was prepared verifying the influence of the following factors:
- Contents of solid and liquid phase
- Loading rate
- Equivalent plastic strain
Total view of the stand
The experimental apparatus can perform both the "indentation test" and "hot upsetting test". The indentation of a thin tool into steel in a semi-solid state, can be used at higher temperatures, i.e. also for a larger liquid phase in the specimen. The "hot upsetting test" of a steel cylinder at very high temperatures of the specimen is second method used for study of behaviour semi-solid metal. On the contrary, the temperature, at which the liquid content reaches a value where the tested cylinder cannot keep its original shape and gets destroyed due to the gravity, limits the second test. These two methods enable to study the steel behaviour within the whole temperature range between the liquidus and solidus curves.
The other experimental method used for study of behaviour steel is the "back extrusion test". Shape of simple product manufactured by back extrusion test and diagram of useful forces are plot in figure.
The dependence force-time of deformation is characteristic of the initial increase in force. In the following section, the material relaxation and the force reduction can be observed. In the final section, the force grows exponentially up to the maximum value. The force grows with the increasing diameter of the upset cylinder. After releasing the motion, the force decreases instantly and the material in mushy state relaxes. After changing the loading conditions (the temperature or loading rate), the curve shifts to other values. But the process remains similar.
Results of experiments were used on the identification constitutive equation. The constitutive equation was chosen from the library of the program system LS-DYNA. This program and ANSYS are used for numerical simulations. For these experiments, a non linear viscoplastic model developed by Perzyna was used.
σ ... material yield stress
ε ... equivalent plastic strain rate
m ... strain rate hardening parameter
γ ... material viscosity parameter
σ0(ε) ... static yield stress of material, which is a function of equivalent plastic strain
The static yield stress for any given temperature and solid fraction depends on the cumulated plastic strain only. Such conclusion is based on the experimental results, where the relaxed static stress drops to the same value shortly after the ram stops, irrespective of its previous velocity – see the static force F stat.
The procedure of evaluation of the constitutive parameters is then based on the computational simulation of the compression test and minimisation of the deviation between the measured and computed values of the compression force.
- Static yield curve σ0(ε) according to figure
- Rain rate hardening parameter m = 0.35
- Viscosity parameter γ = 3.3 x 10-4 s-1
Compression force for ram velocity 0.5 cm/min, experiment and simulation
Good correspondence between the measured and simulated behaviour of tested specimens was observed.
can be found in Publications of the Heat Transfer and Fluid Flow Laboratory.