Canadian and French university teams have joined efforts in carrying out an experimental and theoretical study of the dissolution behavior of the hard-alpha inclusion in liquid titanium alloys. Synthetic hard-alpha dense particles of up to 6 wt pct nitrogen and nitrided sponge of up to 15 wt pct nitrogen were partially dissolved in a titanium or a titanium alloy bath. The metallographic examinations and microprobe analysis show that the dissolution process is always controlled by the outward diffusion of nitrogen into the bath through an external layer of beta phase. The growth of this beta phase layer depends on the velocity of liquid flow in the bath and can lead to an initial increase in the inclusion size. For porous particles, the diffusion of nitrogen from the pellet matrix to the infiltrations gradually leads to a partial densification of the inclusion. A numerical representation of the dissolution problem was developed, including the transient diffusion of nitrogen through intermediate solid phases. The comparison is good between the numerical simulations, the experimental measurements, and the dissolution kinetics given in the literature.

As part of a complete theoretical description of the behaviour of the electric arc in the vacuum arc remelting process, a model has been developed for the column of plasma generated by a single cluster of cathode spots. The model combines a kinetic approach, taking into account the formation of the plasma in the cathodic region, and a hydrodynamic approach, describing the expansion of the plasma in the vacuum between the electrodes. The kinetic model is based on a system of Boltzmann-Vlasov-Poisson equations and uses a particle-type simulation procedure, combining the PIC (particle in cell) and FPM (finite point set method) methods. In the two-dimensional hydrodynamic model, the plasma is assimilated to a mixture of two continuous fluids (the electrons and the ions), each described by a system of coupled transport equations. Finally, a simplified method has been defined for calculating the electric current density and the energy flux density transmitted by the plasma to the anode. The results of the numerical simulation presented are consistent with a certain number of experimental data available in the literature. In particular, the model predicts a percentage of the electric power of the cluster transmitted to the anode (25%) in good agreement with the value indicated in the literature.

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The electron beam cold hearth melting (EBCHM) process has emerged as either an alternative or a complement to vacuum arc remelting, since it is capable of enhancing the elimination of hard-alpha inclusions by dissolution or sedimentation. The present article describes the use of a mathematical model to simulate the electron beam melting of titanium in a cold hearth. The mathematical model is based on the numerical solution of the coupled momentum, solute, and heat transport equations in a transient regime for a three dimension geometry. The model calculates the velocity, turbulence intensity, temperature, and alloy composition in the liquid and the solid phases. The calculation provides the overall heat balance and the volatilization of metallic elements such as aluminum. A postprocessor numerical tool simulates also the behavior of a hard-alpha inclusion during melting (trajectory and kinetics of dissolution). In order to demonstrate the usefulness of this model, the authors examine the influence of the casting rate and of the beam scanning frequency on the volatilization of aluminum and on the capacity of the process to remove hard-alpha defects.

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