Metallurgical Transactions B

A mathematical model has been developed to predict the internal stresses generated in a steel ingot during thermal processing. The thermal history of the ingot has been predicted by a finite-element, heat-flow model, the subject of the first part of this two-part paper, which serves as input to the stress model. The stress model has been formulated for a two-dimensional transverse plane at mid-height of the ingot and is a transient, elasto-viscoplastic, finite-element analysis of the thermal stress field. Salient features of the model include the incorporation of time-temperature and temperature-dependent mechanical properties, and volume changes associated with nonequilibrium phase transformation. Model predictions demonstrate that the development of internal stresses in the ingot during thermal processing can be directly linked to the progress of the phase transformation front. Moreover, the low strain levels calculated indicate that metallurgical embrittlement must be very important to the formation of cracks in addition to the development of high tensile stresses.

Numerical computations were carried out to describe the subsurface trajectories of spherically shaped particles (alloy additions) during simulated furnace to ladle tapping operations in steel-making. Complementing this, experiments in a 0.15 scale water model ladle of a 250 ton teeming ladle were also carried out so as to simulate the subsurface trajectories and total immersion times of various alloy additions as a function of (steel) jet orientation, jet entry locations, particle (alloy additions) entry location, particle shape, density,etc. Similarity criteria for model and prototype were deduced on the basis of Froude modeling. The possibilities of additions of various density being entrained into the bulk liquid and under-going prolonged subsurface motion were examined for a variety of operating conditions. It was found, however, that buoyant spherical particles with apparent densities ranging between 0.4 and 0.9 would, when projected into a recirculating water bath at velocities of 2.7 m/s, record total immersion times of only 0.1 to 40 seconds. The implications of the water model study, together with some idealized sets of computations for an industrial size 250 ton ladle, are analyzed from the viewpoint of industrial alloy addition practices. Finally, the results are examined with reference to different shaped particles and multi-particle addition procedures, since the latter are more typical of industrial practice.

The thermodynamic activities in the liquid Cu-Fe and Cu-Co binary systems were measured by a high temperature mass spectrometric technique. From the obtained data, the heats of mixing in the Cu-Co liquid binary were calculated. Both the Cu-Fe and Cu-Co systems are thermodynamically similar, with large positive deviations from ideality in the activities. The activity coefficients in the liquid Cu-Co system at 1823 K were found to be symmetrical and can be expressed by lnγCu= 1.76X Co 2 The heat of mixing in the liquid Cu-Co system was found to be described by a cubic function δHm = −17.9 Co 3 − 7.6X Co 2 + 25.5Co (kJ/mol) The activity coefficients in the liquid Cu-Fe system at 1873 K were found to satisfy two quadratic formalisms in the binary In γCu = 2.10X Fe 2 − 0.13 0.65 ≤X Fe ≤ 1 In γFe = 1.79X Cu 2 + 0.04 0 ≤X Fe ≤ 0.65

The kinetics of the electrode reaction Fe = Fe slag 2+ + 2e - has been investigated using the single and double pulse techniques. It was found that the exchange current densities are very large increasing from 2 to 10 A cm-2 in the range of Fe2+-concentration from 2 · 10-6 to 30 · 10-6 mole cm−3. The electrode capacitance increases from 50 ΜF cm-2 approximately linearly with the square root of Fe2+-concentration. An attempt was made to explain the concentration dependent part of the capacitance in terms of a model involving electrosorption of the speciesFe at the slag/iron interface. If the adsorbed iron ions are the intermediates in a consecutive charge transfer mechanism, the rate determining step is the transfer of iron between the adsorbed layer and the slag. On the other hand, it may be possible that the transfer is in one step with adsorption occurring in parallel.

A mathematical formulation has been developed to represent the electromagnetic force field and the velocity field in the melt for the electromagnetic casting of aluminum. The theoretical predictions based on fundamental considerations are compared with experimental measurements obtained on a physical model system. The measurements and predictions were found to be in good agreement, regarding both the velocity fields and the electromagnetic force fields. The principal conclusion emerging from this work is of critical importance in achieving the dual objective, that is providing a restraining force, while minimizing the melt velocity perpendicular to the free surface. The mathematical formulation presented in the paper provides the theoretical framework for quantitatively defining these conditions in terms of the coil and the shield parameters.