The recent works carried out by the authors' research group on magnetic field-induced martensitic transformations are reviewed, which are concerned with various kinds of ferrous alloys, such as Fe-Ni poly- and mono-crystals, invar and non-invar Fe-Ni-C polycrystals, discordered and ordered Fe-Pt polycrystals, ausaged Fe-Ni-Co-Ti polycrystals and paramagnetic Fe-Mn-C polycrystals. The works clarified influences of composition, the existence of grain boundaries, crystal orientation, invar characteristic, thermoelastic nature and austenitic magnetism on the magnetic field-induced martensitic trnasformations. In the work on the ausaged Fe-Ni-Co-Ti alloy, the appearance of ''magnetoelastic martensitic transformation'' was newly found. By taking into account the influences of composiiton, grain boundaries, crystal orientation, invar characteristic, thermoelastic nature and austenite magnetism, a new and exact equation was proposed to generally expalin the shift of M_s temperature as a function of critical magnetic field to induce martensitic transformations in those alloys, which consisted of three terms of the Zeeman energy, high field susceptibility energy and forced volume magnetostriction energy. The new and exact equation was experimentally verified to hold in all the alloys studied.

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Using a two-dimensional cold model, the dynamic behavior of particles in blast furnace was studied on a detailed analysis of the flow pattern. The field of the flow was characterized with the stagnant region formed in the central lower part of the apparatus and the flow channels consisting of two regions, i.e., slow moving and fast moving regions. On crossing the boundary between the slow and fast moving regions, the particles experienced a discontinuous, sudden change in the velocity as well as the direction of flow. An approximate method of predicting the flow pattern is described on the basis of plasticity theory. The velocity discontinuous boundary could be theoretically represented by the characteristic curve of the velocity. The boundary of the stagnant region corresponded to the characteristic curve of the stress, so-called slip line. Finally, the flow patern of burden material in a practical blast furnace was simulated, based on the calculas presented.

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A new approach has been developed to analyse the kinetics of heterogeneous gas-solid reactions. The solid reactant is considered as consisting of reactant species having different overall reaction rate constants and thus a rate constant distribution is associated with the solid. This distribution arises due to chemical heterogeneity of the material, availability of varying amounts of gaseous reactants at various locations within the particle due to its microstructural effects, and other physical phenomena which offer resistance to the reaction. Appropriate mathematics has been developed to express the reaction kinetics in terms of this rate constant distribution. The problem of evaluating the distribution is recognized to be equivalent to the problem of finding the inverse of the Laplace transform. A numerical method, based on non-linear optimization, has been used to carry out inversion of the Laplace transform and the rate constant distribution evaluated employing specified kinetic data. The applications of this new concept are illustrated using the kinetic data for reduction of hematite with hydrogen, and gasification of carbon with carbon dioxide. Effects of some of the operating parameters, e.g., temperature, particle size, porosity, gas flow rate and gas composition on the reaction kinetics are discussed in terms of this new concept.

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Desulfurization and simultaneous desulfurization and dephosphorization of molten iron were made by the use of Na₂O–SiO₂ and Na₂O–CaO–SiO₂ fluxes at 1 600°C.
The degree of desulfurization increased with increasing Na₂O/SiO₂ ratio and NaF content in the fluxes, whereas the degree decreased by the addition of CaO. Both of the reactions of desulfurization and dephosphorization took place simultaneously by the use of Na₂O–CaO–SiO₂ fluxes. The degree of dephosphorization was over 80% and not affected by the Na₂/O/CaO ratio of the fluxes, whereas the degree of desulfurization considerably decreased with increasing content of CaO (decreasing the Na₂O/CaO ratio). Some discussions were made on the sulfur and phosphorus partitions obtained at the end of runs.

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Phosphorus distribution between slag and liquid iron has been studied at the temperature range from 1 573 to 1 953 K. The slag system of Fe_tO–P₂O₅–M_xO_y(M_xO_y=CaO, MgO, SiO₂) ternary, and of Fe_tO–P₂O₅–CaO–M_xO_y(M_xO_y=MgO, SiO₂) quaternary were studied to clarify the effect of oxides on the phosphorus distribution equilibrium at steelmaking process.
In view of ionic theory, the approximate validity of regular solution model was examined to formulate the equilibrium reaction of phosphorus distribution between slag and metal. As the results, it was confirmed that the regular solution model was satisfied for all the experimental results including the present work and the previous studies by other investigators, except for extreamly high iron oxide region. The phosphorus and oxygen contents in liquid iron in equilibrium with slag can be estimated within the accuracy of ±10% by the quadratic formalism derived from an assumption of the regular solution of slag.

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The mixing time and slag-metal mass transfer coefficient in gas bubbling and induction stirring were measured by water model and plant scale experiments. The mixing time could be related to parameter εV^–2/3. In the range of low εV^–2/3, the mixing time for induction stirring was shorter than that for gas bubbling. In the range of large εV^–2/3, there was litle difference between the two methods of stirring. These phenomena can be explained by a circulating time of bulk flow in gas bubbling and induction stirring. Metal–phase mass transfer coefficient in water model and plant scale experiments could be related to parameter εV^–2/3. The metal-phase mass transfer coefficient for gas bubbling was larger than that for induction stirring. These phenomena can be explained by the turbulence fluctuation velocity near the slag-metal interface in gas bubbling and induction stirring.

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Magnetic field-induced transformation from paramagnetic austenite to ferromagnetic martensite in an Fe-21Ni-4Mn (wt%) alloy with dual martensitic transformation kinetics has been studied by magnetization measurement and optical microscopy, applying a pulsed ultra-high magnetic field. As a result, the following were found. A magnetic field higher than a critical one is needed to induce the martensitic transformation above Ms. The critical magnetic field increases with increasing temperature, and when plotted against the temperature difference (ΔT) from Ms, it lies on a straight line not passing through the origin. This result and thermodynamical analysis suggest that pulsed magnetic field strongly promotes the athermal martensitic transformation and restrains the isothemal one. The influence of magnetic field on martensitic transformation in the present Fe-Ni-Mn alloy is mainly due to Zeeman effect. The entropy change for athermal transformation at Ms, ΔSΔ_Ms^at is obtained to be 4.13 J/mol·K. The amount of magnetic field-induced martensites increases linearly with the maximum strength of pulsed magnetic field. Lath, plate and butterfly martensites are formed under magnetic field.

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The investigation was conducted on 6 specimens of an identical composition except for N and Ti contents, the specimens were remarkably free of nonmetallic inclusions other than TiN inclusion.
The quasi-dynamic method has been used to investigate the condition of nucleation, growth and propagation of micro-crack from TiN inclusion.
In summarizing the present study the following conclusion can be made:
(1) Fracture toughness K_IC is decreased rapidly with increasing volume fraction of inclusion (f_V) for f_V<0/1% and becomes insensitive when f_V>0.1% where the percentage of cracked-TiN reaches a limiting value.
(2) The percentage of cracked-TiN is determined by the true fracture strain ε_f and its propagation depends mainly on the critical true fracture strain ε_f^*. The ε_f^* can be computed by using both McClintock's model and Wall-Hill method as follows:ε_f^*=0.0345 ln (d_t/a)Thus the ε_f^* can be correlated with the inclusion spacing (d_t) and size (a).
(3) Based on the testing results, we get a similar relation to the ductile fracture model proposed by Rice, that is:K_IC=(E · σ_y · d_t)^1/2

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Effects of volume fraction of α phase and grain size on the creep properties of a series of two-phase titanium alloys were examined. The chemical compositions of α and β phases of the alloys were designed to be constant.
The alloys were quenched after solution-treatments for 1, 100, and 1 000 h at 1 173 K, followed by aging for 4 h at 773 K. The volume fraction of α phase (VFAP) was varied from 17 to 73%. Creep rupture test was carried out at 392 MPa and 773 K in air.
The creep rupture life was the longest at 50 % of VFAP, and the shortest at the minimum VFAP when the specimens were solution-treated for 1 and 100 h. It increased with VFAP when solution-treated for 1 000 h. The steady state creep rates decreased with the increase in VFAP. This might be due to the higher creep resistance of the α phase. Irrespective of the wide range of the average grain sizes, the steady state creep rates become insensitive of grain size as VFAP decreased. This would be attributed to grain boundaries of fine α precipitates generated in the prior β phase. The nucleation of voids occurred in most cases at the α/β and α/α interfaces, and within α phase. The void growth rate decreased with the volume-fraction-ratio of β and α phases and increased with the average transverse grain size of α phase.

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Darken's quadratic formalism is extended to multicomponent solutions. Equations are developed for the representation of the integral and partial excess free energies, entropies and enthalpies in dilute multicomponent solutions. Quadratic formalism applied to multicomponent solutions is thermodynamically consistent. The formalism is compared with the conventional second order Maclaurin series or interaction parameter representation and the relations between them are derived. Advantages of the quadratic formalism are discussed.

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