A theoretical model for the flow behavior of commercial dual-phase steels containing metastable retained austenite: Part I. derivation of flow curve equations

A semi-mechanistic model for predicting the flow behavior of a typical commercial dual-phase steel containing 20 vol pct of ‘as quenched’ martensite and varying amounts of retained austenite has been developed in this paper. Assuming that up to 20 vol pct of austenite with different degrees of mechanical stability can be retained as a result of certain thermomechanical treatments in a steel of appropriate low carbon low alloy chemistry, expressions for composite flow stress and strain have been derived. The model takes into account the work hardening of the individual microconstituents(viz., ferrite-@#@ α, retained austenite- γ _r, and martensite -α′) and the extra hardening of ferrite caused by accommodation dislocations surrounding the ‘as quenched’ as well as the strain-induced(γ _r→ α′) martensite. Load transfer between the phases has been accounted for using an intermediate law of mixtures which also considers the relative hardness of the soft and the hard phases. From the derived expressions, the flow behavior of dual phase steels can be predicted if the properties of the individual microconstituents are known. Versatility of the model for application to other commercial steels containing a metastable phase is discussed.     

残留奥氏体对中碳双相钢冲击性能的影响

采用不同的热处理工艺研究了残留奥氏体对中碳双相钢冲击韧性的影响。利用金相显微镜、扫描电镜、透射电镜和摆锤式冲击试验机,对不同试样的显微组织与冲击韧性进行观察、检测和分析。试验结果表明：中碳贝氏体钢的冲击性能显著高于Q/P马氏体钢（室温冲击功是57J对应15J,-40℃冲击功是33J对应9J）,可能的原因是贝氏体钢中薄膜状残留奥氏体,对裂纹扩展的阻止效应更显著。     

Intercritically annealed and isothermally transformed 0.15 Pct C steels containing 1.2 Pct Si-1.5 Pct Mn and 4 Pct Ni: Part II. effect of testing temperature on stress-strain behavior and deformation-induced austenite transformation

Stress-strain behavior and deformation-induced transformation of retained austenite were studied for intercritically annealed and isothermally transformed Si-Mn and Ni steels as a function of testing temperature between −80 °C and 120 °C. Rapid decrease of retained austenite at small strains dominates at low-temperature testing and in microstructures containing martensite. The austenite transformation in microstructures without martensite shifts to larger strains with increasing testing temperature. The accompanying increase of strain-hardening rates at larger strains deters the onset of necking and improves ductility. The benefits of the austenite transformation lead to a peak in ductility between 20 °C and 70 °C in the Si-Mn steel and at 70 °C in the Ni steel. The peaks are dependent on the nature of the dispersed microconstituents produced in the ferrite during isothermal transformation. Higher testing temperatures enhance the mechanical stability of the austenite and result in lower ductility.     

A heat-transfer model for the rotary kiln: Part II. Development of the cross-section model

A model of rotary kiln heat transfer, which accounts for the interaction of all the transport paths and processes, is presented in a three-part series. In this second paper, the development of a unified model for heat transfer at a kiln cross-section is described. Heat transfer within the kiln refractory wall was solved using a finite-difference approximation for one-dimensional transient conduction. A ray tracing technique was applied to derive coefficients for radiative heat transfer in the kiln freeboard, and the finite-difference model was extended into the contacting bed ma-terial in order to calculate the exchange between the covered wall and the bed. The cross-section model is shown to simulate the measured thermal performance of the pilot kiln for several feed materials: fine and coarse sand, limestone, and pctroleum coke. The interaction among the heat-transfer processes at cross-sections of the pilot kiln was examined, and explanations were made for both the observed close coupling of the bed and inside wall temperatures and the high rates of heat input to the bed occurring near the kiln entrance and in the presence of an endothermic bed reaction. Conclusions regarding the likely effects of kiln internal devices on heat transfer to the bed and the importance of preheaters are reached from the model predictions for a 4 m I.D. prototype kiln.     

A mathematical model for the solution mining of primary copper ore: Part II. leaching by solution containing oxygen bubbles

The one-dimensional model developed previously to simulate thein situ leaching of copper from deeply-buried low-grade copper ore deposits is used to simulate thein situ operation in which the oxygen-saturated solution containing oxygen bubbles is introduced at the bottom of the chimney. The physical and chemical processes incorporated in the present model include the axial convective transport of mass and heat, axial dispersion of mass, mass transfer between the liquid and gas phases, fluid-solid mass transfer, diffusion of oxygen in the pores of ore fragments, and the dissolution of sulfide minerals. The coupled model equations are solved numerically by an implicit finite-difference method. Calculations have been made for various values of the volume fraction of oxygen bubbles (up to 0.1) in the fluid just downstream of the oxygen sparging nozzle. Calculated results indicate that, for a specific chimney considered, the total amount of copper extracted increases with increasing volume fraction of undissolved oxygen bubbles in the inlet fluid and increasing superficial velocity of the solution (up to 20 m per day). However, a further increase in the superficial velocity of liquid or undissolved oxygen bubbles does not enhance copper extraction. Calculated results also indicate that the total fractional recovery of copper increases with decreasing pyrite to chalcopyrite molar ratio, ore grade, particle size, and shape factor.     

A process model for the microstructure evolution in ductile cast iron: Part II. Applications of the model

In the present investigation, the process model developed in Part I has been implemented in a dedicated numerical code to reveal the evolution of the coupled thermal and microstructural fields during directional solidification of ductile iron. In a calibrated from, the model predicts adequately both the variation in the graphite nodule count and the resulting microstructural profiles (i.e., graphite, iron carbide, ferrite, and pearlite) in the length direction of the bar. At the same time, the model has the required flexibility to serve as a research tool and predict behavior under conditions that have not yet been explored experimentally. In this article, the aptness of the model to alloy design and optimization of melt treatment practice for ductile iron is illustrated in different case studies and numerical examples.     

Competitive growth of stable and metastable Fe- C- X eutectics: Part II. mechanisms

The competition between stable and metastable solidification in Fe-C-X alloys has been studied theo-retically, with particular regard to phase stability, nucleation, and growth processes. The effects of small additions of Si, P, Cr, Mn, Ti, Al, and S upon the transition velocities from grey to white and from white to grey in directional solidification are related to their influence on the eutectic tempera-tures, and nucleation and growth undercoolings. It is shown that the consequences of simultaneously adding Si and Cr upon the transition velocities can be deduced from the results of adding of Si and Cr separately only when the detailed effects of these elements upon phase stability, nucleation, and growth are known. The well-known carburizing effect of a high thermal gradient (superheat) has been shown to influence only the nucleation process. A three-phase austenite-graphite-cementite mi-crostructure resulting from the cooperative growth of a double stable/metastable eutectic has been observed for the first time.     

A mathematical model for the dynamic behavior of melts subjected to electromagnetic forces: Part II. Measurement of surface waves and comparison with predictions of the mathematical model

The waves on the surface of a cylindrical mercury pool subjected to a 3 kHz electromagnetic field have been observed. Oscillations were found to correspond to the known eigenfrequencies of a cylindrical liquid pool with a free surface. Which of the eigenfrequencies was dominant depended on the field strength and the relative position of the pool in the surrounding inductor. The amplitude of the oscillations was found to increase with increasing inductor current. The measurements showed fair to good agreement with the predictions of the mathematical model described in Part I. A tentative mechanism for the excitation of the eigenfrequencies by the electromagnetic field is advanced and implications for electromagnetic casting are discussed.     

Predicting the onset of transformation under noncontinuous cooling conditions: Part II. Application to the austenite pearlite transformation

A detailed review of the additivity principle with respect to the incubation of the austenite decomposition was summarized in Part I of this two-part series and led to the concept of an “ideal” time-temperature-transformation (TTT) diagram. This curve is characteristic of the chemistry and austenite grain size in the steel and allows nonisothermal behavior to be described assuming additivity holds. The derivation of mathematical relationships between the ideal and experimental cooling data was presented in the first article. In this second article, an ideal curve for the austenite-to-pearlite transformation was derived from cooling data.The applicability of the ideal TTT curve for predicting the start of transformation under continuous cooling conditions was assessed for a range of cooling rates. Experiments were conducted under both isothermal and varying temperature conditions, including an industrial cooling schedule, using a Gleeble Thermal Simulator. Reasonable agreement was found between the predictions and the observed transformation start temperatures; predictions were consistent and compared favorably against other methods which have been frequently used to estimate the transformation start temperature for nonisothermal conditions.     

Evolution of dislocation structures and deformation behavior of iron at different temperatures: Part II. dislocation density and theoretical analysis

The evolution of dislocation density in iron deformed at 173 K and at room temperature has been examined by transmission electron microscopy (TEM). At room temperature, the dislocation density in the cell walls increases as the deformation progresses up to large strains, whereas in cell interiors, the density evolves toward a saturation value. A linear relationship exists between the flow stress and the square root of total dislocation density both at 173 K and room temperature. The dependence of deformation behavior on the evolution of dislocation structures is discussed in terms of a model considering the dislocation distribution during deformation. Comparison of the calculated result using this model with the experimental curve at room temperature gives excellent agreement. The changes of deformation behaviors at different temperatures can be described by the effect of temperature on the evolution of dislocation distribution.     

Mathematical model of COREX melter gasifier: Part II. Dynamic model

A dynamic model of the COREX melter gasifier is developed to study the transient behavior of the furnace. The effect of pulse disturbance and step disturbance on the process performance has been studied. This study shows that the effect of pulse disturbance decays asymptotically. The step change brings the system to a new steady state after a delay of about 5 hours. The dynamic behavior of the melter gasifier with respect to a shutdown/blow-on condition and the effect of tapping are also studied. The results show that the time response of the melter gasifier is much less than that of a blast furnace.     

A kinetic model of the Peirce-Smith converter: Part II. Model application and discussion

A sensitivity analysis of a kinetics-based model of the Peirce-Smith converter has been carried out, and the model has then been applied to an analysis of copper converter operation. The results of the sensitivity analysis indicate that only factors relating to the mass-transfer rates have a significant effect on the model predictions. However, even with large changes in diffusivities, the model predictions remain within the error of the plant measurements. The converter analysis indicates that considerable improvements to converter productivity can be made, particularly through changes to gas injection practices.     

Inclusion behavior and heat-transfer phenomena in steelmaking tundish operations: Part II. Mathematical model for liquid steel in tundishes

Fluid flow, heat transfer, and inclusion flotation have been modeled mathematically for several types of industrial tundish designs. Computations are presented to illustrate the importance of thermal natural convection currents in mixing the upper and lower layers of steel. The use of flow modification devices was shown to be reasonably effective in further reducing inclusion density levels at the intermediate to larger size ranges. Small inclusions (≦40 μm) were not readily removed with or without flow controls because of their low Stokes rising velocities. Formerly Doctoral Candidate Formerly Postdoctoral Fellow, Department of Mining and Metallurgical Engineering, McGill Metals Processing Centre, McGill University. Macdonald Professor of Metallurgy     

Dimensionless correlations for forced convection in liquid metals: Part II. two-phase flow

An experimental technique has been developed to study the convective heat-transfer characteristics of gas-agitated liquid metals. A sphere made from the same metal as the liquid metal under investigation is immersed in the center axis of the plume. The melting time of this sphere is detected, and from this time, the convective heat-transfer characteristics of the metal bath are deduced. Based on a variety of experimental results, a dimensionless correlation was deduced. This equation has the following form:

Mathematical model of the thermal processing of steel ingots: Part II. Stress model

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. B. G. THOMAS, formerly a Graduate Student at the University of British Columbia     

A study on the kinetic process of reaction synthesis of TiC: Part II. Theoretical analyses and numerical calculation

Based on the experimental results, a mathematical kinetic model of the reaction process to synthesize TiC particles has been built, and a reaction rate expression is developed in this article based on the following mechanism: a Ti-rich Al-Ti complex layer is formed around carbon particles and titanium atoms diffuse from melt, across the layer, to react with carbon to form TiC; the TiC particles precipitate out of melt and diffuse all over the melt. The calculated results have shown that there are four major effect elements—the temperature of the system, the aluminum content of the preform, the thickness of the titanium-rich layer, and the size of carbon particle—to decrease the aluminum content, the thickness of titanium-rich layer, and the size of carbon particle and to increase the temperature, accelerate the reaction rate, and reduce the complete reaction time. In the end, some experiments have been done to investigate the effect of temperature, size of C powder, and Al content on the reaction. The experimental results were in good agreement with the numerical calculated result.     

Mathematical model of the thermal processing of steel ingots: Part I. Heat flow model

A two-dimensional mathematical model has been developed to predict stress generation in static-cast steel ingots during thermal processing with the objective of understanding the role of stress generation in the formation of defects such as panel cracks. In the first part of a two-part paper the formulation and application of a heat-flow model, necessary for the prediction of the temperature distribution which governs thermal stress generation in the ingot, are described. A transverse plane through the ingot and mold is considered and the model incorporates geometric features such as rounded corners and mold corrugations by the use of the finite-element method. The time of air gap formation between mold and solidifying ingot skin is input, based on reported measurements, as a function of position over the ingot/mold surface. The model has been verified with analytical solutions and by comparison of predictions to industrial measurements. Finally, the model has been applied to calculate temperature contours in a 760×1520 mm, corrugated, low-carbon steel ingot under processing conditions conducive to panel crack formation. The model predictions are input to an uncoupled stress model which is described in Part II. B. G. THOMAS, formerly a Graduate Student at the University of British Columbia