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By Vaughan R. Voller

"Numerical methods for dealing with a temperature dependent conductivity are discussed. An approach based on a local application of a Kirchhoff transformation at the discrete level is presented. The application of this transformation - that does not require any inversion- is demonstrated on solving a two-dimensional test problem.IntroductionMuch is said in the recent literature on the modeling necessity of obtaining appropriate thermo-physical properties; in particular the requirement to account for properties that are ""strong"" functions of the depended variables, e.g., Temperature. Of course obtaining appropriate thermo-physical properties serves no purpose unless they can be accurately integrated into a discrete numerical calculation. The purpose of this paper is to examine how temperature dependent conductivities that exhibit discontinuities or rapid changes can be handled in a numerical code.The discussion will be made in the context of a control volume finite element method [1]. After a brief outline of control volume finite element fundamentals basic methods of dealing with discontinuous or rapidly changing thermal conductivity are discussed. This is followed by the presentation of the recently proposed local Kirchhoff method [2,3], The paper concludes with an investigation of the performance of the various conductivity schemes in solving two dimensional problems. This testing clearly shows the advantages (accuracy and implementation) in using the local Kirchhoff method."

Jan 1, 2001

By C. Isaac Garcia, Sihai Jiao, Anthony J. DeArdo

"A practical model based on the Hill analysis has been developed to calculate the Lankford value of interstitial free (IF) steels and its distribution in different rolling directions, by considering only a few selected texture components. The Texture Intensity Ratio (TIR), i.e. (111 ) /(100), was used in the model to describe texture. By using the new TIR parameter, the texture-based prediction models can be used more easily to predict the Lankford value in a rather straightforward way.IntroductionThe deep drawing capacity of sheet steels is generally indicated by the Lankford value, which is mainly determined by the texture in steels1. Traditionally, various models derived from the Taylor model are employed to calculate the Lankford value from the texture2-4. In such models, the plastic deformation of steel is assumed to be the result of the slip of dislocations in certain slip systems, i.e., by either pencil glide or restraint glide. The slip direction is the <111> direction. In the case of pencil glide, the slip is thought to be possible in all crystal planes with the <111> crystal direction. Assuming the material is elongated in the X1-direction by d n and compressed in the X2 and x3-direction by qd n and (l-q)d n, respectively, corresponding to a deformation tensor"

Jan 1, 2001

By Luben Savov

This paper presents recent research works on the removal of the tramp elements Cu, Sn, Zn and Pb from steel. The evaporation of Cu and Sn in iron-based melts treated at reduced pressure of the gas phase was studied in a vacuum induction melting furnace. The effect of chamber pressure, temperature and melt composition was investigated. Since the main source of contamination of steel with Sn and Zn is the recycling of tinplate and zinc coated steel, respectively, possibilities for the removal of meta1ic coatings in a scrap pre-treatment stage were studied, too. Tin was removed in the temperature range 400-5S0°C by treatment with reactive gases featuring high sulphur potential. Zinc can be removed by evaporation or by a combination of thermal and mechanical treatment. The paper discusses the thermodynamics of Pb in carbon-saturated iron melts, too.

Jan 1, 2001

By Di Yang

The influence of high density (104 -105 A/cm2) electric current pulses (70 us duration) and continuous DC (~103 A/cm2) on the flow stress and ductility in tension of a high carbon steel wire were determined at 204°, 427° and 649°C. Electropulsing (100 pulses per second) with an effective current density of 100-200 A/cm2 gave a 10% enhancement in the uniform elongation of the wire at 204°C, but had no effect at 427°C and 649°C. In contrast, continuous DC either had no significant effect on the ductility or gave a decrease. The electropulsing per se decreased the flow stress only slightly at 204° and 427°C, but gave a significant decrease at 649°C. Continuous DC increased the flow stress at all three temperatures. The present results along with those by others suggest that the enhanced ductility by electropulsing and the reduction in flow stress may be further increased by raising the effective current density through increases in either the pulsing frequency, maximum current density of each pulse or pulse duration. This could conceivably increase the reduction per pass during wire drawing or the number of passes between anneals.

Jan 1, 2001

By W. G. Davenport

The offgas from flash furnaces inadvertently contains dust. The dust contains 25 to 30% Cu so it must be treated for Cu recovery. This is almost always done by recycling it back through the flash furnace*. This chapter shows how dust production/recycle is included in our matrix calculations. It then discusses the effects of dust production/recycle on flash furnace industrial oxygen and oil requirements. It concludes that re-smelting of dust requires considerable industrial oxygen and fuel, so that dust production should be minimized. Recycled dust also takes the place of new concentrate in the flash furnace feed system, decreasing Smelter productivity -another reason to minimize dust production. Compositions of industrial dusts are given in Appendix VII and Table 18.3. Industrial quantities are given in Tables 2.1, 3.1, 19.1,20.1&apos; and Appendix VI.

Jan 1, 2001

By Gunnar Eriksson

Computer simulation has become an everyday practice in thennodynamic and materials research. Advanced thennochemical algorithms take into account heat transfer effects and salient reaction kinetics when applied for process models. In particular, the combination of mass transfer or overall reaction rates with multi-component Gibbs energy minimisation provides an effective tool for simulation of industrial thennochemical processes and processing of materials. In this work the combination of rate factors with the Gibbs energy technique was studied by using the novel program ChemSheet, which operates through Microsoft&apos;s Excel® spreadsheets. Such processes as, for example, CVD of pure silicon production, titania pigment manufacturing, vapour pressure of Mercury in amalgams (in Hg-Iamp manufacturing) and melting behaviour of low-temperature alloys have been modelled. Provided that the thennochemical data is available simulations can be performed with any thennodynamic system. The calculation can be performed as an affinity study without a particular reactor model or with a specific reactor scheme.

Jan 1, 2001

By Young-Geun Park

A new decarburization model for the RH system was constructed for calculating the decarburization reaction using a three-dimensional fluid dynamics program. The entire fluid flow in the RH process was calculated by evaluating the shape and volume of the plume zone, formed by Ar gas blown through multiple nozzles on the wall of the snorkel. On the basis of this fluid flow, the decarburizaiton reaction was calculated through establishing the decarburization reaction model, which considers the thermodynamics, reaction kinetics, and the decarburization sites (Ar bubble surface, bath surface, and the CO bubble fomtation at inner sites). The results from this model were compared with a real RH operation results with good agreement. Because it is possible to predict the carbon concentration at various conditions using this model, it may be useful in increasing the decarburizaiton rate. Key words : RH process, plume zone, decarburization, Ar bubble surface, bath surface, inner site, circulation flow rate.

Jan 1, 2001

By V. D. Tathavadkar

Natural chromite mineral is a solid solution of spinet end members namely: chromite (FeCr2O4), hercynite (FeA1204), magnetite (Fe3O4), magnesio-chromite (MgCr2O4), (MgA12O4), and magnesio-ferrite (MgFe2O4). A phase transformation in chromite minerals occurs in oxidising conditions during the soda-ash roasting reaction. This phase transformation plays an important role in improving the extraction efficiency of Cr3+ from mineral phase. The extraction efficiency of chromium (Cr3+) from chromite to a water¬soluble sodium chromate (Cr6+) salt depends upon the decomposition kinetics of the spinet phase. An investigation of the phase changes in chromite ores in the absence of sodium carbonate was carried out in air, argon, and in argon +5 % hydrogen gas mixture. The thermodynamics of phase transformation reaction in chromite solid solution phase is discussed using the solution model proposed by Sack and Ghiorso [1]. The microstructural changes and the changes in elemental compositions of different phases were examined by SEM and electron probe microanalysis (EPMA) respectively. The experimental results indicate that the solid solution spinet phase in chromite mineral undergoes spinodal decomposition under the influence of oxygen partial pressure and temperatures. The structure of phases formed and their morphologies suggest that the phase decomposition may be similar to those observed by Burkert et. a]. 121, although the scale of phase separation in chromite appears to be strongly dependent on oxygen partial pressure.

Jan 1, 2001

By Markus A. Reuter

In this paper various hybrid modelling architectures are proposed for the modelling and metallurgical control of pyrometallurgical reactors. Discussed are architectures in which data reconciliation is combined by thermochemical, neural net and dynamic modelling to improve the models. At the same time the data reconciliation models can act as soft-sensors for estimating unmeasurable data. Cases that are discussed are (i) the modelling of a submerged arc furnace for the production of thermal phosphorous, (ii) the processing of Sn-Pb-Zn flue dust (originating from secondary copper) in a hearth furnace, (iii) modelling of a steel converter, and (iv) dynamic modelling of a flash smelter.

Jan 1, 2001

By Paul C. Turner

In 1998, approximately 57,000 tons of titanium metal was consumed in the form of mill products (1). Only about 5% of the 4 million tons of titanium minerals consumed each year is used to produce titanium metal, with the remainder primarily used to produce titanium dioxide pigment. Titanium metal production is primarily based on the direct chlorination of rutile to produce titanium tetrachloride, which is then reduced to metal using the Kroll magnesium reduction process. The use of titanium is tied to its high strength-to-weight ratio and corrosion resistance. Aerospace is the largest application for titanium, and titanium cost has prevented its use in non-aerospace applications including the automotive and heavy vehicle industries.

Jan 1, 2001

By Andrzej Warczok

Intensive smelting of copper concentrate in Teniente Converter (CT) leads to the production of high grade matte and highly oxidized slag. Smelting slag is processed in Teniente vascular slag cleaning furnace. The slag composition and forms of copper affect the slag cleaning process and final copper content. Converting of high grade matte in Pierce-Smith converter faces some difficulties in proper slagging of iron oxides. Overblowing in copper making stage allows for slag liquidation but leads to high content of copper oxide in converter slag. Converter slag recycling into CT results in the increase of the participation of oxidic copper. Separate treatment of converter slag and its impact on the forms of copper in CT slag has been analyzed. Thermodynamic properties of a system and kinetic limitations pointed out the negative effect of converter slag recycling on the forms of copper and copper recovery in slag cleaning stage. Experimental results of slag cleaning tests in a crucible scale as well as microscopic examination of laboratory and industrial slag samples supported the above analysis and permitted to formulate recommendations of separate processing of converter slag. Keywords: copper, losses, slag, recycling

Jan 1, 2001

By Ravi S. Bellur-Ramaswamy, Daniel A. Tortorelli, Robert Haber, Nahil A. Sobh

We optimize continuous quench process parameters to produce functionally graded aluminum alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard nonlinear programming algorithm. Ingredients of this algorithm include 1) the process parameters to be optimized, 2) a cost function: the weighted average of the precipitate number density distribution, 3) constraint functions to limit the temperature gradient (and hence distortion and residual stress) and exit temperature, and 4) their sensitivities with respect to the process parameters. The cost and constraint functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine the precipitate particle sizes and their distributions. Both the temperature and the precipitate models are solved via the discontinuous Galerkin finite element method. The energy balance incorporates nonlinear boundary conditions and material properties. The temperature field is then used in the reaction rate model which has as many as 105 degrees of- freedom per finite element node. After computing the temperature and precipitate size distributions we must compute their sensitivities. This seemingly intractable computational task is resolved thanks to the discontinuous Galerkin finite element formulation and the direct differentiation sensitivity method. A three-dimension example is provided to demonstrate the algorithm.

Jan 1, 2001

By I. C. Howard, E. J. Palmiere

"Heat transfer and friction in hot flat rolling have traditionally been characterised by an average heat transfer coefficient (h) and an average friction coefficient (p.). However, the presence of oxide scales and asperities at the interface question the use of such averages. The apparent irregularity and lack of pattern of interactions at the interface has prompted this present investigation to move away from averaged h and 11 values, and to study their local evolution based on probabilistic rules. The approach is based on the probability of finding the workpiece surface in a specific configuration at a particular instance of time in the roll gap. These rules are based on observations of surface phenomena such as scale behaviour during hot rolling. The model is implemented using user-subroutines integrated with the commercially available finite element program ABAQUS™. The results show the strong dependence of h and u on the local scale interactions. In particular, the effect of scale thickness, material behaviour and processing conditions on the evolution of hand 11 are discussed. Finally, the development of a Cellular Automata based Finite Element (CAFE) model is proposed to model the combined interfacial phenomenon of friction and heat transfer at the tool-work piece interface.IntroductionIntricate interactions between process variables in hot rolling of steels make it a challenge to the modelling community. For a given material and geometry combination, reducing interfacial power losses can increase the efficiency of the rolling process. The roll-strip interface, therefore, forms the critical zone and is currently the domain of intense investigation, especially to characterize interfacial frictionl • 2 and heat transfer3 • 4 . These interfacial phenomena are inter-related and cannot be studied in isolation. However, very few mathematical models4 • 5 combine an analysis of friction and heat transfer and deformation of the strip-roll interface taking into account the role of asperities and oxide scales."

Jan 1, 2001

By C. Hennesmann, D. Maijer, S. L. Cockcroft, P. Yo

"Die cast aluminum wheels are one of the most difficult automotive castings to produce because of stringent cast surface and internal quality requirements. As part of a collaborative research agreement between researchers at the University of British Columbia and Canadian Auto Parts Toyota Incorporated, work has been underway to predict heat transport and porosity formation in die cast A356 wheels. The basic heat transfer equations have been solved using the commercial finite element package ABAQUS to which specialized routines have been added to predict porosity. Preliminary work on predicting porosity formation focused on using the Niyama parameter as a measure of the probability of porosity. The latest version of the model incorporates a new fundamentally based porosity criterion, which takes into account the effect of hydrogen concentration. The development of this model together with its application to a series of cylindrical test castings as well as a production cast wheel are presented.I. IntroductionDie cast aluminum wheels are one of the most difficult automotive castings to produce because of stringent cast surface and internal quality requirements. Microporosity, in particular, is a common defect that can adversely affect wheel quality. The mechanism of microporosity formation in aluminum alloys is complex owing to its dependence on the interaction of a number of phenomena occurring during solidification including the decrease in hydrogen solubility, the decrease in volume, the development of the solidification structure, and the increase in difficulty in interdendritic feeding [1]. As a result, the amount, size, and distribution of microporosity is affected by a large number of casting parameters including thermal variables, melt composition, grain structure, modification, and inclusion content, making optimization by trial-and-error methodologies difficult.The use of criteria functions, based on thermal conditions during casting, offers a relatively simple approach to predicting microporosity. In practical terms, they are useful because they provide a straightforward method of assessing the impact of varying casting parameters on porosity through various thermal parametersl21 such as thermal gradient, cooling rate, solidification time, and solidus velocity. Drawbacks of criteria functions include insensitivity to varying hydrogen concentration and the limitation to qualitative predictions. Consequently, in aluminum alloys, attempts have been made to develop models incorporating the effects of hydrogen gas and microstructure evolution. However, these types of models represent a significant increase in complexity and sacrifice the simplicity and ease of application of the thermally based criteria functions."

Jan 1, 2001

By T. Tamagawa

Vaporization of zinc and mixing of zinc vapor with CO-CO2 mixtures were studied experimentally to prepare Zn(g)-CO-CO2-Ar mixtures with desired composition for investigating the condensation behavior and efficiency of zinc vapor. The vaporization rate of zinc was generally constant under given conditions, and could be increased by raising the flow rate of the carrier gas, temperature and vaporization area. The Zn(g)-CO-CO,,-Ar mixtures were quenched by a water-cooling sampling tube for measuring the actual composition of the mixtures in the reactor. The oxidation extent of the zinc vapor in the CO-CO2 mixtures had relation to the CO2/CO ratios and the temperatures. Under current conditions, it was necessary to employ the CO2/CO ratio below 0.125 for mixing the zinc vapor with CO-CO2 mixtures without oxidation. In addition, the appearances and zinc contents of the condensed zinc on the sampling tube were also examined.

Jan 1, 2001

By Denise Corrêa de Oliveira

Household zinc based batteries, dry and alkaline, has become the most popular sources of electrical energy, and are widely used. Because of their heavy metals content such as mercury, zinc and manganese, spent batteries cannot be directly placed in common landfills without a pretreatment. As a municipal solid waste, these batteries may cause serious health problems and environmental impacts. These damages can be reduced by recovery (which means saving natural sources and energy), recycling and adoption of cleaner technologies. Although this worry has been increasing recently, and producers are doing efforts to reduce the mercury content, batteries still need proper safe disposal conditions or recycling processes. This work presents the efforts in progress to characterize and recycle mixed - dry and alkaline - spent batteries, by using low cost unit operations. Some possible recycling stages and recovery parameters of metals as zinc and manganese are also discussed.

Jan 1, 2001

By Roderick 1. L. Guthrie, Mei Li

"A mathematical model was developed to study the role of orifice shape in the detection of inclusions in LiMCA (Liquid Metal .cleanliness Analyzer) system. The fluid flow field within the ESZ was obtained by solving the Navier-Stokes equations. The trajectories of entrained particles were calculated using the equations for motion of particles. A numerical study of the effect of orifice shape on signal shape generated by inclusions passing through orifice showed that the signals in a parabolic orifice are gaussian in shape, while those in a cylindrical orifice are trapezoidal in shape. This signal shape difference needs to be taken into account when performing particle discrimination. Orifice shape influences also pass-through fraction of inclusions. Finally, a study of the orifice shape on critical conditioning currents suggested that as the polynominal coefficient of the parabolic orifice increases, the critical conditioning current, which is also the maximum operating current, decreases dramatically. These critical conditioning currents also increase as the fluid flow velocity within the ESZ increases. IntroductionThe presence of non-metallic inclusions in metals often leads to impaired mechanical properties such as a reduction in fatigue strength, and to processing problems such as tear-offs in deep drawing and increased breakage rates in wire drawing operations. Similarly, inclusions cause a variety of surface defects in rolled or extruded products.Prior to the development of the LiMCA system (1) at McGill University in the early 1980's, it was not possible to measure inclusions, in situ, in liquid metals. Compared with other techniques, such as sedimentation, filtration and metallography, which require considerable amounts of labor and time, the LiMCA method has the advantage of providing not only information on the volume concentration of inclusions, but also on the size distribution of inclusions immediately and quantitatively."

Jan 1, 2001

By Rodney L. Williamson

Optimal estimation theory has been applied to the problem of estimating process variables during vacuum arc remelting (V AR), a process widely used in the specialty metals industry to cast large ingots of segregation sensitive and/or reactive metal alloys. Four state variables were used to develop a simple state-space model of the V AR process: electrode gap (G), electrode mass (M), electrode position (X) and electrode melting rate (R). The optimal estimator consists of a Kalman filter that incorporates the model and uses electrode feed rate and measurement based estimates of G, M and X to produce optimal estimates of all four state variables. Simulations show that the filter provides estimates that have error variances between one and three orders-of-magnitude less than estimates based solely on measurements. Examples are presented that verify this for electrode gap, an extremely important control parameter for the process.

Jan 1, 2001

By Yan Beygelzimer, Alexander Spuskanyuk, Victor Varyukhin

"The main idea of the report is that the yield surface can be presented as thick, ""foamed surface"" with dimensionality exceeding two. By other words, perhaps, the yield surface is fractal, i.e. it belongs to the class of geometric objects with fractional dimensionality. Apparently, fractal structure of the yield surface is determined by the fractal structure of natural materials. ""Cloud of internal stresses"" term is introduced to describe the stress distribution in representative volume element. Its plastic flow is determined by the interaction of this cloud with the thick yield surface. Thick yield surface and internal stress cloud concepts allow to determine an additional correlation between micro mechanical models of polycrystals and phenomenological theory of plasticity.1. IntroductionClassical plastic flow models are not satisfying the modem requirements. There are two main directions in their development. The first, mathematical, is connected with the development of the general theory of rheological relationships; the second, physical, is connected with the development of the representative volume element (RVE) models which are based on specific ideas about deformation mechanisms. Within the framework of the first direction, the macroscopic experimental data is formalized; the second approach deals with the generalization of physical research results for the different scale levels that are involved in plastic deformation.These approaches have advantages and disadvantages. In phenomenological theories, the advantages are the mathematical simplicity and laconic formulation of constitutive relations, which allows using them in practical calculations. However, the mathematical models of this class can not be considered as general, they are useful only for the description of limited range of deforming processes. On the other hand, physical theories that are based on the description of real plastic deformation mechanisms are very explanatory and predictive, but they lack mathematical simplicity. The above circumstances lead us to the necessity of compromise that can be found in determining the constitutive relations for RVE, which structure and parameters would bear the information about rnicrolevel and mesolevel phenomena. In this synthesis direction, the fundamental role belongs to [1,2], etc."

Jan 1, 2001

By T. Shi, Q. Yuan, S. P. Vanka, B. G. Thomas

"The quality of continuous cast steel is greatly affected by fluid flow in the mold region, especially involving transient phenomena. Mathematical models are being applied to investigate many different aspects of these phenomena, but their accuracy must be validated before they can be applied with confidence. As part of a long-term effort to develop and apply comprehensive models of the continuous casting process, this work evaluates the relative accuracy of models of three different fluid flow phenomena in continuous casting through comparison with measurements.Firstly, transient flow simulations of velocities in the mold region are compared with digital particle image velocimetry (PIV) measurements in a single phase water model. Large-eddy simulations (LES) are found to reasonably match the flow measurements, including transient flow variations, except at long time scales, which could not be modeled owing to the excessive computation costs. The standard K-e model produced very good agreement with time-averaged velocities for relatively little computation time, although it is inaccurate at predicting the transient variations. Secondly, particle trajectory calculations are compared with water model measurements to study the distribution and flotation removal of inclusion particles. The LES model was able to match the measurements both qualitatively and quantitatively. Thirdly, steady, multi phase flow computations are compared with flow patterns observed in both a water model and an operating steel caster with argon gas injection. For the same conditions, the water model and steel caster produced very different flow behavior. The computational model was able to match the measured flow patterns in both cases.This work suggests that computational flow modeling has the potential to match real processes as well or better than water models, especially when complex related phenomena such as particle motion and multiphase flow are involved. Much work is still needed to further improve the models and to apply them in parametric studies."

Jan 1, 2001