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"Many industrial processes involve materials that are subject to temperature change and thermal stress. Examples range from the casting of large metallic products to the cooling and reliability of small electronic components. Thermally induced stress is a major concern as it can lead to material damage and product failure. Material properties, thermal and mechanical, and process conditions such as the size and location of a feeder in metals casting, or the power dissipation in a computer chip, will govern the magnitude of these stresses. Temperature may also be influenced by fluid flow, for example, the airflow over a computer chip in a laptop will govern the rate of heat extraction, hence the temperature gradients in the chip and the evolving thermal stresses.This paper provides details on the governing equations for heat transfer (temperature) and solid mechanics (stress), their degree of coupling, and the numerical techniques used to solve them. Three examples are discussed to illustrate the use thermomechanical modelling. These also provide an insight into the degree of coupling required between the equations. The first example, involves thermal cycling of electronic components where a prescribed temperature field is applied. As temperature is known, this example only requires the solution of the stress equation. The second example also involves the modelling of an electronic component where the temperature field is also calculated. In both of these examples, the stress calculation is dependent on the temperature field, but the temperature calculation is not dependent of the solution of the stress equation (one-way coupling). The final example provides details on modelling the metals casting process. Both the temperature and stress equations are solved but, unlike the previous two examples, in this case the temperature field is dependent on the results from the stress calculation (two-way coupling)."

Jan 1, 2001

By F. W. H. Dean

A very sensitive sensor for the detection and measurement of hydrogen in solid steel is described. This technique is non-invasive and uses a collector to sweep the hydrogen emanating from a steel surface and feed to it sensor. This method is particularly sensitive, resolving fluxes to < 2 pI cm?2 S?I, with a linear measurement up to 1000 pI cm&apos;2 S?I, The collector is held on the steel substrate by magnets and it is shown that emanation of hydrogen from the steel is controlled by bulk diffusion of the hydrogen through the steel. The technique is demonstrated to have an excellent response time and reproducibility.

Jan 1, 2001

By Deming Wang, R. A. Overfelt

"This paper presents a computer-aided heat transfer simulation method to predict the thermal characteristics of an alloy sample in a special furnace for directional solidification. A two-dimensional transient heat transfer by conduction combined with radiation is developed to calculate the energy exchange between a directional solidification furnace and the sample. Finite difference equations with control volumes are used to calculate the transient heat transfer. A special boundary control volume is used to combine heat conduction and radiation in the transient heat transfer. Heat radiation effects on the surfaces of the special control volumes with a changeable view factor during directional solidification processing are also represented. The simulation results are verified by measurable experimental data. Using the computer simulation model, many thermal properties of the directional solidified castings can be obtained, such as temperature distribution, solidification velocity, the shapes and positions of the liquid/solid interface and thermal gradient at the interfaces. These are very important to analyze microstructure of casting alloys, avoid casting defects and control casting quality. 1 IntroductionIn directional solidification (DS) processing of castings, the temperature distribution, the interface between liquid and solid zone, thermal gradient in the mushy (pasty) zone and solidification rates are very important factors to analyze the microstructure and the casting quality. These variables affect the orientation and size of dendrites, shapes of grains, solute segregation and deleterious casting defects, such as microporosity, freckles and segregation channels. In order to avoid the casting defects, the temperature distribution and thermal gradients of castings during directional solidification must be strictly controlled. However, the structure of furnaces used for directional solidification is often complex. Heat transfer and temperature distribution within a casting not only depend on furnace temperature but also on the thermal properties of the casting alloy, crucibles, retorts etc. A more accurate heat transfer analysis."

Jan 1, 2001

By Akira Kaneda

Mitsubishi continuous process employs an electric furnace for settling matte from slag. Electrodes are immersed into the slag layer in the slag-cleaning furnace and the temperature of the melt is maintained at a predetermined level by Joule&apos;s heat. Electrodes are immersed to the depth where the current of each electrode is kept at a set value, and they are raised or lowered automatically to compensate for the deviation from it. Because electric resistance of the bath is varied with the matte level in the furnace and the composition and temperature of the slag, the immersion depth of the electrodes is affected by them. Therefore by monitoring the immersion depth and its change with time, abnormal situations in the furnace, such a~ rise of matte level or local abnormal state of melt, can be detected. In this paper, relations between state of the furnace and electrode behavior are discussed based on the plant data, and then a new and simple monitoring method of the condition of the furnace is proposed.

Jan 1, 2001

By M. El Ganaoui, P. Bontoux

"A computational model to investigate solid/liquid phase change transitions for binary alloy under directional solidification is presented. Conservation equations are developed by using an homogeneous formulation. A second order accuracy method of time and space based on finite volume approximation has been evaluated by comparing results to spectral solution for time-dependent solutal convection developping in a melted alloy. For extended model to solid/liquid interface effects time amplification of solutal perturbation injected near the interface is described before considering solutal convection is melt.IntroductionThe enthalpy method gives a front fixing approach for energy equation without introducing coordinate transformation. The interfare position is recovered a posteriori [1]. A number of authors have extended this approach so as to include the convection phenomena within the two phase 'mushy region' [2, 3, 4, 5, 6].We have developed a time-dependent enthalpy-porosity formulation for directional solidification [4, 6, 8]. The interaction between solid and liquid phases is modelised by a Darcien type force in the phase change area. The behaviour of the melt is similar with the flow of an incompressible fluid in a porous medium. This force is proportional to the relative phase velocity. It corresponds to a damping force depending on the anisotropic permeability of the 'mushy zone'. The permeability depends on the liquid fraction and on the size of·solidification microstructures. An informative discussion of a new slant on the general approach of continuum mechanics needed to analyze the formation of mushy zone is given in [12]. The method is extended to the presence of species diffusion: the solutal Stefan condition which expresses the solute incorporation or rejection across the interface is accounted implicitly in a species equation valid in all the domain [14, 15]."

Jan 1, 2001

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