1996 Edward DeMille Campbell Memorial Lecture ASM INTERNATIONAL

The Challenge of Quality in Continuous Casting Processes

J.K. BRIMACOMBE

As in any process, the laws of nature are at work in the continuous casting of metals. Heat spills down temperature gradients under the watchful eye of Fourier, while molten metal moves in response to inertial and body forces governed by the Navier–Stokes equations. Tensile strains develop in the solidifying shell subject to changing cooling conditions, the constitutive behavior of the metal, compatibility, and the Prandtl–Reuss relations. Solutes segregate as thermodynamics compete with diffusion to create a heterogeneous solid from a homogeneous liquid. The challenge to the process engineer is to harness these laws to continuously cast a metal section that is free of cracks, has minimal macrosegregation, and has the desired shape. Confronted with the demands of production, cost containment, and an educationally challenged workforce, the obstacles are very real. One response to the challenge is to move knowledge to the shop floor, where wealth is created, through expert systems to educate the workforce and through artificial intelligence to make the continuous casting process “smart.” Harnessing knowledge for wealth creation, and profitability, is the real challenge.

The Edward DeMille Campbell Memorial Lecture was established in 1926 as an annual lecture in memory of and in recognition of the outstanding scientific contributions to the metallurgical profession by a distinguished educator who was blind for all but two years of his professional life. It recognizes demonstrated ability in metallurgical science and engineering. Dr. J. Keith Brimacombe delivered the 1996 Edward DeMille Campbell Memorial Lecture at the ASM-TMS Meeting in Cincinnati, OH. The written lecture was nearly complete at the time of his untimely passing on December 16, 1997 and has been finished and submitted by his colleague, Professor I.V. Samarasekera. On October 1, 1997, J. Keith Brimacombe was appointed the first President and Chief Executive Officer of the Canada Foundation for Innovation. This enterprise, newly established by the Federal Government of Canada, was provided with one billion dollars of funding with the objective of strengthening the nation’s research infrastructure in universities and hospitals. Sadly, Dr. Brimacombe was able to serve only 3 months of his term and succumbed to a massive heart attack on December 16, 1997, at the age of 54. Dr. Brimacombe held the Alcan Chair in Materials Process Engineering, The Centre for Metallurgical Process Engineering at the University of METALLURGICAL AND MATERIALS TRANSACTIONS A

British Columbia, prior to his appointment with the Canada Foundation for Innovation. He was born in Nova Scotia, raised in Alberta, and received his undergraduate education at UBC, obtaining a B.A.Sc. (Hons.) in 1966. With the support of a Commonwealth Fellowship, he traveled to England and studied under one of the great metallurgical thermochemists of this century, F.D. Richardson, F.R.S., at Imperial College of Science and Technology in the University of London, where he received a Ph.D. in 1970. Subsequently, he was awarded the D.Sc. (Eng.) in 1986 by the University of London and an Honorary Doctorate of Engineering degree in 1994 by the Colorado School of Mines. He returned to the University of British Columbia in 1970 to establish courses and a research program in metallurgical process engineering. He remained at UBC, achieving the rank of Professor in 1979, Stelco Professor of Process Metallurgy (a chair endowed by Stelco) in 1980, Stelco/NSERC Professor (a chair endowed by Stelco and NSERC) in 1985, and the Alcan Chair in 1992. One of the finest metallurgical engineers on the world stage in this century, Dr. Brimacombe pioneered the application of mathematical models and industrial and laboratory measurements, to shed light on complex metallurgical processes spanning both the ferrous and nonferrous industries during his 27 year career at the University of British Columbia. For his groundbreaking research, he earned VOLUME 30A, AUGUST 1999—1899

the reputation of being one of the most innovative intellectual giants in the field, for which he earned global recognition. During his tenure at UBC, he built a large collaborative research group in metallurgical process engineering consisting of about 70 faculty, graduate students, research engineers, and technicians. Much of the research was conducted in close collaboration with Canadian companies such as Stelco, Hatch Associates, Algoma Steel, Western Canada Steel, Sidbec-Dosco, Ivaco, Cominco, Noranda, Inco, Alcan, Domtar, Canadian Liquid Air, and Liquid Carbonic. The thrust of the research was the development and improvement of metallurgical processes, such as continuous casting of steel, flash smelting of lead and copper converting, rotary kilns, and microstructural engineering of steel and aluminum, and DC casting processes. This body of work led to 300 publications and nine patents as well as two books. In 1985, in cooperation with faculty colleagues, he founded the Centre for Metallurgical Process Engineering at UBC and was named its Director. The purpose of the Centre is to strengthen the interdisciplinary approach to metallurgical process research and to broaden the field of application to materials other than metals. For this body of research, he was awarded the B.C. Science and Engineering Gold Medal (1985) and the Ernest C. Manning Prize (1987) and, before that, the E.W.R. Steacie Memorial Fellowship (1979) from NSERC. He also received the following awards: TMS-AIME Charles Herty Award (1973 and 1987), AMS Marcus A. Grossmann Award (1976), TMS Extractive Metallurgy Science Award (1979, 1987, and 1989), ISS John Chipman Award (1979, 1985, and 1996), TMS Champion H. Mathewson Gold Medal (1980), ISS Robert Woolston Hunt Silver Medal (1980, 1983, and 1993), ASM Henry Marion Howe Medal (1980 and 1985), TMS Extractive Metallurgy Technology Award (1983 and 1991), the Williams Prize of the Metals Society (UK) (1983), the ISS Mechanical Working and Steel Processing Conference Meritorious Award (1986 and 1996), the ASM Canadian Council Lectureship (1986), and the CIM Metallurgical Society Alcan Award (1988). In 1981, he delivered the Arnold Markey Lecture to the Steel Bar Mill Association. In 1987, he was made a Distinguished Member of the Iron and Steel Society and a Fellow of the Royal Society of Canada. In 1988, he became a Fellow of the CIM and, in 1989, he delivered the TMS Extractive Metallurgy Lecture while being awarded Fellowship in TMS. Also in 1989, he was awarded the Izaak Walton Killam Prize for Engineering by the Canada Council, joined the Board of Directors of Sherritt Gordon Ltd., received the Bell Canada Corporate–Higher Education Award and was appointed an Officer of the Order of Canada. In 1990, he received the Meritorious Achievement Award of the Association of Professional Engineers of British Columbia and a UBC Killam Research Prize. In 1992, he was honored with the Commemorative Medal for the 125th Anniversary of Canadian Confederation and, in 1993, delivered the Howe Memorial Lecture of the Iron and Steel Society and became Fellow of the Canadian Academy of Engineering. In 1994, he presented the D.K.C. MacDonald Memorial Lecture; and in 1995, he was the Inland Steel Lecturer at Northwestern University and received the Ablett Prize of the Institute of Materials. In 1996, he delivered the ASM Edward DeMille Campbell Memorial Lecture and, in 1997, received the AIME Distinguished Service, and he was elected a Foreign Associate of the National Academy of Engineering. In June 1997, he received Canada’s highest scientific honor, the Canada Gold Medal in Science and Engineering from the Natural Sciences and Engineering Research Council of Canada. In 1998, Dr. Brimacombe was posthumously awarded the Benjamin Fairless Award by the AIME and the Inco Medal by the CIM at their centennial celebration. Beyond the quest to generate knowledge and train young people, he was driven by the desire to see the fruits of his research implemented in industry. Not satisfied that publications in peer-reviewed journals are an effective means of reaching out to the shop floor, where knowledge implementation creates wealth, he worked tirelessly at the University–Industry interface to make the transfer of knowledge to industry a reality. A gifted speaker, he was renowned for his ability to translate complex research results to changes that are required to the process for improved quality and/or productivity. Thus, he was sought after by the global metallurgical industry and presented over 50 courses in companies in every continent. A course on continuous casting of steel offered annually in Vancouver, under his directorship, attracted participants from around the world. He seized the opportunities provided by the revolution in computer technology to help further the transfer of knowledge, and since the early 1980s drove the development of user-friendly mathematical models as a means of transferring research results to industry. Brimacombe was also instrumental in developing “smart” systems for the transfer of knowledge and spearheaded the development of an expert system for diagnosing defects in steel billets, which is being marketed commercially. A recent project involving Canadian companies 1900—VOLUME 30A, AUGUST 1999

is the development of a “Smart Process,” in which knowledge is made to work in the process through the use of an on-line expert system and sensors. He gave unreservedly of his time to professional societies, which are a vehicle for knowledge transfer and professional development of materials engineers. He was the only professional who was President of the three major societies serving materials engineers in North America: TMS-CIM in Canada in 1985, TMS-AIME in 1993, and ISS-AIME in 1995. His enthusiasm for professional societies was infectious and has led to the initiation of a very dynamic student chapter at UBC. He served on the Killam Research Fellowships Committee of the Canada Council from 1982 to 1985, where he initiated the Killam Prize in Engineering and worked on other committees of the Canadian Council of Professional Engineers, the Science Council of British Columbia, and the Canadian Steel Industry Research Association. He served on the Boards of the ISS and TMS in the United States. He served on numerous committees in these societies, including Joint Commission and Board of Review of Metallurgical Transactions, Book Publishing Committee, Awards Committee, Extractive Metallurgy Sub-committee, Nominating Committee, and Long Range Planning Committee. In 1989, he assumed responsibilities as Founding Chairman of the TMS Extraction and Processing Division, in 1993–4 was TMS President, and in 1994–5 was Founding President of the TMS Foundation. In 1990, he was named as an Eminent Scientist to the Board of Directors of the Ontario Centre for Materials Research. In 1995, he was Chairman of the Science Policy Committee of the Royal Society of Canada and was a member of the National Materials Advisory Board (United States). In 1996, he was elected Vice President of the Academy of Science of the Royal Society of Canada and was appointed to the Board of the United Engineering Trust. He served on the Board of Trustees of the AIME since 1993; had he lived, he would have become President of the AIME in 1999.

I. ORDER OUT OF CHAOS

THE casting of metals has been central to humankind for millennia, and indeed has shaped and directed the course of civilization. Transforming the chaos of a liquid metal into the relative order of the solid has been a fascination for humans whether in the making of tools or weapons or adornments. Pushing the fast forward button on metallurgical history to this century, a major thrust of casting technology has been the development of continuous or semicontinuous processes. As in earlier times, the development has relied upon other technologies, especially refractories, melting, and refining; but today the role of the computer to monitor and control continuous casting processes is of equal, and growing, importance. This lecture focuses on the continuous casting of two metals—steel and zinc—which the author has had the privilege to investigate over time, with students and colleagues in close collaboration with industry. The purpose of the lecture is not to focus simply on the technical details of the casting processes, but additionally to draw out lessons learned from this splendid intellectual experience which bear upon the generation of knowledge relevant to industrial operations, the use of knowledge on the shop floor to create wealth, the education of process engineers so vital to this task, and the role of the computer. II. THE PROCESSES Although rooted conceptually in the last century, the continuous casting of steel, shown schematically in Figure 1, has entered industrial flow sheets only in the last four decades or so. Rebuilding after World War II, the Japanese steel industry was most aggressive in adopting the process, largely developed in Europe, to cast slabs for the production of sheet and plate. The minimills, which burst onto the steelmaking scene 30 years ago, were quick to adopt continuous casting to produce billets for rolling into long products, viz. rod, bar, METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 2—Schematic diagram of the direct-chill casting process.

contact the surface of the solidifying section (Figure 2), whereas steel casting machines separate the cooling water into two independent systems, one feeding the mold and the other submold sprays. The differences in casting machine design and operation are most interesting. In part, they reflect differences in solidification temperature, thermophysical properties (especially thermal conductivity), and susceptibility to crack formation as well as to segregation effects. But there is more, because the ferrous and nonferrous casting operations stem historically from developments along separate paths. Unwittingly, walls were erected between these great areas of metallurgical activity to create solitudes that now are difficult to bridge. Clearly, the metals industry would benefit from interdisciplinary interaction—the ASM, TMS, and ISS are ideal vehicles for such enhanced communication. Fig. 1—Schematic diagram of the continuous casting of steel.

III. THE CHALLENGE angles, channels, and so on. The last decade has witnessed a technological surge toward near-net-shape casting[1] of thin slabs, beam blanks, and strip (now just being commercialized), which is profoundly transforming and rejuvenating the steel industry in the United States. Today about 500 million tonnes of steel are continuously cast worldwide annually. This is a process to be reckoned with. The continuous or semicontinuous casting of nonferrous metals—zinc, aluminum, magnesium, and lead—is no less formidable. For example, in the aluminum industry, slabs, billets, rod, and strip are cast in large tonnages by a variety of processes. The direct-chill (DC) casting process, with its origins in the 1930s, is depicted schematically in Figure 2. This process is semicontinuous in that a fixed length of section is cast, after which it is withdrawn and the setup repeated. Compared to the continuous casting of steel, the DC casting of aluminum and zinc employs considerably shorter moulds (20 to 50 vs 700 mm) and lower casting speeds (1 to 2 vs 10 to 65 mm/s). In DC casting, water circulating in the mold usually is directed downward to METALLURGICAL AND MATERIALS TRANSACTIONS A

Viewed broadly, the challenge to the continuous metal casting processes is to produce a shape of the desired quality reproducibly at a competitive cost and on time. The same can be said of any materials process. In the competitive environment in which we live, it is the customer who drives the terms of quality and price. It is the materials producer who must meet the property specifications at a cost that sustains a healthy profit over the long term. It was not always so. The steel industry, for example, following World War II, found itself in a bull market for the metal. Countries in Europe and Asia whose industry and infrastructure were badly damaged, or destroyed, were rebuilding. The steel needed for the reconstruction could not be produced indigenously; and this became a boon to the North American steel industry, which had been left untouched by the bombs and disruption of war. Thus, for several decades, virtually every tonne could be sold irrespective of quality as demand outstripped supply. But this situation changed as the Japanese and European steel industries arose from the ashes of war to become world competitors, VOLUME 30A, AUGUST 1999—1901

Fig. 4—Transverse section of a direct-chill cast zinc jumbo exhibiting large cracks. Fig. 3—Macroetch of the transverse section of a steel billet revealing midway cracks.

closely followed by developing countries like Brazil. The competition had become global. Another wave of change about this time was consumer demand for quality. No longer content to own an automobile that rusted quickly on salt-laden winter roads and broke down under limited warranty, the consumer expected more of his purchase—and implicitly of the material(s) from which it was made. The Japanese led the way in the drive to steel quality and forced the North American steel industry to change. Adoption of continuous casting contributed mightily to the transformation, so that the automotive industry could, with a plethora of other improvements, offer multiyear warranties on their product—or die. And so, quality and cost and timeliness of delivery have become the major drivers of metals and materials production. The hard question, of course, is how to maximize quality, minimize cost, and optimize delivery. To seek answers, we could look at specific examples from the continuous casting of steel and zinc, as indicated earlier. Figure 3 shows a macroetch of a continuously cast steel billet section.[2] Ideally, this transverse (to the casting direction) section would be perfectly square, free of cracks and centreline porosity, compositionally homogeneous, and devoid of inclusions. Instead, we are witness to a billet that is not square, exhibits cracks, and has a void at the centerline. The state of cleanliness (presence of nonmetallic inclusions) and macrosegregation cannot be seen, but the latter is a constant companion of center looseness. Figure 4 shows a transverse section of a DC-cast zinc jumbo characterized by a large crack.[3] The customer might expect more of this purchase. The solutions shall follow. The challenge is to cast quality sections that meet customer demands without incurring prohibitive costs. The response is rooted largely in knowledge. What has caused the off-squareness, the cracks, and the centerline cavity in the steel billet? What has happened to generate the cracks in the cast zinc section? Are the defects a result of flaws in machine design, e.g., submold cooling? Has maintenance 1902—VOLUME 30A, AUGUST 1999

been less than adequate, e.g., machine alignment? Have there been upsets in operation of the casting process, e.g., rough or off-center pouring streams into the mold? In fundamental terms, what knowledge do we possess that can link mechanistically the quality, or lack of it, to casting machine design, operation, and maintenance? We can begin with the immutable laws of heat flow as set out by Fourier, Stefan and Boltzman, with the force balances of Navier–Stokes, and the Prandtl–Reuss relations. After all, the laws of nature are at work in any materials process. As shall be seen, these fundamental laws must be comprehended, not necessarily quantitatively at every turn, to underpin our understanding of mechanisms. But fundamentals, although necessary, are not sufficient. If they were, we could readily model the process mathematically in the cool and comfort of a computer laboratory and solve all quality problems. This, of course, assumes that necessary boundary conditions and materials properties were also at hand. But this is rarely the case. The reality is that the continuous casting process, not unlike most materials processes, is complex and must be understood in the context of the system, or flow sheet, of production. It is necessary to enter the real world of heat and dust and people and machines and production schedules where all is not perfect (but then not much is perfect). It is necessary to understand that the liquid metal has its own inherent quality defined by composition, temperature, and cleanliness, all of which are determined by upstream processes in the flow sheet. It is necessary to understand that an industrial process like continuous casting is most easily analyzed at steady state, but upsets can be frequent and damaging to quality at random. Then, clearly, one, or more, variables have slipped from the firm hand of control. Then there is the challenge of the workforce itself, the men and women who manage, operate, and maintain the casting machines, who make the quality and create the wealth. Although dedicated and diligent, few of these people are intimates of Fourier, Navier, and Stokes. Most have not been exposed to the fundamentals of casting quality sections in terms of metal chemistry, fluid flow, heat extraction, and METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 5—Scanning electron micrograph of the surface of a midway crack in a steel billet.

stress generation. The majority have not been to university, where, hopefully, exposure to engineering principles would prepare them to understand the links between their work and the quality of the cast product. If one accepts the notion of the primacy of knowledge workers in the future, clearly the need for education prior to, and during, employment is crystal clear. This applies not only to workers on the shop floor but also to upper-level managers who may have lost touch with the reality of making quality in an increasingly competitive market place. The challenge then is to harness knowledge and put it to work at every level in the casting operation, and indeed throughout the company. IV. PROCESS KNOWLEDGE Knowledge of continuous casting, or of any materials process, is hard won. The process engineer who seeks that knowledge must be prepared to toil by an industrial production unit or by a pilot plant or by a physical model or by other experimental apparatus or in front of a computer screen. He must necessarily work in an interdisciplinary team, which assembles chemical metallurgists, physical metallurgists, mechanical engineers, chemical engineers, computer specialists, and so on, depending on the specific objective. This reflects the real world of processing and perhaps tells us that the discipline “boxes” in which we work have become anachronistic. Thus, the process engineer must marry research/development and production, experiments and computer predictions, and the fundamentals of physics and chemistry that bear on the problem. The paradigm of knowledge generation is driven by the process and what one needs to know to solve a particular problem, to improve an existing process, or to create a new one. A. The Steel Billet To illustrate these points, let us return to the quality problems, or opportunities, shown in Figures 3 and 4. The origin METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 6—Model-predicted axial profiles of the shell thickness and midface temperature showing the position of midway crack formation in a steel billet caster.

of the internal cracks in the steel billet (Figure 3) can be elucidated by examination of the crack surface itself, an example of which is shown in Figure 5. Taken on a scanning electron microscope, the surface of this midway crack is seen to be smooth without any evidence of brittle or ductile fracture. The elongated features are MnS inclusions, while the rosette phase is a manganese silicate. The undulations are dendrite arms. This crack clearly formed while liquid films separated growing dendrites; that is, this is a “hot tear” that formed very close to the solidification front.[4] Indeed with the exception of copper-induced cracking, all cracks found in continuously cast billets are generated, as hot tears, close to the solidification front. This is extremely important knowledge, because it means that, if the axial profile of shell thickness is known, say through computer prediction, the distance below the meniscus (liquid level) at which the crack forms can be determined, as illustrated in Figure 6.[5] The precise location of the crack generation in the casting machine (mold, sprays, or radiation zones) can be pinpointed without guesswork. To reinforce the hot tearing aspect of billet cracks seen in Figure 5, one can turn to ductility measurements made at elevated temperature in the laboratory (Figure 7).[6] Although several zones of low ductility are evident, the most significant for billet casting extends from the solidus to a temperature roughly 70 8C to 100 8C below it. In this region, where, in the absence of microsegregation, only solid steel should exist in theory, sulfur and other solutes indeed segregate between growing dendrites and lower the solidus temperature locally. Sulfur is the major player, because, in combination with iron (FeS), the solidification temperature VOLUME 30A, AUGUST 1999—1903

Fig. 7—The ductility of steel as a function of temperature.

of the microsegregated liquid is reduced to about 1200 8C, well below the solidus temperature of the steel, typically in the range of 1400 8C to 1500 8C depending on carbon content. Thus, it has been found that the sulfur content of the steel, especially above 0.015 to 0.02 pct, has a deleterious influence on crack frequency. A variable offsetting this negative effect of sulfur on crack formation is the manganese content of the steel. Manganese also combines with microsegregated sulfur to form MnS, or in reality (Mn, Fe)S; the solidification temperature of MnS is 1530 8C. Consequently, the net effect of manganese, beyond its influence on final steel properties, is to raise the solidification temperature of the sulfide in the interdendritic zone and to narrow the temperature range of low ductility. Crack susceptibility is thereby reduced. From industrial practice, raising the Mn/S ratio above 25 to 30/L reduces crack formation. Thus, fundamentally, one can see the influence of steel composition on billet internal quality. The liquid steel quality permeates midway crack formation by other means as well, and that is through temperature, or more precisely, temperature of the molten metal above its liquidus. Although fundamentally a misnomer, the industry refers to this temperature as “superheat,” which is usually measured in the tundish (Figure 1). It has been found that with increasing liquid steel temperature, the cast structure of the billet is dominated by columnar dendrites, as shown in Figure 8.[7] Parallel growing dendrites provide easy crack paths in the microsegregated zones between them, as compared to an equiaxed structure in which the dendrites are oriented randomly. The equiaxed structure, appearing at lower liquid steel temperatures, is fundamentally more resistant to midway crack formation. Thus, there is another direct link between liquid steel quality and billet quality. Clearly then, the production of liquid steel upstream in the flow sheet from the casting machine profoundly impacts cast billet quality. To quote an old saw: “it is hard to make a silk purse from a sow’s ear.” But what was the event on the casting machine that actually caused the midway cracks seen in Figure 3? To generate such cracks, a necessary condition is that a tensile strain acts upon a zone of low ductility, in this case, close to the solidification front. The source of the tensile strain can be deduced from Figure 6, which indicates that the midway 1904—VOLUME 30A, AUGUST 1999

Fig. 8—Influence of the liquid steel temperature on the cast billet structure.

Fig. 9—Computer-predicted stress distribution in the transverse plane of the solid shell in a steel billet below the spray chamber.

cracks were forming close to, or below, the spray cooling zone where the surface temperature was rebounding. The rebound stems from the abrupt reduction in surface heat extraction as the billet passes from the spray zone to radiation cooling. Heat, guided by the hand of Fourier, continues to spill down the temperature gradient in the solid shell; but just beneath the sprays, the heat is not extracted as readily from the surface and it effectively piles up. And so, the surface temperature of the billet increases. What is the influence of the surface reheating? An answer to this question can be sought through finite-element analysis to obtain the transverse stress distribution map shown in [4] Thus, we see that tensile stresses (resulting from Figure 9. tensile strains) have been generated close to the solidification front where the key zone of low ductility resides. We can understand these calculated results conceptually (it is a must that we do so!) if the thermal response of the steel shell to surface reheating is considered. For then we comprehend that the reheating surface attempts to expand but is constrained by METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 11—Influence of the steel surface temperature on heat extraction by water sprays. Fig. 10—Design of the spray chamber of a billet casting machine.

the interior of the shell, which has not yet experienced much of a thermal change (steel has a low thermal diffusivity). Thus, the surface is constrained and placed into compression, while tensile forces, not subject to the hand of Fourier (at least not directly), build near the solidification front. If the local structure is columnar, sulfur levels are relatively high, and the Mn/S ratio is low, midway cracks can result. And so, the ultimate cause of midway cracks is the design of the spray cooling zone beneath the mold. The critical factor governing spray design obviously must be minimization of surface reheating below the spray chamber, but also beneath the mold and within this secondary cooling zone. Achievement of an optimum spray design is aided by the computer model rooted in fundamentals, coupled with intuition. Horse sense tells us that the billet should not be cooled too strongly in the spray zone, i.e., that the surface temperature should be maintained close to the mold exit temperature at, say, 1100 8C to 1150 8C. The model then can be applied to quantify three key aspects of spray design. The first is that, viewed axially in the casting direction, the spray cooling just beneath the mold should commence with relatively high heat-extraction rates then taper off with increasing axial distance to the exit of the spray chamber. This can be seen in Figure 10.[5] The reason again is fundamental. As the solid shell grows, the distance between the solidification front and the billet surface over which Fourier’s conductive heat must travel increases and temperature gradients decline; the conductive heat flux falls off. Consequently, if the surface temperature of the billet is to remain unchanged, the rate of surface heat extraction must decline as well. It is simply a matter of balance. The second aspect of spray design is the length of the spray chamber. The computer model revealed that short spray zones, e.g., 1-meter long, cannot adequately cool the billet without subsequent excessive reheating of the surface and the tendency to generate midway cracks. Indeed, the computer suggests that a spray chamber of 4 to 6 meters in length, depending on casting speed, is necessary to minimize surface reheating. The role of the sprays is not only to extract heat from the billet beneath the mold but also to minimize sudden changes in thermal gradients in the solidifying shell as the billet moves from one cooling zone to the next. The third variable in spray design is the overall quantity of water that is directed onto the billet surface through a METALLURGICAL AND MATERIALS TRANSACTIONS A

succession of nozzles pointed at each billet face. Experiments have demonstrated that the spray heat-transfer coefficient varies almost linearly with the spray water flux; the greater the water flux, the higher the heat extraction. From the computer model, laboratory heat-transfer measurements, and experience on operating casters, a desirable overall spray water rate per strand is about 1 kg per kg of steel cast, once again to avoid excessive surface reheating. It turns out that life can be even more complicated, with respect to midway crack formation, because events in the mold can contribute importantly to surface reheating. Under adverse conditions of mold heat extraction, local regions of the solidifying shell can be overcooled, such that upon exiting the mold they appear dark to the observer and they remain dark through the spray chamber. Subsequently, as the billet exits the spray chamber, the surface can be observed to reheat from black to an orange hue, say 1000 8C. To understand this behavior, we need only look at measurements on spray cooling, which have been interpreted in terms of water boiling phenomena. As can be seen in Figure 11, at a typical billet surface temperature of 1100 8C, the rate of heat extraction is virtually independent of the surface temperature, indicative of film boiling, in which a steam film separates the spray water from the billet surface. This boiling regime is desired for good control of billet temperature in the spray chamber, since minor upsets in surface temperature do not largely shift heat extraction. In contrast, a dark patch on the billet surface, as observed in Figure 12, which certainly must be below 600 8C locally, is cooled in the transition boiling regime, where, due to intermittent breakdown of the steam film, the heat extraction accelerates with decreasing billet surface temperature. Under these conditions, cooling is out of control with surface temperature rebounds of possibly 600 8C. Then, even a well-designed and maintained spray system may not prevent the formation of midway cracks. The mold is confounding the good work in the sprays. B. The Zinc Jumbo The story on the zinc jumbo is much shorter, although there are lessons to be learned. At first glance, there is an uncanny resemblance between the cracks appearing in the transverse section of the zinc jumbo (Figure 4) and those VOLUME 30A, AUGUST 1999—1905

Fig. 12—Photograph of a continuously cast steel billet in the spray chamber showing dark, overcooled regions emanating from the mold.

in steel billets (Figure 3). Admittedly, there are differences in proximity to the surface and the width of the cracks; but working toward a remedy, the same fundamental process and material parameters must be considered. Is there a region of low ductility in the zinc? What was the source of tensile strain—reheating of the surface below the spray chamber? Overall, does the zinc industry have something to learn from the steel industry? One can begin by appreciating that the cracks appeared only in Prime Western Grade zinc, which contains about 1 wt pct lead. Hansen[8] tells us that, at equilibrium, zinc has a very low solid solubility for lead, 0.5 to 0.9 wt pct at the monotectic temperature of 418 8C. And pure lead solidifies at a temperature about 90 8C below that of zinc. Thus, it is conceivable to have lead-rich liquid present in the interdendritic region, akin to the liquid sulfide films in solidifying steel, as described earlier. This notion is borne out by examination with the scanning electron microscope of the surface of a crack from a zinc jumbo, as shown in Figure 13.[3] The surface is seen to be smooth, not unlike that of the midway crack in the steel billet (Figure 5). Not surprisingly, the rounded second phase on the surface in Figure 13 is rich in lead, as determined by energy-dispersive X-ray analysis. Clearly, the Prime Western Grade zinc has a low ductility zone close to the solidification front due to lead, much like that of steel arising primarily from sulfur segregation. 1906—VOLUME 30A, AUGUST 1999

Fig. 13—Scanning electron micrograph of a crack taken from a zinc jumbo revealing the smooth nature of the surface. Magnification 1000 times.

Returning to a question posed earlier, is the source of the tensile strain that caused the cracks due to reheating of the jumbo surface below the sprays? A definitive answer was obtained through plant trials and computer modeling of heat flow within the jumbo. In the plant trials, thermocouples were frozen into the shell at the meniscus and permitted, with long lead wires, to travel downward with the descending jumbo. A copper-zinc alloy was also added to the liquid pool to delineate the sump profile, while a steel rod was inserted into the pool to plumb its depth. The latter tests were needed to validate the computer model. The response of two thermocouples, frozen into the zinc shell 23 and 46 mm from the surface of the jumbo, is shown in Figure 14. The computer model was utilized to backcalculate the surface temperature response also presented in METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 14—Temperature response measured at 23 and 46 mm from the surface and calculated at the surface of a zinc jumbo cast at 1.69 mm/s.

Fig. 16—Proposed spray design to prevent crack formation in DC cast zinc jumbos.

Fig. 15—Axial sump profile, location of crack formation (vertical bar), and computed axial profile of midface temperature for a zinc jumbo cast at 1.69 mm/s.

Figure 14. Most importantly, reheating of the surface is observed beyond about 150 seconds; this is below the spray chamber. The sump profile computed under these conditions is given in Figure 15, together with the location (vertical bar) of crack formation below the meniscus, assuming that the cracks formed close to the solidification front. Also shown on the right-hand side of Figure 15 is the computed axial profile of midface temperature based on the thermocouple measurements described previously. Without question METALLURGICAL AND MATERIALS TRANSACTIONS A

then the cracks are caused by reheating of the jumbo surface below the sprays. The solution to the cracking problem, based on this knowledge gleaned from the plant, laboratory, and computer, is the same as that for the midway cracks in the steel billets; reduce surface reheating by lowering the water flux and increasing the length of the spray cooling zone. But, in addition, because the sump depth in the solidifying zinc jumbo is small, slightly less than a meter (compare to that in the steel billet (Figure 6)), the sprays can be extended to below the lower extremity of the low ductility zone. Then, any strains resulting from surface reheating, whatever the magnitude, are not acting on a crack-sensitive region. The proposed new spray design to accomplish this objective is shown in Figure 16; and the effect of this design change on jumbo quality can be seen in Figure 17. Clearly, zinc had something to learn from steel. V. PRINCIPLES AND RULES OF THUMB Even though knowledge may bubble up from the analysis of complex computations and even more complex processes and material behavior, knowledge is most powerful when rendered to essentials—principles and rules of thumb, rooted in fundamentals, but applicable on the shop floor. The creators of wealth in industry need a straightforward knowledge VOLUME 30A, AUGUST 1999—1907

ress hand in hand, not in separate directions. This is not rocket science and does not require a Cray computer, but it has multimillion dollar implications. Then there is the understanding of the generation of tensile strains, which cause cracks in the solidifying shell. One can boil down our knowledge into the following rules of thumb: (1) Rapid cooling of the shell surface results in tensile strains at the surface. (2) Reheating of the shell surface causes tensile strains at the solidification front, as already discussed. (3) Thermally generated tensile strains, due to changing temperature gradients in the shell, act in the transverse plane and, therefore, initiate longitudinal cracks. (4) Mechanically generated tensile strains, due to withdrawal forces, unbending, friction, etc., work primarily in the axial direction and, consequently, cause transverse cracks and depressions.

Fig. 17—Transverse section of a zinc jumbo cast with the new spray system.

structure upon which they can rely to maximize quality, minimize costs, and increase profitability, in partnership with their customers. There must be builders of bridges between the creators of knowledge and the creators of wealth. And so we close the circle of the mind and prosperity. Let us return to steel billet casting and consider the fundamentals that govern this process, once again under the watchful eye of Fourier and Stefan–Boltzmann. The most important lesson that a process engineer learns is “what matters.” The question is a practical one. If a process needs to be cranked up to meet new production schedules, what limits the production rate? If a particular quality problem needs to be solved, what are the key process parameters? Unless one is wedded to endless empiricism, the early answers will spring from knowledge. Take, for example, the fundamentals of heat flow from the solidification front to the external heat-extraction devices, viz. water-cooled mold, water sprays, and thermal radiation. Suppose that, to accelerate production and profitability, the casting speed is to be increased substantially. An immediate concern is the length of the liquid pool in relation to the casting machine design, most notably the distance of the cut-off torches from the meniscus—no one desires to cut billets with a liquid core! The suggestion is made to double the spray cooling water flux and thereby affect the higher throughput of hot steel in the casting machine. The implicit assumption, of course, is that there is a direct relationship between solidification rate and external cooling of the shell. That assumption is both wrong and dangerous. It is wrong because Fourier intervenes; steel has a low conductivity such that conduction through the shell in the spray chamber limits the overall flow of heat from the solidification front to the water sprays—in electrical parlance, shell conduction is the major resistance. The assumption is dangerous because increasing the spray water flux reduces the billet surface temperature, which then enhances reheating below the spray chamber and the formation of midway cracks. For a marginal increase in productivity, the internal quality of the billet is being compromised. Productivity and quality should prog1908—VOLUME 30A, AUGUST 1999

There are exceptions, of course, resulting from bulging and lubrication effects, but these rules of thumb help us to understand and remedy most cracking problems. No need for a computer, just knowledge and an analytical mind. VI. THE SHOP FLOOR Even if knowledge has been boiled down to principles and rules of thumb, it is of little value to a materials production company, if it is not applied where it matters most—on the shop floor where day in, day out, products are made. The first problem is that, frequently, knowledge has not been reduced to its essentials. Fourier and Navier and Stokes and Prandtl and Reuss reside in textbooks and research articles and technical presentations. But the managers and hourly workers do not have time to read the literature, to digest it, to understand it, and to apply it. All too frequently they must rely on experience—some good, some misguided— and word of mouth from industry colleagues and suppliers. The technological receptivity of many on the shop floor may be limited as well by a truncated formal education. Then, fertile ideas, concepts, designs, and procedures, which could contribute millions of dollars to the bottom line of the financial balance sheet and fortify the competitiveness of a company are left to languish. More is the pity. The second problem is that even if knowledge has been rendered into relatively simple principles, how is it imbedded into the collective intelligence of a company and harnessed in the production flow sheet to generate wealth? The answer lies in making the knowledge transfer user friendly in the context of continuing education. Thus, the knowledge could be organized into brief notes and presented by experts, who are sensitive to materials productions operations, in short courses of appropriate duration. The courses can be centralized or delivered on-site at a particular company, usually to persons with widely different education and experience. Clearly, the continuing education programs of the ASM, ISS, TMS, and CIM, although generally centralized, fill an urgent need in this respect and merit strengthening and enrichment. But while short courses are a vehicle for the user-friendly transfer of knowledge (provided they are well presented!), they have limitations. For one, the instructors depart the scene at the end of the course and are available for questions and discussion, thereafter, at reasonable cost only by telecommunication. Fuzzy points may remain unresolved or, worse, METALLURGICAL AND MATERIALS TRANSACTIONS A

residual misunderstanding may spawn misconception and bad practice. Then also, the attendees at the short course are not static. Some move from one process in the flow sheet to another process, e.g., from the billet caster to the scrap bay. Some people retire and some resign and move to another company. And new recruits with little knowledge are hired. The net result is a diffusion of knowledge and a weakening of its concentration in a given operation like casting. Is this to say that short courses are not worthwhile? Not for a moment. Continuing education, however, is a process in itself with emphasis on the word “continuing,” because it must be ongoing to combat knowledge diffusion and the dilution of knowledge concentration referred to previously. Short courses, including hands-on training, may be the most traditional form of continuing education, but the electronic revolution is providing others. Here, I wish to focus on the expert system.

Fig. 18—Depiction of billet quality problems, as appearing on the computer screen to the user during a session with the expert system.

VII. THE EXPERT SYSTEM Expert systems evolved from the human desire to capture knowledge and create systems to emulate human reasoning, i.e., develop artificial intelligence. An expert system essentially consists of a development tool, referred to as the “shell,” which is a software package capable of accepting knowledge on a particular subject; once the knowledge is implemented, the system is capable of drawing on that knowledge much like a human expert to provide insight, train nonexperts, or solve problems as the case may be. We were fortunate to team up with an expert in expert systems, John Meech, who was intrigued, like us, by the possibility of capturing our knowledge on diagnosing defects in billet casting, together with our understanding of the literature, into an expert system. Our goal was to create an expert system that was user friendly to any intelligent individual, regardless of educational level, who had a rudimentary understanding of continuous casting and was familiar with the operation of a personal computer. A fine young graduate student, S. Kumar, who was familiar with the continuous casting process undertook this task as a Master’s project. The knowledge base, developed over 2 decades, consists of a mechanistic understanding of how defects form. The role of steel composition, temperature, and machine design and operation on billet quality was elucidated through extensive plant trials with instrumented molds, mathematical models, and billet evaluation. The system that was created, named CRAC/X, focuses on surface and internal cracks and includes quality problems such as off-squareness, off-corner internal cracks, longitudinal corner cracks, midway cracks, centerline cracks, transverse cracks, transverse depressions, bleeds, and laps.[9] Data provided by casting personnel serve as input to the system and uncertainties in the input data are handled through the application of “fuzzy” logic. CRAC/ X also incorporates a computer model, which predicts shell thickness profile, pool depth, and thermal history of the billet for a given set of design and operating conditions. This information is vital for determining the location of crack origin in the machine; this is accomplished by comparing the observed depth of a crack from the surface of the billet with the predicted shell thickness profile. Obviously, crack depth(s) and type(s) are also user input. Figure 18, taken from the computer screen, of CRAC/X, shows the quality problems that were addressed pictorially. METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 19—Scheme for diagnosing quality problems having complex origins and requiring detailed analysis.[10]

The midway-cracking problem, described in detail earlier in the article, requires an evaluation of both the mold and the sprays, as shown schematically in Figure 19.[10] This logic was incorporated in the expert system to diagnose the likely cause of the defect, which could include an improperly designed spray chamber, nonuniform cooling in the mold, or blocked spray nozzles. The output of the computer model embedded in the expert system, shown in Figure 20, is relied upon to pinpoint the location of crack origin and to assess whether the given spray design leads to excessive reheating either between the mold and the sprays, between spray zones, or beneath the spray chamber. In this way, knowledge rooted in fundamentals is captured to provide the user with a powerful diagnostic tool. Of course, the expert system cannot be expected to anticipate and sleuth all eventualities specific to a particular plant. I recall encountering quality problems, which were eventually traced in one operation to caster misalignment due to VOLUME 30A, AUGUST 1999—1909

Fig. 20—Axial profiles of solid shell thickness (lower plot) and midface temperature (upper plot) of a billet predicted by the computer model imbedded in the Expert System.

deterioration of the steel structure. In this case, the expert system could be expected to suggest misalignment as one of the factors, but it will not tell the user that the steel structure is about to collapse. What the expert system does most powerfully, however, is to dip into the knowledge base in a logical, organized manner that cannot be expected with the level of education found in most minimills today in the pursuit of critical quality problems. Empiricism and argument are replaced with knowledge and logic. VIII. THE INTELLIGENT PROCESS The expert system is a powerful tool in the hands of the workforce, providing empowerment through knowledge developed by experts over many years. However, it does not empower the process, and cannot respond to events such as process upsets that occur in a real situation. In the case of continuous casting, this led us to seek ways of empowering the process. Enter the “Intelligent Mold”—a mold that could sense events, with thermocouples as “eyes” and load cells as “touch” and a modified version of the current expert system as a “brain.” The expert system would contain elements of the system just described for teaching and consultation, but would require new knowledge to link on-line signals to quality and operating difficulties. Over the past 5 years, development of an Intelligent Mold has been underway at the University of British Columbia with the support of industry and government. Figure 21 schematically depicts the basic concept of this development. It has been shown that transverse depressions, bleeds, and laps can be sensed by successive thermocouples embedded in the mold wall. Each of these defects is associated with a local depression of slightly differing magnitude, which locally enlarges the air gap. As each defect passes a given thermocouple, the heat transfer is temporarily lowered, giving rise to a local valley in the temperature signal, as shown in Figure 22. Not only has the work shown that thermocouples are a powerful technique for detecting the presence of such defects on the billet surface, but it has also unambiguously linked the genesis of these depressions to metal level fluctuations and their interaction with the lubricating oil flowing down the mold wall toward the meniscus. Mechanisms for the formation of these defects have evolved from 1910—VOLUME 30A, AUGUST 1999

Fig. 21—The major components of the intelligent mold being developed for billet casting.[11]

this study, and Figure 23 conceptually illustrates the genesis of transverse depressions as a result of metal level fluctuations. Other defects, such as off-squareness, which has plagued the billet industry since its inception, have also been linked to instability of the metal level and consequent variations in solidified shell thickness around the mold periphery. Techniques to detect off-squareness have also been formulated and are based on detecting prescribed differences in temperature between thermocouples on adjacent faces. Meniscus instability may be temporarily caused by a partially blocked tundish nozzle, rough pouring streams, and excessive air entrainment. Such a process upset can be corrected on-line, by the operator, by deblocking the nozzle, or alternatively by plugging it completely and diverting the steel to adjacent strands. On the other hand, meniscus instability in the mold could be related to improper tundish design and excessive turbulence in the tundish, which would require more radical off-line measures to correct. Other process upsets such as high friction and sticking at the meniscus due to a lubrication upset or improper oscillation characteristics as a result of oscillator malfunction can also be detected using mechanical sensors, such as strain gages, linear variable displacement transducers, and load cells. Whatever the source of the process upset, on-line sensors have proved to be valuable in the development of an Intelligent Mold. Developing a system capable of performing in a steel plant environment and interacting with existing plant sensors has proved to be a challenge. It requires interdisciplinary teams of electrical engineers, software specialists, experts in continuous casting, and the cooperation of plant personnel and management to bring it to fruition. This is undoubtedly the next frontier that must be successfully tackled if continuous casting processes are to advance further. METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 23—Proposed mechanism of transverse depression formation near the meniscus due to metal level rise and trapped oil vaporization.[11]

IX. THE POWER OF KNOWLEDGE It is remarkable to think that humankind has moved, by virtue of serendipity, intelligence, and experience, from the hewing of naturally gathered stone to the tailor-making of sophisticated metal alloys and optoelectronic materials. Each development in this technological march through time has inexorably contributed to the knowledge pool of materials processes and properties, which today is vast and accelerating in its growth. The intelligent person, who early in the last century might have comprehended most scientific and engineering knowledge, today struggles to understand a fraction of the knowledge within a specialty. The materials scientist focusing on structure and properties is unaware of the developments in process analysis. The aluminum or zinc expert does not know of the advances in steel processing, despite the obvious similarities in specific processes such as continuous casting, as shown in this article. Perhaps inevitably in the continuum of the materials knowledge pool, we have defined boundaries around specific subjects to cope with the increasing complexity of the atomic world. And, in so doing, we have put ourselves in boxes. Our challenge then is to unleash the full power of knowledge by dismantling barriers that have been built around specific topics within the materials field. The thirst for knowledge by companies who strive to achieve a competitive edge in quality and costs in processes such as continuous casting and many others will be constant in the future. A very real question is whether universities who pride themselves on the development of the intellect, and the creation of knowledge through research, are serious about a commitment to society to harness knowledge in the creation of wealth, which surely underpins our economy. Surely this is the challenge to engineering professors, who are professionals, no less than to professors of medicine who must be concerned about the physical health of society. It will be up to industry to develop the receptor capacity within their workforce through the necessary education to ensure that knowledge is implemented in their processes to give them the competitive advantage that guarantees their profitability. A TRIBUTE

Fig. 22—Thermocouple response above and below the meniscus during the formation and travel of a lap at Company A. [12]

METALLURGICAL AND MATERIALS TRANSACTIONS A

It was September of 1997 and Dr. J. Keith Brimacombe, O.C. had just been offered the position of President of the newly established Canada Foundation for Innovation. He accepted the opportunity to serve Canada without hesitation, excited by the prospect of leading an effort to strengthen the nation’s research infrastructure in universities and hospitals. In leaving his position of Professor and Alcan Chair in VOLUME 30A, AUGUST 1999—1911

Materials Process Engineering at the University of British Columbia, where he had built a reputation as one of the finest metallurgical engineers on the world stage, he said “I have accomplished more than I could have dreamed of in my own career—this is a chance for me to do something for Canada.” His untimely passing, on December 16, 1997, at the pinnacle of his career, is a great loss to Canada and to the materials community worldwide. It was Keith Brimacombe’s dream to create the best process engineering research center in the world and what he accomplished in pursuit of his dream is truly remarkable. One of the most innovative giants of 20th century metallurgical process engineering, Dr. Brimacombe pioneered the application of mathematical models and laboratory and industrial measurements, to shed light on complex processes for the production of metals. For his groundbreaking research, he received over 50 national and international awards, of which the Officer of the Order of Canada was his most cherished honor. He believed passionately in translating the results of his research into practical terms, which would benefit workers on the shop floor and lead to the creation of wealth. Dr. Brimacombe attributed part of his practical bent to his upbringing in a small farming community in Alberta: “On a farm, you have to know how things work, and find ways to make them work better,” he said. He was equally passionate about developing the intellectual potential of young people and the importance of the human resource to the well being of a nation. He would say of his role as an educator that “there is nothing more satisfying than watching the raw intellect and creativity of a student flower and blossom.” And indeed, he had the rare ability to make this happen, even in the most unlikely cases. Keith Brimacombe was born on December 7, 1943, in Windsor, Nova Scotia, where his father was stationed as a flight instructor during WWII. Keith was raised in Alberta and regarded his boyhood in Rosalind, a small farming community near Camrose, as a magic time. His maternal grandparents’ home next door to his own imbued his childhood with an idyllic quality. He loved the early summer morning, when he would creep out of bed to work in the vegetable garden with Grandpa Mac, or the times he would escape to Grandma’s house for milk and cookies when things got tough at home. The generosity and love of his family left a strong impression on Keith, who, through both nature and nurture, embodied these human qualities. Through the Air Force ROTC program, Keith enrolled in engineering at the University of British Columbia. He was attracted to metallurgical engineering because of the complexity of metallurgical processes and the role of the discipline in shaping our civilization. Uniquely gifted, Keith Brimacombe excelled academically and in leadership roles. Upon graduation in 1966, he was awarded both the Athlone and Commonwealth Fellowships, and proceeded to the Royal School of Mines in Britain to work on his doctorate with Professor Denys Richardson, a colossus in process metallurgy. But in Keith’s words, “it was London with its rich history, beautiful parks and outstanding theatre that cast a spell on the boy from the prairies.” In 1970, he completed his doctorate, married Margaret Rutter, and returned to the University of British Columbia, where over the next 27 years he charted an unparalleled career. A devoted father, he spoke

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often, with such pride and deep love, of his two daughters, Kathryn and Jane. Keith Brimacombe was a rare human being, one of the warmest and most caring of individuals. His mischievous sense of humor and ability to tell stories, seldom matched, endeared him to people. He could ad lib a John Cleese skit with astonishing mimicry and loved entertaining you over a drink or a meal. Keith Brimacombe was also a born leader with enviable charisma and charm. Never content with the status quo, he thought deeply about needed change and altered the discipline irrevocably through his creativity; he transformed professional societies, sculpting the finest of stepping stones for those to follow; and he challenged and inspired many around the world with the power of his ideas. Keith had a great love of life and his capacity to enjoy the beauty of his surroundings, whether a sunset on Lake Saima in Finland, or the majesty of Dubrovnik in Yugoslavia, or the pastoral beauty of County Kerry in Ireland was a reflection of his deep sensitivity. Keith was people centered and believed in the richness that flows from men and women working in harmony. I quote from his writings as 1993 TMS President: “Humanity is woven from the souls of men and women—the warp and woof of life’s fabric. The threads of the male and female spirit are profoundly different, and the tapestry is constantly changing. . . . It is time that life’s fabric was woven from threads that mutually enliven the human tapestry in which the colour and strength of one thread meshes with the warmth and texture of another in a vibrant balance.” Inspiring words! For those of us whose lives he touched and nurtured, he was an irreplaceable mentor and a beloved friend. ACKNOWLEDGMENTS Indira Samarasekera was Keith Brimacombe’s research partner over two decades and is a Professor at the University of British Columbia. REFERENCES 1. J.K. Brimacombe and I.V. Samarasekera: Iron and Steelmaker, 1994, vol. 21 (11), pp. 29-39. 2. J.K. Brimacombe: Metall. Trans. B, 1993, vol. 24B, pp. 917-35. 3. V. Venkateswaran and J.K. Brimacombe: Proc. of Modeling of Casting and Welding Processes, J.A. Dantzig and J.T. Berry, eds., Engineering Foundation, New York, NY, 1983, pp. 365-68. 4. J.K. Brimacombe: Can. Met. Q., 1976, vol. 15, pp. 163-75. 5. J.K. Brimacombe, P.K. Agarwal, L.A. Baptista, S. Hibbins, and B. Prabhakar: Steelmaking Proc., NOH-BOS Conf., Washington, DC, ISS-AIME, Warrendale, PA, 1980, pp. 235-52. 6. B.G. Thomas, J.K. Brimacombe, and I.V. Samarasekera: ISS Trans., 1986, vol. 7, pp. 7-20. 7. K. Wunnenberg and H. Jacobi: 4th Japan/German Seminar, Tokyo, 1980, Iron and Steel Institute of Japan, pp. 201-216. 8. M. Hansen: Constitution of Binary Alloys, McGraw-Hill, New York, NY, 1958. 9. S. Kumar, J.A. Meech, I.V. Samarasekera, and J.K. Brimacombe: Proc. Electric Furnace Conf., 1993, vol. 51, pp. 381-93. 10. S. Kumar, J.A. Meech, I.V. Samarasekera, and J.K. Brimacombe: IFAC Workshop on Expert Systems in Mineral and Metal Processing, Helsinki University of Technology, Helsinki, Finland, 1991. 11. I.V. Samarasekera, J.K. Brimacombe, H.M. Adje-Sarpong, P.K. Agarwal, B.N. Walker, and D.P. Lorento: 2nd Canada-Japan Steel Symp., Toronto, Canadian Institute of Mining and Metallurgy, Montreal, 1994, pp. 169-87. 12. S. Kumar, I.V. Samarasekera, and J.K. Brimacombe: ISS Trans., June 1997, pp. 53-69.

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