Modeling of Casting Solidification Stochastic or Deterministic?

Abstract

Solidification modeling has had a phenomenal impact on metalcasting in the last decade. Following its initial success in predicting the occurrence of porosity defects, it has grown to be an essential casting engineering tool. As more complex models have been developed (in response to the realization that simple heat flow models were not adequate to solve the shrinkage problem), they are being used to design more efficient gating and risering systems, which minimize the amount of metal poured to produce a good casting. Models today include predictions of fluid flow during mold filling, casting distortion, mold-metal interface reactions and cast structure.

Until a few years ago solidification simulation was based only on deterministic models. As prediction of microstructural evolution became a contemporary problem, the limitation of deterministic models in predicting such features as dendrite coherency, columnar-to-equiaxed transition, dendrite fragmentation

and movement of dendrites by the liquid, became evident. Recently developed stochastic models for solidification are capable of simulating and displaying the growth of columnar and equiaxed grains. However, the physics of dendritic growth is rather approximate. The growth of dendrite arms and their branching are ignored, and only a bulk representation of the grain growth is provided.

A micro-scale approach for more accurate dendritic growth simulation in casting processes is presented in this paper. The model couples stochastic modeling at a length scale of 10^?6 m, with deterministic modeling at a length scale of 10^?4 m. A deterministic tip-velocity model is used to calculate the advance of the dendrite tip. Arm thickening is also calculated with a deterministic law derived from the dendrite tip velocity law and crystallographic considerations in combination with a deterministic coarsening model. However, the overall growth of dendrite arms is derived from probabilistic calculations. Branching of dendrites arm is allowed to occur based on morphologic instability. Thus the dendrite morphology, rather than the gain structure can be simulated.

A discussion on the advantages and limitations of contemporary deterministic and stochastic models is also included. © 1998 Canadian Institute of Mining and Metallurgy. Published by Elsevier Science Ltd. All rights reserved.

Résumé

La modélisation de la solidification a eu un impact phénomenal sur le coulage des metaux au cours de la derniere decennie. A la suite de son succes initial a predire l'occurrence de porosite, la modelisation est devenue un outil d'ingenierie essentiel pour lecoulage. Puisque des modeles plus complexes ont été développes (suite à la réalisation que de simples modéles d'écoulement de chaleur n'étaient pas adequats pour la resolution du probleme de retrait), ceux-ci sont utilises pour concevoir des systemes plus efficaces d'attaqué de coulée et de disposition de masselottés. Ces systemés minimisént ainsi la quantité de metal versée pour la production d'un bon coulage. Les modéles d'aujourd'hui peuvent prediré l'écoulement de fluide lors du remplissage du moulè, la distorsion des coulages, les réactions à l'interface moule-metal et la structure du coulage.

Jusqu'à il y a quelques années, la simulation de la solidification était basée uniquement sur des modèles déterministes. Puisque la prediction de l'évolution de la microstructure est devenue un probleme contemporain, la limitation des modéles déterministes à prédire des caracteristiques telles que la coherence des dendrites, la transition basaltique-à-équiaxe, la fragmentation et le mouvement des dendrites par le liquide, est devenue evidente. Les modeles stochastiques de solidification, développes recemment, sont capables de simuler et d'exposer la croissance de grains basaltiques et équiaxes. Cependant, la physique de la croissance des dendrités est plutot approximative. La croissance des dendrites et de leurs embranchements est ignorée et seulement une representation en vrac de la croissance de grain est fournie.

Dans ce document, on présente une approche à l'échelle microscopique afin de fournir une simulation plus exacte de la croissance de dendrite, dans les procedes de coulage. Le modele associé la modélisation stochastique, à une echelle de longueur de 10⁶ m, avec la modelisation deterministe, à une échelle de longueur de 10⁴m. Un modele deterministe de velocite a l'éxtremite est utilise pour calculer l'avance de l'extremite du dendrite. L'épaississement du bras est aussi calcule avec une loi deterministe derivée de la loi de velocité a l'extremité du dendrite et de considerations cristallographiques en combinaison avec un modéle de grossissement deterministe. Cependant, la croissance generale des dendrites est derivée de calculs probabilistes. L'embranchement des dendrites est permis en se basant sur l'instabilite morphologiqué. Ainsi, on peut simuler la morphologie de dendrite, plutot que la structure de grain.

On inclut également une discussion des avantages et des limites des modéles deterministes et stochastiques contemporains. © 1998 Canadian Institute of Mining and Metallurgy. Published by Elsevier Science Ltd. All rights reserved.     

Analysis of solidification behaviour of low alloy steel ingot casting – simulation and experimental validation

Abstract

Solidification in a small experimental steel ingot casting was studied using finite element based simulation. Using the model, the phenomenon associated with fluid flow, temperature distribution, mushy zone formation, thermal gradient ahead of solidification front, local solidification time at various instances of solidification was examined. The heat transfer was found significant till a critical thickness of the solidified ingot. Air gap analysis during the solidification showed that, in spite of high ferrostatic pressure of liquid metal there is notable air gap in the ingot bottom. The model predicted the final piping shrinkage and some small zones of axial porosity formation. The experimental ingot showed a good match on piping shrinkage and porosity obtained from simulation. The microstructure formation in the experimental ingot could be correlated with simulation results. The approximate regime of columnar to equiaxed transition was estimated form the simulation and was matched with that obtained in the actual experimental ingot. The microstructures of the ingot at typical zones were examined in the ingot and correlated to local solidification time.     

Evolution or revolution?—a new era in billet casting

The billet industry was born in the mid-1960s as a series of scrap recycling plants, at a time when environmental awareness was not even in vogue. Out of the determination and vision of the individuals who forged this industry, a new philosophy of steelmaking emerged. A philosophy based on low man-hours per tonne, and profit sharing gave birth to the highly profitable minimill concept that has now gripped steel production in the flat-rolled area. The billet industry has evolved from being primary suppliers of reinforcing bar to being competitive in high quality products while retaining the original production philosophy. A quiet revolution is now underway in this industry with casting speeds approaching those of thin slab continuous casting. Mould powder lubrication and other practices common to slab casting, such as controlled feeding of liquid steel from tundish to mould in place of metering nozzles are becoming common place. This paper delineates some of the challenges facing the industry which is in the throes of a revolution. Professor Alexander McLean’s early work on the importance of controlling fluid flow in the tundish and its impact on turbulence in the mould is emerging as being critical to the challenge of producing high quality billets at high casting speeds.     

Influence of mechanical factors on solidification structure of thin strips of Fe–6.5wt-%Si alloy by twin roll casting process

Strips (1.6?mm thick) of Fe–6.5wt-%Si alloy were prepared by twin roll casting. The microstructure was found to be mainly columnar and equiaxed grains. The plastic deformation of the strip is inhomogeneous in the thickness direction. The most serious deformation is located at a certain depth from the strip surface. The influence of mechanical factors on the solidification structure of the strip is discussed. As the two solidifying shells contact with each other at the end of solidification, the columnar growth fronts break into fragments, which finally grow into equiaxed grains. At the hot rolling stage, the inhomogeneous deformation of the strip is attributed to the fact that the ductility of the alloy is sensitive to temperature. There is a large temperature gradient in the thickness direction, which can be up to 510°C?mm^??1.     

Unidirectional solidification of dilute PbBi alloys

The morphological stability of a planar solid-melt interface during unidirectional solidification of dilute PbBi alloys is studied. It is shown that an approximate control of the growth rate may affect significantly the breakdown line. Observations are reported on the shape of the cells which emerge for growth conditions not too far from the ones corresponding to the non planar transition. Then the solid-liquid interfacial free energy is evaluated from an application of the condition of marginal stability for the observed cells; the obtained values compare favorably with what is presently admitted for pure lead.     

Women's experiences of treatment of depression: Medicalization or empowerment?

An interview study was conducted in which women's experiences of diagnosis and treatment for depression were explored. Nine women (aged 19–66 yrs) who had been diagnosed by a physician participated in the study. Topics explored in the interview included how women came to be diagnosed as depressed, how treatment was experienced, how they understood the causes of their depression, and how being diagnosed had affected their view of themselves and their futures. Analysis involved a thematic approach guided by the topics addressed in the interview. The women's accounts also were analyzed with respect to the themes of medicalization and empowerment. All of the participants gave medicalized accounts of their depressive experiences, which were characterized by biomedical explanations and identification of anti-depressant drugs as beneficial in alleviating their distress. Based on this analysis of the women's accounts, it is concluded that a medicalized understanding and treatment of women's depressive experiences cannot readily co-exist with personal empowerment. Suggestions are made for developing strategies for treatment of women's depressive experiences that offer the benefits of medicalization without precluding the possibility of personal empowerment. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Selection of the slag-forming mixture in continuous casting of 45ХГМА steel

TSK-K-25 slag-forming mixture is chosen for the production of 500 × 500 mm square billet on a vertical continuous-casting machine. This mixture permits the casting of 45ХГМА steel at reduced speed (0.07–0.14 m/min).     

Effect of modification on the solidification of Al–Si aluminum alloys

The solidification of the AK12 alloy processed by a standard flux and a combined modifying flux, which significantly increases the mechanical properties of the alloy at a significant increase in the modifying effect time, is studied. The experimental results are simulated using the ProCAST software package.     

Water Modeling of Optimizing Tundish Flow Field

 In the water modeling experiments, three cases were considered, ie, a bare tundish, a tundish equipped with a turbulence inhibitor, and a rectangular tundish equipped with weirs (dams) and a turbulence inhibitor. Comparing the RTD curves, inclusion separation, and the result of the streamline experiment, it can be found that the tundish equipped with weirs (dams) and a turbulence inhibitor has a great effect on the flow field and the inclusion separation when compared with the sole use or no use of the turbulent inhibitor or weirs (dams). In addition, the enlargement of the distance between the weir and dam will result in a better effect when the tundish equipped with weirs (dam) and a turbulence inhibitor was used.     

Modeling of Flotation Process—An Overview of Different Approaches

The modeling of flotation has been reviewed with the aim of identifying their usefulness, significance as well as limitations. From literature it is clear that, various flotation models have been developed on the basis of the processes and sub-processes occurring in flotation. An overview of the literature indicates that various approaches have been adopted in quantifying the process. Flotation models based on kinetics have prevailed in almost all flotation conditions regardless of the ore type and ore characteristics as well as flotation cell configurations. It may be concluded that the classical first-order kinetic model is comparatively a better model and can be utilized to optimize the flotation process as it is applicable to both batch and continuous flotation processes with high confidence level.

Finally, it is suggested that future work should focus on improving the models which can more accurately predict the prevailing conditions and enable better optimization of the flotation process.     

Overview 12: Fundamentals of dendritic solidification—II development of sidebranch structure

Experiments have been carried out to study the development of the dendritic sidebranch structure in succinonitrile. Results obtained provide the first insights into such fundamental problems as the origin of sidebranch perturbations, the mechanism of sidebranch evolution, the influence of anisotropy in solid-liquid interfacial energy, the kinetics of isothermal coarsening, and, finally, the mechanism of dynamic sidebranch coarsening during solidification. All of the problems addressed have applications to the interpretation of microstructures arising from both conventional and rapid solidification processes.     

On a stochastic theory of grain growth—II

The stochastic theory of grain growth proposed previously [C. S. Pande, Acta metall.35, 2671 (1987)] is developed further in this paper. This theory leads to a Fokker-Planck equation for the grain size distribution. Two different “deterministic” terms for this equation, one proposed by Hillert and other by Pande, are compared. It is found that contrary to expectations Hillert's determistic term even with the addition of a “diffusion” like term does not lead to a grain size distribution which could be in agreement with experiments. The deterministic term proposed by Pande, leads to a grain size distribution which is similar to lognormal distribution, and closer to experimental results.     

Origin of laparoscopy: coincidence or surgical interdisciplinary thought?

The history of laparoscopy illustrates the interaction between the many areas of medicine and technology; in fact, the development of that technique is a cumulative effort of internists, gynecologists, and surgeons. At the beginning of our century, however, neither group was particularly open to the idea of scholarly exchange. In this respect, an early pioneer of laparoscopy, Georg Kelling (1866-1945) of Dresden and the story surrounding the invention of the laparoscopy are interesting exceptions. Although Kelling regarded himself a surgeon, he devoted a great deal of energy to the development of "nonsurgical" methods of treatment. He spent a great part of his life determining stomach capacity, constructing a semiflexible tube endoscope (straightened after the insertion), and attempting to alleviate gastrointestinal bleeding by means of high-pressure pneumoperitoneum (lufttamponade). To observe the effects of insufflation on abdominal organs, Kelling introduced a cystoscope into the abdominal cavity. In fact, the invention of "celioscopy" or laparoscopy (1901) can be called a synthesis of Kelling's work with insufflation and his fascination with endoscopy.     

Payment or repayment? The problem of private practice.

"From Freud on, it has been recognized that there is always a 'masochistic element' in neurotic and functionally psychotic individuals… . We need to be very sure that, in the fees which are charged for that otherwise doubtful service known as psychotherapy, we do not fall into the trap of merely gratifying this need for punishment on the part of the patient… . We need to be very certain… that 'therapy' does not become merely a form of expiation, much as electrically induced convulsions or hospitalization (with its overtones of imprisonment) does for others, who cannot afford 'psychotherapy."' The greatest weakness and defect of private practice "lies precisely in the fact that it offers as treatment what, in reality, is the very essence of the disease itself, namely continued privacy and personal withdrawal. Now we are coming to see that the way to feel better is to be better, in the ethical and interpersonal sense of the term." The neurotic's insecurity "stems from real guilt, which can be satisfactorily resolved only by radical openness and restitution." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Recall of interrupted tasks under stress: A phenomenon of memory or of learning?

The study proposed to answer three questions: "1. Is superior recall of successes in an intelligence test situation (S-recall) a function of selective forgetting (repression) of failures or selective learning in favor of successes? 2. Is superior recall of failures in this situation (F-recall) a function of selective remembering or selective learning in favor of failures? 3. Is there a mnemonic reaction to the test as a whole?" Findings indicate that: "1. Both the S- and f-recall tendencies were due to a selective learning rather than a selective remembering mechanism. 2. A repression was demonstrated for S-recallers with regard to the stress situation as a whole. 3. A comparable process of enhanced retention of the total stress situation was not demonstrated for F-recallers; rather the effect here was due to enhanced registration." Implications of results are discussed. It is suggested that "experimental tests of repression… fulfill a criterion of cognitive relevance of test materials." 23 references. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Optimisation of geometry of 185 × 185 mm square billet mould of Sidenor continuous casting machine

Abstract

Industrial trials conducted at Sidenor Basauri Works, and numerical modelling at Centro Sviluppo Materiali (CSM), have been combined in order to find a square 185 × 185 mm billet peripheral geometry that improves the quality of cast products by eliminating the occurrence of off corner cracks and depressions, and reducing the percentage of rejection. The idea is to change the square shape of the mould section to a new profile having a larger corner radius and outward bulging faces. Experimental trials using moulds with convex faces and larger corner radii resulted in an interesting decrease in the percentage of rejected bars. The presence of longitudinal defects has not been completely eliminated, but the adoption of moulds with larger corner radii has been demonstrated to be successful. Numerical modelling has been used to verify that the larger corner radius is the most important variable that guarantees the improved result, while it is less sensitive to different deflections of the faces. This encourages the use of moulds with flat faces, which produce billets that are much easier to handle with conventional tools for their transfer. It can be concluded that by using moulds with a corner radius of 40 mm, instead of conventional moulds with 10 mm corner radius, and flat faces, the risk of longitudinal off corner defects is significantly reduced.     

Intoxication--suicide or not?

It is often impossible to decide whether a death due to poisoning with drugs and/or alcohol is accidental or intentional. In 1965 WHO introduced the category "uncertain cases of death" in the official statistics. The number of cases in this category has increased and constitutes at present in Sweden between 30 and 70 per cent of the total number of suicides. In Malm? (1972-1973) most of these deaths were due to lethal poisoning with drugs and/or alcohol. When discussing suicidal rates it is important to include those cases.     

Paradox or contradiction?

Notes that in the April, 1955 issue of the American Psychologist, two young psychologists note the discrepancy between theory and practice in the clinical field, particularly during training, and a veteran says that he itches too but offers no suggestions for relief. It seems clear that our society can use many clinicians, a few experimentalists, and fewer who are half-and-half. On the other hand, scholarly tradition requires publication and the age requires it to seem scientific. Training is institutional for ends that are individual. Such observations could be compounded and argue for much franker facing of the sociology and economics of clinical psychology than has been given them. The author concludes that no one should be certified for the use of a clinical technique unless and until he can prove competence through results in the judgment of a group of his peers. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Authoritarianism or acquiescence?

The hypothesis that scores on the F scale and similarly constructed inventories are primarily measures of acquiescence rather than authoritarianism is tested by testing subjects on a G scale composed of opposite statements to those of the F scale. Response set to acquiescence was measured by obtaining each individual's tendency to support both F and G scale statements. If individual fluctuations from one scale to another are ignored, they tend to differ significantly from each other in tendency to acquiesce. Response set to acquiescence increased as items became more ambivalent. It is suggested that a much more parsimonious explanation can be given to account for the positive relations between authoritarianism, misanthropy, xenophobia, and ethnocentrism. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Opinions or Data?

Replies to comments by W. Wood (1962) to the original article by M. R. Feinberg and J. Lefkowitz (see record 1963-02029-001), which assessed the image of industrial psychology among corporate executives. The author discusses five points made by Wood, including issues regarding opinion vs. research findings and original study's methodology. (PsycINFO Database Record (c) 2010 APA, all rights reserved)