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By G. K. Manning, C. H. Lorig

TWO metallurgical tools have acquired wide use within the past several years as a means of studying the transformation characteristics of steel. One is a technique used first by Bain and Davenport for determining the transformation characteristics of a steel at constant temperature; the second is the end-quench hardenability test. Constant-temperature transformation curves like those of Bain and Davenport have done much to rationalize the metallography of steel; however, in commercial practices, constant-temperature transformation is seldom encountered, therefore only rarely can such curves be directly applied. The real reason for the determination of such curves lies in the fact that they provide a way of thinking about transformation that is both convenient and productive. The end-quench hardenability test is a more practical means of studying transformation, for, by correlating positions on the hardenability bar with shapes of different masses, an almost direct application of the results can be made. Unfortunately, the end-quench test, though practical, can do very little toward improving the metallurgists' way of thinking about transformation. These two metallurgical tools, dealing with precisely the same phenomenon, should be very closely associated in metallurgists' minds. Actually, they are frequently pushed into separate mental corners and considered as being more or less distinct and unrelated. The reason for this is that no strong connecting link between them has been developed. An attempt is sometimes made to relate these two tools by projecting the critical cooling rate on the isothermal transformation plot as illustrated in Fig. I. The critical cooling rate is considered as a constant rate-though in practical applications, cooling rates are never constant—and this constant cooling rate is given uniform significance from the Ae temperature down to the temperature of initial transformation. A little thought indicates the errors of such a procedure. Certainly the time interval spent just below point A of Fig. I cannot be as effective in promoting nucleation as is the time interval spent just above point B. Yet the procedure represented in Fig. I considers all the time spent between temperatures A and B to be just as effective in promoting nucleation as though all the time were spent at temperature B. Furthermore, change the shape of the isothermal curve between points B and C in any way desired, and the required critical cooling rate is not changed one iota. This cannot possibly be true. Such a way of thinking about critical cooling rates not only is incapable of giving any results that are quantitatively satisfactory but is likely to give very misleading qualitative results.

Jan 1, 1947

Jan 1, 1923

Jan 1, 1923

By Earl S. Greiner, Bradley Stoughton

As a part of the systematic study of the alloys of iron under the auspices of the Engineering Foundation, and preliminary to the commencement of comprehensive work on this larger subject, the authors have undertaken an investigation of the available literature dealing with the alloys of iron and silicon. The purpose is to collect all the data in English and foreign languages and present them in two monographs, one of a more scientific and the second of a more industrially useful nature. Of course, a great deal of information upon the constitution of the iron-silicon alloys was found specificially upon the changes of phase in the equilibrium diagram and the different phases present, such as solid solution, chemical compounds (iron silicides), etc. While no extended research was contemplated in the particular study undertaken, nevertheless the data collected proved to be so contradictory in many respects that a simple study of some of the outstanding problems involved in the constitution and equilibrium diagram was undertaken. Because research was not a primary object of the work, and also because of the extreme industrial importance of the silicon alloys between 0.80 and 14 per cent. silicon, and finally because of the unsatisfactory state of knowledge existing as to these alloys, the experimental investigation was limited entirely to alloys with less than 10 per cent. silicon. Discussion oF Continuous Series It has often been said in print that the iron-silicon alloys form a continuous series of solid solutions from 0 to 15 per cent. silicon. This claim the authors are inclined to doubt: first, because the alloys from 0 to 4.25 per cent. silicon are ductile and malleable at atmospheric temperature, while those with 5 per cent. or more of silicon are comparatively hard and brittle. Furthermore, the alloys with more than 4.25 per cent. silicon are comparatively hard and low in ductility at atmospheric temperature, but become much more ductile when heated slightly. It is well known, for example, that the alloy containing 4.75

Jan 1, 1930

By Robert Palmer

So MUCH has already been written on this vast subject of ground movement and subsidence, and so many data collected and commented upon, that in this paper the author proposes to confine himself to the submission of some plans showing what has actually occurred in the mining of several of the orebodies which have, come under his direction during the last 20 years or so at Rio Tinto, Spain. Some notes are added for the purpose of describing the plans. The author does not attempt to give his opinion as to the reasons why the subsidences have occurred in the manner in which they are found, but confines himself to giving as true a picture as possible of the movements that have taken place.

Jan 1, 1930

By Harold V. Pearce

(Chattanooga Meeting, October, 1908.) THE fire which occurred in the fall of 1906, at the works of the Boston & Colorado Smelting Co., Argo, Colo., destroyed entirely the gold- and silver-refinery of the plant; and in view of the development of modern practice in the refining of copper-mattes, etc., the management decided that it would be inadvisable to rebuild that part of the works for the continued use of the process which had been conducted therein for so many years as a metallurgical secret. This decision probably removes altogether from the sphere of practice the " Pearce " method for the separation of gold. At all events, it removes the business reasons which have prevented hitherto the publication of the principles involved. At the suggestion of Dr. Raymond, Secretary of the Institute, my father, Richard Pearce, the former manager of these works, has requested me to prepare a brief description of this process for the benefit of our members. Since I severed my connection with the Boston & Colorado Smelting Co. some time ago, I am indebted for some practical details to the present superintendent, Charles Rees, whose friendly assistance I would gratefully acknowledge. With regard to the history of the inception and development of this process by its inventor, Richard Pearce, I cannot do better than quote freely from his own notes and papers. HISTORY OF THE PEARCE PROCESS.' "In 1874 my entire time was directed to the improvements and additions to the plant at Black Hawk. The changes which I had made in the construction of the furnaces at Black Hawk proved so beneficial that I was requested to introduce the improvements at the branch works at Alma. These changes were carried out as speedily as possible, and proved of great advantage as compared with the old system. "The separation and refining of the gold from the matte now engaged my attention, and since previous experience in the treatment of gold-bearing matte and

Feb 1, 1909

By G. B. Walker, S. A. Falconer, S. J. Swainson, H. H. Vogel

During the past few years much interest and attention has been focused on a relatively new method of ore concentration, which utilizes the principles of sink and float and employs as the heavy medium a suspension in water of a finely ground solid, such as galena or ferrosilicon. Although a relatively recent development, much progress has already been made in applying heavy-media separation processes to a considerable number of ores. Eight plants in this country and abroad are now treating approximately 10 million tons of ore annually by heavy-media separation (sink-float) processes, including lead-zinc, lead, iron, garnet, tin and tungsten. At the annual meeting of the A.I.M.E. in 1941, three interesting papers (unpublished) dealing with heavy-media separation (sink-float) processes of ore concentration as practiced in four commercial units in the United States were presented by Victor Rakowsky, Grover Holt, Elmer Isern and Robert Ammon. These papers gave an excellent exposition of the principles of sink and float, as well as the operating practice in two iron-ore-beneficiation plants, the Harrison and the Merritt, of Butler Brothers, in Minnesota; the Central mill of the Eagle Picher Mining and Smelting Co.; and the Mascot mill, of the American Zinc, Lead and Smelting Co. Augmented by pictorial descriptions and a working model demonstrating the processes, these papers evoked a great deal of interest and discussion. In fact, in reporting the high lights of the meeting in the April 1941 issue of Mining and Metallurgy, Professor Taggart made the statement that " preconcentration by heavy suspension was Miss A.1.M.E 1941 so far as milling is concerned." Although to date the greatest application of heavy-media separation from the tonnage point of view has been for the treatment of lead, zinc and iron ores, these processes have a much wider field of usefulness. In this regard, it is to be noted that recently new heavy-media separation plants for treating cassiterite ore and garnet ore have been placed in successful operation. Moreover, numerous other types of ores have been found to respond well to these processes when tested on a semi-commercial scale, and it is expected that in the near future a considerable number of new plants will be erected. In view of the fact that heavy-media separation processes offer such attractive possibilities, particularly now, when the mining industry is being called on for an even larger production than ever before has been attempted, despite shortages of labor and supplies, it was felt that a description of some of the successful separations that have been worked out during the past year in the Ore Dressing Laboratory of the American Cyanamid Co. on a variety of ores of strategic importance would be of interest. The purpose of this paper, therefore, is to present the essential data relating to investigations of heavy-

Jan 1, 1943

By G. B. Walker, S. J. Swainson, S. A. Falconer, H. H. Vogel

During the past few years much interest and attention has been focused on a relatively new method of ore concentration, which utilizes the principles of sink and float and employs as the heavy medium a suspension in water of a finely ground solid, such as galena or ferrosilicon. Although a relatively recent development, much progress has already been made in applying heavy-media separation processes to a considerable number of ores. Eight plants in this country and abroad are now treating approximately 10 million tons of ore annually by heavy-media separation (sink-float) processes, including lead-zinc, lead, iron, garnet, tin and tungsten. At the annual meeting of the A.I.M.E. in 1941, three interesting papers (unpublished) dealing with heavy-media separation (sink-float) processes of ore concentration as practiced in four commercial units in the United States were presented by Victor Rakowsky, Grover Holt, Elmer Isern and Robert Ammon. These papers gave an excellent exposition of the principles of sink and float, as well as the operating practice in two iron-ore-beneficiation plants, the Harrison and the Merritt, of Butler Brothers, in Minnesota; the Central mill of the Eagle Picher Mining and Smelting Co.; and the Mascot mill, of the American Zinc, Lead and Smelting Co. Augmented by pictorial descriptions and a working model demonstrating the processes, these papers evoked a great deal of interest and discussion. In fact, in reporting the high lights of the meeting in the April 1941 issue of Mining and Metallurgy, Professor Taggart made the statement that " preconcentration by heavy suspension was Miss A.1.M.E 1941 so far as milling is concerned." Although to date the greatest application of heavy-media separation from the tonnage point of view has been for the treatment of lead, zinc and iron ores, these processes have a much wider field of usefulness. In this regard, it is to be noted that recently new heavy-media separation plants for treating cassiterite ore and garnet ore have been placed in successful operation. Moreover, numerous other types of ores have been found to respond well to these processes when tested on a semi-commercial scale, and it is expected that in the near future a considerable number of new plants will be erected. In view of the fact that heavy-media separation processes offer such attractive possibilities, particularly now, when the mining industry is being called on for an even larger production than ever before has been attempted, despite shortages of labor and supplies, it was felt that a description of some of the successful separations that have been worked out during the past year in the Ore Dressing Laboratory of the American Cyanamid Co. on a variety of ores of strategic importance would be of interest. The purpose of this paper, therefore, is to present the essential data relating to investigations of heavy-

Jan 1, 1943

By Sir Robert Hadfield

Introduction.-I esteem it a great honor to be asked by this Institute to give them an address chiefly devoted to metallurgy. While it is with great regret that I find myself unable to be present to deliver this in person, I take this opportunity of wishing your society every success in its continued career of usefulness to the metallurgists of the great Republic. To be elected, eight years ago, along with Dr. J. E. Stead, F. R. S., as one of your Honorary Members, was a privilege which I greatly esteemed, for I consider that no society in America has done so much as ours for the advancement of metallurgy. Those who have Served our Society.-Where many have served so well, it is difficult, without appearing to make unavoidable distinctions, to select names from those of your members who have done so much for the cause we have at heart-the advance and progress of metallurgy. As typical, however, and not in any way meant as a complete list, there are among others the following names which in the past and to-day stand out prominently in this science of ferrous metallurgy. With most of those now mentioned I have personally come in contact, or by correspondence in some few cases, and have exchanged views, since I first came over to America 30 years ago. Holley; Jones; Weeks; Andrew Carnegie; Thomas Carnegie; Fritz; Sterry Hunt;. Egleston; Maunsel White and Taylor, who did so much for high-speed tool steel, and helped to revolutionize machine-shop practice; W. J. Taylor; Robert Hunt; Alfred Hunt of Pittsburg, who did so much in the early history of aluminum, and, alas! did. not live to see the wonderful progress which has been made in that particular branch of metallurgical industry; James Douglas; C. B. Dudley; Birkinbine; Howe; Metcalf; Barus; Langley; Raymond; P. H. Dudley; H. H. Campbell; W. R. Webster; E. D. Campbell; Talbot; Spilsbury; Gayley; Dinkey, under whose supervision and responsibility modern armor has been so successfully produced in this country, which the writer can testify from personal knowledge of , test results possesses very high Figure of Merit; Schwab; Kennedy; Wellman; Garrison; Wood; Moldenke; Webster; Swank; Unger; Richards; Sauveur; Strat-

Jan 5, 1914

By George Enos

As the coating formed affects the corrosion rate, duplicate samples of eight non-ferrous alloys were placed in flowing mine water. The alloys tested were as-cast or as-rolled and machined or polished. The paper describes the tests and gives the corrosion losses and the appearance of the samples at the end of the test. AN IMPORTANT factor affecting the rate and nature of corrosion of metals and alloys is the film, or coating, formed on the surface; and this may accelerate or retard corrosive action once started. The formation of films and coatings is intimately associated with the chemical composition and physical constitution of both the metal and the corroding medium. A film or coating may be either the corrosion product resulting from oxidation; that is, an oxide or salt, or a deposition of suspended matter from the corroding media upon the surface of the metal, or a mixture of both. The coating may adhere tightly or loosely to the surface of the corroded metal. In short, a film or coating is the reaction product of the corroding medium and the metal, which adheres to the surface of the metal and with which may be intermingled material from the attacking media not concerned in the chemical reactions. As the, terms film and coating are used by different writers for very different things, distinction is made between the two, by the present writers, on the basis of thickness. Thus, a film is defined as a corrosion product or deposition, on the surface of a corroded metal, that is of such thickness that it cannot be measured by the metallurgical microscope. A coating, on the other hand, is of such thickness that it can be measured. If the resolving power of the 2 mm. (equivalent focal length) apochromatic oil immersion objective (N.A. 1.4) is taken as the limit of the microscope, the limiting resolution is two lines that are 0.0002-0.0004 mm. apart. It is thus possible to measure coatings that are greater than 0.0002-0.0004 mm. thick. This thickness is equivalent to 200,000-

Jan 7, 1924

By Carl E. Swartz

For many years kettles used in the melting and refining of lead and other nonferrous metals and alloys have been made of cast iron. The logic of this probably lies in the fact that cast iron has been known as a material of construction for vessels of this type much longer than steel, and satisfactory fabrication from it has been more easily accomplished and better understood. As the capacity of lead refineries has increased, it has been only natural to increase the size of kettles. Today kettles of 150 to 250 tons are not uncommon. As the size of the kettles increased and better shapes were designed, the uniformity of material of construction became more important. Records kept over comparatively long periods of time have shown that the length of service of kettles has not been uniform. Many causes contribute to this and the importance of each has not yet been evaluated. Kettle design, kettle setting, method of firing and material of construction have been changed from time to time to obtain better service, but the variation in length of service is still great. A kettle may fail during the first few heats or may last through more than one thousand heats. The purpose of this article is not to present the conclusions of a finished piece of research on kettle manufacture and use, but to present a series of observations made over considerable time in the hope that others will publish data and that all may be correlated into a logical scheme which will result in better service and longer kettle life.

Jan 1, 1931

By Byron M. Bird

JIGGING is the stratification of a mass of solid particles in upward pulsations of water or in alternating upward and downward pulsations. The stratification usually is effected in a rectangular open-top container having a perforated bottom through which the pulsations of water are applied to the materials to be separated; in separating coal, to a mass of coal and refuse. Jigging usually is a continuous process involving three steps: (1) the reception of the raw coal, (2) the stratification of the coal and refuse so that the refuse settles to the screen plate, and (3) the overflow of the cleaned coal and the withdrawal of the refuse collected on the screen. The jig is the most universal washer ever devised. It is handling in practice a wide range of closely sized coals and ores, mixed sizes of coal from 8-in. to 0 through ¾ -in. to 0, and mixed sizes of ores down to 7/32-in. to 0 and even smaller. It is treating materials ranging in specific gravity from that of gold at 19 to that of coal at 1.30. It is handling feeds in which the proportions of high-gravity materials range from 90 per cent or higher, as for some iron ores, to 10 per cent or less for some coals. It is handling feeds containing all shapes of particles-round, rectangular, and , flat. It is handling simple separation problems and difficult separation problems. Thus, it is an almost universal separating device. One might add that it has been one of the most misunderstood types of washers, from both a theoretical and a practical point of view. Although considerable progress has been made in coal jigging in the past 10 years, the jig probably has more unexplored possibilities than any other type of washer. In this chapter the object has been to treat the jigging process in a practical manner and to give information that will help the reader to improve his particular operation. Inasmuch as performance data from operating plants would contribute little of value, none has been given. Instead, the emphasis is upon jigging principles as a foundation for attacking the problems that arise. These principles are in reality tentative conclusions from research in the field of jigging during the past 10 years and most of this chapter should be regarded as a progress report on an investigation still under way. As all really difficult problems in jigging arise from an attempt to treat a large range of sizes in one operation, nearly the entire discussion will be

Jan 1, 1943

By A. S. M’Creath, E. V. d’Invilliers

The rapid development of the southern coal and iron-ore fields during the past few years, and especially in the latter half of the year 1886, and the avidity with which everything relating to the industrial situation there is read and absorbed by the professional and non-professional public, has led to the preparation of a brief paper for the Institute upon a comparison of the raw materials available on or about January 1st, 1887, at three prominent centers of consumption. While disclaiming any originality or priority in the treatment of the resources of these districts, where so much valuable and interesting work has been performed in the past by several members of the Institute, we hope that the presentation of some analyses of samples personally secured by us in the several districts selected, and prepared for a comparative study of the character of the materials actually used and to be used by the furnaces of the "New

Jan 1, 1887

By L. Weyher, H. L. Lovell

This discussion is restricted to a very specific application of the cyclone - its use as a hydro-cyclone in the cleaning of fine coal. It is hoped that the development of the present data will assist in the further elucidation of existing qualitative models, and also in an enhanced application of the hydrocyclone and provide a base for further research. Discussed are the mechanisms of gravity separation in hydro-cyclones, test procedures, experimental observations, and industrial applications from these studies. Within the general area of unit operations, a considerable effort has been expended in theoretical and empirical research associated with cyclone operations. The motivation involves the industrial requirement for devices and techniques to manipulate small particles at low operating costs, a situation required in coal preparation. There are good reasons why the cyclone helps to satisfy this demand, because it combines operational simplicity (no moving parts) with versatility and high throughput capacity per unit area. The cyclone is one of the most widely applied tools in the process technologies. There are areas for potential cyclone application which have been only meagerly explored or not considered at all. This discussion is restricted to a very specific application of the cyclone - its use as a hydrocyclone in the cleaning of fine coal. It represents an initial presentation of a more comprehensive report. Coal preparation can appropriately claim the hydrocyclone since most of its predominant industrial uses have originated in this area and have spread into other applications, including the broad field of ore dressing, the petroleum industry, chemical processing, nuclear engineering and food technology. There is one operational principle common in all cyclones: A fluid is tangentially introduced into a cylindrical or conical container under pressure. A predominantly irrotational flow field1 is established within the cyclone (Fig. 1). The uniqueness of this flow is indicated by the variation in tangential velocity across the cyclone radius, which reaches a maximum a short distance from the center and decays toward the cyclone wall. In contrast, the tangential velocity in a centrifuge increases uniformly toward the wall. Usually two products are discharged from the cyclone. They differ in that one discharge consists predominantly of that portion of the feed fluid which moves along the wall axially away from the feed inlet, while the other consists predominantly of fluid spiralling along the central regions of the cyclone, in an axial direction opposite to that of the wall current. Fig. 2 indicates these discharge points schematically. The latter product may be termed the vortex-product, since it is discharged with the central vortex-current. In the case of conical cyclones, the former product may be referred to as the apex-product. Although the names "over- and underflow" are widely used, many cyclones are operated from extreme angular positions thus the proposed terms are less ambiguous. The cyclone feed fluid can be laden with solid particles or nonmiscible fluid drops. Such a feed component is discharged from the cyclone, after some residence time, into the one or the other product. Yet, the orifice through which a particle will leave the cyclone is dependent upon a number of factors. These factors, in a statistical sense, determine the path of the particle within the cyclone. Thus, different separation phenomena are possible and different process results attainable by the controllable variation of the particle path. It is then, to attain a fuller understanding of this particle path, to which this study is ultimately directed. It is anticipated that the detailed study of the data being developed will allow further elucidation of existing qualitative models. However, the development of a quantitative description of cyclone operation in terms of a mechanism is not currently feasible. The flow conditions in a cyclone are not fully understood even for a pure fluid, without the added complexity of the inclusion of multiple size-density particles. It is hoped that the development of the present data will also assist in an enhanced application of the hydro-cyclone and provide a base for further research. Some practical applications drawn from the data are suggested. Cyclone operations have been classified according

Jan 1, 1967

By H. S. Martin

ALTHOUGH it was known some years ago at the- Utah Copper Co. mills that fine grinding improved flotation recoveries, no accurate data were available until recently as to just how far the grinding could be carried economically. In 1923 the ultimate degree of fineness for flotation feed was supposed to be about 10 per cent. on 65 mesh, with approximately 55 per cent. through 200 mesh, which meant that most of the mineral would pass 100 mesh. At this time Garfield and Wilfley tables were used ahead of flotation and a good deal of the coarse mineral removed prior to the ball mill regrind. Shortly afterwards, mill-scale tests developed the fact that on a feed containing not over 10 per cent. +65¬mesh material flotation alone would give a copper recovery equal to that obtained by the combination of tables and flotation, but that on much coarser feed the recovery with flotation alone was lowered. This was at a time when all the sulfide minerals were floated if possible, so that the only requisite was to grind fine enough to free the mineral from gangue. EARLIEST USE op MICROSCOPIC EXAMINATION OF TAILINGS As early as 1921, the writer had attempted to determine by chemical analysis the relative proportions of copper minerals in tailings from an ore that made extremely poor flotation results. Chemical analysis was not satisfactory or conclusive, and samples of these tailings were sent to the U. S. Bureau of Mines Station at the University of Utah for micro-scopic examination. The question at that time was to determine, if possible, which copper minerals had been lost and why, but R. E. Head, in his report, revealed other interesting data. He said in part: Briefly stated, the mineral particles or grains may be classified into separate groups as follows: 1. Free grains of pyrite, chalcopyrite, chalcocite and bornite, respectively, which contain no other included sulfides; 2. Grains in which all three of the copper sulfides are represented (the core may he of chalcopyrite, partially altered to bornite, these two minerals being entirely surrounded by a shell of chalcocite); 3. Grains composed of equal amounts of bornite and chalcocite or chalcopyrite and chalcocite.

Jan 1, 1929

By William E. Ford, Edward Salisbury Dana

The important BARITE GROUP is the only one among the anhydrous sulphates and chromates. Mascagnite. Ammonium sulphate, (NH4)2S0,. Orthorhomhic. Usrially in crusts and stalactitic forms. p = 1.523. Occurs about volcanoes, as at Etna, Vesuvlus, etc. Taylorite. 5K2SOa.(N&)ySOd. 111 small compact lumps or concretions. From the guano of the Chincha Islands. Thenardite. Anhydrous sodium sulphate, Na2S04. In orthorhombic crystals, pyrarnidal, short prismatic or tabnhr; also as twins (Fig. 384, p. 160). White, to brpwnish. 0 tically +. p = 1.477. Soluble in water. Often observed in connection with salt lates, as on the shores of Lake Balkhash, Central Asia; similarly elsewhere; also in South America in Tarapaca, Chilc. In the United States, forms extensive deposits on the Rio Verde, Aria. In Cal., at Borax Lake, San Bernardino Co. Aphthitaiite. Arranite. Glmerite. (Ii,Na)&O1. Rhombohedral; also massive, in crusts. Color white. From Vesuvius, upon lava; at DouglashaU near Weateregeln, Ger- many, in hloditc; Stassfurt, Germany; Rocalmuto, Sicily.

Jan 1, 1922

Jan 1, 1899

By M. L. Samuels

In a recent paper the authors1 discussed the reactions to tempering of hypereutectoid steels quenched from 1000' C., as revealed by studies on changes in hardness, electrical resistivity, coercive force and metallo-graphic charaeteristics. The data, which related specifically to tempering temperatures of 550°, 650" and 710" C., for varying periods up to 125 hr., permitted the following important conclusions: 1. The rate of softening of the steels at the temperatures examined differed markedly although the steels were of "similar" general chemical composition. 2. The temperature of maximum softening spread over a range from about 650" C, to the eutectoid inversion. 3. The divergence in behavior was ascribed, at least in part, to a profound difference in tendency to graphitization on annealing at sub-eutectoid temperatures. 4. The mode of spheroidization of the cementite, as revealed by metallographic studies, also varied considerably in the different steels. The purpose of the present investigation is to pursue further the study of the difference in behavior of the steels on tempering over a wider range of temperature. To this end the following features have received particular attention: 1. Comparison of temperatures of maximum softening of the various steels when the quenched samples were tempered for 5 hi. and for 75 hr. followed by furnace cooling and by quenching in water. 2. Deterrnirlation of the effect of quenching temperature, prior to tempering, on the rate of softening. Quenching temperatures of 1000" and 850" C. were used in the investigations. 3. Examination of the microstructures obtained with the various heat-treatments employed.

Jan 1, 1938

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By M. L. Samuels

In a recent paper the authors1 discussed the reactions to tempering of hypereutectoid steels quenched from 1000' C., as revealed by studies on changes in hardness, electrical resistivity, coercive force and metallo-graphic charaeteristics. The data, which related specifically to tempering temperatures of 550°, 650" and 710" C., for varying periods up to 125 hr., permitted the following important conclusions: 1. The rate of softening of the steels at the temperatures examined differed markedly although the steels were of "similar" general chemical composition. 2. The temperature of maximum softening spread over a range from about 650" C, to the eutectoid inversion. 3. The divergence in behavior was ascribed, at least in part, to a profound difference in tendency to graphitization on annealing at sub-eutectoid temperatures. 4. The mode of spheroidization of the cementite, as revealed by metallographic studies, also varied considerably in the different steels. The purpose of the present investigation is to pursue further the study of the difference in behavior of the steels on tempering over a wider range of temperature. To this end the following features have received particular attention: 1. Comparison of temperatures of maximum softening of the various steels when the quenched samples were tempered for 5 hi. and for 75 hr. followed by furnace cooling and by quenching in water. 2. Deterrnirlation of the effect of quenching temperature, prior to tempering, on the rate of softening. Quenching temperatures of 1000" and 850" C. were used in the investigations. 3. Examination of the microstructures obtained with the various heat-treatments employed.

Jan 1, 1938