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By A. L. Mular

The flotability of crushed zinc oxide pellets which were doped to produce more n-type or less n-type (more p-type) properties was studied with a Halli-mond tube. Flotation data are presented to show that the pH at which 50% recovery occurs and the collector concentration for 50% recovery depends upon the concentration of doping agent added substitu-tionally for zinc in zinc oxide. The time of sintering of pellets has a slight effect on flotation behavior. A speculative model is proposed to explain the observed behavior in light of the fact that zinc oxide is a semiconductor and has a space charge region at the surface. Experimental verification is necessary before the proposed model can be established as correct. In recent years, the attachment of flotation reagents to minerals has been shown to depend upon the behavior of an electrical double layer which exists in the liquid near the mineral-liquid interface.' Thus, a mineral placed in water will undergo a surface re-arrangement, most likely be preferential dissociation of lattice atoms or by surface adsorp-tion-desorption reactions, to form a dissociation electrical double layer with the solution. Among the many factors which influence adsorption processes, the past history of the mineral itself is one of the most important. Because of trace impurities, minerals from different localities may exhibit marked differences in flotation behavior. This is not unexpected, since investigators who have studied the detailed structure of the double layer's3 have known for some time that the impurity content of many minerals may exert strong influence on double layer variables. For this reason, their studies were usually made with minerals of high purity. The precise relationship between impurities in a mineral and double layer parameters such as capacity and electrostatic potential has been obscure. However, impurities in a semiconductor type mineral which is in contact with a solution have been recently shown to produce changes in the properties of a space charge layer which extends into the bulk of the semiconductor to a distance of one micron or more.4 The double layer is influenced by the space charge layer, whose origin is best discussed in terms of the band theory of solids. A qualitative description of the behavior of impurities in the bulk of a semiconductor, from a chemical point of view, is useful at this point. Briefly, impurities or defects (lattice vacancies, interstitials, etc.) in semiconductors such as PbS, ZnS, FeS2, Cu2S, NiS, NiO, Fe2O3, ZnO, CdS, MnO2 and many others, behave somewhat like acids or bases in water. For example, water dissociates into hydrogen and hydroxyl ions according to

Jan 1, 1965

By D. K. Atwood

Experiments resulted in a satisfactory laboratory method for restoring permeability to clay-containing cores damaged by fresh water. Clay contents of a number of field cores were measured, and permeabilities of plugs from these same cores were then deliberately reduced with fresh water. This damage is attributed to swollen and dispersed clays occupying the pore space. After damaging, a number of experiments were performed to meaJure the amount of damage and to establish some means by which permeability could be restored. The experiments included flooding the damaged cores with water-miscible fluids such as salt water, acetone, isopropyl alcohol and ethanol. Permeability was not successfully restored in these experiments. However, part of the damage was repaired by flooding with oil; when water was removed by distillation in the presence of immiscible fluids such as air or toluene, permeability was completely restored. This evidence suggested that swollen and dispersed clays could be collapsed to their original volume by strong interfacial and capillary forces. It was further postulated that the required forces could be generated by flooding the damaged cores with a solvent partially miscible with water. The flooding experiments were repeated using n-hex-an01 as the partially miscible solvent. Permeability was restored to five of six damaged cores and substantially increased in the sixth. A large fraction of the restored permeability was retained even after water saturation was raised to its original value with 12 per cent salt water. INTRODUCTION Sharp reductions in permeability often occur when relatively fresh water contacts clay-containing formations during drilling and workover operations. These permeability losses are caused by removing inorganic ions from the environment surrounding the clay, and consequent swelling and/or dispersion of clay minerals into the available pore space.' This phenomenon is generally termed clay damage, fresh-water damage, or simply formation damage; it causes large losses in current revenue by preventing oil wells from making their allowable production. Attempts to repair the damage and restore permeability by flowing salt water solutions or brines through clay-damaged cores containing montmorillonite have been unsuccessful.' This irreversibility is thought to result from formation of brush-heap, or edge-to-face, structures when the dispersed clay is flocculated. The brush-heap structures occupy much more space than the close packed domains present before damage.' One solution of the problem is to destroy the clay-water brush-heap and thus restore permeability. Because no satisfactory method existed for restoring permeability to clay-containing formations damaged by fresh water, the work described in this paper was under taken. The laboratory experiments generally consisted of deliberately damaging fresh cores containing clay and then attempting to repair this damage by various means. Results indicate that generating strong interfacial forces within the pore space of damaged cores collapses the clay brush-heap and restores permeability. These forces are most conveniently generated by flowing partially water-miscible solvents, such as n-hexanol, through a core. THEORY OF THE DAMAGE PROCESS The most common clay mineral groups known to cause permeability damage to formations are the mont-morillonites, kaolins, chlorites and illites. These clays are constructed of particles which can adsorb water on their surfaces and edges and, in the case of montmorillonite, between layers of the basic particle itself. This adsorption increases as water salinity decreases. At low salinities the particles disperse into the aqueous phase. When the clays present in the formation are kaolin, chlorite and illite, dispersion accounts completely for permeability damage to porous media. However, unlike the other clays, montmorillonite particles can imbibe water and adsorb ions between layers of sub-particles, or platelets. These platelets have net negative charges on their faces and are held together by exchangeable (or removable) cations such as Na and Ca decrease in ion concentration (salinity) in the fluid surrounding a particle causes migration of water into the clay layers and disperses the basic particle, while diffusion removes the original exchangeable ions from between the platelets. Once these ions are removed, the facing negative platelets repel each other, causing the montmorillonite to swell until, for all practical purposes, the individual platelets are dispersed. For this reason, fresh-water* damage is much more severe in sands containing montmorillonite than it is in sands containing other clays. Many investigators have shown that even trace amounts of montmorillonite can be responsible for marked reduction in the permeability of reservoir sands in the presence of fresh water." ." Monaghan and others have shown that fresh-water damage in montmorillonite-containing cores cannot be

Jan 1, 1965

Jan 1, 1949

By J. R. Campbell

IN order to discuss the subject intelligently, it will be necessary to touch briefly on the forms in which sulphur is supposed to exist in coking coal to be carbonized in beehive or byproduct ovens. Sulphur is known to exist in coal as sulphides and sulphates, as can be determined experimentally. Then there is the so-called organic sulphur, i.e., sulphur in combination with the carbon, hydrogen, and oxygen of the coal, about which much has been written, but nothing definitely proven in an experimental way. In fact, so far as we know, there never has been developed a satisfactory and conclusive method in the laboratory for the direct determination of organic sulphur. For most coking coals, it can be safely assumed that the preponderance of sulphur is in the form of pyrite (FeS2). When exposed to comparatively low temperatures during the coking process, it loses its sulphur according to the following chemical reaction: 7FeS2 = Fe7S8 + 6S. It will be seen, therefore, that six out of the 14 atoms of sulphur (or 42.8 per cent.) are expelled, or volatilized. Fe7S8 remains in the coke as pyrrhotite, or magnetic sulphide of iron; this accounts for the highly magnetic properties of the powdered coke. A more commonly accepted reaction is FeS2 = FeS + S, in which the straight sulphide of iron is produced with 50 per cent. volatilization of sulphur. In the beehive methods of coke making, air is introduced in sufficient amounts to carry on the distilling and the coking processes, and the sulphur is oxidized along with the other volatile products: First, into sulphur dioxide (SO2), known by the pungent and suffocating odoremitted from the trunnel head; second, into sulphuric anhydride (SO3); and, finally, into sulphuric acid, as it comes into contact with the air and moisture. In a properly regulated draft on a beehive oven, there is never complete combustion of the gases. In other words, the coking process should be carried on in a reducing atmosphere, and a low-grade producer gas kept issuing from the trunnel head. For coals of about 30 per cent. volatile matter, the ratio of air to gas is 3 ½ to 1. In complete combustion, the ratio is 6 to 1, producing an extremely high temperature

Jan 1, 1916

By William Kent

(Read at the Philadelphia Meeting, February, 1878.) IN the paper by Mr. Fernow, on Red Charcoal, read at the first session of this meeting, it was suggested that this fuel might be used in the blast furnace with greater economy than ordinary or black charcoal. In the discussion which followed the paper, it was stated that the charcoal furnaces of the Lake Superior District have used imperfectly burned charcoal with success, and that these furnaces have given the best results in fuel economy on record. On consulting some of our well-known metallurgical authorities the writer finds that the question of the use of red charcoal, or other imperfectly burned charcoal, or charred wood, is not at all new. In Percy's late work on Fuel, pages 409-414, are given a few facts, which are here condensed, as follows:

Jan 1, 1878

Total U.S. mineral production reached an estimated $17.8 billion for 1960, 4 pct above 1959 and second only to the record high of $18.1 billion established in 1957. As a group, metals achieved a rise from $1.6 billion in 1959 to $2.0 billion this year, an increase of 28 pct. Similarly the value of nonmetallic production including fuels (i.e., natural gas, petroleum, natural-gas liquids, asphalt and related bitumens, carbon dioxide. anthracite. bituminous and lignite coal, peat, and helium) rose from $15.5 billion in 1959 to approximately $15.8 billion in 1960. However, this 2 pct increase in the total value of non-metallic production was due to an increase in the value of the fuels ($11.8 billion in 1959 to $12.2 billion in 1960) which offset a drop in value of the other nonmetallic minerals ($3.7 billion in 1959 to $3.6 billion in 1960).

Jan 2, 1961

By E. C. Bitzer

THE primary object of the work described in the following pages was to simplify the equipment in the separating circuit of the heavy-media process by substituting a spiral classifier for the separatory cone. Mechanical considerations were the leading attraction and the best that was hoped for on metallurgical performance was that the new vessel would give results equal to those obtained by conventional equipment. Tests have demonstrated in commercial operation on iron ore that the mechanical advantages of the spiral separator are about as predicted; also, the metallurgical performance is superior to the cone on the ores treated. Treatment of iron ore involves the separation of two products: a concentrate that sinks and a float product that contains true float material plus a controlled division of interfering middling. The middling material is heavier than the average specific gravity of the separating medium. Recent work with the spiral separator on Tri-State zinc ore showed that the middling material had to be recovered as concentrate because this fraction contained the bulk of the-zinc in the ore. It has been demonstrated that it is possible to make three products with the new separator on an ore such as this: a float tailing, a float middling, and a high grade heavy sink product. It appears from this last work that the new separator has definite mechanica1 and metallurgical advantages over any type of separating cone for treating feed that contains large amounts of material of a specific gravity close to that of the separating medium. However, either type of separator should perform equally well, metallurgically, on feed that is free of middlings. Each series of experiments with the spiral separator as required additional work to fully develop the possibilities of the machine. For this reason the paper is divided into chronological parts. History of Development A drag-type classifier was first proposed as a substitute for the cone separator by Butler Brothers technicians during the initial tests with galena medium at Crosby, Minn., in 1937. The desire for finding a substitute for the cone arose from trouble with interfering middlings and certain operating disadvantages of the cone. The possibility of using a spiral classifier was also suggested at this time by Emmett Butler and C. J. Abrams. However, inability to satisfactorily recover fine galena, which was used as a medium, terminated all development work at Crosby. During the winter of 1937--1938 investigation started on magnetic medium with concurrent s development of the inverted or closed- top cone, which was found necessary to eliminate iron-ore middlings with the float product. About

Jan 1, 1947

By David J. Selleck, Eugene P. Pfleider

9.61. Introduction. Open pit mining methods produce more than 80% of all raw materials today in the United States. Much of this comes either from properties that formerly employed underground methods and were converted to open pit or from mines that ultimately must go underground when the economic stripping limit is reached. Generally the ores are transported over large vertical distances and techniques have been developed to do this economically. One approach is to combine conventional surface trucking, over relatively level roads, with the use of gravity and underground facilities. There are various modifications, depending upon the character of the orebody and the topography. Several schemes, as used in Sweden, Canada, and the United States, merit describing. One of the critical problems involved in the transference of ores from surface to underground is that of flow of bulk solids. Must it be crushed? Will it hang up in the transfer? What size and inclination of ore pass are required. How is the ore best fed onto the transporting device underground? As an example, the planning engineers for the Carol Project of the Iron Ore Company of Canada faced these problems in making their designs for the production and transportation of some 55,000 tpd from their Smallwood Mine in Labrador. Other operations, facing somewhat similar conditions, used other approaches of interest. This chapter describes some of the factors involved in the design, construction, and operation of a combination surface underground transportation system as applied to open pit mining operations. 9.62. Tunnel-Ore Pass Systems. The type, shape, dip, and size of the orebody, as well as the surface topographic features, generally estab-

Jan 1, 1968

By D. D. Bolstad, S. M. Dar, T. W. Smelser, H. C. Pettibone

The use of roof bolt supports has reduced the number of fatal and nonfatal roof fall accidents in coal mines. Roof fall accidents, however, still occur far too frequently. Roof bolting plans are based almost entirely on trial and error, which inevitably leads to underdesign or overdesign with regard to bolt length, spacing, tension, and bolt type for the specific conditions. Underdesign poses safety problems, and overdesign leads to unnecessary costs. Guidelines are needed to select and design optimum roof-bolt plans that will maximize safety and minimize cost. Despite the use of 100 million roof bolts per year, the theory of roof bolting remains underdeveloped. Underground tests designed to provide this knowledge have been only partially successful owing to the many uncontrollable geologic variables present in underground mining situations. The Bureau of Mines believes that the best approach is to conduct a laboratory model study in correlation with finite-element analysis (FEA) and field verification, where these variables can be tightly controlled and measured. A physical model allows precise performance measurement of different bolt types as a function of a wide range of precisely measured parameters. Although the model being used is idealized and limited in size, it serves as a reliable basis for confirming the mechanism of rock reinforcement by bolting and the accuracy of the computer FEA approach to modeling mining problems.

Jan 1, 1984

By P. Barnes

If it be admitted that the use of the metric system of measurement is desirable, and that it will be well, as urged by one of our engineering societies, to show upon all our plans or drawings a metric scale in addition to a scale of inches, then it becomes important to introduce some ready means of drawing these scales. For many present purposes it is quite sufficient to space off and to draw them with the common dividers and the right-line pen, but if the number of drawings made or copied in an engineer's office, and upon which scales must be shown, is more than two or three daily, then some more mechanical or automatic means should be provided. For a great majority of detail drawings, a simple transcript of the surface of a good two-foot rule would answer every purpose, and probably the best comparative showing of the metric scale would be made by drawing a line of millimeters close by the side of the line of sixteenths. This would be in fact little more than the

By N. G. Johnson

ALL of us are only too familiar with the fact that first the defense program, and finally the war, required vastly increased production from existing sources, and the discovery and development of new sources of minerals and metals. For this vast program, the explosives industry was well prepared. I use the term "well prepared" to cover all the phases of explosives service, which include formulation, design, manufacture, distribution, and application.

Jan 1, 1944

By Wallace W. Wilson

This DaoerAA calls to attention for the first time, to the writer's knowledge, a purported recovery of oil by substantially horizontal gas cycling that is considerably in excess of 50 per cent of the oil originally in place. The average angle of dip along the path of travel of the gas is less than one degree of arc. The best recovery by gas cycling previously brought to the writer's attention1 occurred in the case of the Mile Six Field in Peru, where about 68 per cent of the original oil in place has so far been recovered. In this case, however. the recovery was greatly aided 1)y the high dip angle of about 17.5". An approximate estimate of recovery was made by the method developed by the writer' for the case of the Cook Ranch Field, using an average relative permeability ratio function dictated by past experience with a number of good quality sandstones. A result of about 40 per cent recovery of the original oil in place wa* obtained after the 8.5 pore volumes of cumulative gas cycling undergone by the Cook Ranch Field. Tile writer desires to emphasize what appears to him as the sound engineering practiced at Cook Ranch, and also the care attending the taking of data and the high quality of the calculations made. It is impossible to take issue on factual grounds with any of the conclusions drawn in the paper. It is, however, desired to point out the difficulty of explaining the unexpectedly favorable oil recovery on ordinary theoretical grounds. It would be of interest to know whether relative permeability ratios have been measured on the Cook sand. The operator is inclined to attribute some of the excess benefit to settling of the oil across the bedding planes into the lower part of the sand. It is difficult for the writer to appreciate the importance of such an effect, inasmuch as the concomitant opening of excessive vacated pore space in the upper part of the sand would he expected to cause excessive bypassing of the gas. REFERENCE 1. Welge. H. J.: "A Simplified Method for Computing Oil Recovery by (Gas or Water Drive." Trans. AIME, (1952), 195, 91. AUTHOR'S REPLY TO MR. WELGE Welge has poined out clearly the difficulty of applying material-balance procedures in calculating the Performance of low-pressure, dispersed gas injection operations. There can be no argument that even with the most favorable assumptions of K,/K,, and with cumulative gas cycling in excess of normal expectations, the calculated oil recovery will be considerably less than the 72.5 per cent recovery realized from this project to Jan. 1, 1951. There probably are at least two reasons for the unusually high recovery from this reservoir, the effects of which would be difficult or impossible to calculate by known methods: 1. The operator did not use the same injection wells for the entire operation, and exercised considerable control over producing GOR by changing the locations of injection wells whenever well performance indicated excessive bypassing. Fifty-six wells were used for injection, not over 29 of which were in use simultaneously. This procedure resulted in frequent shifting of the fluid movement patterns in the reservoir and undoubtedly increased the ultimate recovery. The writer knows of no satisfactory procedure for calculating the effect of this practice. 2. Vertical movement of oil across the bedding planes of the reservoir rock hy gravity drainage tended to maintain a relatively high oil saturation, and hence a favorable K,/K, ratio, in the lower sections of the reservoir. As pointed out by Welge, this condition has aggravated the tendency for high producing GOR, but at the same time it has resulted in increased oil recovery. As may be seen from the performance charts for the various battery areas, operating (GOR'S have been quite high for the last several years of reported history.

Jan 1, 1952

By John T. Norton

FoR many years the copper-bearing steels have been of considerable interest to the metallurgist because of their corrosion-resistant properties. More recently the discovery of their definite age-hardening characteristics has focused attention on them again. In a recent paper, Smith and Palmer(l)† have given an admirable description of the behavior of a considerable number of steels of this type and a study of their results suggests two questions of a more or less fundamental sort. In the first place, it has been plainly shown that the hardening effect of added copper does not increase up to the maximum solubility of copper in iron as given by earlier investigators, but reaches its greatest value considerably below this point. This fact suggests that either the solubility is not so great as previous investigators have stated, or that the age-hardening mechanism is not the simple precipitation phenomenon that has been postulated. In the second place, the nature of the aging mechanism in this particular system should be determined. Recent developments in the study of age-hardening processes have shown that the increase of hardness is often, but not always, accompanied by precipitation and the action of a particular system is not predictable on the basis of its components or type of phase diagram. It would be of considerable interest to study the aging of the iron-rich iron-copper alloys in detail. One would like to know whether the aging mechanism is different at high and low aging temperatures, and whether the extreme sluggishness of the system may perhaps represent some new type of aging process. The experiments to be described were carried out in an endeavor to answer these questions. Obviously, in such experiments it is important to confine the hardening effect to the single element, copper, so that iron and copper of high purity must be used in the preparation of specimens. An observation of lattice changes during the aging process, correlated with the hardness changes, seems to be the best available method of

Jan 1, 1935

By John T. Norton

FoR many years the copper-bearing steels have been of considerable interest to the metallurgist because of their corrosion-resistant properties. More recently the discovery of their definite age-hardening characteristics has focused attention on them again. In a recent paper, Smith and Palmer(l)† have given an admirable description of the behavior of a considerable number of steels of this type and a study of their results suggests two questions of a more or less fundamental sort. In the first place, it has been plainly shown that the hardening effect of added copper does not increase up to the maximum solubility of copper in iron as given by earlier investigators, but reaches its greatest value considerably below this point. This fact suggests that either the solubility is not so great as previous investigators have stated, or that the age-hardening mechanism is not the simple precipitation phenomenon that has been postulated. In the second place, the nature of the aging mechanism in this particular system should be determined. Recent developments in the study of age-hardening processes have shown that the increase of hardness is often, but not always, accompanied by precipitation and the action of a particular system is not predictable on the basis of its components or type of phase diagram. It would be of considerable interest to study the aging of the iron-rich iron-copper alloys in detail. One would like to know whether the aging mechanism is different at high and low aging temperatures, and whether the extreme sluggishness of the system may perhaps represent some new type of aging process. The experiments to be described were carried out in an endeavor to answer these questions. Obviously, in such experiments it is important to confine the hardening effect to the single element, copper, so that iron and copper of high purity must be used in the preparation of specimens. An observation of lattice changes during the aging process, correlated with the hardness changes, seems to be the best available method of

Jan 1, 1935

Executive JVW REYNOLDS, Chairman SYDNEY H BALL E DEGOLYER WILLIAM H BASSETT SAMUEL A TAYLOR Finance GEORGE D BARRON, Chairman H A GUESS GEORGE OTIS SMITH Membership ] H CALLOW, Chairman GEORGE D BARRON WILBER JUDSON JOHN A CHURCH, JR H N SPICER Alternates LEWIS W FRANCIS LOUIS D HUNTOON F T RUBIDGE

Jan 1, 1923

US 4,185,077 - In the recovery of uranium from a solution produced by leaching uranium ore, the leach liquor is contacted with a polymeric crosslinked vinyl benzyl chloride anion exchange resin and eluted with sulfuric acid to recover uranyl sulfate Such a resin is resistant to attrition and thermal degradation during elution. R.L. Albright, assigned to Rohm & Haas Co Jan. 22, 1980. 6 pp (423-7). Filed: 10-31-75 (627,829).

Jan 1, 1982

By P. Barnes

IF it be admitted that the use of the metric system of measurement is desirable, and that it will be well, as urged by one of our engineering societies, to show upon all our plans or drawings a metric scale in addition to a scale of inches, then it becomes important to introduce some ready means of drawing these scales. For many present purposes it is quite sufficient to space off and to draw them with the common dividers and the right-line pen, but if the number of drawings made or copied in an engineer's office, and upon which scales must be shown, is more than two or three daily, then some more mechanical or automatic means should be provided. For a great majority of detail drawings, a simple transcript of the surface of a good two-foot rule would answer every purpose, and probably the best comparative showing of the metric scale would be made by drawing a line of millimeters close by the side of the line of sixteenths. This would be in fact little more than the

Jan 1, 1877

By Sheldon P. Wimpfen

RESEARCH is undertaken to find out what must be done when what we are doing now is no longer adequate. To accomplish this end, researchers apply the truths of nature to industrial evolution. A survey conducted with the co-operation of 58 universities and colleges offering degrees in mineral engineering was the basis for the table accompanying this article. This survey was undertaken with the object of presenting to faculties and student bodies, as well as to industry, all available information on what action the educational institutions of the country have taken to provide the properly trained researchers so vitally needed. A hoped for result is that the great variety of opportunities available will encourage some undergraduate students to continue in their field beyond attainment of a B.S. degree.

Jan 1, 1947

S. F. EMMONS RESEARCH FELLOWSHIP. The movement was started by a number of the friends and admirers of the late S. F. Emmons, Economic Geologist of the United States Geological Survey, to perpetuate his name through a fellowship to be known as the ?S. F. Emmons Research Fellowship," and they have succeeded in raising some $13,000 for the purpose of carrying on research work in economic geology. The Committee in charge of this Memorial Fund has succeeded in obtaining the co-operation of Professors Kemp, of Columbia, Irving, of Yale, and Lindgren, of Massachusetts Institute of Technology, in the administration of this fellowship. These three gentlemen are respectively geologists of the institutions mentioned and are exceptionally qualified to determine in what direction the fund can be best administered. It is hoped that additional contributions will be forthcoming from many who have heard of this movement. Subscriptions are invited and may be sent to any one of these gentlemen, or to Benjamin B. Lawrence, Treasurer, No. 60 Wall Street, New York City.

Jan 10, 1913

By N. L. Svensson

The model developed by Tuylor for the calculation of Polycrystalline yield strength has been applied to the case of an aggregate hawing a preferred orientation. In general this procedure requires the specification of texture by means of weighting factors applied to specific orientations. The problem to which the model has been applied is that of the yield-strength aniso-tropy of cold-rolled aluminum whose rolling texture was described as a combination of (110)[112] and (311) [112] In this case yield-strength anisotropy is defined by the rutio of yield strength measured at an angle 8 to the rolling direction to that measured along the rolling direction. The method of calculation of yield-strength ratio as a function of ? is described and the results show good agreement with experimental values. The orthotropic yield criterion suggested by Hill has been applied to the results and the strain ratio R also calculated as a function of ?. This has been compared with calculations using the method suggested by Elias, Heyer, and Smith which does not exhibit suck good agreement with observation. one deficietlcy of the method presented is that the strain ratios used by are those applying to iso-Irobic materials. The method should therefore be reg-clrded only as a first abbroximation to the prediction of anisotropy. THE problem of calculating the stress-strain characteristics of polycrystalline aggregates from the properties of single crystals has attracted attention for a number of years. The most important contributions to this study have been those due to: Sachs,' Cox and sopwith,2 Taylor,3 Kochendorfer,4 Batdorf and Budiansky,5 Calnan and Clews,6 Bishop and Hill,7,8 Kocks,9 Budiansky, Hashin, and sanders, 10 Kroner,11 Cyzak, Bow, and payne, 12 Budiansky and Wu,13 and Lin.14 While the earlier work has been largely superseded, recent developments tend to support Taylor's solution" within the restriction imposed by his assumptions. The essential features of Taylor's approach were: 1) the material is rigid-plastic; 2) each grain experiences the same strain components as the aggregate as a whole (the problem was that of uniaxial deformation with principal strain components in the ratio 3) all regions of each grain deform uniformly; 4) work hardening occurs equally on all slip systems. While Bishop and Hill7 have generally validated this approach, there has been some criticism offered. Kocks? as pointed out that since multiple slip must occur the single-crystal data must be determined from orientations arranged such that polyslip takes place. Boas and Hargreaves,15 and others, have shown experimentally that the strain distribution within grains is not uniform, the strains in the vicinity of grain boundaries being less than those in the center of the grains. Both of these criticisms can be largely offset by the suitable choice of single-crystal critical shear stress. However, for the problem analyzed below, the critical shear stress is not directly used and, consequently, these criticisms lose their importance. The more recent contributions have attempted to obtain a more complete analysis by considering an elas-toplastic material and considering interactions between grains of differing orientations. Lin14 has considered the early stages of yielding for a polycrystalline aggregate having specific regions of defined slip plane orientations. On the other hand, Budiansky and Wu13 have allowed for these interactions for randomly disposed grain orientations and have calculated the polycrystalline stress-strain curves for crystals exhibiting either elastic-ideally plastic or kinematic hardening characteristics. This work has shown that yielding commences when the macroscopic stress is 2.2 times the critical shear stress for slip in a single crystal (7,). The yield stress-strain curve then rises becoming asymptotic to a value of 3.072 7,. This is close to the value obtained by Bishop and Hill (3.06) in their confirmation of Taylor's method. This, of course, is to be expected since, at large strain values, the elastic strains are negligible and the rigid-plastic model is satisfactory. The results of Budiansky and Wu indicate that the result obtained by Taylor is 7.7 pct high at a plastic strain which is two times the elastic strain at the initiation of yield. By defining the anisotropy in terms of relative values, the ratio of yield strength at orientation ?, to that measured in the rolling direction, the effect of the discrepancy in Taylor's solution is considered to be of lesser consequence. Therefore, it is anticipated that an analysis based on Taylor's solution, which can be quite straightforward, should provide a reasonable estimation of the anisotropy of materials having a preferred orientation texture. OUTLINE OF TAYLOR'S METHOD In fee metals there are four possible slip planes (the octahedral planes) and in each there are three possible slip directions (the edges of the octahedron), that is a total of twelve possible slip systems. von Mises16 has shown that at least five independent slip systems must become operative in each grain of the polycrystalline aggregate in order to preserve continuity of strain. With this geometrical requirement as basis and the assumptions previously listed, Taylor determined the operative slip systems for a number of orientations of the tensile stress axis specified in the unit stereographic triangle. For the ith slip system, the critical shear stress

Jan 1, 1967