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By W. B. Morrison

The principal factors influencing the total percent elongation of a lead-tin eutectic and several low-alloy steels which exhibit superplasticity were investigated. These factors are: a) Strain-rate sensitivity of the stress (m). b) Specimen geometry; in particular, diameter-to-length ratio (d0/l0), and surface irregularity (e.g. notches). A feature of the tensile deformation of a superplastic alloy is the early appearance of a neck which continues to extend throughout the test. As a result the total elongation is directly related to the diameter-to-gage-length ratio. The strain-rate sensitivity of the stress varies during extension, mainly because of microstruc-tural changes. A satisfactory correlation exists between the minimum strain-rate sensitivity and total elongation, as indicated in the equation shown below. Notches cause a considerable reduction in total elongation and their effect is greatest at high values of strain-rate sensitivity. An initial notch depth exists below which there is no appreciable effect on elongation. An equation relating elongation to strain-rate sensitivity and specimen geometry is proposed, THE total percent elongation of a tensile specimen is usually regarded as a measure of superplasticity. However, little attention has been given to the fact that total elongation is also a function of specimen diameter and gage length, even though the importance of geometry has long been recognized in the tensile testing of materials in which elongations are relatively small.* In the present study, the effect on superplas- tic extension of the ratio of specimen diameter to length was investigated and an analysis was made of strain distribution along the gage length. Superplastic alloys are characterized by having a flow stress sensitive to strain rate but relatively insensitive to strain.2"' In an earlier study,5 it was found that the strain-rate sensitivity of several low-alloy steels changed during the test and that the minimum value correlated best with total elongation. In the present study, the variation of strain-rate sensitivity during the straining of a lead-tin alloy was investigated. EXPERIMENTAL PROCEDURE Lead-tin eutectic alloy (32 pct Pb 68 pct Sn), made from high-purity lead and tin, was cast in the form of 1-in. diam rod. The rod was cold-rolled in stages to 0.25 in. diam and then swaged to 0.125 in. diam. Samples were cut from the rod at various stages of the mechanical working process. Tensile test specimens were then made by attaching threaded steel ends to the rods by an epoxy-base thermosetting adhesive which required a setting treatment of 2 days at room temperature. The rods were seated in the steel ends in holes approximately 0.01 in. oversize. The test pieces thus made were of various diameters and gage lengths. These were stored at a temperature of about -70°C (-94°F) until required for testing. The distribution of strain along the gage length of a specimen was determined at various stages of the tensile test. The lead-tin alloy was superplastic at room temperature and direct observations during testing were simple. The gage length was divided by reference marks into five initially equal units. These reference marks were made with ink and were reinforced during the test when the initial marks became faint. Photographs were taken, at intervals, of the deforming specimen and measurements of the elongation in each of the gage units were made on these photographs. Tests were also done on several superplastic low-alloy steels whose properties were described earlier.5 The chemical compositions of these steels are given in Table I. A diagram of the notched tensile specimen used in the steel tests is shown in Fig. 1. The specimens were tested at 900°C (1650°F) in a furnace through which a mixture of He + 2 pct H was continuously circulated.5 RESULTS Strain Distribution. Approximately 20 tests on lead-tin alloy specimens were conducted to determine the strain distribution during the test. An example is shown in Fig. 2 of the strain distribution in the gage

Jan 1, 1969

By R. L. Fullman, J. W. Cahn

A method is derived for obtaining the distribution of sphere diameters and plate thicknesses (or pearlite spacings) from size distribution functions obtained along randomly oriented lines. The method described offers several advantages over existing methods. IT is often of interest to measure not only the average particle size but also the distribution in sizes of particles dispersed in an opaque material, such as an alloy. Particles of a single size will exhibit a range of apparent sizes on the plane of polish. If the sample contains a distribution of particle sizes, the distribution of observed sizes on the plane of polish is related to the distribution of actual particle sizes by an integral equation, For example, a distribution of sphere sizes, N(r),

Jan 1, 1957

By Herbert R. Hanley

THE One Hundred and Twenty-sixth meeting-of the Institute, held in San Francisco, Sept. 25 to 29, 1922, was a success in every way. Character-istically, San Francisco presented climate suited, to the occasion, while the Committees on Arrangements left nothing undone that would contribute to the interest and entertainment of the members and their wives. There was a registration of over 230, and all sections, save three, were represented. In the technical meetings, under the leadership of Albert Burch in the mining session and C. W. Merrill in the milling session, the greatest interest was manifested in ore-hunting geology and modern ore-dressing methods. The general geologic phase developed numerous discussions and had for its aim the study and correlation of known data and the application-of these to the finding of commercial orebodies. The geologic features of the Comstock and their significance to the development of the present orebodies were discussed. This brought out matters of much technical interest as well as those of romantic nature in the history of the early life of that camp. The profitable application of modern milling methods to ores, non-commercial a short time ago, was discussed with much interest. The recent work on the Comstock ores occupied a conspicuous part in these discussions. Basic principles delineated by mathematical study of mechanical devices for the milling of ore came in for a prominent part in the program as well as the physical-chemical side of the processes devised for the winning of precious metals as a profit.

Jan 11, 1922

By Paul Hunt

UP TO June, 1923, the Park-Utah mine had shipped about 94,000 tons of a direct-smelting ore of a gross value of $4,200,000, or about $45. a ton. These values were in gold and silver only, although the ore carried small amounts of lead, copper and zinc. Freight, treatment and deductions had averaged $15.40 a ton. At the expiration of the Pittman Silver Act there was in sight about 30,000 tons of a similar ore with a gross value of about $15 a ton in gold and silver, and a large body of partly developed lead-zinc ore of a gross value of about $20 a ton, 40 per cent. of which was represented by the lead-zinc content and the balance by the silver and gold. Mine costs had been high during the life of the Pittman Act, but as a large part of the profits had gone into equipment of the mine and the orebodies were large and had good walls, we knew that mine costs could be greatly reduced. We were therefore faced by the necessity of getting lower freight and smelter rates or of concentrating the ore. We did obtain better freight rates on lower grade ore, and a favorable smelting rate on the small tonnage of siliceous silver-gold ore, but this smelter rate could not be applied to the lead-zinc ore with any profit to ourselves. The Judge mill of the Park City Mining & Smelting Co., with which we were affiliated, was running to capacity; if we built our own mill it meant a 5-mile freight haul to a satisfactory millsite and a year's delay. Fortunately, the International Smelting Co. had just inherited a mill at Tooele which, with some changes, was about double the capacity required for its own ores. Flotation tests were run on Park-Utah ore and a contract entered into with a low base treatment charge per ton, the tariff being largely fixed by the metallurgical deductions. This contract has been admirably calculated so that the miner can follow a lean orebody to its limit. Such a procedure has no doubt made it difficult for the smelting company at times, but it has resulted in finding ore extensions that otherwise might have been missed, so in the long run it has profited too. A flat rate per ton would have been like mining up to the claim endlines in a great many of the stopes. In order to offer such a contract it can be inferred that the smelting company must have been able to make high recoveries and high-grade products on a very lean ore.

Jan 1, 1928

By Paul Hunt

UP to June, 1923, the Park-Utah mine had shipped about 94,000 tons of a direet-smelting ore of a gross value of $4,200,000, or about $45. a ton. These values were in gold and silver only, although the ore carried small amounts of lead, copper and zinc. Freight, treatment and deductions had averaged $15.40 a ton. At the expiration of the Pittman Silver Act there was in sight about 30,000 tons of a similar ore with a gross value of about $15 a ton in gold and silver, and a large body of partly developed lead-zinc ore of a gross value of about $20 a ton, 40 per cent. of which was represented by the lead-zinc content and the balance by the silver and gold. Mine costs had been high during the life of the Pittman Act, but as a large part of the profits had gone into equipment of the mine and the orebodies were large and had good walls, we knew that mine costs could be greatly reduced. We were therefore faced by the necessity of getting lower freight and smelter rates or of concentrating the ore. We did obtain better freight rates on lower grade ore, and a favorable smelting rate on the small tonnage of siliccous silver-gold ore, but this smelter rate could not be applied to the lead-zinc ore with any profit to ourselves. The Judge mill of the Park City Mining & Smelting Co., with which we were affiliated, was running to capacity; if we built our own mill it ineant a 5-mile freight haul to a satisfactory millsite and a year's delay. Fortunately, the International Sillelting Co. had just inherited a mill at Tooele which, with some changes, was about double the catpscity required for its own ores. Flotation tests were run on Park-Utah ore and a contract entered into with a low base treatment charge per ton, the tariff being largely fixed by the metallurgical deductions. This contract has been admirably calculated so that the miner can follow a lean orenbody to its limit. Such a procedure has no doubt made it difficult for the smelting company at times, but it has resulted in finding ore extensions that otherwise might have been missed, so In the long run it has profited too. A flat rate per ton would have been like mining up to the claim endlines in a great many of the stopes. In order to offer such a contract it can be inferred that the smelting company must have been able to make high reeoveries and high-grade products on a very lean ore.

Jan 1, 1928

By W. L. McMorris, A. H. Brisse

IN the last several years the coal industry has intensified its effort to solve the growing problem of cleaning and recovering fine mesh coals. On one hand these has been increasing civic pressure for cleaner streams, and on the other hand there has been increasing production of fine mesh coal, resulting directly from adoption of the modern mining methods so essential to the economy of the coal mining industry. Cleaning fine coal with the same precision possible with coarser coals is a difficult task, and for coals finer than 200 mesh it has been impractical. Furthermore, the inclusion of —200 mesh material in the final product markedly increases costs of de-watering and thermal drying, which are necessary steps if coal is to meet market requirements. Consequently these extreme fines have generally been wasted. As a result, problems have been created in many districts because there has not been enough area for adequate settling basins. Wasting of coal in the -200 mesh slimes may account for a loss in washer yield equivalent to 2.0 to 2.5 pct of the raw coal input. With rising mining costs the value of such a loss is constantly increasing and a need for a better solution to the fines problem becomes more pressing every day. From an operating viewpoint, also, continuous removal of extreme fines from the washing plant circuit permits good water clarification practice, improving significantly the overall cleaning efficiency. The obvious desirability of recovering a commercially acceptable coal from washery slimes prompted U. S. Steel Corp. to investigate the merits of the Convertol process developed in Germany." Although this process has been used commercially in Europe for some time, little if any consideration has been given to its possible adoption in the U. S. until very recently. Fundamentals of the Convertol Process: In the Convertol process, droplets of dispersed oil are brought into intimate contact with the solids suspended in the coal slurry to be treated. This contact causes oil to displace the water on the surface of the coal by preferential wetting, or phase inversion, after which the coal particles are allowed to agglomerate in a manner permitting their re- moval from the slurry by centrifugal filtration. The clay and other particles of mineral matter suspended in the slurry do not have the affinity for oil the coal particles have. Consequently the oil treatment is preferential to coal to the extent that more than 95 pct of the oil used reports with the clean coal recovered. Figs. 1 through 3 will clarify the steps involved in the process. Fig. 1 shows the suspended material in the slurry to be treated, which is a thickened product containing 40 to 45 pct solids. Oil is now injected into the slurry under vigorous agitation to produce good oil to coal contact conditions, which result in preferential oiling of the coal particles. These coal particles are then permitted to agglomerate by gentle stirring in a conditioner to form flocs, as shown in Fig. 2. At this point in the process the agglomerated oiled coal can be washed and partially dewatered on a vibrating screen, as shown in Fig. 3. Finally, the washed flocculate can be further dewatered in a high-speed screen basket centrifuge or in a solid bowl centrifuge. Commercial Application of the Convertol Process in Germany: The original Convertol process was developed by Bergwerksverband zur Verwertung von Schutzrechten der Kohlentechnik, G.m.b.H., a German research organization controlled by the Coal Operators Assn. of the Ruhr Valley. The process as reduced to commercial practice in Germany' is shown in Fig. 4. In this process a thickened slurry (40 to 45 pct solids) mixed with a predetermined percentage of oil is fed from a surge tank to the phase inversion mill. After the phase inversion step, the slurry is usually discharged directly to a highspeed screen centrifuge. From 3 to 10 pct oil is used, depending on type of oil, size consist of coal to be recovered, and operating temperature. The top size of fine coal cleaned in Germany by the Convertol process is limited by the size of the openings in the centrifuge screen basket. Any mineral matter coarser than the basket opening, which is generally 60 to 80 mesh, must remain with the oiled coal. If the coal fines have been effectively cleaned down to about 80 mesh, the cleaning performance of the process is practically unaffected by the presence of coarse coal particles. However, since recovery of coal much coarser than 80 mesh is mow economical by conventional methods, it normally becomes more costly to allow substantial percentages of this coarse coal in Convertol process feed. Where the general plant layout does not permit effective cleaning of coal sizes down to 80 mesh or lower. there is some justification for a coarser Con-

Jan 1, 1959

By George Asmus

CLOSED front, or open front for blast-furnaces, has been for a number of years a much discussed question among the furnace-men in every country where iron is made. As blast-furnaces are costly structures, and as the whole question is one of economy, I hope to be excused for entering a little into details. The ('fore-hearth " is a prolonged opening in the lowest part of the hearth, from two to three feet wide, four to six feet long, and two to three feet high. It is a more or less fire-proof box, cooler than

Jan 1, 1876

By K. Verghese, R. W. Rousseau, R. P. Gardner

A radioactive tracer method and a size-discretized, mass balance model are formulated and demonstrated in a feasibility experiment for the determination of crystal growth rates in MSMPR crystallizers. The system studied is aqueous KN03 with K-42 as the radioactive tracer. The results indicate that the method should prove to be very valuable for this application, particularly when systems exhibiting size-dependent growth rates are of interest. An indicated refinement to the tracer method is the simultaneous use of an additional tracer in the liquid to determine the amount of radioactivity from the liquid that is adsorbed on the samples of filtered crystals.

Jan 1, 1980

By A. R. Troiano, E. A. Steigerwald, F. W. Schaller

The initiation of localized cracking in hydrogenated high strength steel was dependent on the developmeni of a critical hydrogen conceniration and relatively insensitive to the magnitude of the applied stress. The stress was believed to influence the deluyed failure process by providing the means for grouping the hydrogen. On the basis of an assumed distribution law the observed changes in the lower critical stress as a function of notch acuity, yield strength, and temperature were predictable over a significant range of these variables. THE phenomenological characteristics of delayed failure in high-strength steel have been comprehensively investigated and the behavior has been attributed to the strong embrittling action of hydrogen.1-3 Delayed failure or, as it is also termed, static fatigue, is the most sensitive means of detecting hydrogen embrittlement since it allows the maximum time for hydrogen diffusion during a test.3 The nature of delayed failure cail be aptly described by four parameters which are schematically depicted in Fig. 1. The upper critical stress corresponds to the rupture stress in a conventional notch tensile test. The lower critical stress or static fatigue limit is the stress below which no delayed failure will occur. The incubation period is the time required for the formation of the first crack and the fourth parameter is the failure time. An increase in hydrogen content, notch acuity, or strength level of the material increases the susceptibility for delayed failure by decreasing the lower critical stress, the incubation period, and the time to failure.lY3 A decrease in test temperature prolongs the incubation period in accordance with the lower diffusion rate of hydrogen, and also de-

Jan 1, 1961

By E. P. Polushkin

This work has for its purpose the establishment of a new method for determining the structural composition of alloys. The area occupied by a constituent on a few representative photomicrographs of the alloy is measured, by a planimeter, especially designed for metallographic work, and the volume and proportional weight of the constituent calculated. Experiments have shown that the results are accurate enough to justify the application of the method to many problems in metallographic research instead of chemical analysis. The advantage of the method is the possibility of determining the amount of the constituents without separating them from the alloy; their composition may also be determined if the ultimate chemical analysis of the alloy is known. Suppose Fig. 1 represents a part of a photomicrograph on which the total area of the black figures is to be found. By a system of parallel lines drawn short equal distances apart all figures may be divided into trapezoids. As the area of a trapezoid is equal to its median multiplied by its altitude, the relation between the total areas of the black and the white figures comprised within each strip is equal to the relation between the sums of medians for these figures respectively. This is also true for the whole area of the photomicrograph. Therefore, to determine the total areas of the black and white figures we must first find the proportion between the sums of the medians and then divide the area of the whole photomicrograph in the same proportion.

Jan 1, 1925

By AIME

COAL, its acquisition and consumption, has loomed large enough in the lives of many of us at one time or another, not from a technical standpoint, perhaps, but on a utility basis, to keep the house warm and the plant going. The Chairman of the Coal Division was much like many of us in that respect until after his graduation from Northwestern in 1928. Then he went to work as geologist for the Zeigler Coal Co., investigating strip coal possibilities in western Illinois, and also did research in the microscopy of coal at the Illinois Geological Survey. His interest in coal was originated and stimulated by Gilbert H. Cady, of the Illinois Geological Survey. With his advice, and with the co-operation of M. M. Leighton, Survey chief, the results of his research work on the mineral constituents of coal at the Survey were accepted as a thesis for his doctorate which he received from Harvard in 1935. Nine days before the Christmas of 1906, Clayton Garrett Ball was born at Wauconda, Ill. His father was professor of geology at Northwestern until he retired in 1946; retirement didn't lessen his active interest in his profession; he's still teaching geology at the University of Kansas City. So it was only natural for Clayton to study at Northwestern. In 1937, following a year's connection with the Bell &

Jan 1, 1948

Reynolds Jamaica Mines, Ltd., has received a $3+ million loan from ECA for the development of what are termed the largest bauxite deposits in the world in Jamaica, B.W.I. This amount is in addition to $11 million already provided. The new agreement calls for delivery of 750,000 tons a year beginning in early 1952. Inco has announced a new alloy containing 35 pet Ni which can be used for many purposes served by the old alloys which ran up to 70 pet Ni. The new alloy "Incoloy" is 35 pet Ni, 20 pet Cr, and the balance iron.

Jan 8, 1951

By Ira B. Joralemon

The sampling of disseminated copper deposits has been describeu often but the method of combining assays to give the true shape and value of the orebody as it will be mined has received less attention. As the ore mined during five or ten years at several of the great disseminated properties has averaged materially lower in grade than the published estimates, the question of the sampling and estimating of these orebodies seems timely. In this paper, attention is given particularly to factors that may cause errors in the final estimate. Sampling of diamond-drill holes, churn-drill holes, and underground workings is briefly described in the first part of the paper; then the method of combining assays to give the average grade and tonnage that will be mined is taken up in some detail. The necessity of study of the geology of the deposit and of probable costs is emphasized. Finally, the methods of calculating tonnages are outlined. DlAMOND-DRILL SAMPLING There are three main requisites for accurate diamond-drill sampling. First, the core should be removed and the hole cleaned out at the beginning of every sampling interval, usually 5 ft. (1.5 m.). After the rods are let down, water should be run through them until it becomes clear. The water must be clear before drilling starts. 'In this way the material knocked down from the sides of the hole by the descending rods is washed away, instead of being left to salt the sludge sample. The second requisite is to save all the sludge and all the core from every sampling interval. Where the material is uniformly heavy, the cuttings will settle suffciently in a box, through which the sludge flows s1owly.l Where part of the material is too light to settle readily, the sludge should be run into barrels, and allowed to settle until the water becomes clear. Then the clear water is siphoned off, and the sludge evaporated to dryness over a slow fire, sacked, and assayed.2 To obtain

Jan 1, 1925

THE refining period of an open-hearth heat blends imperceptibly into the finishing period, during which final adjustments are made in slag composition, in bath action and temperature, and in composition of the steel, in order to prepare it for casting into ingots. Operations must be governed by the consideration that alterations in the character of the heat during the finishing period must be held to a minimum. In a broad sense, the finishing and deoxidation period of a heat may be said to begin when the action of the last ore addition has ceased, and to end when the teeming of the ingots is completed. INGOT STRUCTURES A survey of the relative advantages and disadvantages of different types of ingot structure is required because deoxidation treatments during the finishing period control the amount of gas evolved during solidification and consequently determine the type of ingot structure. Four classes of ingots are recognized, depending upon the degree of deoxidation to which the steel has been subjected. These types are killed, semikilled, capped, and rimmed; typical examples of their structures are represented by ingots 1, 2, 5, and 7, respectively, of Fig 9-1. The actual ingots from which these cross sections were sketched were all poured to the same height (indicated by the dotted lines) in the same type and size of bottle-top molds. The eight drawings of the figure represent selected types of ingot structure in a continuous series from "dead killed" to "wild," resulting from variations in the total quantity of gas evolved, from none at all to copious amounts, during solidification of the steel in the mold. Killed and semikilled steels are adjacent at the "quiescent" end of the ingot structure series where only small amounts of gas are evolved. The term "quiescent" describes the action of the molten metal during and subsequent to the teeming of killed and semikilled steels. Capped and rimmed steels are adjacent at the

Jan 1, 1951

By P. Raffinot, M. Rey, V. Formanek, G. Sitia

Six years of laboratory study, followed by three years of mill operation treating more than 10,000 tons of ore, have established the flotation of oxidized zinc ores with fatty amines as an efficient process. Recently the method has been applied with success to partially oxidized sulphide ores. In this paper the authors give an account of their research and the milling results obtained in Sardinia since 1951. CONCENTRATION of oxidized copper and lead ores by flotation has been practiced for 30 years, but flotation of oxidized zinc ores has remained unsolved until a few years ago. This problem is, however, of great importance in mining districts where large tonnages of oxidized zinc ores exist in underground mines or in dumps. Some sulphide ores also possess a degree of oxidation high enough to justify recovery of oxide zinc minerals. Various attempts have been made to float the zinc carbonate, smithsonite. It is well known' that smithsonite can be collected with fatty acids, but as the predominant gangue constituents, limestone and dolomite. are floatable with the same reagents, fatty acids are difficult to use. Gaudin has shown,' on mixture of pure minerals, that smithsonite can be floated with higher xanthates, or better, with higher mercaptans. Another procedure, briefly mentioned by Davis," consists in sulphidizing the ore, activating the zinc carbonate with copper sulphate, and floating with ordinary xanthates. This process was attempted in the writers' laboratory in 1946, but results were erratic. It has since been taken up by Italian engineers and is in operation on certain types of ores. Two other research projects should be mentioned. In 1942 Erlenmeyer and others' floated synthetic mixtures of smithsonite and gangue minerals with hydroxyquinoline, an analytical reagent for zinc. On the other hand, Bunge, Fine, and Legsdin published in 19465 Some interesting results obtained on Missouri oxidized zinc ores. With sodium oleate as a collector and a combination of sodium hydroxide, sodium silicate, and citric acid as a limestone depressor, they secured, after four cleaning operations, a good grade of concentrate. With many ores this reagent combination lacks adequate selectivity. In 1939 M. Rey initiated a program of research on this important problem. Work was pursued first at the School of Mines in Liége, Belgium"' and later in Paris in the laboratories of Société Miniére et Mbtallurgique de Penarroya and Société Minerais et Métaux. Reagents used in the beginning were higher xanthates and mercaptans, later fatty amines. Sulphidization with sodium sulphide was found necessary. These conditions make possible the flotation of zinc carbonate and zinc silicate. Two milling plants were put in operation in Sardinia in 1950 and several others are now contemplated." ' It should be mentioned that unknown to the present writers McKenna, Lessels, and Peterson were

Jan 1, 1955

By H. H. Campbell

The following pages discuss some problems connected with the manufacture of steel by the open-hearth process. The methods employed necessarily enter into the domain of what is called theory; but the results are eminently practical. The determination of the various losses of thermal power and the investigation into the chemical reactions in the bath, are important to every manufacturer. It will be understood that definite figures concerning one furnace and one system, will not apply to all other furnaces and systems; but it is hoped that methods are developed, which are capable of general application and which will shorten the labors of others. The gas-calculations contain nothing entirely novel; but certain methods appeared to be very convenient and they are here elaborated in order that others may have a model to follow. The determination of the loss of iron by weighing the slag and finding the percentage of iron therein, is probably unusual. If so, the fact is to be regretted, since this is the only way that an accurate result can be obtained. The common method of estimating the loss in open-hearth work, is to subtract the weight of metallic products from that of the materials charged. Nothing could be more unsatisfactory, inaccurate and meaningless. Pig-iron, steel, wrought-iron and ore are charged into the furnace; complicated chemical reactions occur; the sand of the pig-iron, the slag from the wrought-iron, the gangue of the ore, all rise to the top ; the silicon, manganese and carbon burn and leave the metal; some of the iron oxidizes and goes into the slag; some of the ore is reduced and gives up metallic iron ; the recarbonizer is added, the mission of which is to waste itself; in the pouring of the steel, pit-scrap is made in the ladles, around the moulds and under the spout; the errors in weighing the products join hands to make accuracy impossible; and then the " loss" is determined by diffrence !

Jan 1, 1891

By S. A. Hovanessian

The method of characteristics which reduces the Buckley-Leverett mnlineur, partial differential equation to two first-order, linear differential equations is applied to the solution of a waterffood recovery problem for multiple lines of producing wells and one line of injection wells. The application of the method is described by a numerical example, and a brief theoretical background is given. From the results of this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple sets of producing wells. INTRODUCTION In this paper, the method of characteristics is applied to the solution of a waterflood recovery problem with multiple lines of producing wells and one line of injection wells. The application of the method to this type of recovery problem considerably simplifies the procedure of obtaining a numerical solution. It differs from the method described by Kern1 because it eliminates the need for integration in obtaining saturation fronts. In addition, the saturation history at any location within the field is obtained from a single diagram (time vs distance with saturation as a parameter)'. The paper includes a brief theory of the method of characteristics and its application to the solution of oil recovery problems. A numerical example is worked out, and the cumulative oil recovery-vs-time curve for a system with multiple sets of producing wells is obtained. This curve is then compared with the recovery curve of a system with only one set of producing wells. From this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple lines of producing wells. However, the recovery time is considerably longer for multiple sets of producing wells.

By M. L. Fuller

The fundamental mechanism of the deformation of zinc has been thoroughly described by several prominent investigators, particularly Mark, Polanyi, and Schmid,1 Mathewson and Phillips,2 and Schmid and Wassermann.3 The deformation of zinc occurs primarily through slip along basal planes (00.11, and secondarily through twinning on pyramidal planes of the form (10.2). In addition to these basic studies on single crystals, there have been a number of determinations4,5 of preferred orientations developed in rolled, polycrystalline zinc. In no case, to our knowledge, has there been described the development of oriented structures in zinc as a result of a systematic series of rolling treatments. The work included in the present paper shows the changes in orientation produced in a zinc alloy by successively increasing degrees of cold-rolling reduction. This alloy has the same crystal form, hexagonal close-packed, as zinc, but its susceptibility to hardening for a given degree of working is much greater because of its higher recrystal-lization temperature. Experimental Procedure Composition of the Alloy and Rolling Treatment The alloy used in this investigation consisted of zinc of 99.9 per cent purity to which 1 per cent of copper and 0.01 per cent of magnesium had been added.

Jan 1, 1934

By Louis A. Panek

Ground movements in the zone adjoining an active cave were measured at four sites in the San Manuel Mine. Measurements were made to detect extension and inclination, basic components of displacement, which can readily be duplicated by mine personnel using relatively simple equipment. The displacements demonstrated the development of a zone of strain relief surrounding the active cave, within which the ground tends to migrate toward the cave, and extension cracks develop tangential to the cave. This expansion of the ground surrounding an active cave can be exploited to promote future caving; it also creates special problems with respect to the design of an effective ground support system for mine openings in the production area.

Jan 1, 1981

By S. J. Burns, W. W. Webb

The dislocation arrangements formed during unsteady propagation of cleavage fractures on (010) planes in LiF have been investigated by high-resolution etch-pit techniques and by X-ray diffraction topogvaphy. In impurity-hardened crystals, cracks propagating in any direction on (010) planes at velocities of about 103 cm per sec are usually accompanied by light plastic deformation which is enhanced wherever the crack is allowed to hesitate. Dislocations with [011] type Burger's vectors are often formed looped around the crack tip. They are dragged along with the crack tips leaving edge dislocations lying nearly parallel with the clearage surface about 5µ from it. These dislocations are easily overlooked since they may initially intersect with the cleavage surface infrequently and later may disappear from the crystals due to image forces during aging at room temperature. Although the plastic work associated with these dislocations is only comparable with the reversible (010) surface energy, an instability in crack propagation appears due to a limit of the velocity with which dislocations can be dragged along with the crack. Transition to a fully brittle nonplastic fracture mode occurs when the crack velocity exceeds the velocity with which dislocations can be moved by the stress field of the crack. TRANSITIONS between brittle and ductile modes of fracture appear to be common processes in the behavior of materials in which the flow stress is close to the stress at which brittle cracks can propagate. High-strength engineering alloys fit into this category and the transition from ductile to brittle modes of crack propagation may be associated with catastrophic failures in these important materials. The methods of theoretical mechanics indicate the geometrical conditions in which these processes may occur but the detailed mechanisms controlling the generation of dislocations in the initiation of the plastic mode and the process by which the loss of plasticity occurs on transition to the brittle mode are not yet clear. Since these mechanisms are not amenable to direct observation in engineering alloys we have chosen a semi-ductile alkali halide LiF as a model system in which to observe transition mechanisms between plastic and brittle modes of crack propagation. Cleavage cracks in this system are known to undergo a plastic-elastic transition at velocities between 103 to 104 cm per secl and dislocation configurations in LiF are amenable to study by optical-microscopic observation of dislocation etch pits2 and by X-ray diffraction topography.3 We have been able to identify a dislocation mechanism responsible for the transition from brittle to slightly plastic modes of crack propagation in LiF. A model based on this mechanism permits calculation of the critical crack-propagation velocity for this transition and indicates the importance of the stress dependence of dislocation velocity in determining the critical crack velocity. Of course, this model cannot be carried directly over to more complex materials but it is quite possible that its qualitative features are generally applicable. Dislocations intersecting fresh cleavage surfaces in LiF were reported by Gilman,4 by Forty,5 and by Wash-burn et a1.6 Such dislocations were construed to have been nucleated where the cleavage crack hesitated or stopped, near stress concentrators, such as cleavage steps, on the crystal face. The loci of such dislocations deposited On the cleavage plane in bands were called "stop lines" or "deformation zones". Gilman, Knudsen, and walshl measured the velocity of cleavage cracks in lithium fluoride by evaporating thin resistive strips on the crystal side and recording

Jan 1, 1967