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By F. R. Jones

T Tahawus, N. Y., National Lead Co. operates the MacIntyre development. Here the world's largest titanium mine produces 5200 long tons of ore per day and pours 8000 long tons of waste rock over its dumps. Concentrated ilmenite is sent by rail to National Lead Co. pigment plants, and a second product, magnetite, is sold to steel producers in raw form or is agglomerated and shipped as sinter. Several earlier attempts had been made to produce iron from the deposits, which have been known since 1826. These attempts failed, chiefly because of titanium impurity. In 1941 the present owners re-established the operation for production of war-scarce ilmenite, and the impurity became the main product.

May 1, 1956

By N. O. Johnson

THE Hog Mountain mine is a pyritic-gold property in the north central part of Tallapoosa County, Alabama, at an elevation of 800 ft. in the southern Appalachian region. It is 13 miles by a good secondary road from Alexander City, a station on the Central of Georgia Railroad. Since its discovery in 1839, the mine has been worked intermittently. The records of past operations are few and are scattered over a long period of time; however, available information indicates a production of approximately 12,000 oz. of gold prior to the present company's activities, which started in 1933. Additional 7844 oz. has been produced under the direction of the present management. The ore from stopes has averaged 0.200 oz. gold per ton; the ore from development, 0.136 oz. gold per ton. Silver, copper, iron and sulphur are also present but to date are of minor importance. The grade of ore in comparatively narrow veins makes necessary extreme vigilance in the methods of mining. Geology Wall Rock.-Hog Mountain consists of a quartz-diorite intrusion approximately 5000 ft. long by 1200 ft. wide. Its resistance to weathering, as compared to the surrounding schists, has led to the formation of a conspicuous ridge rising 400 ft. above the adjacent country. All the mining operations are confined within the limits of this quartz-diorite formation. . Except where there is excessive shearing, either parallel or at flat angles to the quartz veins, all the walls of the stopes within the limits of the veins are strong enough to make timbering unnecessary. Where shearing exists, there may be a sloughing off of the walls, especially in the process of drawing the ore. When this occurs, stulls are placed in the stope, either while the stope is advancing, or while ore is being drawn from a completed stope. In general, very little timber is required. Veins.-The quartz veins have been deposited along fracture planes in the quartz diorite. There are 20 principal veins, all of which are roughly parallel and strike at right angles to the long axis of the formation.

Jan 1, 1937

By K. C. Carriere

INTRODUCTION The purpose of this section is to introduce the reader to the concepts of computer control of grinding circuits, and to flag some of the opportunities to be encountered, but without becoming overly involved in details of process, equipment or software. It is assumed that the reader has some familiarity with computer hardware and software, and in particular with the grinding process. The paper is organized into four parts: a general commentary of the need for computer control of grinding, a discussion of the process considerations involved, a more detailed elaboration on the current state of applicable computer technology, and a case study indicating one approach towards such a project. A brief installation survey and references for further reading are also given. This section will primarily deal with supervisory computer applications. Direct Digital Control and microprocessor systems are generally used as replacements for analog controls and thus are not considered in depth. Many configurations of grinding circuits exist, necessitating certain assumptions. Since many new concentrators use an open circuited SAG mill feeding a closed circuit ball mill, this configuration is used as a model although the principles stated can be extrapolated to any circuit. Motivation The use of computers for industrial control has been one of the dreams of control engineers and operators alike for many years. The concept of a plant running at optimal conditions with minimal operator involvement is very attractive from economic and technical standpoints. Accomplishment of this goal has been a long struggle, but today likelihood of success of such a project is very high, considering the reliability of modern hardware and the sophistication of available software. The primary motivation of any control system must be economic, i.e. it must pay for itself and make money for the owner, directly or indirectly. In grinding control the benefits which can be expected include: a) Higher through-put b) More uniform product in particle size, density and volumetric flog: c) Reduced operating costs including media consumption, power consumption and liner wear

Jan 1, 1982

By W. T. Allan

RAW bituminous coal has been in general use as a blast-furnace fuel in Scotland for the last century, and although its use has now been largely abandoned and it has been replaced by coke in the majority of the few furnaces which are at, present in blast in this country, coal-smelted pig iron is not yet a thing of the past; it is still being produced and mar-keted in competition with the more cheaply smelted product of the coke-fired furnace. Various factors have influenced this change in practice; the once plentiful deposits of coal of a suitable nature for the blast furnace are now not so easily obtainable; native blackband and clayband ironstones which are easily smelted in the coal-fired blast furnace, although still far from being exhausted, are not available except at a. cost that is somewhat higher than that of imported ores, making them unattractive to the ironmaster that is compelled by circumstances to smelt his iron at the lowest possible cost. Within the last 15 years overproduction of synthetic nitrogen has led to progressive reductions in the price of sulphate of ammonia, the recovery of which together with the other by-products before that time materially assisted in reducing the working costs of the coal-fired furnace. Now the sale of the by-products recovered yields a diminished profit. When the cost of the product is the only consideration the small, slow-smelting, coal-fired blast furnace cannot compare with its large, modern, coke-fired competitor. Other `considerations do not by any means all support the same side of the argument. In the smelting of pig iron to be used in the manufacture of steel where the quality of the final product depends so largely upon the control of the conversion process and so much less upon the physical quality of the pig iron used, the physical properties of the pig iron do not exert any appreciable influence upon the quality of the steel produced, therefore the methods employed in the smelting of the pig iron matter but little so long as the requisite chemical composi-tion is reached. On the other hand, in ironfounding where the simple melting of the pig iron, which is the only treatment it receives before being cast into its final form, does little or nothing to modify its original charac-

Jan 1, 1937

By C. H. Li, R. J. Stokes, T. L. Johnston

Sodium chloride crystals are brittle in the presence of surface microcracks. Water immersion leads to an enhancement of ductility which is retained indefinitely in dry air providing the crystal is dried without leaving a surface precipitate. Storage in a damp atmosphere results in a surface reaction and consequent rembrittlement. Although elimination of surface flaws in ionic solids does not necessarily enhance ductility, there is always a change in the location of the fracture origin. EVER since the original experiments of Joffel there has been controversy over their interpretation and no satisfactory generalized explanation has yet been given. It is generally admitted that when sodium

Jan 1, 1961

By Wilson Blake

Rock deformation and failure taking place around underground openings is usually both accompanied and preceded by the phenomena of rock noise or microseismic activity. These small-scale releases of seismic and acoustic energy can be detected with special geophysical monitoring equipment. Use of this equipment allows one to look inside a rock mass to determine how an opening is behaving under the applied loading system. Microseismic equipment and monitoring techniques are briefly reviewed, and use of the microseismic method as an engineering tool in monitoring rock structure stability is illustrated by case histories. Examples cited range from evaluating roof stability using single-channel portable equipment, to rock burst monitoring using sophisticated computer controlled, multichannel monitoring systems.

Jan 1, 1983

By George F. Becker

Complexity of Rock-Fractures.—The strains to which rocks have been subjected are manifestly very complex, and it is entirely safe to presume that every possible mode of deformation and rupture is exemplified. The most superficial inspection of any ordinary mountain region is sufficient to assure the observer that the rocks have been pressed, stretched, bent, buckled, twisted, and shorn. The study of torsional rupture cannot fail, therefore, to throw light on geological phenomena. The question is how areas which have been broken in this manner are to be distinguished from those which have yielded to other systems of forces. Phenomena of Joints.—It is well known that a large part of the more homogeneous rocks and some very heterogeneous rocks are intersected by partings often ailed joints. These partings are frequently flat surfaces even when seen in very large exposures, but are sometimes surfaces of moderate, single, or double curvature. Joint, usually occur in groups, in each of which the several partings are parallel to one another, and several such groups often intersect the same rock-mass. In such cases the different systems make large angles with one another. Nearly all students of the subject of jointing have reached the conclusion that joints are faulted surfaces, the dislocations usually being of small amplitude; and this conclusion receives abundant support from the study of thin sections under the microscope. It has thus been shown that much even of what would be regarded in hand specimens as mere slaty cleavage

Jan 1, 1895

By C. R. Pelley

Abstract-This paper describes the analytical characteristics of Western subbituminous coal and the manner in which these characteristics apply to their use in a utility-sized steam generator. It compares these characteristics with those of typical Midwestern coal and Eastern bituminous coal. The paper also reviews in detail the design considerations that must receive attention when various blends of these three coals, or any combinations thereof, are planned to be used. This research paper describes variations in analytical and utilization characteristics when coals from different origins are blended in order to achieve a predetermined sulfur content for the purpose of predicting sulfur oxides emissions as they affect environmental regulations and the resulting alterations in utilization characteristics such blending would cause, and how such blends of coal would affect a utility-sized steam generator.

Jan 1, 1978

By Robert A. Melton

Since many of the easily mined, continuous, thick coal seams in the Appalachian Region have been exhausted, new exploration and mining is being directed toward less continuous seams that are under more cover and are more difficult to mine. The direct results of this are that more money and time and more expertise and data are needed to plan and open new coal mines today. It is also becoming apparent that the old methods of assimilating and preparing information needed for mine planning are inadequate to meet the needs of today's modern mining engineer, especially in the areas of data gathering, storage, retrieval, preparation, and interpretation. The system described here allows assimilation of old and new core data in a relatively quick, accurate, and efficient manner. The system is a set of computer assisted procedures consisting of the following four basic steps: 1) raw data collection, computer input, storage, and graphic preparation, 2) geologic profile correlation and establishment of seam continuity, 3) computerized data posting of important seam parameters, 4) geologic and planimetric analysis for mine planning.

Jan 1, 1977

A discussion of the paper by Mr. Campbell, which was read by title at the Lake Superior meeting, but first presented at the New York meeting of the Iron and Steel Institute, October, 1904 (see p. 772). These papers are here published onder a mutual agreement between the Councils of the two Institutes, and will also be found in the Journal of the Iron and Steel Institute for the year 1901, vol. ii. Mr. William R. Webster, Philadelphia, Pa., said: We are under great obligation to Mr. Campbell for his exhaustive investigation, and the results he has put before us to-day. They are the most conlplete series of tests that have ever been made, where all the conditions of rolling, etc., were kept uniform. In discussing Mr. Campbell's first investigations, I claimed first, that the method of least squares, then used, would of necessity only gire the average value of any element, and that if the effect of any element was greater in the presence of high carbon than with low carbon this would not be shown by the method of least squares. Secondly, that the effect of manga nese should be considered on acid steel as well as on basic steel, instead of ignoring all the eff'ect of that element when it was below 0.60 per cent., as was then recommended by Mr. Campbell. I am pleased to note that the results of his present investigation confirm my views on these points. In presenting the results of his first investigation, Mr. Campbell referred to my investigation of 1893-94, and took exception to the value of phosphorus varying (depending on the amount of carbon present) from 800 to 1,500 lb. for each 0.01 per cent. He claimed that one might just as well consider the effect of phosphorus as being constant, and of carbon varying. I refer to this, as he now has introduced very similar conditions in his present tables, in that he gives variable values for manganese (depending on the amount of carbon present) for both acid and basic' steels. Can we now say, with more certainty than formerly, which element should be considered as haviup a constant effect ? There is one other point that I took up in my former discus-

Jan 1, 1905

By Albert J Hoskinson

Progress on the earth depends to a large extent upon the rapid interchange of ideas and commodities between the various nations of the world. The smooth flow of commerce, by which these ideas and commodities move, is accelerated by accurate and complete maps of the various land and water areas of the earth. The production of accurate maps depends upon a complete knowledge of the figure and dimensions of the object to be charted, therefore a knowledge of the shape of the earth is a prime necessity for accurate charting purposes. Gravity observations were first undertaken to aid in determining the shape of the earth so that the geodetic surveys of its land and water areas might be more accurately connected to form an undistorted map. A large part of the earth's surface is water and it is therefore necessary to get gravity values at sea as well as on land before a complete and accurate figure of the earth can be determined. Dr. F. A. Vening Meinesz, of Holland, was the first scientist to perfect a pendulum instrument that would accurately measure gravity at sea. He had previously developed a multiple pendulum apparatus for measuring gravity upon swampy and unstable land areas in Holland and it was therefore quite natural that he should adapt the instrument to give accurate results upon a still more unstable support, the surface of the sea. His instrument as perfected gives satisfactory results when mounted in gimbals on any vessel where the roll and pitch are not more than about 5" and where the vibrations from rotating machinery and wave action are not large enough to cause the pendulums to shift on the knife-edges. This degree of stability can be obtained on surface craft only in protected waters or on very calm days. Therefore, Dr. Meinesz mounted his instrument in a submarine so that he could submerge below the disturbed surface waters and get the desired stability in nearly any kind of weather by simply diving to greater depths. Most of the gravity-at-sea work has been done with a Meinesz instrument and a very large number of the observations have been made by Dr. Meinesz himself. He has occupied nearly 1000 sea, stations and probably has traveled as many miles by

Jan 1, 1940

By Albert J. Hoskinson

Progress on the earth depends to a large extent upon the rapid interchange of ideas and commodities between the various nations of the world. The smooth flow of commerce, by which these ideas and commodities move, is accelerated by accurate and complete maps of the various land and water areas of the earth. The production of accurate maps depends upon a complete knowledge of the figure and dimensions of the object to be charted, therefore a knowledge of the shape of the earth is a prime necessity for accurate charting purposes. Gravity observations were first undertaken to aid in determining the shape of the earth so that the geodetic surveys of its land and water areas might be more accurately connected to form an undistorted map. A large part of the earth's surface is water and it is therefore necessary to get gravity values at sea as well as on land before a complete and accurate figure of the earth can be determined. Dr. F. A. Vening Meinesz, of Holland, was the first scientist to perfect a pendulum instrument that would accurately measure gravity at sea. He had previously developed a multiple pendulum apparatus for measuring gravity upon swampy and unstable land areas in Holland and it was therefore quite natural that he should adapt the instrument to give accurate results upon a still more unstable support, the surface of the sea. His instrument as perfected gives satisfactory results when mounted in gimbals on any vessel where the roll and pitch are not more than about 5" and where the vibrations from rotating machinery and wave action are not large enough to cause the pendulums to shift on the knife-edges. This degree of stability can be obtained on surface craft only in protected waters or on very calm days. Therefore, Dr. Meinesz mounted his instrument in a submarine so that he could submerge below the disturbed surface waters and get the desired stability in nearly any kind of weather by simply diving to greater depths. Most of the gravity-at-sea work has been done with a Meinesz instrument and a very large number of the observations have been made by Dr. Meinesz himself. He has occupied nearly 1000 sea, stations and probably has traveled as many miles by

Jan 1, 1940

Discussion of the paper of IRVING A. PALMER, presented at the Salt Lake meeting, August, 1914, and printed in Bulletin No. 91, July, 1914, pp. 1447 to 1460. L. S. AUSTIN, Salt Lake City, Utah.-With the union of the Guggenheim interests and the American Smelting& Refining Co. in 1900, competition among the lead-smelting companies appeared to have been largely eliminated. This condition prevailed for but a short time, owing to the erection of smelteries by competing companies. Naturally, as competitors, the older companies endeavored to keep improved methods to themselves, not realizing, it would appear, that such knowledge could never be bottled up, but would drift into the common field of practice. Of late it has begun to be felt that more is gained than lost by adopting a franker and more open policy. The line, however, is drawn in. giving details of costs, which, fully known, it is felt, would be taken advantage of by a rival. As Mr. Palmer says, steady and substantial progress has been made, and latterly, I may add, the improvements have been radical. Sintering by the Huntington-Heberlein method or with Dwight-Lloyd machines has effected an important saving over reverberatory roasting, the cost being, say, 50 to 75c., as compared With $2 per ton by the older method. Moreover, the .large use of a sintered product has resulted in doubling blast-furnace tonnage. However, the change has not been an unmixed blessing, as in the machine roasting little time can be given to the breaking up of the blende, and it has been impossible to decompose largely the zinc sulphide, so detrimental in later blast-furnace treatment. The satisfactory roasting of the blende is still an unsolved problem. Nor is this all. For the best reduction it has been found that a part of-the change should be crude (unsintered) ore, indicating that the already fused material is only too ready to change to slag, thus lessening the opportunity for better reduction.

Jan 11, 1914

By M. H. Merriss

Some years ago, at the plant of the Baltimore Copper Smelting & Rolling Co., the receipt of large quantities of copper blister running high in lead, nickel, and arsenic resulted in the formation of a great amount of very foul slag, in the anode furnaces. A typical analysis of this slag was: Gold, oz. per ton......... 0.09 Arsenic, per cent.......... 0.60 Silver, oz. per ton......'.. 13.20 Antimony, per cent........ 0.50 Copper, per cent......... 19.50 Silica, per cent............ 28.30 Lead, per cent........... 11.90 FeO, per cent............. 19.20 Nickel, per cent.......... 4.60 CaO, per cent............. 1.60 The problem was to get out the copper in marketable form, to save the gold, silver, and particularly the nickel, and to get rid of as much as possible of the lead, arsenic, and other elements that were valueless to the Baltimore plant. In a copper refinery that does not take custom material for matte smelting, the usual method is to smelt the anode slag with coke in a reducing furnace, the black copper thus formed being sent back to the anode furnaces; this was the custom at Baltimore. An average anode slag will contain, perhaps, 40 per cent. copper and such small quantities of lead, nickel, etc., that smelting will get rid of most of these impurities in the black-copper furnace slag. To treat such an impure slag in this way, however, would result in a large nickel loss, and would send back to the anode furnaces all the lead and nickel not so lost, where it would be slagged off again and returned to the black-copper furnace as a slag still more concentrated in impurities. The result would probably be a constantly increasing amount of anode slag containing a likewise constantly increasing percentage of impurities. To avoid such a disastrous closed circuit some other process had to be devised. A small multiple-tank room, built for impure copper as an adjunct to the main series electrolytic refinery, was available, so the following standard process was suggested:

Jan 1, 1924

By J. C. Smock

The magnetic and polaric properties of magnetite, or magnetic iron ore: are fundamental facts in magnetism. The disturbing erect of this mineral upon the magnettic needle in land surveying must have been very early observed. The difficulties arising from this source are still almost insurmountable in making accurate surveys in districts where this ore occurs to any extent, either as a rock

By R. G. Patterson

The usual procedure in determining the magnetic susceptibilities of rocks and formations has been to take samples in the field and measure their volume susceptibilities in the laboratory, using one of numerous methods available. In none of these methods is the measuring instrument suited for field use. Usually the sample is pulverized; sometimes it is machined to a desired sue and shape, and in one method1 a cast of the sample is made and the susceptibility of the rock compared with that of a material of known susceptibility of the same size and shape, made from the cast of the original sample. Some writers assert that the difference in susceptibility of a rock sample in powdered and solid forms is negligible, and while doubtless this is true in many cases there are others in which the difference becomes appreciable. Further, the susceptibility of a small specimen may differ from that of the rock from which it is taken, owing to the stresses produced by the hammering or other forces used to obtain the sample and shape it for testing. Wilson2 found that an individual specimen of granite had about the same susceptibility in the solid as in the powdered form, but that pieces from different parts of the rock varied as much as 750 per cent because of unequal distribution of magnetite. The most accurate value of susceptibility would, obviously, be obtained from averag- ing a number of tests on the undisturbed rock instead of from one or two samples. No such procedures have been published, to the writer's knowledge. It is the purpose of this paper to describe a method by which susceptibilities of rocks may be determined in place by means of a portable instrument. Method The principle involved in this new method is that there is a change in inductance of a coil due to the presence in its magnetic field of a paramagnetic or dia-magnetic medium. In this case, however, the windings of the coil do not enclose any part of the rock under test. Instead, the coil is circular, being small in cross section as compared to its radius, and consists of several hundred turns of fine wire. It is placed flat on the rock of which the susceptibility is to be measured. Thus only part of the magnetic field from the coil penetrates the rock under test. The relation between the change in field strength or inductance of the coil and the susceptibility of the medium will be developed later. To measure the change in the inductance of the coil due to the presence of a magnetic material an alternating-current inductance bridge was chosen. Description of Apparatus Of many alternating-current bridge methods applicable,3 the one shown in Fig. 1 (Owen's bridge') was adopted for its simplicity and sensitivity. In Fig. I, the test coil is indicated by PlL1. It is connected to the bridge by about

Jan 1, 1946

By R. G. Patterson

The usual procedure in determining the magnetic susceptibilities of rocks and formations has been to take samples in the field and measure their volume susceptibilities in the laboratory, using one of numerous methods available. In none of these methods is the measuring instrument suited for field use. Usually the sample is pulverized; sometimes it is machined to a desired sue and shape, and in one method1 a cast of the sample is made and the susceptibility of the rock compared with that of a material of known susceptibility of the same size and shape, made from the cast of the original sample. Some writers assert that the difference in susceptibility of a rock sample in powdered and solid forms is negligible, and while doubtless this is true in many cases there are others in which the difference becomes appreciable. Further, the susceptibility of a small specimen may differ from that of the rock from which it is taken, owing to the stresses produced by the hammering or other forces used to obtain the sample and shape it for testing. Wilson2 found that an individual specimen of granite had about the same susceptibility in the solid as in the powdered form, but that pieces from different parts of the rock varied as much as 750 per cent because of unequal distribution of magnetite. The most accurate value of susceptibility would, obviously, be obtained from averag- ing a number of tests on the undisturbed rock instead of from one or two samples. No such procedures have been published, to the writer's knowledge. It is the purpose of this paper to describe a method by which susceptibilities of rocks may be determined in place by means of a portable instrument. Method The principle involved in this new method is that there is a change in inductance of a coil due to the presence in its magnetic field of a paramagnetic or dia-magnetic medium. In this case, however, the windings of the coil do not enclose any part of the rock under test. Instead, the coil is circular, being small in cross section as compared to its radius, and consists of several hundred turns of fine wire. It is placed flat on the rock of which the susceptibility is to be measured. Thus only part of the magnetic field from the coil penetrates the rock under test. The relation between the change in field strength or inductance of the coil and the susceptibility of the medium will be developed later. To measure the change in the inductance of the coil due to the presence of a magnetic material an alternating-current inductance bridge was chosen. Description of Apparatus Of many alternating-current bridge methods applicable,3 the one shown in Fig. 1 (Owen's bridge') was adopted for its simplicity and sensitivity. In Fig. I, the test coil is indicated by PlL1. It is connected to the bridge by about

Jan 1, 1946

By John M. Lovejoy

I take pleasure in transmitting herewith "Petroleum Development and Technology in 1927," in which we have attempted to set out in a series of 40 papers with attendant discussions the advances made in Production Engineering and Refinery Engineering during the year. The volume also contains a digest of round table discussions on Petroleum Engineering Research problems and Petroleum Engineering Education. In addition to the above we set out in 16 papers a review of production of each producing area of the United States and of the more important foreign countries, together with a review of the world's production and forecasts for 1928. We also include 8 papers on the Economics of the oil industry. The papers and discussions included herein represent the contributions of more than 200 engineers, including the foremost in each line. These papers were presented at technical sessions held in Fort Worth in October, 1927, and at the annual meeting in New York in February, 1928. We desire to express our thanks and appreciation to all those who have contributed to this volume. As in previous years, we have attempted to emphasize the value of both written and impromptu discussions. -We have made a practice of returning all impromptu discussions to the authors for correction and amplification, and because of this practice we feel that the discussions contained herein are in very presentable and readable form. It was decided by the nominat,ing committee when meeting for thc purpose of nominating officers for 1928 to eliminate the vice-chairrnanship for Transportation Engineering, as that branch of the industry seemed to come more naturally under the activities of the American Petroleum Institute. It was also decided by this committee to institute a new vice-chairmanship for Petroleum Engineering Research. Wc have had heretofore round table discussions on engineering research, but through the newly created vice-chairmanship, to which Mr. L. C. Uren was elected, we expect to have more comprehensive sessions on engineering research than heretofort.

Jan 1, 1928

By W. T. Lankford, Edward Saibel

During the course of an investigation of the plastic flow of aluminum aircraft sheet under combined loads, several problems arose in which analyses of the conditions leading to unstable plastic flow were needed. In order to provide these analyses, and in the hope of attaining a better understanding of the general problem of unstable plastic flow, the present study was undertaken. It is well known that unstable plastic flow is associated with a form of mechanical instabi!ity frequently observed during the plastic deformation of ductile metals. This instability is characterized by the fact that, at its onset, plastic straining mill proceed at a constant magnitude of the externally applied forces. It is further typical that the resulting unstable flow is generally accompanied by the formation of a neck, a local bulging, or some other form of heterogcneous deformation. Perhaps the most familiar example of unstable plastic flow to the metallurgist is the formation of the neck in the ordinary tension test. It is well known that in this test most metals exhibit a maximum in the externally applied load, followed by the process commonly referred to as "necking down." Instability in the simple tension test has been frequently discussed and numerous investigators1'2'3'12 have derived the criterion for instability in terms of a critical rate of strain hardening. It is the purpose of the present study to extend the criterion for unstable flow to the more general case where the body undergoing flow is subjected to combined loads. It is hoped that the problems considered will provide a more consistent picture of the general features of this important form of mechanical instability. The most practical implications of instability in plastic flow arise in connection with sheet metal forming operations. In the formation of a great many sheet metal parts, the deformations are produced primarily by stretching. If the conditions which lead to unstable flow are fulfilled in such a formation, and if the resultant instability leads to a pronounced localization of flow, then the useful limit of ductility of the material will have been reached. It i; also essential that the effects of instability be taken into consideration in any study of the plastic flow and rupture of metals under combined stresses. In general, when unstable plastic flow is initiated, straining becomes localized, the geometry of the test splecimen changes, and the state of stress in that portion of the specimen undergoing plastic flow is no longer under external control. In many past studies of the effects of combinetl Metals On flow and rupture) account has not been taken of the fact that, although a given test may be started under constant

Jan 1, 1947

By Edward Saibel, W. T. Lankford

During the course of an investigation of the plastic flow of aluminum aircraft sheet under combined loads, several problems arose in which analyses of the conditions leading to unstable plastic flow were needed. In order to provide these analyses, and in the hope of attaining a better understanding of the general problem of unstable plastic flow, the present study was undertaken. It is well known that unstable plastic flow is associated with a form of mechanical instabi!ity frequently observed during the plastic deformation of ductile metals. This instability is characterized by the fact that, at its onset, plastic straining mill proceed at a constant magnitude of the externally applied forces. It is further typical that the resulting unstable flow is generally accompanied by the formation of a neck, a local bulging, or some other form of heterogcneous deformation. Perhaps the most familiar example of unstable plastic flow to the metallurgist is the formation of the neck in the ordinary tension test. It is well known that in this test most metals exhibit a maximum in the externally applied load, followed by the process commonly referred to as "necking down." Instability in the simple tension test has been frequently discussed and numerous investigators1'2'3'12 have derived the criterion for instability in terms of a critical rate of strain hardening. It is the purpose of the present study to extend the criterion for unstable flow to the more general case where the body undergoing flow is subjected to combined loads. It is hoped that the problems considered will provide a more consistent picture of the general features of this important form of mechanical instability. The most practical implications of instability in plastic flow arise in connection with sheet metal forming operations. In the formation of a great many sheet metal parts, the deformations are produced primarily by stretching. If the conditions which lead to unstable flow are fulfilled in such a formation, and if the resultant instability leads to a pronounced localization of flow, then the useful limit of ductility of the material will have been reached. It i; also essential that the effects of instability be taken into consideration in any study of the plastic flow and rupture of metals under combined stresses. In general, when unstable plastic flow is initiated, straining becomes localized, the geometry of the test splecimen changes, and the state of stress in that portion of the specimen undergoing plastic flow is no longer under external control. In many past studies of the effects of combinetl Metals On flow and rupture) account has not been taken of the fact that, although a given test may be started under constant

Jan 1, 1947