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By Carel Robinson

THE little coal mine at Otsego, in the Winding Gulf field of southern West Virginia was dying. In the history of coal mining thousands of mines have been successful at first, but usually a change occurred and profits ceased. Often be change was so gradual and extended over such a length of time that the fundamental causes did not stand out in sharp relief and their significance was not realized. Studies often reveal that the cause for failure was in the arteries that connect the producing places with the mine entrance. Profits continued so long as the working places were close to the tipple and while the thrill of newness aid ease of access resulted in effective supervision from day to day. The air- way and haulageway, the wire line and manway, may have been sufficient when the distance from the entrance was a few hundred feet, but were inadequate when this was extended for thousands of feet.

Jan 1, 1937

By O. U. Bradley

The extent of losses, due to evaporation, sediment, and water, in crude oil stored in steel tanks, is a very interesting question, and particularly so at this time, when every reasonable measure should be employed to eliminate all possible losses of this important natural product. Available information on this subject is incomplete; e.g., during the development of the Cushing Field, considerable surplus oil was stored in steel tanks, but from time to time, owing to changes in weather, some losses by evaporation and short storage room on the leases, these tanks were topped out, thus rendering inaccurate any system designed to determine the average rate of evaporation or other losses of the oil over a given period. Furthermore, the losses, as shown by the records at the time, as a result of hasty gages, failed to take into account the temperature and gravity of the oil. Losses may be classified roughly as occurring from evaporation, presence of sediment and water, and leakage. The coefficient of expansion and contraction of crude oil, in relation to temperature conditions, is of material importance; also, the rate of evaporation is dependent upon the gravity of the oil, as the escape of the lighter hydrocarbons in fresh Cushing oil, of from 40 to 42 gravity, on a warm day is considerable, and from available records of temporary storage, it is safe to assume that a loss of 1 to 11/2 per cent. in volume will easily occur in light crude oil of Cushing grade over a period of 6 months, including the summer season. The presence of sediment, water, and other impurities, in the oil will also cause more or less deterioration in quality, particularly when the fresh production is run direct from the gage tanks, or from the wells on the lease to steel storage, as is often the case when an oil field is being rapidly developed. The bad oil will settle to the bottom of the tanks and may be determined by thiefing and running a centrifuge test on the sample. The amount of water in the oil depends entirely on the conditions under which it is produced. Sometimes in large producing wells, with heavy gas pressure, some water may come in with the oil, particularly if the well has been drilled to the top of a water sand. Under these conditions, cut oil is often produced, which, if not settled out, is carried over into the steel tanks. The losses by leakage in steel tanks are difficult to determine, for

Jan 1, 1920

By A. B. Kinzel

SILICON, unfortunately, is not in the same category as some other metals with respect to the absolute value of the highest purity material prepared. Tucker, in England, and Becket, in this country have devel-oped procedures for the purification of silicon, and Becket's process has made industrially available silicon of a purity of 99.8 per cent or better. However, even the term "silicon metal" may be a paradox to some people, although not more so than the term "amorphous" as applied to silicon. These terms come from commerce, and "metal" is used to distinguish industrially high-purity silicon from ferrosilicon, silicon-aluminum, and other high-silicon alloys. Alloys of iron and silicon with 95 per cent Si or less are known as ferrosilicon, with a designation of silicon content where necessary, and the terns "silicon metal" is invariably applied to the grades containing 96 per cent Si and higher. The Becket method of purification was referred to in a monograph on the Alloys of Iron and Silicon, and the Tucker procedure was described in some detail in that publication.1 In order to get silicon of still higher purity, a sample, prepared by the Becket method, analyzing 99.84 per cent Si, 0.020 Fe, 0.016 Al, 0.005 Ca, 0.025 C, 0.033 per cent 02, 0.006 H2, 0.006 N2, and 0.001 per cent Mn, was crushed to pass a 100-mesh sieve said further purified by a modification of Tucker's procedure. This modification differs from Tucker's method in that after treatment the 100-mesh alloy was centrifuged to remove the last traces of acid. Our directly determined analysis of this purified sample shows: Si, 99.952 per cent; Fe, 0.009; Al, 0.012; Ca, 0.003; C, 0.006; or 99.982 per cent. Silicon by difference equals 99.97 per cent. The variation between silicon by difference and silicon as directly determined is important. Although Tucker mentions the amount of insoluble matter in commercial silicon both before and after his treat-ment, he does not mention the existence of carbon in the alloy; neverthe-less, lie reports silicon by difference. Any final figure as to purity obviously results from agreement between direct determination and

Jan 1, 1939

By Alfred Weiss

Over the past 25 years hard-rock mining companies have developed a number of profitable computer applications which appear applicable to operations in the coal industry. The evolution of these applications are described and the most profitable discussed. The basic nature of these systems is that they must cut across organizational boundaries. While technological advances contributed significantly to the successful implementation of computers within mining, the human aspects related to organization, management and control of systems projects remain as key to future success in coal as they were and still are in hard-rock mining.

Jan 1, 1983

By Joseph W. Roe

MaNY questions arising in the work of the mining engineer may be solved quickly and with suffcient accuracy by the methods of descriptive geometry; but, unfortunately, this subject is more often considered from a mathematical view-point than as an effective tool for solving practical problems. Some of the principles involved are merged into the ordinary operations of mechanical drawing, and are used unconsciously by the engineer in his every-day work. The rest are stowed away on the book-shelf with his forgotten or rarely-used college text-books. One reason for this condition of " innocuous desuctude " may lie in the uifortunate and often cumbersome notation which it has been found necessary to introduce. If some of these principles can be recalled to the engineer's attenti011 in terms of' every-day use they may prove of practical hearing. Recently, in talking with several mining engineers, I used some of the drawing-room methods of a machine-designer, to the evident surprise of those around me. These men were perfectly familiar with the methods, but their application to mining-work had not occurred to them. At their suggestion the present paper is offered, not in ally way as a treatise, but merely to suggest a certain point of view, in hope that it may lead others far more familiar with mining-problems to pursue the subject further. I. To Find the Strike. As the simplest and most fundamental problem, let it be required to find the strike of a vein when the location and elevation of three points on the outcrop are known. It mill be assumed for the present that the rein is a plane.

Jan 1, 1911

By John L. Schroder, Woods G. Talman

EXPERIENCE has shown that certain known natural conditions and other indefinite characteristics combine to make a mining area vulnerable to mountain bumps. Some of the known conditions are heavy overburden, an overlying stratum of strong non-elastic rock, a structurally strong coal seam that does not crush easily and yet is the weakest stratum in the series, and a floor stratum of more than ordinary firmness. The indefinite characteristics could include resistance of top or bottom of a coal seam to lateral flow, effect of immediate top and bottom strata, nature of the coal seam, and other factors about which very little is known. It is in this area that exhaustive study is needed to achieve positive control of the dreaded mountain bump hazard.

Jan 8, 1958

By W. G. Pfann

In zone-melting, a small molten zone or zones traverse a long charge of alloy or impure metal. Consequences of this manner of freezing are examined with impurerespect to solute distribution in the ingot, with particular reference to purification and to prevention of segregation. Results are expressed in terms of the number, size, and direction of travel of the zones, the initial intermsofsolute distribution, and the distribution coefficient. IF a charge of binary solid-solution alloy is melted and then frozen slowly from one end, as for example in the Bridgman method of making single crystals,' coring usually occurs, with a resulting end-to-end variation in concentration. Such coring, or normal segregation, is undesirable where uniformity is an object. On the other hand, for certain systems, it can be utilized to refine a material by concentrating impurities at one end of the ingot.'. ' In the present paper a different manner of freezing will be examined with respect to the distribution of solute in the ingot. A number of procedures will be indicated which have in common the traversal of a relatively long charge of solid alloy by a small molten zone. Such methods will be denoted by the general term zone-,melting, while the process described in the preceding paragraph will be called normal freezing. It will be shown that, in contrast to normal freezing, zone-melting affords wide latitude in possible distributions of solute. Segregation can either be almost entirely eliminated or it can be enhanced so as to provide a high degree of sttparation of solute and solvent. A number of simplifying assumptions will be invoked which, while not entirely realizable in practice, nevertheless provide a suitable point of departure for more refined treatments. Moreover, our own experience with zone-melting has shown that, for certain systems at least, the analysis holds quite well. The present paper will be confined to a discussion of principles and a general description of procedures. Comparison with experiment is planned for later publication. Normal Freezing Before considering zone-melting, segregation during normal freezing will be reviewed briefly. If a cylinder of molten binary alloy is made to freeze from one end as in Fig. 1, there usually will be a segregating action which will concentrate the solute in one or the other end of the ingot. If the constitutional diagram for the system is like that of Fig. 2, then the distribution coefficient k, defined as the ratio of the concentration in the solid to that in the liquid at equilibrium, will be less than one and the solute will be concentrated in the last regions to freeze. If the solute raises the freezing point, then k will be greater than one and the solute will be concentrated in the first regions to freeze. The concentration in the solid as a function of g, the fraction which has solidified, can be expressed by the relation: C = kC0 (1-g)k-1 [I] where C, is the initial solute concentration in the melt. Eq 1 is based on the following assumptions: 1—Diffusion in the solid is negligible. 2—Diffusion in the liquid is complete (i.e., concentration in the liquid is uniform). 3—k is constant. Concentration curves representing eq 1 for k's from 0.01 to 5.0 are plotted in Fig. 3. This equation, in one form or another, has been treated by Gulliver,³ Scheuer,4 Hayes and Chipman5 for alloys and by McFee2 for NaCl crystals. It is derived in Appendix I. It should be pointed out that the k which is calculated from the phase diagram will be valid only in the ideal case for which the stated assumptions are correct. In all actual cases, the effective k will be larger than this value for solutes which lower the melting point, smaller for solutes which raise the melting point, and will probably vary during the beginning of the freezing process. For simplification it will be assumed that the ideal k is valid. Zone-Leveling Processes The processes of this part are designed to produce a uniform, or level, distribution of solute in the ingot. Single Pass: Consider a rod or charge of alloy whose cross-section is constant and whose composition, C2, is constant, although permissibly varying on a microscopic scale." Such a charge might be a rapidly frozen casting or a mixture of crushed or powdered constituents. Cause a molten zone of

Jan 1, 1953

By S. F. Shaw

MINING conditions in Mexico during the current year have been most unfavorable, synchronizing with conditions in the United States, but the outlook for the near future is improving. The chief difficulties met with are because of the following conditions: severe drop in prices of metals; high smelting rates; high prices of supplies; inadequate means of transportation; low efficiency of labor. In comparison with pre-war prices for metals it cannot be said that prices are low, particularly for silver, which recently has gone to a level that would have been considered exceedingly good in 1912. But conditions have changed so greatly that only the most favorably situated properties can operate without loss.

Jan 1, 1921

By H. E. Gross

A plausrsle method of drilling beyond the continental shelves is set forth with limitations of the method. The continental shelves comprise the water-covered portions of land masses out to 600 ft. of water, or roo fathoms. The problems and possibilities of drilling beyond this depth are discussed in this paper. Introduction Much attention is being given the problem of developing petroleum beneath the open sea. Geophysical surveys have been made 26 miles offshore1 from the continental United States, and onco offshore ownership is established it is likely that there will be drilling for oil on the continental shelves. More than two years ago the author presented the means for drilling in deep water.2 at the fall meeting of the Petroleum Division of the AIME at Los Angeles. His concepts then were based on the use of rigid foundations suitable for drilling in water up to 600 ft. deep. The present paper suggests a method for drilling in deeper water. Possibilities and Problems of Drilling beyond the continental shelves It being conceded that because restricted deep-water portions of the hydrosphere might contain oil in commercial quantities, and that at any rate it is pertinent to know more of the nature of the lithosphere beneath the hydrosphere, the possibilities and problems of drilling beyond the continental shelves should be set forth. Drilling in open water would offer few if any advantages over drilling on land. These are: 1. The ocean transportation is available to deep-water drilling sites, and extensive pipe lines and roads are unnecessary. 2. Refinery facilities and markets perhaps are established on the near-by shore where adjacent fields on land are nearing depletion. 3. There is freedom from jungle pests and tropical diseases. 4. Competitive drilling is less likely. 5. Extensive areas attractive for development arc not yet under lease or concession. Disadvantages are great and numerous: 1. Storm hazards from wind and wave. 2. Expensive foundations, either rigid or floating. 3. Shutdown times because of weather. 4. Marine Regulations of Federal Bureaus in addition to customary regulations on land. 5. Frequent difficulty in moving men and materials to and from drilling platforms. 6. Extra precautions required in open sea. For drilling in water more than 500 or 600 ft. deep, rigid foundations2 become too costly, and floating foundations must be used, and they must meet the following requirements:

Jan 1, 1947

By H. E. Gross

A plausrsle method of drilling beyond the continental shelves is set forth with limitations of the method. The continental shelves comprise the water-covered portions of land masses out to 600 ft. of water, or roo fathoms. The problems and possibilities of drilling beyond this depth are discussed in this paper. Introduction Much attention is being given the problem of developing petroleum beneath the open sea. Geophysical surveys have been made 26 miles offshore1 from the continental United States, and onco offshore ownership is established it is likely that there will be drilling for oil on the continental shelves. More than two years ago the author presented the means for drilling in deep water.2 at the fall meeting of the Petroleum Division of the AIME at Los Angeles. His concepts then were based on the use of rigid foundations suitable for drilling in water up to 600 ft. deep. The present paper suggests a method for drilling in deeper water. Possibilities and Problems of Drilling beyond the continental shelves It being conceded that because restricted deep-water portions of the hydrosphere might contain oil in commercial quantities, and that at any rate it is pertinent to know more of the nature of the lithosphere beneath the hydrosphere, the possibilities and problems of drilling beyond the continental shelves should be set forth. Drilling in open water would offer few if any advantages over drilling on land. These are: 1. The ocean transportation is available to deep-water drilling sites, and extensive pipe lines and roads are unnecessary. 2. Refinery facilities and markets perhaps are established on the near-by shore where adjacent fields on land are nearing depletion. 3. There is freedom from jungle pests and tropical diseases. 4. Competitive drilling is less likely. 5. Extensive areas attractive for development arc not yet under lease or concession. Disadvantages are great and numerous: 1. Storm hazards from wind and wave. 2. Expensive foundations, either rigid or floating. 3. Shutdown times because of weather. 4. Marine Regulations of Federal Bureaus in addition to customary regulations on land. 5. Frequent difficulty in moving men and materials to and from drilling platforms. 6. Extra precautions required in open sea. For drilling in water more than 500 or 600 ft. deep, rigid foundations2 become too costly, and floating foundations must be used, and they must meet the following requirements:

Jan 1, 1947

By W. M. Peirce, R. K. Waring

Zinc of high purity offers definite advantages in certain fields. A process by which zinc of 99.99 + per cent purity is produced by pyro-metallurgical methods is described in this paper. The process consists of a fractional distillation following the primary reduction; this fractional distillation employs the principles of rectification for the separation of lead and other high-boiling impurities and cadmium and other low-boiling impurities. Theoretical Considerations Involved in Production of High-purity Zinc by Distillation Fractional distillation, fractional condensation, and rectification are recognized methods of separating mixtures of liquids. In the field of organic liquids these methods are widely used but not commonly to effect as complete a separation of liquids as is done in the problem under consideration. Zinc boils at 905" C., cadmium at 778" C. and lead at about 1620" C. Zinc may contain from several hundredths of one per cent to over one per cent each of cadmium and lead, and the problem is to reduce these impurities to a few thousandths of one per cent. For lead and zinc, the spread in boiling points is substantial, 715° C., while for zinc and cadmium it is only 127" C. The basic limitation of any separation by distillation may be found from the relation between the equilibrium composition of the vapor and the liquid for all mixtures of the two substances involved. If a mixture of constant boiling point is found, or if a stable compound that vaporizes without dissociation occurs, there is a definite theoretical limit to the degree of separation that is possible when operating at atmospheric pressure with respect to that mixture. Otherwise, any degree of separation is theoretically possible. The equilibrium composition of vapor in contact with liquid mixtures of zinc and cadmiurn at the boiling point has been determined experi-

Jan 1, 1937

By D. J. Jr. McAdam

PART I.-OUTLINE OF INVESTIGATION, DESCRIPTION OF METHODS AND MATERIAL Previous Investigation of the Influence of Stress on Corrosion IN 1917 Haigh1 presented evidence that under simultaneous corrosion and cyclic stress metals may fail at lower stresses than if the corrosion is prior to the cyclic stress. In 1926 the author, while investigating the cooling effect of water on the fatigue resistance of metals, found that under these conditions steel specimens fail at stresses far below the endurance limit.2 (By "endurance limit" is here meant the fatigue limit obtained with specimens as free as possible from stress concentration and corrosive influences.) This led to an investigation (at the Naval Engineering Experiment Station, Annapolis, Md.) of the influence of cyclic stress on corrosion. This investigation maybe divided into three parts. The first part was a general survey of the conditions necessary to cause complete failure under corrosion and cyclic stress of relatively high frequency. The entire process by which metals fail under these conditions was-called "corrosion-fatigue." "Corrosion-fatigue limits" for a large number of metals were determined and the relationships of these limits to chemical composition, heat treatment and physical properties were established. The conclusion was reached that corrosion-fatigue is due to the accelerating influence of cyclic stress on corrosion. Results of this part of the investigation were presented in five papers.2-6 The second part of the investigation was a preliminary study of the influence of cyclic stress on corrosion. Each experiment was conducted in two stages. The first was a corrosion stage in which the specimen was corroded under cyclic stress; the second was a fatigue stage, in which the previously corroded specimen was tested (without further corrosion) to determine its fatigue limit. The difference between this fatigue limit and the endurance limit was used as a criterion of the "damage" due to

Jan 1, 1931

Meeting, June 26, 1913).-On the petition of 29 members residing in and near San Francisco, Cal., the San Francisco Local Section was established. The territory of the St. Louis Local Section was established to include the following States and parts thereof: All the State of Missouri ; That part of the State of Illinois south of and including the city of Urbana ; That part of the State of Indiana south of and including the city of Indianapolis ; That. part of the State of Kentucky west of and including the city of Frankfort ; That part Of the State of Tennessee west of and including the city of Nashville That part of the State of Arkansas north of and including the city of Little Rock.

Jan 7, 1913

By Stanley D. Michaelson, Norman Weiss

This was a year of realization. Some years are for planning and development, some for designing and building, others for fulfillment. With greater hopes and plans for the future than ever before, the year 1954, nevertheless, will be remembered principally because of project completion. Among copper mines, for example, there were Silver Bell, Copper Cities, Bisbee, Yerington, and White Pine. In iron, there were the Humboldt, Coleraine, Cerro Bolivar, and Eagle Mountain. In asbestos, Johns-Manville's new mill at Asbestos, Que. In uranium, completion of the ninth mill on the Colorado Plateau-Kerr-McGee's at Shiprock, N. M. In research, 1954 marked the completion of Kennecott's Research Center in Salt Lake City, one of the historic forward strides in the science of minerals beneficiation. The year was fruitful in other directions as well. Investigations of a fundamental nature were on the upswing, and pilot plant projects have also increased in size and number. Progress in new reagents and equipment was greater than normal. It can already be conservatively predicted-from the technological point of view-that 1955 and 1956 will be tremendous years.

Jan 3, 1955

Have your name and address on the first page of your manuscript. Typewritten manuscript is preferred, but is not essential. If you have the manuscript typewritten, have it double spaced and written on one side of the page only; send two copies to us if convenient; only one copy of the illustrations is desired. In typewritten manuscript, formulas are better inserted by hand. Keep a copy of your manuscript in case of loss in the mail. ILLUSTRATIONS.-Photographs reproduce best when printed on glossy paper. Solio is one of the best varieties. A good print is preferable to a negative. Blueprints, drawings, or pen or pencil sketches can be used for line engravings, but care should be exercised to make them legible and clear, especially in the case of blueprints. Tracings or photographs of drawings are preferable to blueprints. Rough sketches can be used, if necessary. Photographs should be sent flat, not rolled. Do not put reference letters or other marks on photographs; if such letters or marks are necessary, fasten a piece of tracing paper to the top edge, trace a rough outline of the picture upon it and then place all letters, etc. on the tracing paper lithe exact position you wish them to appear. Restrict the number of micrographs as much as possible on account of the considerable expense involved. Standard magnifications for non-ferrous metals and alloys are recommended as follows: 10, 25, 50, 75, 100, 150, 250, 500, 750, 1000, 1500. Micrographs should be trimmed to 2 1/4 X 2 1/4 in. (six micrographs to a plate), or, if larger, up to 3 1/2 X 4 in. (two to a plate). The smaller size should be adopted if consistent with adequate representation of the subject. With each micrograph should be attached an explanatory title, together with the actual magnification, etching medium, treatment, etc., indicating what the author intends to show.

Jan 1, 1919

By F. W. Hillnhutter

In plant tests with a 9.7 m hearth diameter high top pressure blast furnace the influence of disintegration of sinter during low-temperature reduction on blast furnace performance was evaluated. The blast furnace burden during the test period consisted of 74% self-fluxing sinter with a basicity of CaO/Si02 = 1.3, 15% pellets, 6% lump ore, and 5% recirculated slags. The sinter for the test was produced in a modern sinter plant. By changing the fuel rate and/or the MgO content at a constant basicity CaO/Si02 sinters with different low-temperature disintegration properties could be produced. The blast furnace was equipped with pressure monitoring devices at medium height of the furnace stack wall. This device provided in addition to the normal operating data readings of pressure losses in the upper and lower part of the furnace. The basic physico-chemical factors determining low-temperature disintegration are explained. The testing devices and the extent of quality control measures of sinter during the test period are outlined. Conclusions are drawn from the plant test in relation to sinter properties.

Jan 1, 1977

By C. V. Millikan

TEMPERATURE measurement in wells is an old practice and geothermal gradients have been of interest to geologists for many years.1,2 Their application to the operation of oil wells is a more recent practice. It has long been recognized that temperature anomalies occur in drilling and producing wells but thermometers that could obtain a satisfactory record of the anomalies were not available.3 The normal geothermal gradient is con-sidered as being about one degree Fahren-heit for each 60 ft. of depth.4 This "nor-mal" gradient varies in different areas, but whatever it may be in an area there is little variation from the surface to as deep as the drill penetrates. The normal gradient is appreciably changed by gas expanding from the reservoir into the borehole or by the movement of fluid through a borehole while drilling, producing, or circulating. It is the resulting anomalies and abnormal gradients from which conditions in wells can be interpreted. Some of the applications of such interpretations are locating the position of oil or gas sands, permeable strata in a reservoir zone, gas-oil contact, source of water, casing leaks, and the top of cement behind casing.

Jan 1, 1940

By Milo W. Krejci

(Butte Meeting, August, 1913.) THE plant and quarries of the Inland d Portland Cement Co.. are located- at Metaline Falls, Wash, about 128 miles north of Spokane, on the Fend Oreille river, and 10 miles, of the Canadian border. The plant is one of a chain of cement plants controlled by the Lehigh Portland Cement Co., of Allentown, Pa. Work on this plant was commenced in June, 1910, and was completed in April, 1911, but on account of some delays in the construction of the power plant, the works were not put into operation until August., 1911. Since then it has been in continuous operation and has furnished the Inland Empire with a high grade of cement. Fig. 1 is a, view and Fig. 2 is a plan of the works. Water Power Development.-The source of the water supply for the hydro-electric plant of the Inland Portland Cement Co. is Sullivan lake, a body of water approximately 5.5 miles long and 0.5 mile wide, situated in the Kanisku Forest Reserve. A wooden crib dam was installed so as to raise the elevation of the lake 25 f and the additional storage capacity was taken up by the diversion of Sullivan creek into the lake by means of a wooden flume, 0.25 mile long, 6 by 8 ft. in crosssection, and a ditch 1,200 ft. long. The water from the lake follows the natural water course to an intermediate storage reservoir, which was created by the construction of an earthen dam. This pond was used in connection with the saw mill which was installed at this point. Besides the earth dam, there was also built a crib, at the point shown in the sketch map, Fig. 3. This crib dam is 35 ft. high. From this point the excess water follows the natural -course of Sullivan creek to the Pend Oreille river.

Jan 7, 1913

P. W. BRIDGMAN.-Owing to a misunderstanding, I did not see Dr. McAdam's and Dr. MacGregor's remarks on my paper on Flow and Fracture (Metals Technology, December 1944, Pp. 32-38), until after their publication. Both Dr. McAdam and Dr. MacGregor speak of my analysis for the stress distribution at the neck of a tension specimen as containing several assumptions; in particular, that the strain is uniform across the section of the neck, that there is no hoop tension at the periphery, and that the plasticity conditions of von Mises hold. As far as the mathematics goes, the situation is no different in this problem of plastic flow than in a conventional problem of elasticity. That solution is unique which satisfies the boundary conditions on the stresses, the stress equations of equilibrium, and in addition the constitutive equations connecting stress and strain in the elastic case, or a corresponding set of equations, of which the von Mises relations are a special form, in the plastic case. In the particular case of the necked tension specimen I have found that there is a solution satisfying the boundary conditions, the stress equations of equilibrium, and the von Mises plasticity conditions in which the strain is uniform across the section, and there is no hoop tension at the periphery. This is therefore the solution, and the uniformity of strain and vanishing of hoop tension at the periphery are to be described as discoveries, over which the operator has no control, rather than as assumptions. The only part of the solution that can properly be described as an assumption is the von Mises plasticity condition. With regard to this it is to be noted that the condition is needed only in a much weakened form, for the analysis uses the condition only at the neck, where the strain is approximately constant. Thus, in the extreme case referred to in a footnote of my paper (p. 37, Met. Tech. Dec. 1944) the actually measured strain across the section varies from 2.4 to 2.6. Obviously it is a much weaker assumption to postulate that the von Mises condition holds in the strain range 2.4 to 2.6 than to assume it to hold for the entire range of strain from o up to 2.6, which would be necessary if the solution applied to the entire tension specimen rather than to the immediate region of the neck only. Furthermore, it is to be commented that under the special conditions of this problem the von Mises condition becomes identical with the maximum shearing-stress criterion of plastic flow; this amounts also to a weakening of the restrictions imposed by the von Mises condition. Dr. MacGregor refers to actual experiments of his own in which the strain was found not to be uniform across the neck. It is to be emphasized, however, that these were experiments on bars of rectangular section, and that the nonuniformity established was a nonuniformity around the perimeter, not a nonuniformity from the surface toward the axis. My method of solution applies only to a circular cross section. It can be said that the solution that satisfies the boundary conditions, etc., would definitely not be expected to demand a uniform strain for noncircular sections. In discussing my results, Dr. McAdam uses a definition of "flow stress" different from mine, so that the immediate applica-

Jan 1, 1945

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946