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By R. Costantini

The author discusses the promising future of the use of pipelines for transportation of ore slurries over long distances, citing existing installations. Various criteria and factors affecting the use and size of pipelines are considered. Among the factors influencing the use of pipelines are particle size, specific gravity, abrasiveness, minimum velocities, and pumping considerations. Long-distance transportation of solids by hydraulic pipelines holds the promise of great economic benefits. Today within the confines of most mineral processing plants, the moving of solids about in slurry form by pipeline is commonplace, since the method offers great advantages when conditions are suitable. Yet, this method is surprisingly slow in being adopted on a broad scale for transportation of solids over long distances (arbitrarily the term will be applied to one over five miles long). This is especially surprising in view of the successful realization in this country within the last five years of two daring ventures in long-distance solids pipelines. A 72-mile long, 6-in. diam pipeline of the American Gilsonite Co. has been satisfactorily transporting 700 tpd of gilsonite from the mine at Bonanza, Utah, to the processing plant at Grand Junction, Colo., since April 1957. The 108-mile long 10-in. diam pipeline of the Pittsburgh Consolidation Coal Co. has been transporting about 4000 tpd of finely crushed coal from the mine at Cadiz, Ohio, to the Eastlake power plant of the Cleveland Electric Illuminating Co. on Lake Erie since January 1958. However, besides two projects in the operations of The Anaconda Co. there have been hardly any other significant solids pipeline developments in the minerals industry during the last three years. The two projects are the 14-mile long, 6-in. diam copper concentrate gravity pipeline at Anaconda's El Salvador project in Chile which has been transporting about 800 tpd since January 1959. The second is a 16-in. diam tailings pipeline at the Anaconda Reduction Works, Anaconda, Mont., designed to transport about 20,000 tpd of deslimed flotation tailings for dam building. This pipeline, which is currently undergoing tryout tests and which will be about seven miles in length, will have a maximum of three 20-in. rubber-lined centrifugal pumps in series at the starting point, each developing a maximum of 100 ft of head, to supplement gravity. It is the writer's opinion that the major reason for the hesitation in considering pipeline operations is confusion due to an inadequate understanding of the basic physical principles affecting the slurry flow process by many engineers in the industry. This in turn begets an attitude of fear and trepidation instead of confidence on the part of many management executives, which leads to a minimizing of the advantages and exaggeration of difficulties when considering the possibility of a long-distance solids pipeline. The promotion of better understanding and consequently the promotion of greater confidence in the potentials of long-distance solids pipelines when conditions are suitable is thus the main purpose of this article. To this end, after considering several examples of the possibilities for solids pipelines in the minerals field, the relative significance of the major factors affecting pulp flow, and some major aspects of slurry pumping will be discussed on a general qualitative level. Then a brief outline of the semi-empirical quantitative methods developed to date for estimating slurry flow behavior will be presented. SOME POSSIBILITIES To give an idea of the magnitude of the possible economic benefits, it should be interesting to mention briefly some of the projects currently under consideration and to suggest some likely future possibilities. At Anaconda's El Salvador Project in Chile (Fig. 1) it is eventually planned to extend the existing 14-mile pipeline by another 60 miles to bring the copper concentrates down to the coast of the Pacific Ocean. Preliminary tests indicate that the projected 6-in. pipeline will be able to transport approximately 2000 tpd of concentrates at a pulp density of 40 to

Jan 1, 1961

By F. Bahnemann

IN discussing the problem of abnormal magnetic polarization, C. A. Heiland1? emphasized the unfortunate fact that our knowledge of the geological and physical conditions relating to such occurrences is very limited and that a more detailed insight into their physical causes would be extremely valuable for interpreting measured anomalies. He also pointed out that to arrive at quantitative physical formulas that would express the conditions that cause abnormal polarization many more occurrences of the kind would have to be recorded. The first part of this paper is a contribution to such descriptions.

Jan 1, 1935

By Thomas V. Falkie

The use of operation research and computer techniques in the mineral industries continued to gain acceptance during 1966. There are generally at least five sources of information for researchers and practitioners in the field: (1) Technical periodicals like MINING ENGINEER- ING, Mining Congress Journal, etc. (2) Proceedings of the Symposium and Short Course on Computers and Operations Re- search in Mineral Industries, held last year at Penn. State University and jointly sponsored by the University of Arizona, Stanford University, Colorado School of Mines, Penn. State University and the Society of Mining Engineers of AIME. (3) Various local conferences, such as the 1966 Rocky Mountain Minerals Conference held in Denver. (4) United States Bureau of Mines publications. (5) The AIME annual meeting in New York and the SME Fall Meeting in Tampa.

Jan 2, 1967

By George M. Bouton, Lawrence Ferguson

The experiments described in this publication were inspired by the Bell System's large interest in lead-alloy sheathed cables and by the wide range of fatigue and corroding conditions to which they are sometimes subjected in service. The first experiments consisted of operating specimens of lead + I per cent antimony telephone cable sheath alloy in a fatigue test while they were immersed in water taken from a manhole. Because of many published reports concerning corrosion-fatigue phenomena of various metals and alloys, a reduction in fatigue life was expected(1)2 Instead, however, the fatigue test ran on for many times the normal number of cycles an4 was finally stopped without failure. Because of this, the experiments were broadened to include the effect of many media on the fatigue properties of four lead alloys over a wide range of testing speeds and strains. One material, a viscous tacky polymerized isobutylene3 used in

Jan 1, 1945

By C. A. Heiland

Geophysical methods are playing an ever increasing part in various engineering fields. About ten years ago, geophysical exploration was first applied in civil engineering to the study of foundations and the location of construction materials and water. Its usefulness is now being extended into the field of structural engineering. Almost every structure has to be so designed that it will withstand any force to which it may be subjected. Such forces may result from its own weight, applied loads, pressures of various kinds, including those due to wind and water, ground subsidence and vibrations. The last two, problems involving the nature and dynamic behavior of surface and subsurface formations, are within the scope of geophysical investigations. In the design of any structure, the disposition and dimensions of its members as well as their materials must be so selected that they will withstand any or all of the forces enumerated above. In other words, its "resistance" to such forces must be sufficient, allowing for a definite margin of safety. Often a static treatment of the problem leads to satisfactory results, but the static method entails serious errors when vibrations are involved, as in resonance with an impressed vibration the displacements of a structure or parts thereof may dangerously exceed the allowable values. The principle of "dynamic design"† is, therefore, avoiding or reducing resonance by suitable selection of the natural frequency of a structure, or by the provision of damping. Methods of Investigation Dynamic design of structures is required where ground vibrations occur naturally or are produced artificially. Earthquake regions fall in the first group; areas of industrial activity where vibrations are produced by machinery, blasting, etc., fall in the second. In either case, dynamic

Jan 1, 1940

By Albert Ladd Colby

PAGE I. Introduction,...........577 11. PRocess of Manufacture. 1. American Specifications. 2. Foreign Specifications, . ......... 580 III. Chemical Properties. I. Chemical Composition: (a) American Specifications ; (b) Foreign Specifications. 2. Chemical Analysis: (a) American Specifications ; (b) Foreign Specifications ; (c) Number of Analyses Required ; (d) Sample for Analysis ; (e) Check-Analyses Impracticable ; (f) Rejection Solely on Variation in Com-' position,............581 IV. Physical Properties. 1. Drop-Test and Drop-Testing Hachine: (a) American Specifications ; (b) Foreign Specifications ; (c) Limits in Deflection. 2. Tensile Test: (a) American Specifications; (b) Foreign Specifications ; (c) Test-Pieces are not Representative ; (d) Specified Tensile Strength is Affected by the Section ; (e) BpeciBed Tensile Strength is Often Inconsistent with Specified Chemistry ; (f) Specified Tensile Strength is Often Inconsistent with Specified Elongation ; (g) Amount of Tensile Testing Required is Excessive ; (11) Conclusions. 3. Dead-Weight Test: (a) American Specifications; (b) Foreign Specifications; (c) Number of Tests Specified. 4. Bending-Test: ((1) American Specifications ; (b) Foreign Specifications,..........589 V. Section. 1. American Specifications. 2. Foreign Specifications: (a) Templets ; (b) Sample Piece of Rail; (c) Allowable Variation from Templet,...........601 VI. Weight. 1. American Specifications. 2. Foreign Specifications,. . 603 VII. Length. 1. American Specifications. 2. Foreign Specifications, . . 604 VIII. Drilling. 1. American Specifications. 2. Foreign Specifications, . 604 IX. Finish. 1. American Specifications. 2. Foreign Specifications, . . 50.5 X. Branding. 1. American Specifications. 2. Foreign Specifications : (a) Data to be Rolled in Raised Letters on Web of Rail ; (b) Marking of the Blow-Number on Each Rail; (c) Additional Marking and Painting of Rails,........605 XI. Inspection. 1. American Specifications. 2. Foreign Specifications: (a) Prior Notice of Rolling; (b) Free Access to the Works ; (c) Cost of Inspection, Analyses and Tests to be Borne by the Manufacturer ; (d) Rails after Inspection by Manufacturer to be Sorted into Lots Prior to Inspection by the Engineer ; (e) Disposition of Rejected

Jan 1, 1907

By C. A. Heiland

Geophysical methods are playing an ever increasing part in various engineering fields. About ten years ago, geophysical exploration was first applied in civil engineering to the study of foundations and the location of construction materials and water. Its usefulness is now being extended into the field of structural engineering. Almost every structure has to be so designed that it will withstand any force to which it may be subjected. Such forces may result from its own weight, applied loads, pressures of various kinds, including those due to wind and water, ground subsidence and vibrations. The last two, problems involving the nature and dynamic behavior of surface and subsurface formations, are within the scope of geophysical investigations. In the design of any structure, the disposition and dimensions of its members as well as their materials must be so selected that they will withstand any or all of the forces enumerated above. In other words, its "resistance" to such forces must be sufficient, allowing for a definite margin of safety. Often a static treatment of the problem leads to satisfactory results, but the static method entails serious errors when vibrations are involved, as in resonance with an impressed vibration the displacements of a structure or parts thereof may dangerously exceed the allowable values. The principle of "dynamic design"† is, therefore, avoiding or reducing resonance by suitable selection of the natural frequency of a structure, or by the provision of damping. Methods of Investigation Dynamic design of structures is required where ground vibrations occur naturally or are produced artificially. Earthquake regions fall in the first group; areas of industrial activity where vibrations are produced by machinery, blasting, etc., fall in the second. In either case, dynamic

Jan 1, 1940

By R. W. Baldwin

On page 309, column 1, the second equation should read: Ma-M1 = dlog_Pa M2-M1 d log P2

Jan 1, 1961

By C. T. Cox

W. A. Reich.*—I should like to ask Mr. Cox if he has any information on the change in

Jan 1, 1945

By E. G. Spilsbury

AS a fresh illustration of the advances made in the past few years in the overhead-cable systems of hoisting and conveying, as applied to open-cut deep mining and quarrying, I would call attention to a further development of this system of transportation which has lately been put in operation i-n this State. A few miles above Williamsport, on the Susquehanna river, the Glen Union Lumber Company, of Pottsville, Pa., owned a large tract of valuable timber-

Jan 1, 1892

Adams, Benjamin C., Jr., Student, Univ. of Oklahoma Norman, Okla. '36 Adams, Ernest C., Student, Univ. of Illinois 908 W. Green St., Urbana, Ill. '35 Adams, George H., Student, Colorado School of Mines Golden, Colo. '36 Adams, Robert Keller Mitchell Hotel, No. 18, Golden, Colo. '35 Afshar, Hadji Khan A., Student Box 63, Univ. Sta., Moscow, Idaho. '36 Ahrenholz, Herman William, Jr., Student, Lehigh Univ Bethlehem, Pa. '35 Alger, Robert P., Student, Missouri School of Mines & Met.Rolla, Mo. '36 Allen, Paul W., Student, Mass. Inst. of Tech Cambridge, Mass. '35 Allen, R. M., Jr., Student, Virginia Polytechnic Inst., "G" Co.Blacksburg, Va. '35 Alley, John Arnold, Student, Montana School of Mines Butte, Mont. '36 Amberger, R. H., Student, Michigan College of Min. & Tech Houghton, Mich. '35 Ambrosiani, F. Peter, Student, Michigan College of Min. & Tech Houghton, Mich. '36 Andersen, Burton Lee, Student, School of Mines, Univ. of Washington Seattle, Wash. '36 Anderson, Carlos, Student, Univ. of Oklahoma Norman, Okla. '36 Anderson, J. Wendell, Student, Pennsylvania State College State College, Pa. '36 Anderson, Joseph S. Cornelia Hotel, Ajo, Ariz. '35 Anderson, R. C., Student, Univ. of Washington Seattle, Wash. '35 Anderson, Roy A., Student, Washington State College Pullman, Wash. '35 Anderson, Willard. Student. Univ. of Oklahoma Norman, Okla. '36

Jan 1, 1936

By L. B. Slichter

Prospecting is certainly the world's biggest and best gambling business. It is a game where the chips cost many thousands and where many millions, even billions, can be won. An attractive feature of this gamble is the fact that the players are free to rig the odds as favorably as possible. Only the limited bounty of nature, the restrictions of the laws of the land, the competition from other players, the limited sagacity of the player himself— only these, and other factors, restrict the possibilities for large winnings. Today probably about half the land surface of the earth remains to be searched for signs of ore visible at the surface. It is fortunate that so much land still remains for exploration by relatively economical methods. Looking to the future, it is a good guess that the costs of finding ore will increase in response to increasing technical difficulties. To continue to achieve profits from prospecting, it will become necessary to analyze the business more skillfully, in a more and more sophisticated manner. Whenever feasible, qualitative concepts must be replaced by their quantitative equivalents, improvements, and extensions. THE GAMBLE The fact that prospecting is a gambling business reminds us at once of the elementary rule known as the law of gambler's ruin. I hesitate to mention so simple a rule in this company of experts. This rule expresses the rather serious chance of going broke when the odds for success are small, merely by a normal run of bad luck regardless of the long-run expectations of gain. The only sure way of avoiding this special risk of gambler's ruin is to have enough capital, and the will, to continue the play many times and thus ride out the inevitable runs of bad luck. For example, if the probability of success is one in ten for each venture, there is a 35 pct chance that ten successive ventures will fail in a row. But if one has the capital to continue the play through a run of 100 failures, then the chance of gambler's ruin is only 5 in 100,000. Almost any management, I suppose, would be under terrific pressure to cease the play during a long run of bad luck. To continue to prospect under such circumstances requires great confidence in the premises, and a firm conviction in the long-term expectation of profit. There is evidence which I shall mention that in the future even the strongest companies may not have the necessary capital to prospect on the ideal scale. Joint ventures will be very desirable as a means for extending the available venture

Jan 1, 1961

By R. Ward Grosz

Reasonable and timely solutions to the complicated mathematical calculations involved in the mine planning, economic evaluation and slope stability studies related to the Ruth Mine would not have been feasible without the modern digital computers. The Ruth Mine was a prosperous underground copper operation in east central Nevada from 1915 to 1948, when rising mining costs finally exceeded the value of the ore. A substantial reserve of porphyry copper remained in the ground, but until recently all economic evaluations indicated that it was at best a marginal operation and a relatively poor risk of capital. There has been a steady progress in improving all aspects of surface mining since the first steam shovel started stripping overburden; however, developments in just two rather specialized areas proved to be critical in changing the Ruth Mine from a reserve of mineralized rock to an economically attractive orebody. One involved the progress made in recent years in the science of slope stability. Applying the latest techniques in this field to mine planning resulted in reducing the stripping ratio from 6.0:l to 4. 2:l. The other major factor was the efficiency and cost performance of large capacity haulage trucks which made it feasible to go down over 1100 ft. in an open pit and recover ore with a high stripping ratio economically.

Jan 1, 1969

By Albert R. Ledoux

With the improvements in design and efficiency of machinery the element of danger in its use is becoming less, but it is a question whether the strain involved in operating modern plants is not increasing somewhat the danger of accident due to human fallibility. I propose to describe a somewhat uncommon casualty resulting from a not infrequent incident in the use of air-compressors. It is not necessary to state the location of the mine in which the accident occurred nor the makers of the compreseor, and the object of this brief paper is more to draw out suggestions from members more familiar than am I with the practical handling of mining machinery, than to point a moral. The compressor in question was a three-drill machine of standard make. At the time of the accident it was furnishing air to a single drill working in an upraise from a well-ventilated tunnel, and giving ventilation to a winze below the tnnnel where two men were hand-drilling. The compressor also furnished power to a small hoist in the winze, but the hoist was only operated occasionally, and never while the drills were working. The drills were located about 1200 ft. from the compressor. The engineer testified that he never had been short of air, and that there had been no complaillts that the

Jan 1, 1904

All the TECHNICAL PUBLICATIONS and PREPRINTS published in 1932 are available at Institute headquarters. They are also on file in public,, university and technical libraries and, when so indicated in the list, may be found in the TRANSACTIONS. Copies of the TECHNICAL PUBLICATIONS have been mailed to those members of the Institute who are registered in the different classes: A-Metal Mining; B-Milling and Concentration; C-Iron and Steel Division; D-Nonferrous Metallurgy; E-Institute of Metals Division; F-Coal Division;. G-Petroleum .Division; H-Nonmetallic Minerals; I-Mining Geology; K-Mining Administration; L-Geophysical Prospecting. Other members may obtain copies by writing to the Secretary. Copies of PREPRINTS may also be obtained from the Secretary's office. Additional copies are sold at the rate of 1 cent per page; minimum charge, 25 cents. Nonmembers may purchase the papers at the prices mentioned. METAL MINING TECH- NICAL PUBLI- - TITLE AUTHOR MEETING TRANS. CATION VOLUME No. AND PAGE* 484-A.45 Propeller Type Mine Fan at Moose A. S. Richardson New York 102, 86, 93 F.52 Shaft, Butte, Montana (13) Feb., 1932 487-A.46 Progress in the Improvement of Max H. Barber New York, Methods and Equipment at Feb., 1932 Open-pit Iron Mines on the Lake Superior Iron Ranges (9) Pre. Sand Filling through Pipes and Lucien Eaton New York, 102, 33, 41 Boreholes (9) Feb., 1932

Jan 1, 1932

By B. B. Zavoico

There were no radical changes in the petroleum situation in the Russian Soviet Union during the 1926 to 1927 operating year. The developments of the previous year were continued, but the major undertakings were far from being completed. The pipe lines from Baku to Batum and from Grozny to Touapse, and the large refineries on the Black Sea are delayed in their completion by the insufficient authorizations; until their completion the changes in the general situation will be necessarily of a halfway nature. The marketing situation was subject to much controversy during the past year and, though certain statements are quite true, the bulk of the criticism against the petroleum industry hardly deserves mention. The home market in Russia is steadily growing, with the per capita kerosene consumption already exceeding the prewar figure and fuel oil consumption obviously gaining. The foreign trade is making rapid and well-grounded success, but continues to suffer from low world quotations. There is no apparent sacrifice of home consumers in favor of export trade. The production of all Russian fields increased by 13,750,000 bbl. as compared with the 1925 to 1926 operating year, and next year's program anticipates a further increase of 9,720,000 bbl. (Table 1). The increased and improved refining facilities will make the real gain in production in the next year even larger than these figures indicate.

Jan 1, 1928

By F. E. Harris

It has been said that carbon is "ubiquitous" with reference to iron alloys. Certainly at temperatures where carbon and iron form the solid solution, austenite, it may be readily added to, or removed from, steel surfaces. Differences in concentration potential are the sole requirements for carbon flow. To measure the rate of carbon flow, a proportionality factor, D, is arbitrarily expressed in units of (length)2 X (time)-'. If the term used for carbon concentration is weight Pet C, as is customary, then a factor must be found, changing this term to One of weight Per unit volume when the diffusion coeficient, D, is used in flow formulae. The determination of D values for carbon is complicated since D varies with the concentration itself. The Matano method has often been employed for systems involving a variant D. This method expresses all evaluation of unsteady flow whereby D is given a relationship with the numerical value of C-x slopes. The author contends that this solution is incorrect, except when D is invariant. The primary purpose of this paper is to support this contention. Here diffusion is controlled under two conditions of flow. The first part deals with the steady state; the second part considers unsteady flow under definite restrictions. Beginning with the fundamental concept, the development is continued until equations for C-x curves are obtained. The solution is then subjected to experimental data. It is realized that a great amount of reliable data is required for a rigorous proof. KO such research is claimed. Instead an attempt is made to set forth the physical significance of the diffusion mechanism, and particularly to express the factors which influence the flow of carbon in austenite. Of equal significance is the implication that gaseous media may be employed with reasonable accuracy in making these determinations. The Steady State Diffusion of Carbon in Au~tenite The fundamental experiment defining diffusion in solid metals may be readily performed for carbon in gamma iron.' For this experiment a thin plate of medium carbon steel is chosen. The surfaces of this plate may be taken as two parallel planes which may be considered infinite for points well in the Center of the planes. These two planes are held at different concentrations of carbon at a constant temperature. This temperature, 1700°F for example, is one where the single phase: carbon in solution with gamma iron, exists. When these conditions are held for a sufficient time the concentration of carbon of the different points of the solid ment down towards its steady state value. At points well removed from the ends, the concentration will remain the Same along planes parallel to the surfaces of the plate.

Jan 1, 1948

By F. E. Harris

It has been said that carbon is "ubiquitous" with reference to iron alloys. Certainly at temperatures where carbon and iron form the solid solution, austenite, it may be readily added to, or removed from, steel surfaces. Differences in concentration potential are the sole requirements for carbon flow. To measure the rate of carbon flow, a proportionality factor, D, is arbitrarily expressed in units of (length)2 X (time)-'. If the term used for carbon concentration is weight Pet C, as is customary, then a factor must be found, changing this term to One of weight Per unit volume when the diffusion coeficient, D, is used in flow formulae. The determination of D values for carbon is complicated since D varies with the concentration itself. The Matano method has often been employed for systems involving a variant D. This method expresses all evaluation of unsteady flow whereby D is given a relationship with the numerical value of C-x slopes. The author contends that this solution is incorrect, except when D is invariant. The primary purpose of this paper is to support this contention. Here diffusion is controlled under two conditions of flow. The first part deals with the steady state; the second part considers unsteady flow under definite restrictions. Beginning with the fundamental concept, the development is continued until equations for C-x curves are obtained. The solution is then subjected to experimental data. It is realized that a great amount of reliable data is required for a rigorous proof. KO such research is claimed. Instead an attempt is made to set forth the physical significance of the diffusion mechanism, and particularly to express the factors which influence the flow of carbon in austenite. Of equal significance is the implication that gaseous media may be employed with reasonable accuracy in making these determinations. The Steady State Diffusion of Carbon in Au~tenite The fundamental experiment defining diffusion in solid metals may be readily performed for carbon in gamma iron.' For this experiment a thin plate of medium carbon steel is chosen. The surfaces of this plate may be taken as two parallel planes which may be considered infinite for points well in the Center of the planes. These two planes are held at different concentrations of carbon at a constant temperature. This temperature, 1700°F for example, is one where the single phase: carbon in solution with gamma iron, exists. When these conditions are held for a sufficient time the concentration of carbon of the different points of the solid ment down towards its steady state value. At points well removed from the ends, the concentration will remain the Same along planes parallel to the surfaces of the plate.

Jan 1, 1948

By George A. Moore

A recent survey of existing analytical results, and an attempt to correlate them with each other and with the known history and behavior of the samples, indicated that none of the commonly applied methods could be considered established as intrinsically reliable. It was. therefore, desired to attempt to establish the reliahility of some one method by external evidence. If this were to be accomplished, other methods could then be evaluated in terms of the method establibhed. The correct method was accordingly to be chosen without regard for cost, speed, or convenience; with the requirements for routine application to be reserved for 1ater consideration. The method of total combustion was chosen and submitted to a limited number of tests against primary standard samples. Considerable experimental difficulty was encountered, indicating that additional work on the experimental arrangements is desirable. While the work to (late by no means represents a completed investigation, it is helieved that the combustion method is basically sound and that its development should be continued. Choice of Method Of the several available methods, mechanical disintegration. electrochemical methods'2'3 modifications of the Sieverts experiment,% and vacuum fusion, were all judged to contain one or more factors of un- certainty not at present completely cvaluated or suhject to complete control. These methods, therefore, were considered currently unsuitable for referee purposes. Solid evolution was considered to be of doubtful significance when conducted in the alpha range. A reasonable chance for a true analysis was found for evolution in the gamma range. Preliminary tests have indicated a very slow rate for evolutioll from gamma iron. indicating a running time of possibly 100 hr. for a one-centimeter sample. Difliculty in distinguishing such slow. evolution from blank gas was anticipated, hence the method was not consitlerctl the most suitable for the present purpose. The combustion method was evaluated as being most sound on fundamental principles. The only important unknown would be to determine that the iron oxide formed did not occlude water at the tcmperaturv of the combustion.with the odvious precautions of using a sound and clean specimen, providing a system sufficiently tight to give acceptable blanks in longtime runs, and providing a suficicntly sensitive measuring system, reasonable, precise, and truthful analytical results could be logically expected. Apparatus The equipment as originally operated is shown in Fig. I, and the glassw-are in its latest modification in Fig. 2. The sulphuric acid drier and small safety tube in the upper right of Fig. I were replaced by a KOH drier and combined manometer safety tube, to permit operation at reduced

Jan 1, 1945

By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill' put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor's minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor's minimum work problem imply the solutions of Bishop and Hill's maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970