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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

By Lendall P. Warriner, Blandford C. Burgess

Jasper County lies just north of the geographical center of Georgia, bounded on the west and north by the Ocmulgee River. The county seat, Monticello, is approximately 65 miles east-southeast of Atlanta and 40 miles north of Macon. It is served by the Macon-Athens branch of the Central of Georgia Railway Co. and by five paved highways converging from adjoining county seats. Farming and lumbering are the principal local occupations. About half the county is covered with pine and mixed hardwoods; a large part of the forested land is owned by the Soil Conservation Service of the Department of Agriculture in its Piedmont Land Utilization Project. The topography is one of gently rolling field and forest with occasional hills rising 100 ft or: more above the creek beds. Though annual rainfall is in the neighborhood of 60 in., most of it falls in torrential downpours of short duration which tend rapidly to erode the red soil and convert the country roads to greasy tracks of red mud.

Jan 1, 1949

By Leo Behr

RECENT years have seen important practical advances in the construction of recording instruments for use with thermocouples. The difficulties of the problem will be appreciated when it is remembered that a 10° F. change in temperature of a base-metal couple at 1500° means a change in the electromotive force of about 0.00035 volt. In a circuit having a resistance of 350 ohms, this means a change in the current of 0.00000,1 amp.; and despite this requirement of great sensitivity the instruments must be sufficiently robust to withstand the rough usage which is so often their lot. Two methods are in common use for the measurement of the electromotive force produced by a thermocouple: 1. The milliammeter method, in which the current produced by the thermocouple in a circuit of known resistance is measured and from. this the electromotive force is deduced by Ohm's law. 2. The potentiometer method in which a known potential difference is opposed to the thermocouple electromotive force. The use of thermocouple and milliammeter for measuring temperature introduces some possible sources of error, for the reading depends on a number of factors, including the following: (1) Electromotive force set up at the hot junction, (2) electromotive force set up at the cold junction, (3) resistance of the circuit including thermocouple, lead wires, and meter, (4) field strength of magnets, (5) strength of controlling springs in meter, (6) friction at pivots, of pointer on paper, etc. It is obviously necessary to so design and maintain the installation that the reading is independent of all the factors except the first. The electromotive force set up at the cold junction can easily be taken care of provided it is constant. This has been approximately accomplished by burying the cold junction in the ground or actually secured by locating it in a container, the temperature of which is kept constant by means of a thermostat.

Jan 9, 1919

In reply to inquiries and comments which have reached me since the publication of this paper, and in explanation of some seeming discrepancies between my statements in the text concerning the amount of displacement of the faults, on one hand, and certain figures in the plates on the other hand, I give here, with some additional remarks, my measurements of the displacements in the different sections, which it originally seemed unnecessary to print : By displacement, I mean neither the throw, i.e., the vertical distance apart of the two edges of a faulted bed (what Mr.

Jan 1, 1896

By Sallie McCabe Johnson

LIFE IN RUSSIA for the foreign woman is hard. It is up to her whether her days are spent in tearful longing for ironic or whether she :hakes the real effort to ferret out the interesting or amusing side of such exasperating conditions as ooh a Russian can conjure. So to begin Discard all promises.. This is perhaps the most difficult thins- to learn but promises in Russia are nut what they are at home. There are many reasons for ibis, sonic good and some bad but whatever the reason. the fact remains that they are usually worthless- as each of us must slowly learn In, disappointment after disappointment. Also we must learn that we cannot expect to get or to do a certain thing just because someone else has done so. What we did yesterday perhaps cannot be dune today. What we purchased air hour ago, oxen ten minutes ago- we cannot purchase now. What our neighbor did this morning we cannot do this afternoon. Changes arc continuous. Every person's experience is different from that of another aid this in a great measure accounts for the conflicting stories brought horns. In a land of chaos we live only from hour to hour and this is one of the exceedingly exasperating conditions to face. When I wished to visit Leningrad, an overnight nip from Moscow, more than a week's lime w as required to obtain a ticket, vi en through the efficiency of lntourist: alone I might have spent a month at it. Each day

Jan 1, 1932

By W. G. Matteson

The Gulf Coastal plain of the southern United States is that area bordering for a large part, the Gulf of Mexico and extending inland and northward to the main interior highland region. It is more or less V-shaped and includes the States of Florida, extreme southern Alabama, all .of Mississippi and Louisiana, the eastern and southern half of Arkansas, and the eastern, southeastern, and southern portions of Texas. While the contents of this paper apply to. the Gulf Coastal plain in general, they are intended to refer more specifically to that portion of the plain included between the 90th and 97th meridians, and the 29th and 33d parallels, an area that may be described geographically as comprising western Mississippi, all of Louisiana, part of eastern and all of south-eastern Texas. It is within this area that numerous and prolific oil pools have been developed during the last 17 years.

Jan 2, 1918

By Joan Melcher

The oil embargo and increasing disillusionment with nu- clear power have put this country's abundant coal reserves in growing demand. Both the government and industry are looking toward increased coal mining, and with this goes an increased interest in new and advanced methods of coal utilization. One advanced coal system stands out among the rest-magnetohydrodynamics (MHD). Its high efficiency, strong probability of sulfur dioxide control, and limited consumption of cooling water place MHD in a unique position to help the power generation industry. Another point in MHD's favor is the capital costs of operation, which are lower than those of other advanced technologies. However, initial costs are higher and realization of a commercial MHD plant in this country may be more than a decade away.

Jan 12, 1977

By Gilbert Soler

PRODUCERS of alloy steels recognize the importance of chemical composition in rela-tion to the hot-working properties and the typical surface defects found in their prod-uct. Each analysis of steel has its own peculiar characteristics. Under conditions of standard mill practice each analysis is susceptible to certain types of defects. Mill practice must be varied to obtain the best combination of surface and internal quality in the product. Chemical composition influences the cast structure and crystallization character-istics of the ingot. It also determines the rate of heating and cooling, the plastic hot-working range, and the phase structure of the steel at various temperatures as well as the tendency toward scale formation and decarburization, This paper endeavors to emphasize the manner in which chemical composition affects the various properties of steel, and to indicate the relative impor-tance of these factors in relation to the hot-working properties and surface charac-teristics of killed steel. The influence of chemical composition may be outlined as follows: I. Effect on the cast structure of steel, including: A. State of deoxidation, and type of inclusions. B. Gas content of steel. C. Freezing point and melting point of steel.

Jan 1, 1940

By A. J. Williams

THE province of Saskatchewan, situated in the center of the Great Plains region of Canada, has, like most prairie areas, an essentially agricultural economy. Most of its population of about 860,000 is located in the southern half of the province in the farming and ranching areas. To the north of the prairie is a broad forested belt supporting a considerable timbering industry, and the northern one third of the province is glaciated pre-Cambrian rock formation. This latter area is relatively barren of vegetation, but the presence within it of a considerable variety of radioactive, noble and base metals, and industrial minerals has been shown by prospecting in recent years.' Glacial Geology The Keewatin ice sheet, considered to have accumulated in the country to the west of Hudson Bay in Pleistocene time, covered at its maximum advancement almost all of Saskatchewan and extended south of the international boundary. Only in the Cypress Hills in the southwest and around Wood Mountain in the south central portion of the province did the preglacial formations escape the action for this glacial period. The bedrock of the plains and forest areas therefore is overlain by moraines and modified glacial drift, which vary in thickness from a few feet to 400 or 500 ft.' Glacial action in the pre-Cambrian area of the province was largely erosional, most of the more recent formations and some of the pre-Cambrian rock being transported out of the area to the south and west. It has been estimated that about 13 pct of this area is composed of lakes and rivers not too adaptable to rail or water transportation, so that until the use of aviation for exploration purposes became general, development of the area was slow. To the south, the heavy mantle of glacial drift has to some extent deterred the discovery of industrial minerals in the bedrock underlying the forest and prairie regions3 At the same time, this drift contains numerous deposits of those most elementary and necessary industrial minerals, sand and gravel. Sedimentary Basin The major feature of the sedimentary deposits underlying the plains regions is the basinal structure known as the Moose Jaw syncline, which runs from the southeast corner of the province in a northwesterly direction. To the west of this syncline the formations curve upward, then have been faulted and further upthrust to appear at the surface in the foothills of the Rockies in Alberta; to the east and north they curve upward into Manitoba and northern Saskatchewan, but the surface contacts are covered mostly with glacial drift.238 The axis of the syncline dips to the southeast, so that there is also an upward trend of the formations along the axis to the northwest. In illustration of the regional structure underlying the province, the pre-Cambrian basement has been logged in drillholes at the following depths in several locations: Ogema (south central), 9390 ft; Gronlid (northeast), 2599 ft; Vera (northwest), 4422 ft; Big River (north northwest), 2348 ft. Fig. 1 indicates the general surface geology of the province, ignoring such glacial overburden as may overlie many of the bedrock formations. Also indicated is the approximate location of the axis of the Moose Jaw syncline.' Industrial Minerals Clays: The province is fortunate in possessing a widespread distribution of clays of ceramic value, ranging from those used for heavy structural products to the high grade pottery and china clays. Shales suitable for brick and tile production are found in the Upper Cretaceous and Tertiary formations across the south of the province where the glacial drift is thin or nonexistent. Many deposits of glacial lake clays suitable for such wares are found scattered over the rest of the province south of the pre-Cambrian area. The Whitemud formation of the Upper Cretaceous is a narrow sedimentary band of secondary clays found intermittently at points across the south of the province where glacial action did not disturb or remove them.' In the southwest corner of the province, around Eastend in the Frenchman River valley, the refractory clays of this formation are contaminated somewhat with iron compounds or other alteration products of basaltic rocks. This eliminates the use of those clays in true whitewares, as they fire to creamy buff shades at the lower temperatures and to a blue-specked grey at cone 8 to 12, (2280°F to 2390°F), the range commonly used in firing whiteware. However, for use in the production of colored artware, caneware, stoneware or crockery, and sewerpipe, this type of clay makes an excellent body that requires little or no addition of flint, feldspar, or other fluxing materials such as are required in the higher class of ware.' It is not a grade of clay that can be shipped great distances to the manufacturing centers, but a market for considerable tonnages has developed at nearby Medicine Hat, where cheap natural gas is available for the firing of the ware. Farther east in the south central portion of the province, the clays of the Whitemud formation are generally more refractory and white burning. The formation is divided into three zones, consisting of white clays, brown shale, and white sandy clays.

Jan 1, 1953

By R. A., Pallanch

SO many variations of lead-zinc ores occur in nature that it is impossible to state any rules that will apply to the concentration of ores of this type. Some have lead and zinc in approximately equal amounts; others may have pre- dominant amounts of one or the other metal. There are gradations from all sulfide to completely oxidized minerals. Some such ores carry little pyrite, others contain much more pyrite than they do lead and zinc combined. The behavior of ores in flotation is largely a function of their lead-zinc ratios. their content of pyrite or pyrhotite, the nature of existing soluble salt conditions, the character of the gangue constituents: and the speed with which the minerals float. For the purposes of this paper only those lead-zinc ores handled commonly in present-day flotation practice will be considered. These are practically all-sulfide ores with relatively minor degrees of sulphatization or oxidation.

Jan 1, 1936

By Hans Lundberg, Basil T. Wilson, H. Steuart Scott

FOR the benefit of those readers who may not be in close touch with present practices in the geophysical prospecting for ore, brief reference will fiat be made to the advantages and shortcomings of the methods to be discussed. Magnetic and electric methods are generally accepted as the most useful for ore prospecting. By magnetic methods, magnetic intensities that are not normal may be recorded and outlined. From these can he located concentrations of such highly magnetic minerals as magnetite or pyrrhotite, which sometimes occur in such large masses that they are of economic value in themselves. More often. however, these magnetic min¬erals are associated with others, such as copper, zinc, lead, gold, and silver, which, if existing in sufficient concentration and quantity, may constitute valuable ore bodies. It is therefore only when pyrrhotite and magnetite are present in these bodies that the magnetic method can be used to indicate their presence.

Jan 1, 1945

By Howard S. Bryant

FROM the viewpoint of the oil producer, the oil refiner, the oil marketer, and the investor, in oil securities, a brief picture of the crude oil supply and demand in the present critical season of the year will be timely and interesting. Although crude oil production has been in a comparatively poor statistical position this year, increased sales and sustained refinery and crude oil prices have allowed increased profits for many oil companies. The large amount of crude oil going into storage during the present period of peak consumption, just previous to the major yearly fall decline in consumption, has caused oil producers to make plans to leave the oil in the ground for the present in several of the areas of large flush production. The present moment is looked on as the turning point in the current year.

Jan 1, 1929

By W. F. Holbrook

THE problem of sulfur control is important in all blast-furnace operations but particularly for certain grades of steel because of the rigorous specifications. During the past decade the tendency has been to produce pig iron, and, hot metal of lower sulfur content. As most of the sulfur in the ion originates in the fuel, the use of high-sulfur coke demands modifications in practice to meet sulfur specifications. While it is generally known that high temperatures and more basic slags favor desulfurization, operators as a rule produce the most acid slag that will permit proper desulfurization. The viscosity of blast-furnace slag has been thought to be related to desulfurization and has been investigated by Feild and Royster1, also McCaffery and his associ-ates2, but apparently no systematic effort has been made to determine the relative desulfurizing powers of slags over the range of composition encountered in practice.

Jan 1, 1936

By F. B. Plummer

PRODUCING operations abroad during 1940 were shrouded in the fog of war. Little, if any, concrete information is available, and the data that issue from the belligerent countries are too frequently distorted for military purposes, for the volume of supply of gasoline and fuel oil has become an important strategic secret. Despite this lack of information signs indicate the spread of a slow paralysis which is gripping producing operations in foreign countries. Only in the Caribbean area are developments proceeding normally and even there the destruction of the Western European market is being seriously felt. This creeping paralysis is being brought about partly by the serious shortage of materials so necessary for drilling and other producing operations such as steel, machinery, and the like-together with a scarcity of that prime munition of war-money. Markets too have been curtailed by the operation of exchange control as all exchange is needed to support war efforts. As a result, gasoline is tightly rationed in all belligerent countries. The growing casualties in shipping are fast restricting the water-borne trade in petroleum, but have had a local stimulating effect in some areas where the risk is less or where water-borne transport can be efficiently used as for instance Trinidad and Egypt. The type of product needed for war effort, particularly the great demand for aviation gasoline, has changed the schedules of .refinery operations. As a result of all these influences the world oil picture outside the United States- has vastly changed during the year.

Jan 1, 1941

By N. H. Jensen

SINCE the sixties, Utah has been one of the leading metal mining states of the Union. During the last fifteen years its mines have supported the largest smelting center in the world. Its rank as a metal producing state is reflected by its 1924 production which had a value in excess of $65,000,000 making it the leading silver producing state, third in both copper and lead and sixth in gold production. During the past year, metallurgical developments for the recovery of zinc contained in lead ores has made rapid progress so that the future zinc output will be of substantial importance. The largest silver mines of the nation and the world's largest open cut copper mine are within its borders. Settlement of Utah started in 1847, with the advent of the "Mormons," and originally the area of the state was much greater than now. The first metal mining

Jan 1, 1925

By AIME AIME

FEATURES of the second fall meeting of the Petroleum Division for 1941, held at the Ambassador Hotel, Los Angeles, Oct. 29-30, were the forum on the Paloma Plan on Thursday after- noon, the large attendance from east of the Rockies, and the dinner on Wednesday evening sponsored by the Southern California Section and at which President Suman spoke on the strategic minerals and metals situation. The attendance was large and the technical fare uniformly good ; the presiding officers had the proceedings well in hand at all times and kept things humming. Some- times it was necessary to taper off the discussion because of pressure on time. All this was due to careful groundwork before the respective sessions. These presiding officers deserve citation: L. W. Huebel, Howard Pyle, E. K. Parks, Carlton Beal, E. G. Trostel. R. W. French, Jr., John Dodge, and H. N. Marsh. The Los Angeles local commit- tees and the Southern California Section deserve much credit for the arrangements, which were recognized by suitable resolutions at the end of the meeting.

Jan 1, 1941

By Ernest A. Hersam

IN every commercial establishment,' it is customary and necessary to take inventory, periodically, and to account for profits and detect losses, to achieve productiveness and enhance efficiency. So, too, in the ordered life of every individual, there is the need of periodic introspection. The exercise of the Sabbath for rational thought, the utilization of pause, or rest, from the technique of daily occupation, orient the efforts. These are the constructive opportunities by which we grow always better than we were. Thus, also, there' is need of a periodic analysis of the organizations to which we belong and toward which we con- tribute. So we find' reason for the fitness of our loyalty. There seems to be no half-ground for the engineer. Whatever presumes to bear his name demands either the crushing pressure of his heel or the supporting pressure of his hand.

Jan 1, 1929

By P. W. Bridgman

DURING the war, the Navy undertook the construction, under my direction, of an experimental gun embodying features designed to lessen the cost and time of production. These experiments were initiated after representations as to their, desirability had been offered by myself, by the Naval Consulting Board, and by the National Research Council. The first drawings were made in June, 1917, and the experiment was completed in November, 1918. For the sake of clearness it will pay to recapitulate briefly the fundamental idea of gun construction. It is well known that if a hollow cylinder is subjected to internal fluid pressure, the maximum stress occurs in the inside layers, the outer parts carrying much less than their due share of the stress. This inequality of stress is more pronounced the thicker the walls of the cylinder. If such a cylinder is pushed to the elastic limit, failure in elasticity will take place long before the outer layers have reached the limit of their capacity. Economical use of the material would demand, however, that all parts of the cylinder reach the limits of their capacity simultaneously. This may be brought about, at least in cylinders of not too great thickness, by producing in. the inner layers an initial compression, and in the outer layers an initial tension. The effect of internal pressure is at, first to relieve the compression of the inside layers, while increasing the tension of the outside layers. If the initial stresses are properly distributed, all parts of the cylinder will reach their elastic limits simultaneously, thus giving a cylinder of maximum strength for its weight. In gun construction as hitherto practiced, this initial distribution of stress is produced either by winding the inner tube with wire, a common English practice, or by shrinking hoops over the inner tube, which has been the standard American practice. Either process is long and expensive, particularly with the larger guns, 12- or 14-in., which require

Jan 2, 1920

By AIME AIME

THE fall meeting of the Petroleum Division, held at Tulsa, Okla., on Oct. 11 to 14, devoted two days to technical sessions and two to field excursions. A representative attendance of 250 to 300 engineers and operating officials engaged in oil production marked the sessions and paid close attention throughout to a notable series of highly technical papers. Restricted as the program was to consideration of production problems only, the time proved too short for discussion or even the presentation of the 20 papers submitted. Much informing and pertinent discussion none the less took place, and the sentiment was general to the effect that the meeting was one of the best ever held by the Division. The meetings were held in the auditorium of the Municipal building and local arrangements were well looked after by the Mid-Continent Section of the Institute and the Oil and Gas Association. The combination of the three organizations served to bring together engineers and operators most usefully. F. Julius Fohs, chairman of the Division, presided at the sessions on Monday. Tuesday morning John M. Lovejoy of the local section took over this responsibility in the absence of T. E. Swigart, who was detained in California. The afternoon session was presided over by A. G. Heggam of the Oil and Gas Association and the Tuesday evening banquet by W. C. Franklin of the same organization.

Jan 1, 1926

By R. I. Jaffee, J. G. Dunleavy, W. Hodge, H. R. Ogden

Jan 1, 1949