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By D. Harrington

WHEN the word gas is mentioned in connection with mining, almost invariably it is inferred that the explosive gas, methane, is in mind and that it must refer to coal mining. While it is true that methane occurs, or is likely to occur, in almost any or all coal mines, it is also a fact that the metal mines of the world have in them by far a greater variety of gases than have the coal mines. In many cases the gases in metal mines are as dangerous to individuals as the gases likely to be found in coal mines; in some instances the metal mine gases are even more deadly. The coal mine is more likely to have methane than the metal mine, in rare instances it may have high percentages of nitrogen or high carbon dioxide, or there may be a deficiency of oxygen where the air is confined in a blind end or in a sealed region; much more rarely there are found in coal mines in relatively small percentages, ethane, or other hydrocarbons with odor of ether, gasoline or kerosene, or there may be minute percentages of hydrogen sulfide. In time of coal mine fire or explosion, there is likely to be high carbon monoxide (4 per cent. or over in some cases) and if the coal contains much sulfur, there may be some sulfur dioxide in the fire fumes. In metal mines there are a number of cases of occurrence of methane and attendant explosions; some metal mines have appreciable percentages of the decidedly explosive hydrogen; in some metal-mining regions carbon dioxide flows into the mine, fills the workings and overflows just like water. In other regions, at many working faces there are high-temperature gases containing a mixture of gases of sulfur (sulfur dioxide, hydrogen sulfide and possibly SO3 in some cases) together with carbon dioxide and nitrogen, and the deadly hydrogen sulfide in lethal proportions is found in some high-sulfide metal mines at blasting time. Carbon monoxide constitutes a decidedly dangerous day by day hazard in connection with metal-mine blasting, because of the heavy charges of dynamite that are used and the use of fuse, which in burning gives off much carbon monoxide. The poisonous gas hazard is accentuated because of the relatively small openings where metal-mine blasting is done and to the inefficient ventilation of the usual metal mine.

Jan 1, 1930

By W. R. Ingalls

IN THE years immediately preceding 1914, the American people earned an aggregate income of 33 to 34 billion dollars, of which they saved about five billion, the annual saving being expressed mainly in the form of houses and railway extensions; to a less extent in public utilities, public improvements, factories and mines; and to a very small extent in foreign investments. It appeared needful that we should save and invest annually in these ways about 15 per cent. of our aggregate income in order to keep the development of our plant, so to speak, ahead of our steadily growing needs. The common knowledge that at present our housing and railway facilities are inadequate suggests immedi-ately that we have been running behind the pre-war ratio of reinvestment. Since 1919, we have not had any carefully prepared, authoritative estimates of the national annual income. However, with some experience in this subject, I have ventured to make rough estimates, which rest on solid foundations, although some rather empirical develop-ments are involved. Such estimates would be consid-ered good work in this field if they fell within limits of 10 per cent., plus or minus. Even so, these data are more useful when quickly available than more accurate data that are belated; for recognizing that there is a margin of error we can at least get a reasonable and approximate idea of how things are going.

Jan 2, 1923

Jan 1, 1951

By Felix Shay

THE Agua Fria mine is in eastern Honduras at Lat. 140° 06' N., Long. 86° 36' W. Danli, the seat of the local municipal government, is the nearest town. The property is approximately 44 miles east of Teguci-galpa, the terminus of a truck road from the Pacific coast. The mine lies at an altitude of 3300 ft. with surrounding elevations as high as 6000 feet. For 20 years the oxidized croppings of the Agua Fria vein had been worked intermittently when in 1927 an attempt was made to open the property. A shaft was sunk 300 ft. and considerable ore was blocked out, but before a mill could be installed financial difficulties arose and the mine reverted to the original owners. Erle P. Halliburton, of Los Angeles, purchased the property in 1934. At that time a careful consideration of all factors involved showed that air transport was the only practical method of moving the equipment and machinery necessary to commence production. The other alternative was by muleback, which required sectionalizing all equipment to a maximum load of 200 lb., and during the rainy season this type of freighting was subject to serious delays. It was decided to purchase a trimotor Ford powered by three Pratt and Whitney Wasp B motors developing 400 hp. each. There were several reasons for the choice: (1) this type of plane was available at a reasonable price, owing to its replacement by faster models on most of the airlines in the United States; (2) the ship was capable of carrying a pay load of 3000 lb. over the required distance; (3) since this airplane had been widely used there would be no difficulty in securing competent personnel or in purchasing spare parts. It was necessary to rebuild the plane for cargo service. The windows were removed and the fuselage was entirely covered. A hatch was cut in the top of the fuselage to receive heavy crane loads and pieces of freight that were too large or too long to go through the rear door. The seats were removed and the interior of the plane was lined with Duralumin sheets. A heavy-duty landing gear was installed and the floor was reinforced.

Jan 1, 1940

By Richard F. Moe

INTEREST in developing White Pine, considered since 1942, was renewed by the Korean conflict and its shortage of domestic sources of copper. In view of this Morris F. La Croix, president of Copper Range Co. of Boston, and of its wholly owned subsidiary, White Pine Copper Co., worked an agreement out with Government officials. Essentially the contract called for a construction loan of $57,185,000 at 5 pct interest, with $13 million additional supplied by Copper Range. Defense Materials Procurement Agency contracted for 243,750 tons of copper from the first 275,000 tons produced, at a base price of 25.5& per lb, the contract to expire Dec. 31, 1961.

Jan 4, 1954

By T. W. Healy, P. Somasundaran, D. W. Fuerstenau

The flotation behavior of quartz in the presence of alkyl ammonium acetates as a function of alkyl chain length has been interpreted in terms of hemi-micelle formation at the solid-liquid interface. The van der Waals cohesive free energy that is responsible for hemi-micelle formation has been found from these results to be 1.0 kT per CH2 group. This is in excellent agreement with literature values obtained from research on the properties of micelles in bulk systems. Collectors of the type CH3(CH2)n-2CH2-P, where P is a polar group and n is the number of carbon atoms in the straight alkyl chain, will induce flotation of an appropriate mineral at lower concentrations as n increases. This reduction in collector concentration with increasing n has been reported for such systems as xanthates on sulfides1,2 and amines on quartz.' The effect of chain length of alkyl surfactants on such solution properties as conductivity,' surface tension,' and solubility6 and such interfacial properties of solids as contact angle7 and electrokinetic potential8 have received considerable attention, but only limited quantitative descriptions of the effects have been given. The electrokinetic studies of alkyl amine salts on quartz indicated that the solution concentration of collector at which the marked change in electrokinetic potential of quartz occurs decreases systematically as the length of the alkyl chain increases. The aim of the present work was to obtain a quantitative description in terms of current theories of flotation of the effect of the hydrocarbon chain of alkyl ammonium acetates on the flotation behavior of quartz. BASIC PRINCIPLES The marked changes in electrokinetic potentials of quartz in dodecylammonium acetate (DAA) solutions were postulated to result from the association of adsorbed collector ions into two-dimensional aggregates, called hemi-micelles.9 Subsequently, the rapid increase in flotation rate of quartz was shown to coincide with hemi-micelle formation." We would like to discuss briefly the concept of hemi-micelles in terms of recent interpretations of micelles in bulk solution. Micelle hypothesis: In dilute solutions, alkyl ammonium and related salts behave as ordinary strong electrolytes, but at a certain concentration there is a marked change in physical properties of the solutions, e.g., in equivalent conductance, transport number, freezing point lowering and viscosity. To account for these phenomena, McBainl1 introduced the concept of micelles, which are aggregates of long-chain ions. It is believed that the ionic heads of the constituent ions of the micelle are in contact with water, whereas the nonpolar groups turn away from it and are in contact with each other. Work must be done to bring these charged polar groups together, but energy is gained (i.e., so called van der Waals cohesive energy) when hydrocarbon chains are expelled from the water and allowed to associate. For a given polar group, the tendency to form micelles will therefore strongly depend on the hydrocarbon chain length. Theoretical treatments of micelle formation by Shinoda12 and Phillips13 and others lead to the following expression for the concentration at which micelles form (the critical micelle concentration or cmc) in aqueous solutions of long- chain electrolytes

Jan 1, 1964

By FREDERICK W. BRADLEY

MINING methods are evolved rather than devised; and the process is slow. The advance in no particular year is phenomenal, but progress is un- questionably being made constantly in several directions: (a) better adaptation to given conditions of various "systems" of mining; (b) better utilization of mechanical equipment ; (c) improvement in working conditions so as to promote the health, safety and efficiency of the workers. During the year 1930 operations were commenced at a number of important new mines. Methods adopted are not new, except in minor detail, but the fitting of methods to conditions is interesting, because, as the engineers presumably started from scratch, they have selected the methods that experience under similar conditions has indicated as being the best.

Jan 1, 1931

Jan 1, 1933

By M. C. Fuerstenau, J. D. Miller

The response of calcite to flotation with saturated fatty acids and alkyl sulfonates of various chain lengths is presented. The amount of collector re-quired for flotation is shown to decrease systemati-cally with increasing carbon content from 8 to 12-carbon atoms per molecule. This systematic flotation response is correlated with the solubilities of the calcium-collector salts, which were established with a nephelometer. The 14-carbon collectors deviate from this systematic behavior, and no flotation is possible with the 16-carbon homologs. As determined by infrared analysis, the mechanism of collector adsorption involves a specific chemical reaction be-tween the collector and the surface. A reaction of the form CaCO3(s)+ 2 RCOO"=*=Ca(RCOO)2(s) + C03= is suggested. The pH of the system is also shown to be a most important parameter as it controls the carbonate, calcium, and collector ion concentrations in solution and thus controls flotation response. The importance of hydrocarbon chain length of collectors was recognized early, and various studies have been made on this aspect of flotation. Wilkinson, ' for example, noted that as the chain length of alkyl xanthates is increased, the amount of collector required for flotation of sphalerite is decreased. The same effect has been shown in the flotation of galena.2 Similar results were obtained when malachite3 and calcite4 were floated with various fatty acids. DeBruyn5 has shown that a similar phenomenon occurs when quartz is floated with amines at constant pH. Recently, Fuerstenau, Healy, and Somasundaran6 correlated this phenomenon with the van der Waals cohesive free energy of association of the hydrocarbon chains. It seems unlikely, however, that chain association could be involved in the sulfide and carbonate systems with the collector additions employed, especially with the short-chain xanthates. Rather, it would seem that the decrease in collector concentration with increase in chain length noted for flotation is related to the solubility of the metal-collector salt. The purpose of this investigation is to verify this premise and also quantify this phenomenon if possible. Calcite was selected for study with both alkyl sulfonates and saturated fatty acids as collectors. EXPERIMENTAL MATERIALS AND METHODS The collectors used in this investigation ranged from 8 through 14 carbon atoms per molecule. The fatty acids had a reported purity of greater than 99%. The sodium alkyl sulfonates were provided by the Marathon Oil Cot, Littleton, Colorado, and had the

Jan 1, 1968

By C. S. Barrett

WhEN a collimated beam of protons or other energetic particles is scattered by a single crystal, the emerging particles produce patterns that contain much crystallographic information. Calculations of the trajectories of individual particles can predict with reasonable accuracy the complete pattern (which is related reciprocally to channeling, now studied in detail6) but the task is a lengthy one which has been completed for very few cases. A many-beam dynamic diffraction calculation of the patterns would be even more difficult and in some cases may be invalid. Because of these complexities, simple methods that will predict to a rough approximation the relative intensities of the lines in films of the back-scattering patterns of a given crystal are wanted. I have found a method which, although it is not a valid computation of intensities or of film darkening by either dynamic or kinematic diffraction principles or by trajectory calculations, nevertheless is found to be useful in practice. It has been tested on several crystal types,7 and is here tested on additional ones. The method consists in first calculating the structure factor F(hk1) for the (hkl) plane, of spacing d, by the familiar equation: where the summation extends over the atoms in the unit cell and fj is the atom scattering factor of the jth atom (using tables computed for electron diffraction, preferably those computed without exchange). Then the F values are squared and summed over all the orders, n, for which F2 has an appreciable value, giving a quantity: Finally, I, is expressed as a percentage of Ic for the

Jan 1, 1970

By Irving Fatt, R. M. Weinbrandt

Efforts have been made for many years to observe pore structure of sedimentary rocks on a microscopic scale. A better description of the pore structure in reservoir rock would aid in the development of relations between flow through tube network models and flow in consolidated reservoir rock. The unique qualities of the scanning electron miscroscope (SEM) make it the ideal tool to use in a study of pore structure. Previous methods of studying pore structure included plastic casts of pore space and optical microscopy.l-7 There is now available a new method to observe three-dimensional flow channels in reservoir rock: a scanning electron microscope having variable magnification from X20 to X20,000 and approximately 1000 times the depth of focus of the conventional light microscopes. This microscope also can obtain stereoscopic images and can measure and diagram flow channels so that it is possible to construct a network of tubes that will model consolidated reservoir rock. THEORY OF THE SCANNING ELECTRON MICROSCOPE The scanning electron microscope (SEM) functions by projecting a beam of electrons through magnetic focusing lenses at a specimen and recording secondary electrons excited by the primary beam. The amount of secondary electron emission portrays the topography of the specimen because more secondary electrons are emitted from high points than from low points. A schematic of the SEM is shown in Fig. 1. The property of the SEM that is of most importance in this study is its great depth of focus. The depth of focus results from using electrons

Jan 1, 1970

By F. Louis Grammer

The difference between blast-furnace gas and ordinary producer-gas is chiefly that blast-furnace ga,s is higher in CO2 and lower in hydrocprbons and hydrogen, as is shown in Table I. Table I.— Volume-Composition of Producer-Gas and Blast-Furnace Gas. Producer-Gas. Blast-Furnace Gas. Per Cent. Per Cent. (Volume.) (Volume.) CO......22 to 33 25.5 CO2........ 6 to 3 13.0 H...13 to 7 1.5 CH4........ 3 to 1.5 0.0 N..54 to 60 60.0 If natural gas, water-gas, or by-product coke-oven gas be available, blast-furnace gas can be made to resemble very closely in calorific value the average producer-gas by merely mixing in one of these products, which are richer in hydrocarbons and hydrogen. Blast-furnace gas, however, possesses a virtue which is sometimes absent in producer-gas, especially with coals very high in sulphur—namely, that blast-furnace gas is relatively free from sulphur. In some regions the sulphur in coal is an acute problem, and it is highly desirable to find uses for the mine-products which are specially high in sulphur-content. An advantage would be gained if the coal were coked before charging into the gas-producers, but this adds to the expense. Sulphur may be partly eliminated from coal by washing it, the success depending upon the form in which the sulphur occurs, and upon the efficiency of the washer, but it cannot always be removed to the extent desired at most American plants. It is not practicable to remove all the sulphur from producer-gas by washing it, though Mr. Reinhardt, of Germany,

Jan 1, 1909

S. LE FEVRE, Forest Glen, N. Y. (communication to the Secretary*).¬F. L. Nason thinks I could not have studied Mr. Witherbee's paper and doubts the arithmetic used, but in his discussion arrives at practically the same conclusion. He says 10 ft. thickness of ore over a square mile should give 27,878,400 tons, allowing 10 cu. ft. per ton of ore. This is correct, but if he reads carefully he will see that this depth of ore was figured as covering one-tenth of the surface, which reduces the figures to those used by Mr. Nason. I did not say, however, that there were 2,300,000,000 tons of ore in New Jersey, but that applying the same method of computation as used by Mr. Nason, to the area of the iron ore-bearing gneisses in New Jersey, we would get a total of 2,300,000,000. I did say, "In this area are located 366 magnetite mines that have been worked more or less. These lenses may easily be capable of producing (on an average) 1,000,000 tons each, and there are probably double the number listed not opened up." Thus my estimate for New Jersey, as far as any was made, would be: Probable ore 366,000,000 Possible ore in addition 732,000,000 1,098,000,000 Mr. Nason's final conclusion of his personal estimate was one-half of what he erroneously read to be the estimate given in the paper, or half of 2,300,000,000, which equals 1,150,000,000. So the two estimates seem to differ less than 5 per cent., and we have the two sister States of New York and New Jersey on an equal footing of productive possibilities in magnetic ore.

Jan 6, 1917

PLANS for the World's Engineering Congress in Japan are rapidly taking shape. The Congress itself will be held in Tokyo in the week beginning Oct. 30, and will be followed by a second week of short excursions to points of interest, and this, in turn, by a two weeks' excursion through the Inland Sea and to Manchuria. Aside from the time each may desire to spend in Japan, from 30 to 42 days, according to route, must be allowed for travel from New York to Tokyo and return, with correspondingly' shorter time from intermediate points. The American Express Co., which has been appointed official travel agents by the American committee, has fur-nished the following estimates:

Jan 8, 1928

By Robert L. Clayton, Arthur Baker

Two massive sulfide zinc-copper ore bodies are in quartz-sericite schist (probably formed by regional metamorphism of sediments) and andesite of the Precambrian Yavapai Series, on opposite sides of a large rhyolite mass. The Copper Queen ore body is conformable with bedding of its schist host rock, but the Old Dick ore body probably crosscuts the strata. A lens of low-grade mineralization in chlorite schist, associated with the Old Dick ore body, crosscuts through 150 feet of strata. The ore bodies are almost entirely enclosed by premineral faults with less than 150 feet of displacement. The minerals of the ores are pyrite, sphalerite, and chalcopyrite, with minor arsenopyrite and galena and small amounts of intimately associated chlorite, sericite, and calcite. Old Dick sphalerite-chalcopyrite intergrowths have mutual boundaries, and sphalerite grains contain abundant exsolved chalcopyrite. Copper Queen sphalerite-chalcopyrite intergrowths have extremely ragged boundaries, the sphalerite contains no exsolved chalcopyrite, and the ore overall has a schistose texture. The pre-mineral fault on the hanging wall of the Copper Queen ore body has had 100 feet of post-mineral displacement. Wall rocks of the Old Dick ore body locally have been sericitized. Andesite and quartz-sericite schists for at least several hundred feet around both ore bodies have been chloritized erratically and contain traces of copper.

Jan 1, 1968

By T. S. Hutchinson, C. E. Kemp

The bottom water drive analysis presented by Muskat has been extended to include fields with wider well spacings. Curves are presented from which volumetric sweepout, water-oil ratio, and rate relations may be calculated. The effects of non-unity ratios on sweepout eficiency and productivity decline have been studied by an approximate method. Also, the effect of gravity on volumetric sweepout has been approximated for a particurlar geometry. INTRODUCTION The purpose of this paper is to report work done in applying the analysis of bottom water drive reservoirs given by Muskat1 to a larger class of reservoirs, to extend this analysis to include the effects of gravity and non-unity mobility ratios in an approximate manner, and to investigate the rate of decline of productive capacity. The bottom water drive type reservoir is one where the oil is underlain by a water zone of sufficient thickness that water movement is essentially vertical. This system is defined in more detail in the appendix and a one well element is shown diagrammatically in Fig. 1. Muskat obtained solutions to the equations describing the volumetric displacement efficiency of idealized bottom water drive systems by assuming that gravity effects due to differences in density betwecn oil and water were negligible and that the mobilities of oil and water were the same. If either of these assumptions is not made, the complexity of the system makes an analytical solution well nigh impossible at the present stage of mathematical development. Coles and Stade' developed an approximation to consider these factors. The authors have refined approximations, starting with the same basic assumption, which should give a somewhat quantitative picture of bottom water drive performance when mobilities are not equal and the effects of gravity are not negligible. The results of these approximate calculations can then be used to obtain the decline in well productivity as the field is depleted.

Jan 1, 1957

By Leo F. Reinartz

Part II of a four-part series on the history of steelmaking in the US, points out the inadequate safety and living conditions that existed in steel mills at the turn of the Century. Also defined are furnace and process developments. OPERATIONS in steel plants today are highly mechanized. Men work in light, clean, orderly melting shops, making it difficult for old timers to convince young men that primitive, hazardous conditions existed in steel plants at the turn of the century. Working conditions then were very poor as compared to present day standards. In small plants especially, sanitary, locker, and washroom facilities, first-aid practices and stations were un- known Accidents were frequent and severe. Workers had a fatalistic attitude toward getting hurt. He who had an accident was looked upon as a hero. A dirty bandanna often served as a bandage. Infections were frequent. Electric cranes were in their infancy and broke down often Cables had not as yet replaced chains. Pig iron and scrap iron were loaded by hand in the stockyard, and stockyard locomotives were un- known; mules served as the usual motive power. It was not unusual to see recorded a delay of ½ hr in charging a furnace because of a balky mule. Furnace operations A few plants had primitive charging machines, but most furnaces were charged by placing scrap or pig iron on the paddle of a long peel, which rested on a bar across the furnace door opening. Laborers at the handle end of the peel, using the bar as a fulcrum, would heave the material into the furnace by a down and sideward motion of the peel handle. In time they became expert in placing these materials in the furnace, but it was hard, hot work, and a long time was required for charging. Cold charges of 25 tons required more than 12 hr for melting and re- fining the steel. Ports, doors, and frames were not water cooled. The charging and working area in front of the furnace was covered with steel plates. They were hot and often warped by the intense heat of the un- insulated checker chambers directly below. In the summer, working conditions on the charging floor were almost unbearable. Silica refractories were of poor quality. Because of this, and the inadequate training of furnace men in fuel control and furnace operations, roofs, front and back walls, and ends burned out rapidly. Dolomite machines were unknown; consequently, furnace banks and hearths were fettled with dolomite by the use of hand shovels. The round system required six or more men. Each man took a shovelful of dolomite and, in his turn, deposited it on the back wall and bank by a dexterous forward swing and twist of the shovel. The upward swing of the shovel partially protected his face from the searing heat of the furnace coming out through the wide-open door. Considerable skill and stamina were required to do this job properly. Reverse valves, usually of the cast-iron butterfly type, were located below the charging floor. They were operated by long levers on the charging floor level men they became warped, because of heat and abuse, great strength and skill were required to reverse them. Furnace operations were difficult. The quality and quantity of producer gas coming from irregularly stoked, hand-operated gas producers was uncertain and unreliable. Furnace Linings and ports were quickly burned out. Poor bottom and side-wall refractories, indifferent and inexperienced crews, as well as irregular re-

Jan 1, 1961

By E. H. Tenney

A discussion of the probable future use of coal for power development involves the study of several basic factors, such as future demand for power, the quantity and availability of fuels in direct competition with coal, the price of coal, and a closely related factor—the efficiency and cost of fuel utilization. Predictions based on purely statistical analyses of past coal consumption have definite limitations. For example, statistics showing the relation between coal utilization and total energy consumption from all sources between the years 1890 to 1930 indicate that during that period the energy consumption per person in the United States increased five times, while the coal consumption per person increased only twice1, and there has been an actual decrease in per capita coal consumption since 1920. Figures such as these, compiled by authentic agencies, emphasize the need for caution in attempting estimates as to the future use of coal, and, incidentally, would seem to offer little basis for optimism in the coal industry. They also suggest the value of analyzing broadly the part played in the past by the related factors of power consumption, competitive fuels, coal prices and the efficiency of utilization. Proper weight must also be given in such a study to the present status and limitations of power-plant developments, arid to the question of what the coal industry itself can do to further its own interests arid influence the consumption of its product.

Jan 1, 1936

By E. H. Tenney

A discussion of the probable future use of coal for power development involves the study of several basic factors, such as future demand for power, the quantity and availability of fuels in direct competition with coal, the price of coal, and a closely related factor—the efficiency and cost of fuel utilization. Predictions based on purely statistical analyses of past coal consumption have definite limitations. For example, statistics showing the relation between coal utilization and total energy consumption from all sources between the years 1890 to 1930 indicate that during that period the energy consumption per person in the United States increased five times, while the coal consumption per person increased only twice1, and there has been an actual decrease in per capita coal consumption since 1920. Figures such as these, compiled by authentic agencies, emphasize the need for caution in attempting estimates as to the future use of coal, and, incidentally, would seem to offer little basis for optimism in the coal industry. They also suggest the value of analyzing broadly the part played in the past by the related factors of power consumption, competitive fuels, coal prices and the efficiency of utilization. Proper weight must also be given in such a study to the present status and limitations of power-plant developments, arid to the question of what the coal industry itself can do to further its own interests arid influence the consumption of its product.

Jan 1, 1936

By R. M. Douthwaite, G. Birkbeck

The effect of grain size and specimen dimensions on the occurrence and magnitude of a yield point drop in pure iron has been examined. The tests were done at room temperature. The results indicate that gain size is the critical factor determining whether a yield drop occurs. The specimen diameter:gain size ratio does not influence the magnitude of the yield drop for the range of gain size and specimen diameters investigated. HUTCHINSON,' petchY2 and worthington3 have investigated the grain size dependence of the upper yield stress (uUYP) and the yield point drop, ouyp - aLYP, in Armco iron, mild steel, and Si-Fe, respectively. These authors used center-annealed wires to avoid stress concentration from specimen shoulders and to ensure uniformity of the applied stress. Coarsegrained specimens show no yield point drop; the yield point drop then increases as d-'I2 increases (where d is the grain diameter). These results can be understood in terms of Petch's analysis2 in which the magnitude of amp depends on the strain rate in the (limited) number of grains deforming plastically at the upper yield point. If N grains per unit volume are undergoing plastic deformation, the strain rate in the deforming grains is l/Nd3 times higher at the upper yield stress than when the whole specimen deforms homogeneously. If N is constant and independent of grain size at uUyp, then all the grains are deforming when ~d~ = 1, so there is no yield point drop. At finer grain sizes, the yield point drop is given by: where AU, is the friction stress increase corresponding to a tenfold strain rate increase. Christ, Smith, and Burton studied the upper yield point in 0.050-in.-diam wire specimens prepared from zone-refined iron. Each end of the 2; -in. specimens was soldered to a & -in. diam steel ball and the load applied through the two balls. There was a yield point drop in specimens with grain diameters less than 0.1 mm; no drop was observed in specimens of grain diameter greater than 0.1 mm that were free from veining substructure, but specimens of grain diameter 0.129 mm, annealed in the y range, showed an upper yield point. and this was associated with the presence of a veining substructure in these specimens. Christ et al. suggested the upper yield point occurs when more than a specific number of grains fill the specimen cross section so a multiplicity of slip is required to initiate plastic deformation. Table I summarizes the published data on the grain size at which the yield drop disappears. On the basis of this data the ratio of specimen diameter:grain diameter = 5 to 27 appears to be the critical value for the occurrence of a yield point drop. Thus, petch2 interprets the appearance and magnitude of the yield point drop in terms of the limited number of grains deforming plastically at uuyp, whereas Christ et a1. consider that the occurrence of the yield drop depends on the ratio specimen diame-ter:grain diameter. The published data cover a wide variety of materials so some variation between the results is to be expected, but the size range covered in the data of Table I is rather limited. In an attempt to discover whether the specimen diameter:grain size ratio or the grain diameter is critical in determining

Jan 1, 1969