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By Ralph W. M. Lai, D. W. Fuerstenau

This paper presents the results of a study of the principles which control the distribution of ultrafine particles between an oil phase and an aqueous phase. Alkyl sulfonates were used to control the wettability of fine alumina particles and to stabilize the water-isooctane emulsion system in the extraction process. The effects of sulfonate chain length, sulfonate adsorption, pH, and oil-water ratio on the recovery of solids in the oil phase were investigated. Higher extraction was found under conditions which yield higher hydrophobicity and large interfacial area of the oil-water emulsion. Today there is considerable interest in developing methods for the recovery of fine particles from disseminated ores. One such method might be the extraction of fine particulate solids from aqueous suspensions into an oil phase, and one example of a successful industrial process based on oil-water distribution phenomena is the emulsion flotation process used in concentrating manganese ore.' The oil agglomeration process of Farnand, Smith, and Puddington has been suggested for concentrating tin ore. Patents 3-4 for oil flotation processes extend back to that of William Haynes in 1860. The basis of all these processes is directly related to the stabilization of emulsions with solid particles. The first extensive study of oil-water emulsions stabilized by finely divided solids was made by Pickering. Later, Briggs,6 weston, 7 Chessman and King,8 and Leja and Schulman9 experimentally demonstrated how solid particles control water-oil and oil-water systems. Hildebrand10 suggested that fine particles can stabilize an emulsion because the fine particles are partially wettable by both oil and water, that is, that the contact angle must be finite. Takakuwa and Takamori 11 recently applied emulsion inversion to the study of collector adsorption in flotation systems. At the Royal School of Mines, Shergold and Mellgren12 are currently carrying out a comprehensive study of the extraction of fine particles into an organic liquid phase. In the present study of the liquid extraction or oil flotation of ultrafine particles, the recovery of hydro-philic alumina particles of 0.1-µ average diameter was determined after separating an isooctane-water mixture (emulsion) into its two phases. Alkyl sulfonates of different chain lengths were used to change the wettability of the alumina and to effect emulsifi-cation of the oil-water mixture. The effects of the oil-water volume ratio, sulfonate adsorption, and pH on the recovery of the fine particles were investigated. Since the surface charge on an oxide such as alumina is determined by the adsorption or interaction of H+ and OH- with the surface, pH control is extremely important. Furthermore, since the zero point of charge (zpc) of alumina13-14 occurs at pH 9 to 9.4, major adsorption effects with anionic collectors in these systems will occur below pH 9. The results of the foregoing investigation are discussed in terms of the recovery of the fine particles, the oil-water ratio, contact angles, surface tension, the adsorption of sulfonate onto the solid surface, and the emulsifica-tion of oil. MATERIALS AND EXPERIMENTAL METHODS Materials: The particulate solid used in all the experiments was Linde "A" alumina, a high-purity, readily available form of a-alumina. The surface area of the alumina, as evaluated from measurements of stearic acid adsorption from benzene, was 14.5 sq m per gm, based on a value of 20.5 sq Å for the cross-sectional area of stearic acid.13 All aqueous solutions were prepared from triply distilled conductivity water. Other materials included high-purity crystals of sodium alkyl sulfonates, isooctane, and, for pH adjustments, reagent grade hydrochloric acid and sodium hydroxide-Because sulfonic acids are strong acids, they are

Jan 1, 1969

By V. A. Phillips, M. Safdar Ali

The tensile properties of Cu-0.20 pct Al, Cu-0.45 pct Mg, Cu-0.27 pct Cr, and Cu-0.22 pct Be solid-solution alloys were studied at -196°, 18°, 2509 and 500°C on wires internally oxidized at 900°and 1000°C. Internal oxidation produced marked increases in yield strength relative to pure copper, particularly at low temperature. The yield strength decreased with increase in temperature to a much greater extent than predicted by current theories of dispersion hardening. The strengthening effect of internal oxidation persisted throughout the entire stress-strain curve, but since a marked loss of ductility occurred at all test temperatures, only modest increases in tensile strength were realized. INTERNAL oxidation involves the preferential oxidation of a baser solute in a relatively noble solvent by diffusion of oxygen into the solid. Since the process is diffusion controlled, it is expedient to carry it out at a high temperature often approaching the melting point. The amount of solute is limited and the oxidation conditions adjusted so that oxygen diffuses inwards to meet the solute causing reaction to progress inwards and form subscale instead of only sur face scale. The reaction can be made to occur throughout the thickness of thin material producing a fine dispersion of oxide inside the metal. C. S. Smith1"3 appears to have been the first to recognize the true nature of the process of internal oxidation. Although extensive kinetic and metal-lographic studies followed by Rhines and coworkers,4-5 Chaston7 andMeijering and Druyvesteyn8 working independently were the first to report hardening effects due to internal oxidation. These results prompted detailed studies of the effects of internal oxidation on the hardness, tensile, creep, and fatigue properties of a number of alloys by G. C. Smith and coworkers9-12 in England, on hardness by Gottardi13 in Italy, and on hardness and tensile properties by wood14 in the U.S.A. Publications dealing with other aspects of internal oxidation will not be reviewed here. Internal oxidation of solutes having a high affinity for oxygen provides a means of obtaining very fine dispersions stable in a suitable atmosphere at temperatures well above those at which most age harden ing precipitates coalesce. The process therefore offers a method of producing thin sheet and wire of possibly outstanding creep resistance. The size limitation might be overcome by internally oxidizing porous powder compacts made from alloy powder before final sintering. PREPARATION OF ALLOYS The alloy ingots, which were approximately 5 1/2 in. long by 1 in. diam, were made up in a high-frequency furnace, using as raw materials OFHC copper, 99.99 + pct Al, high-purity magnesium, and master alloys of Cu-4.19 pct Be and Cu-10 pct Cr. The alloys containing aluminum and magnesium were melted ii closed high-purity graphite crucibles and solidified in the crucible which was lowered partly Out of the coil to give a hot-top effect. The alloys containing beryllium and chromium were made by melting in vacuo in alumina-lined sillimanite crucibles. The magnesium, chromium, and beryllium

Jan 1, 1960

By G. E. Keller, G. D. Coe

Several methods have been devised for rapid determination of sulfur in coal using a high-temperature combustion furnace. The fundamental principles of the various methods are similar but the techniques vary widely. The method described herein is no different in principle from some of its predecessors but varies considerably in technique. Originally devised to overcome the low-accuracy criticism leveled against the others, the tube-furnace method has proved successful for limited applications. Work is being done to widen the applicability of the technique. Subsequent to the work of A. Vita1 in 1920, a number of investigators have published data dealing with the rapid determination of sulfur in coal using a high-temperature combustion furnace.2-5 These, together with several unpublished methods, involve wide differences in technique although they are all similar in principle. Investigation of typical details of procedure showed that poor precision or accuracy could be attributed to one or more of the following: 1) inadequate quantity of sample to be representative, 2) a delivery tube temperature too low to confine condensation to a washable area of the tube, 3) no provision for back washing the delivery tube, 4) incomplete absorption of the sulfur compounds due to inadequate bubbler, and 5) the false assumption that all of the sulfur is evolved as sulfur dixoide. The method herein discussed is no different in principle from some of its predecessors; the differences are in technique. Although the method is rapid—a determination can be completed in 5 min— accuracy has riot been sacrificed in order to achieve speed. MATERIALS AND EXPERIMENTAL WORK Fig. 1 shows the arrangement of the equipment. A metered volume of oxygen is passed through calcium chloride for removal of moisture, then through Ascarite for removal of carbon dioxide, and thence through a glass tee to the feed end of the combustion tube. Connected to the side arm of the glass tee is a rubber tube that is closed with a pinch clamp during combustion of a sample. The products of combustion are expelled through a Vycor bubbler, the end of which is submerged 3 cm below the surface of a 1 pct hydrogen peroxide solution contained in a 300 ml high-form beaker. At the completion of the 4-min combustion period the contents of the beaker are titrated to a yellow end point, using a methyl red indicator, with 0.05 N sodium hydroxide (or sodium tetraborate). The pinch clamp on the tube leading from the tee in the oxygen line is then opened and mouth suction applied to draw the hydrogen peroxide up into the bubbler past the ell, almost to the rubber tube connecting the bubbler to the combustion tube. This washing of the bubbler is repeated until no further acid reaction with the indicator is obtained. The hydrogen peroxide-sul-furic acid solution is then titrated to the final yellow end point. Test work conducted at the Robena Laboratory disclosed the following critical conditions that had important bearing on the precision of the method: Weight of Sample: Several series of tests wherein the sample weight ranged from 0.1 to 0.5 g of -60 mesh coal showed that the lowest variance (standard deviation squared) resulted from the use of 0.5-g samples; the variance was slightly greater when 0.3-g samples were used, and with less than a 0.3-g sample weight the variance increased rapidly with decrease in weight. Although the use of a 0.5-g sample invariably resulted in a very slight explosion as soon as the sample entered the hot zone of the combustion tube, this did not detract from the precision of the method. Temperatures: Mott and Wilkinson5 found that a combination of low temperature (1250°C) and low oxygen flow rate (less than 700 ml per min) tended to give high results due to formation of oxides of nitrogen. Although the method herein employs a much higher oxygen rate than 700 ml per min, as an additional precaution to assure accurate results, 1315°C (2400° F) is recommended as the most desirable furnace temperature. The temperature of the elbow of the bubbler should be at least 75°C to minimize condensation

Jan 1, 1961

By K. H. Coats

This paper describes an approximate technique for handling the problem of percolation of evolved gas upwards through the oil column in computer simulation of natural depletion. This technique has been incorporated into a general model for simulating three-phase flow in one, two or three dimensions. The mathematical model for perfonning these calculations is described in detail in a separate article. 1 While vertical gas percolation occurs during natural depletion in a reservoir of any configuration, it is especially pronounced in the pinnacle reel or bioherm. The reel may have an areal extent less than one section with a thickness of up to 800 It. The upward percolation of evolved gas often limits the time step in calculations as little as one day. Using this small time step, computer expense for a single 30- to 40-year simulation on even a one-dimensional basis has exceeded 92,000. The method described here for handling the percolation allows time steps of 60 days or more (depending on reservoir size and production rate), resulting in a considerable reduction in computing expense. The method also allows calculations in which secondary gas caps build up in tight zones of the oil column below the main gas cap. The validity of the method is indicated in connection with an example pinnacle reef field. Calculated results using a 2-day time step (where the method in question is not needed and not invoked) are compared with results using the method and a 60-day time step. The comparison shows good agreement. Results from one- and two-dimensional simulations of the reef are presented along with the corresponding computing times on the CDC 6600 computer. A three-dimensional simulation was also performed and the required computing time is given. INTRODUCTION A general analysis for simulating three-dimensional, three-phase flow in reservoirs has been developed. 1 In applying this model to reservoirs undergoing natural depletion, a time-step restriction was encountered due to the flow of evolved gas upwards through the oil column and toward the gas cap. A remedy for this problem has been incorporated in the analysis and is described here. The time-step restriction is encountered only in calculations which include flow in the vertical or near vertical direction. The restriction occurs to some extent in reservoirs of any geometrical configuration, but it is especially pronounced in the pinnacle reef or bioherm where the ratio of thickness to areal extent is unusually large. This paper describes the problem, a method of handling it, incorporation of the method in the three-dimensional, three-phase model, and, finally, a test of the method's validity in an application to an example pinnacle reef reservoir. THE PROBLEM During the early stages of reservoir depletion, pressure falls below bubble point in progressively lower regions of the oil column. Continuing production results in evolution of dissoived gas throughout the oil column. This gas then percolates upwards toward the top of the reservoir. If the gas encounters a sufficiently low permeability zone in its travel upward, then it can accumulate and form a secondary gas cap. If no zones are encountered which are tight enough to hold gas against the gravity forces, then the gas travels on until it reaches the top of the sand or the main gas cap. Numerical simulation of multiphase flow in reservoirs is generally performed with time steps such that the flow of a fluid into or out of a block in one time step is a fraction (considerably less than one) of the total amount of that fluid present in the block. Use of a time step where the time step's

Jan 1, 1969

By E. C. Carris

THE particular field of application of machines utilizing air cur¬rents as the primary separating medium is in the cleaning of the fine sizes of bituminous coal. Approximately 12,000,000 tons of bituminous coal were cleaned by air machines during 1940. They have not found any application for cleaning anthracite. Since the development and introduction of the first successful com¬mercial pneumatic oscillating machine for cleaning bituminous coal in 1916, by the Sutton, Steele and Steele Co., Dallas, Texas, and the Ameri¬can Coal Cleaning Corporation, formerly of Welch, W. Va., four other successful pneumatic coal-cleaning machines have been developed and introduced to the American coal-mining industry: 1. Peale Davis: "Pneumo-Gravity" machine, 1924. 2. Arms "Concentrator," oscillating table, 1924. 3. Heyl and Patterson oscillating table, 199.7. 4. "Stump Air-Flow," pulsating air jig, 19391. Out of these five developments only the Sutton, Steele and Steele, or American Oscillating, and the Stump Air-Flow Jig remain on the market. They are the predominating pneumatic coal-cleaning machines in use in the United States. HISTORY OF AMERICAN TYPE SEPARATOR The first successful American machine, the CJ table (Fig. 1) was developed by the Sutton, Steele and Steele Co. The SJ table was the first standard model designed specifically for the cleaning of coal. It was installed in the original Crane Creek plant, owned and operated by the American Coal Co. at McComas, West Virginia. This plant was designed by The Roberts and Schaefer Co., Chicago, Ill., working in cooperation with the American Coal Cleaning Corpora¬tion, which had taken over the patent rights and sale of the pneumatic separators. Eight machines were installed in this plant. They were known as the type SJ. They were 60 by 84 in., the short dimension being the width of

Jan 1, 1943

By J. H. Schulman, M. H. Buckenham

Although much interest has been taken in the use of mixed collectors in flotation, this investigation is probably the first in which oppositely charged collectors have been considered. The results obtained and the techniques used could well be applied in the behavior of other mixe the behavior of other mixed collector systems and could possibly explain the effective flotation results which have been reported when various collector combinations have been used. Collectors conventionally employed in flotation systems are soluble in water, but many of their homologs of longer hydrocarbon chain length are insoluble. The properties and behavior of these insoluble compounds may be conveniently studied when they are spread as monolayers at the air/water interface on the Langmuir-Adam trough. Although some extrapolation is involved in applying effects observed at this interface to the solid/liquid interface where the action of collectors is most important in flotation, the technique nevertheless is most useful for the study and interpretation of flotation phenomena. Of particular interest in this field are investigations on the insoluble monolayers of the fatty acids, alkyl sulfates and alkyl amines; the penetration of these insoluble monolayers by soluble surface active components and their interaction with metal ions from the underlying solution.'-' Unfortunately, the insoluble xanthates and related compounds do not exhibit stable monolayer properties due to rapid oxidation at the air/water interface and, therefore, cannot be studied directly in this way. These approaches have enabled Leja and Schulman8 to suggest mechanisms explaining dynamic attachment of mineral particles to air bubbles involving collector-frother interaction and the adsorption of collectors onto mineral surfaces. In this and other papers 9-12 considerable evidence is presented to support the concept of collector-frother and metal ion-monolayer interaction and to emphasize the value of monolayer techniques in elucidating the flotation system. Molecular interactions resulting from monolayer penetration are determined by the nature of and the association between both the polar and nonpolar groups of the two molecules concerned. Stable complexes are formed on penetration when interaction takes place between both the polar and nonpolar groups, and although the resultant complexes are not necessarily true chemical compounds, the properties of the molecularly associated complexes are very different from those of the individual components. Shortening of, or changes from, a straight hydrocarbon chain in one of the reacting molecules reduces considerably the stability of the associated complex as do changes in temperature, pH and substrate composition. The effect of hydrocarbon chain length becomes most important when observed effects are to be applied in flotation studies where soluble homo-logs and, therefore, much shorter hydrocarbon chain lengths are used. The present investigation is based on Langmuir trough work carried out by Bowcott,l3 who studied the penetration of insoluble amine monolayers by potassium lauryl xanthate. Bowcott observed that cetyl amine monolayers were readily penetrated by xanthate, but found that with time the high film pressures resulting from penetration and association fell off, indicating decomposition and ejection of xanthate from the film. This decomposition was pH dependent. Of particular interest in this work were studies on an equimolecular mixed monolayer of the fully N-substituted ammonium compound, for example, cetyl trimethyl ammonium iodide (CTAI) and potassium cetyl xanthate. Despite the fact that the CTAI is water soluble and the xanthate on its own is incapable of forming a monolayer, the mixed film was stable up to a surface pressure of 67 dynes per cm. In this condensed state the xanthate was stabilized against atmospheric oxidation, although iodine injected beneath the film caused an immediate collapse. The stabilizing of xanthate against oxidation by association with an alkyl trimethyl ammonium bromide (TAB) could be important in flotation, and a study of the performance and behavior of mixed collectors therefore was undertaken. A modified Hallimond tube operated under controlled conditions was used to evaluate flotation. Surface tension measurements were made to investigate the properties of the soluble

Jan 1, 1963

By J. T. Raleigh, D. L. Flock

This study investigated the nature of formation plugging with bacteria and attempted to relate its characteristics to physical rock properties. Fifteen core samples of four specific formation types were defined and plugged using a commonly occurring, uniform sized dead bacteria, Bacillus subtilis. Two of the formation types were fairly uniform-grained sandstones and two were heterogeneous carbonates. The injection rate and concentration of solids in the brine were held constant during the test runs. The pore geometry factor G was a significant petro-physical rock characteristic for correlation with depth of plugging, but lacked importance as a parameter for rate of plugging. Although the G factor may not completely describe porous rock geometry for plugging predictions, for reservoirs with multi-pore systems, there is evidence that the pore geometry factor might form a basis for establishing injection water specification in more llornogeneous reservoirs with only primary porosity development. INTRODUCTION GENERAL PURPOSE Injecting water into oil-bearing formations to increase recovery is common practice in the petroleum industry. One of the most serious operational problems involved with water injection wells is the tendency of the porous rock immediately adjacent to the injection wellbore to plug partially. This results in increased injection pressures and/or a decrease in the rate of injection. This plugging in injection wells can result from a number of causes, including bacteria contained in the injected water.1 The purpose of this work was to investigate the nature of injection plugging with bacteria and to attempt to relate its characteristics to physical rock properties. Many variables exist in research of this type, so, to reduce them, injection rate and concentration of bacteria in brine were held constant. The bacteria used for plugging was a uniform-sized, dead bacteria, Bacillus subtilis, a micro-organism commonly found in water, air and soils. Four specific porous rock types were plugged—two consolidated sandstones and two heterogeneous carbonates. The experimental work involved two distinct phases. The first concerned determining the physical rock properties and the second was the experimental work of actually plugging the selected core samples. PORE GEOMETRY FACTOR Capillary pressure is necessary to displace a wetting fluid from a capillary opening with a nonwetting fluid. The factors which govern capillary pressure are the surface or interfacial tension of the fluids involved, the system wettability and the equivalent pore radius. Thus: P,= 2ucososrd..........(1) Thomeer used the idea that the location and shape of the capillary pressure curve reflect characteristics of the pore structure of any porous media sample.' He presented the mathematical description of capillary pressure curves and of indicated differences in pore geometry of samples. where G = pore geometry factor PC = capillary pressure Pi = displacement pressure (V,)p, = fractional bulk volume occupied by the displacing fluid at any capillary pressure (V,), = fractional bulk volume occupied by the displacing fluid at infinite pressure or total interconnected pore volumes. The shape of the curve is defined by the pore geometry factor G. The curve shape is related directly to the sorting and interconnection of the pores of the sample. The location of an infinite number of curves can be defined by the same asymptotes. However, these curves differ in shape, each curve being described by a specific value of G. Thus, the description of a curve is unique when, in addition to the position of its asymptotes, its shape is defined. These curves can be used graphically to determine the characteristic parameters of any arbitrarily located curve. Those parameters that can be approximated from any capillary pressure curve are: (1) total interconnected pore volume, represented by (V,),- ; (2) extrapolated displacement pressure, the abscissa axis; and (3) pore geometry factor, by the curve shape. PROPERTIES OF BRINE AND BACTERIA The fluid used throughout this study was an aqueous solution of sodium chloride, 25,000 ppm by weight. The addition of salt to fresh water was intended to eliminate clay swelling in the sandstone cores and to retard leaching in the limestone cores. The viscosity of the brine solution at 100F, the temp-

Jan 1, 1966

By C. W. Allen, L. C. Moore

The Mather mine, of the Negaunee Mine Co., is within the limits of the City of Ishpeming. on the Marquette iron range in Michigan's Upper Peninsula. It is named for William G. Mather, who has served as President, and Chairman of the Board, of The Cleveland-Cliffs Iron Co. for well over 50 years. The property comprises nearly the square mile of section 2, T.47 N. R.27 W., which, except for 20 acres in the northeast corner, was leased by The Cleve-land-cliffs Iron Co. to the Negaunee company. The latter is a partnership of Cleveland-Cliffs and the Bethlehem Steel Co., organized to equip the property, retaining Cliffs in charge as operator. Shipments of ore from this area are mainly through Marquette, which is 16 miles to the northeast on Lake Superior, or through Escanaba, a Lake Michigan port, 65 miles to the south. Cleveland-Cliffs, in 1943, operated 12 mines in the Lake Superior district, with shipments of 6,635,576 tons for the year. Geology The north footwall of the Marquette Range synclinorium outcrops near the north line of set. 2, the iron formation dipping to the south at an angle of about 40. The south side of the trough reappears at a distance of 4J5 miles on sec. 26 and the surface geology between shows iron forma- tion or intrusive diorites. The latter are harder than most phases of the iron formation and, as a result of glacial action, appear as buttes or low-lying hills. The general elevation of sec. 2 is about 1450 ft. above sea level, or 850 ft. above Lake Superior, and the higher diorite outcroppings about 1600 ft. above sea level. The geological structure has been complicated by a series of major and minor faults, one of which may be illustrated by the diorite sheet, which tilts south with the iron formation in the north half of the section and then reappears near the center to repeat this sequence. Sectionally the geological series includes a nearly eroded capping of Goodrich quartzite followed by the considerable thickness of Negaunee iron formation, which is cut by intrusive dikes or diorite sheets, and underlain by the Siamo slates grading into quartzites. The ore deposits occur mainly in troughs formed by the intersection of impervious dikes and the footwall slate, but include locally enriched lenses or bands in the iron formation and also interbedded with the Siamo slate. The ore is a soft red hematite with an indicated dried analysis from the surface drilling to date of 61.50 per cent Fe, 0.134 Per cent P, 5.40 per cent Si, 2-87 Per cent A1 and 0.015 per cent S. Exploration A diamond-drilling campaign started in 1937 actually had its inception in 1917, when a number of shallow test holes were put down for the purpose of locating ore that might be quickly developed and mined

Jan 1, 1946

By S. H. Moll, R. E. Ogilvie

The investigation of solid-state diffusion phenomena may lead to much information concerning binary alloys. In particular, a study of the concentration gradients present in multiphase diffusion couples can lead to the determination of the solubility limits of the single-phase fields in the phase diagram. The specific concentration gradient which results from the heat treatment of a diffusion couple depends not only upon the time and temperature of diffusion, but also upon the number of phases existing in equilibrium at the diffusion temperature. Such concentration gradients possess sharp discontinuities whose terminal points correspond to the solubilities existing at the limits of the two-phase field in the phase diagram at the diffusion temperature. In general, there will be a discontinuity in the concentration curve for each two-phase field which exists in the phase diagram between the concentration limits of the couple. A number of investigators have analyzed the gradients present in multiphase diffusion couples. 1-8 The iron-titanium phase diagram exhibits a y loop in the temperature range from 900" to 1400°C, and the limit of the a + y field lies at some composition which is less than 1 wt pct Ti for any temperature. It was felt that a diffusion study could yield values not only for the diffusion coefficients involved, but also for the chemical solubilities in the phase diagram. The concentration gradients were analyzed by an X-ray absorption technique developed by Ogilvie.6 The absorption of a monochromatic X-ray beam is measured in steps parallel to the diffusion direction and the resulting intensity gradients are transformed into concentration gradients by applying the laws of X-ray absorption in a binary system. This technique has been applied by ogilvie6 to the systems Ni-Au, Cu-Au, Fe-Cr, and Ni-Cr; by Gelles7 to the systems Be-Fe, and Be-Ni and by Hilliarde to the system Al-Zn. Linear X-Ray Absorption Analysis—The use of X-ray absorption analysis as a tool for determining concentration gradients arises from the fact that the beam is absorbed according to the quantity and species of elements present in the sample and not according to their state of aggregation. This method is more advantageous than the chemical analysis of machined layers since it is less time consuming and less expensive and can analyze a very small area. IF a homogeneous binary alloy (A + B) is analyzed with two different monochromatic X-ray beams I0(2) and lo(2) the following relation between the transmitted intensities, the intrinsic absorption coefficients of A and B for the two different radiations and the weight fraction of each element may be derived.' In (I/Io) (a+b) xa(u/p)a(2) + xb(u/p)8(2) Eq. [1] is independent of specimen thickness and density, but requires that either element A or B possess an absorption edge between the wavelength limits of the two monochromatic beams. I, is evaluated for each radiation by measuring the transmitted intensity through a varying number of foils of a suitable absorber. A plot of the natural logarithm of the transmitted intensity as a function of the number of foils, when extrapolated to zero foils, yields the value of I,. If a plot of the ratio in Eq. [ I] is calculated as a function of xA, then a master curve results. From

Jan 1, 1960

By W. Ivanick, Frank W. Glaser

ORDERING reactions of Fe-Si compositions in the a region have been mentioned in a number of review articles.7-8 However, little is known in regard to the critical temperature, T at which this transformation takes place. Greiner and Stoughton,' in a study of the constitution of iron-rich Fe-Si alloys below 800°C, placed the onset of order at a composition of about 4 to 5 wt pct (7.5 to 9.5 atomic pct) Si. They observed that at this composition the ductility and strength begin to decrease sharply and brittleness develops. During X-ray studies they observed only the appearance of superlattice lines for compositions containing 12.5 atomic pct Si. More recent X-ray diffraction studies- etected the appearance of superstructure lines (corresponding to the calculated positions of [Ill] and [ZOO] reflections) for alloys containing 9.5 atomic pct. This fact confirms Greiner and Stoughton's original hypothesis in regard to the onset of order at compositions containing about 7.5 to 9.5 atomic pct Si. The physical properties.of Fe-Si alloys containing more than 10 atomic pct Si have been studied only to a limited extent. Their extreme brittleness and difficulties of sample preparation render them of little industrial use in comparison with alloys in the 0 to 10 atomic pct Si range. The properties of Fe-Si alloys reported to date are mostly properties measured at room temperature on ordered compositions It appears that because of experimental difficulties fully disordered alloys could not be produced in the critical composition ranges and their properties could therefore not be reported. In Figs. la, lb, and lc, a summary of physical properties of Fe-Si alloys, measured during recent investigations of the influence of silicon additions to iron, is presented. No mention of determination of the critical temperature, T for disorder could be found in the literature. The following is an account of work done in an attempt to: 1) produce the disordered state of various Fe-Si alloys and establish the critical temperature, T for disordering, and 2) compare the electrical and thermal conductivity characteristics of the ordered and disordered phases as functions of composition. Materials, Preparation of Test Samples, and Testing Methods Fe-Si alloys with high silicon contents (about 10 atomic pct) are usually prepared using powder metallurgy techniques. This method insures accurate compositions and high purity through the use of protective atmospheres during solid state diffusion alloying of the mixed powders."" Iron and silicon powders were mixed in the desired proportions, cold or hot pressed, and then homogenized at 1150°C for periods ranging from 6 to 12 hr under a protective getter and in a hydrogen atmosphere. Fully homogenized samples were quenched in water from various and successively higher temperatures to establish the critical temperature for disorder. Temperatures were determined using Pt—Pt-Rh thermocouples in contact with the test samples. Test bars were approximately 0.6x1.25x7.5 cm. Electrical measurements were made at room temperature by determining the potential drop over a 1.5 cm span for a current of 10 amp. Densities of the samples were determined by immersion. High temperature electrical resistivities were measured using previously described techniques.'" Specific heat conductivity up to 200°C was measured by heating one end of the test bar and water-cooling the other; heat conductivity was then obtained by subtracting the rate at which heat entered the water from the

Jan 1, 1957

By Worthen Bradley, R. G. Hall

THIS paper will attempt to show how a metallurgical problem at one California quicksilver mine was solved, and how the solution was applied successfully at another mine. The pronouns "we" and "our," as used below, refer to the Bradley Mining Co. of San Francisco. The term "concurrent firing" for the purpose of this paper can be defined as feeding and firing a rotary kiln at the same end-that is, of course, the upper end. This is as opposed to "counter-current firing," the orthodox method, in which a kiln is fed at the upper and fired at the lower end. The terms "quicksilver" and "mercury" are used interchangeably. EARLY REFERENCES The earliest work on nonferrous metallurgy, we believe, was The Pirotechnia of Vannocio Biringuccio,1 its first edition having been printed in Italy in 1540. Quoting from its chapter entitled "Concerning Quicksilver and Its Ore": Quicksilver . . . is one of the gods and has divine strength in itself, and also, to the annoyance of the alchemists, it is winged. Hence, when it sees that it is in gravest danger, it loosens itself from . . . every bond . . . and flies away into the heavens, escaping from the hands of those who crucify it. Almost laughing, it leaves all its adversaries mocked and scorned, with their phials and filters empty . . . How thorough a job, under certain conditions, it can do of mocking its adversaries and leaving their phials and filters empty, was found out four centuries later at the Sulphur Bank mine, on the east shore of Clear Lake, in Lake County, California. The other mine mentioned in the title is the Reed, in Yolo County, California, 35 miles by road southeast of Sulphur Bank. Reed and Sulphur Bank ranked respectively fifth and seventh in U. S. production in 1943. The earliest direct reference we can find to furnacing troubles at these mines was by Thomas Egleston in 1890.2 Speaking of Sulphur Bank, Egleston says: Sometimes there is more sulphur than cinnabar in the ore, which is a detriment to both . . . making the sulphur impure, and rendering the cinnabar difficult to work on account of the soot. In some of the early . . . furnaces the accumulation of soot from the excess of sulphur has been known to penetrate as far as the fan blower at the end of the . . . condensers, and completely prevent its revolution. In order to get rid of the inconvenience of this accumulation . . . , as well as to get a commercial value from the sulphur, it (the sulphur) is now separated by steam and sold. It is claimed that the sulphur alone pays all the expenses of . . . the mine. The mine was first worked for sulphur, and the cinnabar it contained was considered to be an inconvenience, and was carefully picked out and thrown away. as its richness and value were not

Jan 1, 1945

By R. W. Kewish

The preparation of massive uranium metal containing very low concentrations of a number of light elements by bomb reduction of UF4, with calcium is described. Details of procedures are given for preparing high-purity ingredients for the bomb reduction. The as-reduced uranium metal contained, on the average, less than the following amounts of light element impurities, in ppm: Li, 0.1; Be, 0.1; B, 0.1; C, 25; 0, 70; Na, 1; Mg, 3; Al, 2; and Si, 7. Other impurities for which the metal was examined averaged, in ppm: Ca, < 10; V, < 10; Cr, 2; Mn, 6; Fe, 50; Co, < 5; Ni, 8; and Cu, 1. THE preparation of very high-purity uranium metal in massive form for research purposes is of great importance. Recently the kilogram-scale preparation of uranium metal containing less than 70 ppm of detected impurities was accomplished by Blumen-thal and coworkers by vacuum remelting of high-purity crystals of uranium obtained by fused salt electrolysis.1"3 Albert and coworkers4 have reported successful experiments in lowering the concentrations of certain impurity elements in uranium, notably iron, to a few ppm by the zone-melting method. The present paper describes the preparation of high-purity massive uranium metal by the bomb reduction of UF4, with calcium. Early in 1951 a program was undertaken at the Los Alamos Scientific Laboratory to prepare uranium metal of very high purity with respect to a number of the light elements. The methods considered for this purpose were 1) bomb reduction of a uranium halide with calcium, 2) electrolysis of fused salts, and 3) hot wire decomposition of UI4, The first of these processes had been used extensively at Los Alamos since 1943 (and still is used) for the production of uranium metal.5 In considering the three processes it was evident that either of the last two would require an extensive development program with no certainty of success. On the other hand, a study of available data showed that uranium metal of very high purity with respect to some light elements had occasionally been made in routine processing by the first method. It was therefore decided that an intensive study of the bomb-reduction process would be made to see if it could be improved to yield uranium metal with very low concentrations of light elements. DEVELOPMENT OF PROCEDURES The bomb-reduction process used at Los Alamos consists of reducing UF4 with calcium, using iodine as a booster. The reaction is carried out in a magnesium-oxide crucible enclosed in a steel bomb. Argon is used in the bomb to avoid objectionable side reactions which would occur in the presence of air. All ingredients for this bomb-reduction process were examined as possible sources of light elements. It was known that high-purity UF4 was required. The calcium used in the reductions was a source of carbon and magnesium. The magnesium-oxide crucibles were sources of boron, silicon, and magnesium. The iodine did not appear to be a source of any impurities. Pure UF4- The UF4 for bomb reduction is prepared from U3O3 , by successive reduction to UO2, with hydrogen and hydrofluorination of the UO2, with anhydrous HF. Since it was known that no impurities were normally introduced during the gas-solid reactions, effort was directed toward the preparation of high-purity U3O3. Of the many possible procedures for the purification of uranium solutions the following were investigated: 1) Precipitation of uranium peroxide. (Two procedures were tried. The first consisted of simultaneously adding hydrogen-peroxide and ammonium-hydroxide solutions to a uranyl-nitrate solution, containing citric and malonic acids, at such relative rates that precipitation was carried out at a constant pH of 1.5 The second consisted of simultaneously adding uranyl-nitrate, ammonium-hydroxide, and hydrogen-peroxide solutions to an aqueous solution

Jan 1, 1960

By A. J. Griest, P. D. Frost, J. R. Doig

During the past 5 years, research directed toward the development of titanium alloys having improved strength-ductility relationships and heat treatability has been carried out at Battelle for the U. S. Air Force.1"3 In the course of this work, a method of heat treating ß-stabilized titanium alloys was developed which produced a wide range of useful properties.4 The heat treatment consisted of two steps: a) solution treating at temperatures in the a-ß phase region, and b) overaging at a lower temperature in the range 800°to 1100°F. Corollary to the alloy development work, research was conducted on the mechanism of the heat-treatment reaction. The investigations of Frost and co-workers on isothermal transformation in Ti-Cr5 and Ti-Mn8 alloys disclosed the existence of the transition phase, w, during the course of the decomposition of metastable ß phase. Subsequent work at Battelle7,8 &apos;and at Case Institute by Brotzen and co-workerss further clarified the nature of the decomposition process. Beta decomposition was found to proceed by the following series of reactions: 1 2 3 4 a + Ti, My (in eutectoid systems). ßo, ßr, and ßU refer to ß phase of original, enriched, and ultimate alloy contents, respectively. Omega is a transition phase having a complex structure. 10-13 Step 4, of course, occurs only in ß-eutectoid systems. This paper presents data correlating transformation behavior with mechanical properties for the following alloys: Ti-8Mn, Ti-8Mn-2A1, Ti-4Mn-4A1, Ti-6Al-4V, and Ti-4Fe. The isothermal decomposition of ß in titanium-manganese alloys of similar composition has been investigated by Frost and coworkers8 and the effect of various annealing treatments on alloys in this system has been studied by Holden, Ogden, and Jaffee.14 The compositions Ti-8Mn-2Al, Ti-4Mn-4A1, and Ti-6A1-4V, were studied in the present work in an effort to define more clearly the effect of aluminum on the response to solution and aging treatments. Ogden, Holden, and Jaffee15 have invesitgated the effect of aluminum on the response of a similar alloy (Ti-8.8Mn-2.46A1) to annealing treatments, and Luini and Lee16 have made an exploratory investigation of the heat-treatability of the Ti-4Mn-4Al alloy. The Ti-4Fe alloy was studied as an example of a moderate1y active eutectoid system. Holden, Ogden, and Jaffee 17 have studied Ti-Fe alloys and have presented some hardness data for aging at 400°C for alloys of Ti-2.56, 5.01, and 7.35 iron after quenching from the a-ß field (750°C). EXPERIMENTAL PROCEDURES The experimental procedures generally used in the precipitation-hardening study are outlined in the following sections. Departures from these techniques are noted in the discussions of the individual alloys. Table I presents the nominal and actual compositions of the alloys studied, together with the swaging and rolling temperatures. In all cases, these temperatures were in the a-ß field and the microstructures consisted of an equiaxed a-ß mixture. Melting and Fabrication—Except for the commer-

Jan 1, 1960

By Albert G. Zima

According to recently puhlished statistics, it is predicted that as much oil must be produced during the next 16 years as has been produced during the past 75, in order to satisfy the high rate of consumption of petroleum products. During 1934, over 17,000 oil wells were completed in the United States, and it is expected that over 20,000 additional wells will be drilled during the current year. Were it not for the remarkable progress made during recent years in the improvement of drilling technique and in the development of equipment used in the production phase of the oil industry, it is doubtful whether sufficient oil could be produced to meet present requirements. A few years ago, wells seldom were deeper than 3500 to 4000 ft., owing to the limitations of the drilling methods and equipment employed. Today, however, through the application of scientific drilling methods and the adaptation of modern equipment and improved materials, many wells range from 6000 to 8000 ft. in depth, and a few recent completions exceed 10,000 feet. Drill Tools Modern rotary drilling tools are the product of ingenious design and careful selection and adaptation of materials used in their construction. They must withstand terrific abrasion and, because of their compactness, must be designed to resist exceedingly high unit stresses. In bits, core drills and reamers, the bodies are made of either forged or cast alloy steels, heat-treated to develop a combination of high strength and toughness. To provide sufficient strength to the threaded portions and to protect the threads from distortion or damage, the box or pin sections of the tools are hardened to approximately 310 to 330 Brine11 hardness number. Drill and reamer cutters are generally of the movable type; i.e., serrated cones, cylinders or disks, which can readily be replaced when

Jan 1, 1935

By N. A. Stockett

Southeast Missouri is the largest and oldest lead-producing district in the United States. For the year 1941, the statistical picture of pig-lead production, stated in short tons (partly estimated by the Engineering and Mining Journal) is as follows. Tons World production................. 2,000,000 United States Production .........- 460,000 Southeast Missouri production..... 142,000 The consumption of primary lead in the United States in 1941 was approximately 900,000 tons, or almost double the country&apos;s production. The largest previous year&apos;s in in the United States was 718,000 tons, in 1926. The largest quantities of lead are used for cable sheathing, storage batteries and white lead. During 1941 tetraethyl lead for auto and aviation gasoline consumed 50,000 tons of lead. The entire lead production of Southeast Missouri is now mined by the St. Joseph Lead Co., whose dominant position as the largest producer in the United States of lead directly from ores is best shown by the fact that in 1941 it produced approximately 31 per cent of the lead production of the United States from its mines in southeast Missouri, where 22,000 tons of ore, averaging over 3.00 per cent lead, is mined per working day. It is known that lead was mined at Mine La Motte, Madison County, Missouri, by Renault in 1723. Other white men and Indians probably did some mining prior to that time. Since 1865, the recorded production to Jan. I, 1942, shows that the St. Joseph Lead Co. and the various other companies that have operated in St. Francois County mined lead ore, which, after milling and smelting losses produced 5,980,000 short tons of pig lead. • About 95 per cent of the present lead production of Southeast Missouri is mined in St. Francois County. The northern part of this area is 60 miles south of st. Louis. The remainder of the lead is obtained at Mine La Motte, about 25 miles southeast from the center of the producing area in st.Francois county, Prospecting In this district, most of the ore is discovered by surface and underground diamond drills and by prospect drilling underground with rock drills. Each 2-ft. length of the cuttings from these Jack-hamer prospect holes is assayed for lead. These holes are marked and the records are entered on maps. It has been found that close drilling—100-ft. centers of holes, and sometimes less—is necessary in order to locate most of the smaller commercial ore bodies, many of which previously had been missed by drilling the areas with holes spaced 200-ft. centers or more. To date, geophysical and other methods of prospecting, apart from diamond and Mining Practices of the St. Joseph Lead Company in Southeast Missouri

Jan 1, 1943

By C. E. Brown, D. C. Helms, O. W. Shimer

The early history and progress of anthracite stripping, from the first known operation at Summit Hill in 1821 through 1917, was covered in 1917 in a paper by J. B. Warriner,1 then chief engineer, now president of the Lehigh Navigation Coal Co., and stripping methods between 1917 and 1931 were the subject of a paper in 1931 by H. H. Otto,2 of the Hudson Coal Company. . The present paper is confined to methods used today on pitching beds in the western middle and southern anthracite fields. The anthracite industry, not unlike other large industries, had been affected for more than a decade by the adverse economic conditions of the country. High development and operating costs and the competition of other fuels caused some collieries to be closed temporarily, while others were permanently abandoned. In order to obtain a larger tonnage at a lower development cost, a larger stripping program was put into effect by many companies. In 1932, stripping operations accounted for 3½ million tons, or 7 per cent of the total anthracite production of the year, and in the next 10 years this increased until more than double that amount, or over 14 per cent of the total production, was from stripping operations. These figures represent the total production of the entire anthracite region; unfortunately, the figures have not been separated from the different fields. There are some operations in the southern and middle western fields where the tonnage obtained from stripping amounts to more than 30 per cent of the total colliery production. Stripping operations on pitching beds present difficult problems. Owing to the various geological formations, a different situation is encountered in nearly every stripping pit; and because of the proximity of an overlying bed, it is very often necessary to load the entire overburden into trucks and haul it out of the pit to the dump area, although back filling and casting is done whenever possible. Beds in the areas described in this paper pitch from 20" to 90 and some are on the invert in many sharp folds and faults. Planning The more successful strippings have had adequate engineering analysis. Some work is being done without much preliminary planning, but many strippings would have failed completely if close supervision by the engineering department had not been . maintained. Locations of stripping areas are determined as follows: I. By constructing cross sections over the areas and drilling sufficient diamond-drill or well drill holes to study the strata and to determine the location, thickness

Jan 1, 1944

By P. W. Andrews, R. B. Toombs

ECONOMIC STRUCTURE OF MODERN INDUSTRIAL ECONOMIES The role of minerals in modern industrial economies may be examined in several ways. There are relationships with the various sectors of the economy: the primary, secondary, and tertiary industrial groupings and activities. Mineral supply and demand activities can be measured in terms of national accounts criteria. The economic policy objectives of the modem industrial economy are based to a considerable extent on the needs of the nation for economic supplies of miner- al materials. There is an important role for minerals relative to national security in peace and in wartime and many national policies are directed toward ensuring adequate sup- plies of minerals. Environmental control in the modem industrial economy is increasingly concerned with matters related directly to the production and use of minerals and these matters, in turn, bear importantly on conservation in mineral supply and demand. Mineral polices include specific provision for research and development activities concerned with the production and the use of minerals. In all, national policy objectives will be shaped in considerable part by the circum- stances of mineral supply and demand: the relative degree of availability from domestic and foreign sources, the state of the mineral-processing industries, and the degree of development of the mineral-using industries, and per capita and total changes in requirements. Goods made from mineral raw materials are the basis of all advanced societies and although this is taken for granted, every country is continually dealing with problems of mineral supply and demand. Considering that in the first 50 years of this century the consumption of mineral materials in a highly Industrialized country such as the United States increased by six times while the population was doubling, it becomes apparent that if a country is to enjoy rapid economic growth it must have access to huge and ever-growing supplies of mineral materials at lowest possible cost. Adequate supplies of mineral materials and wise usage of mineral resources have always been among the most important determents of a nation&apos;s survival The importance of access to adequate mineral supplies is increasing every year and this has significant international, as well as national, implications because of the unique locational characteristics of mineral resources. It is generally acknowledged that no particular type of natural resource is essential to a high level of national income or to economic progress. A country&apos;s endowment of natural resources need not exercise a determining influence on the course of its national income over time, provided it is able to trade. What is required for economic progress is the availability of a substantial quanti-

Jan 1, 1976

By N. F. Schulz, H. A. Lex

Representative samples of typical manganiferous iron ores from the Cuyuna Range, Minn., were reduced to the metallic iron state at temperatures just short of fusion with an excess of coke in the manner prescribed by the R-N Direct Reduction Process. The magnetic separation characteristics of the reduced ores were determined at several grinds by means of the Davis magnetic tube concentrator. The efficiency of metallic iron concentration by magnetic separation was a direct function of the degree of metallization of the ore sample and of the degree of liberation at-tained in grinding. Some improvement of liberation characteristics was observed if a small amount of sodium chloride was present in the ore during reduction. Despite the extremely fine-grained structure of the crude ores, iron concentrates containing more than 90% Fe at iron unit recoveries of 90% or more were obtained from well-metallized samples of three of the four ores tested. The rejection of manganese to the tailings corresponding to such separations varied from 80% to 95%. The manganiferous iron ores of the Cuyuna Range in Minnesota constitute a major potential source of manganese in the United States provided that a technically and economically feasible process can be devised for its recovery. The iron and manganese of these ores occur chiefly as oxides or carbonates in the form of very small, irregular, discrete grains embedded in a matrix of quartz or other siliceous gangue. The present investigation was undertaken as a sequel to an earlier one conducted jointly by the U.S. Bureau of Mines and the R-N Corp. Those results indicated that the R-N Direct Reduction Process might be a means for recovering both a metallic iron concentrate and a marketable manganese by-product from Cuyuna manganiferous iron ores.&apos; The R-N Process is one of many proposed schemes for the treatment of crude iron ores involving the di- rect reduction of the iron content to metallic iron followed by physical extraction of the iron. In general, it consists of the following stepsz2 1) Iron oxide in crushed natural ores or iron concentrates is about 95% reduced to metallic iron at elevated temperatures but without fusion in a rotary kiln in the presence of a solid carbonaceous fuel (usually coke), limestone, and combustible gases. 2) The kiln product, consisting of metallized ore, excess coke, lime, and coke ash is cooled. The excess coke is recovered and recycled to the kiln feed. 3) The metallized ore is ground for liberation and magnetically separated to yield a metallic iron concentrate. 4) The metallic iron concentrate is agglomerated by a briquetting process. The reduction kiln temperatures must be high enough for the desirable chemical reactions to proceed at practical rates without causing fusion of any of the ore constituents. The time of exposure of the ore to the reducing conditions must be ample for 90% to 95% metallization of the iron oxides present. If more than 95% of the iron is metallized, however, difficulties may arise in the briquetting step, presumably because of accompanying higher carbon content of the metallic iron. Although not always necessary, powdered limestone or dolomite may be added at some time during reduction to aid in eliminating sulfur and phosphorus from the final product.3,4 Other additives, notably sodium chloride, when present during reduction, result in improved liberation characteristics of the metallic iron from certain reduced ores.&apos;v6 Under the reducing conditions normally employed, P(co + H2)= 1 atmosphere, and 1830&apos; to 2150°F (1000° to 1170°C), the R-N Process is claimed to be adaptable to a wide variety of low, medium, and high grade iron and manganiferous iron ores. The manganese oxides and carbonates are reduced mostly to nonmagnetic MnO which is rejected to the nonmagnetic tailings. Manganese-bearing pyroxenes of the original ore, however, may be rejected poorly, if at all, apparently because these minerals occur within the iron lattice or are entrapped in the metal particles.7 The investigation was limited to studies of the Cuyuna ores listed in Table I, which were reduced to the metallic iron state under various conditions

Jan 1, 1969

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&apos; 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&apos;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&apos;s minimum work problem imply the solutions of Bishop and Hill&apos;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 R. I. Jaffee, F. C. Holden, H. R. Ogden

Ti-Mn alloys were studied in order to determine the factors affecting the mechanical properties of &stabilized titanium alloys. The principal compositional factors have been found to be solid-solution strengthening, the martensitic transformation, and instability of the P phase. Structural factors, such as grain size and shape, were found to have more influence on ductility and toughness than on strength. THE alloys of titanium with the &stabilizing elements offer the chief hope for developing useful heat treatments. Conversely, the heat-treatment response possible with the p-stabilizing elements causes difficulties such as weld embrittlement and thermal instability during service at elevated temperature. Therefore, it is of considerable technical importance to understand the factors that govern the heat-treatment responses in these alloys, so as to be able to soften the alloys if they are embrittled by an adventitious heat treatment, to render them stable in service, or to harden them while maintaining adequate ductility and toughness. The Ti-Mn system is a good example with which to demonstrate the factors that govern strength and heat-treatment response in. a P-stabilized system. The region of the a-j3 transformation, after the work of Maykuth, Ogden, and Jaffee,&apos; is shown in Fig. 1. The a solubilities are low. This means that, in the two-phase a-p field, partition of manganese between the two phases occurs practically only to the P phase. The solid-solution effects are therefore chiefly the result of solution in the ,8 phase. The eutectoid occurs at 20 pct Mn and 550°C, and proceeds very sluggishly. It can be ignored in heat treatments in hypo-eutectoid alloys, except for long-time storage at low temperatures below the eutectoid temperature. Even here, there is some question that diffusion proceeds far enough to involve eutectoid decomposition. Three compositional factors bear on the mechanical properties and structure of titanium a-P alloys. These are: 1—solid-solution strengthening, 2—mar-tensite transformation, and 3—P instability. Combined with the purely structural factors of grain size and shape, these govern the properties of the alloys. Perhaps the most important factor is solid-solution strengthening. The facts that manganese dissolves in a titanium to a maximum of only 0.5 pct and most of the manganese partitions to the p phase dominate the structure and properties of the a-/3 alloys. Because of the overwhelming preference of manganese for the ,3 phase, the P phase is harder and the a phase is softer. The relative amounts of both phases may be modified by heat treatment in the a-P field as application of the lever rule in the two-phase field clearly shows. A critical temperature in the Ti-Mn diagram is 800°C. This is the P transus temperature of the 6.4 pct Mn alloy, which has the lowest manganese content which will form all retained-P phase on quenching to room temperature. Any quench performed from below 800°C will produce a structure consisting of only a, a plus retained P, or retained p, for alloys of the compositions used in this work. For alloys containing less than 6.4 pct Mn, any quench from above 800°C will always result in structures

Jan 1, 1955