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By Schlanger H. P

A theoretical model for gas outbursts in underground coal mines is as follows. An outburst is the structural failure ofcoal due to excess stress resulting from body forces caused by gas pressure gradients. These body forces influence the stability of a mine face in the same manner that gravitational body forces affect the stability of the roof of a mine. The magnitude ofthese body forces can be appreciated when it is realized that for an average density coal, the gravitational body force is equal in magnitude to the force from a gas flow with a pressure gradient of 14 kPa m-I. Gas pressure gradients and the resultant stresses within a seam can be calculated with numerical methods. Thus, providing the necessary parameters can be measured or estimated, in principle the theory can be applied to compare the outburst risk of various mining arrangements.

Jan 1, 1985

By Josef K. Alter

Crosshole Sonic Logging (CSL) of drilled shafts requires 1.5-in (38-mm) or 2-in (51-mm) I.D. sonic access tubes to be installed inside the steel reinforcement cage. The sonic access tubes do not contribute to the structural capacity of the drilled shaft. The proposed use of Ischebeck TITAN T73/56 CSL/Hollow Threaded Rebar for Cross Hole Sonic Logging Access Tubes Combined with Longitudinal Concrete Reinforcing in Drilled Shafts (patent pending) is discussed as an alternative method of construction and CSL probe access. The T73/56 hollow threaded rebar/sonic access tube performs as a high strength rebar while at the same time creating a 2.2-in (56-mm) I.D. sonic access tube. The deformed high strength hollow bar provides better adhesion to concrete thus reducing the problem of debonding associated with smooth PVC and steel pipe. A cost comparison using conventional rebar with added sonic access tubes is discussed. The use of T73/56 CSL/Hollow Threaded Rebar as a value engineering alternative can reduce both material and labor costs for drilled shaft construction and can provide an advantage where anchor bolt cages and longitudinal reinforcing create congestion.

Jan 1, 2011

By Wittenberg J. C, Reid A. F

A method is described for the rapid and effective production of polished section mounts of ore and mineral particulates to the standards required for automated image analysis. This requires mounting without segregation of particles by mass or density, and it is also preferable to avoid having particles in contact so that they can be recognised as individuals. To achieve this, the particle samples are first split to an appropriate degree in a rotary riffle, and the sub-sample mechanically diluted and thoroughly mixed with an inert filler of the same size range as the particles. Just sufficient epoxy resin is added to make the mixture fluid. During setting, the ore particles are mechanically supported by the inert filler particles, thus maintaining the particles in a random three-dimensional distribution. A rapid two-stage grinding process, based on the successive use of 600 mesh silicon carbide and 1200 mesh (10 um) corundum on cast iron plates, is followed by three stages of mechanical diamond polishing on cloth laps. Hand polishing is entirely avoided, as is the use of papers.

Jan 1, 1984

By K. Mulukhov

Introduction The depth of open-pit mines continues to increase. The typical designed depth for large quarries is now in the 300 to 600 m (1,000 to 2,000 ft) range, with some quarries even reaching depths of 700 to 800 m (2,300 to 2,600 ft). The cost of handling material from such deep mines can be 60% to 70% of the total cost. The capacity of using a cyclic means of transport, such as trucks or skip hoists, continues to drop as the depth of the mine increases. In addition to the problem of maintaining relatively low slope angles for haul roads, increases in environment pollution and increased fuel consumption make the use of trucks ineffective below 100 to 150 m (300 to 500 ft). In handling large quantities of bulky materials, i.e., more than 15 to 20 Mt/a (16 to 22 million stpy), under fixed terminal points, belt conveyors are preferable in almost in all cases. An exception is when the lump size of the load is too high for the conveyor to handle. Belt conveyors in mines can handle loads having a maximum lump size of no more than 250 to 300 mm (10 to 12 in.). The use of a movable crusher prior to the belt conveyor in an open-pit mine would make the process very expensive. Such an operation could not compete with truck haulage on a cost basis. Belt-car conveyor The main factor that restricts the lump size for conventional belt conveyors is collision impacts between the load-carrying belt and idlers. These impacts are completely eliminated in the belt-car conveyor, which was previously described by Mulukhov (1977). The unique feature of the conveyor is that the load-carrying belt is supported by moving cars. Each car consists of a troughed cross strap that supports the belt with the load and two rollers, on which the cars move along upper and lower rails. Cars are connected by two endless chains revolving over sprockets. The system uses conventional drive pulleys, tail pulleys and return idlers. There are no fasteners between the carrying belt and the car cross straps. The conveyor belt simply drives the cars along by the force of friction between the belt and the straps. A belt-car conveyor was first installed in 1970 at the Karatau mining operation in Kazakhstan. The system was an elevating conveyor with an inclination of 20° and was located on the final part of the truck haul road. The conveyor transferred blasting phosphate ore from the quarry to the crushing plant. A bunker was mounted between the trucks and the conveyor. The maximum lump size was typically 1,200 mm (48 in.). However, there were some lumps as large as 1,500mm (60 in.), which was greater than even the belt width (Fig. 1). Because the prototype belt-car conveyor was intended only for industrial trails, it had a relatively short length of about 50 m (160 ft). Nevertheless, the conveyor yielded a substantial profit over the cost of truck haulage. Naturally, the first question one might ask is why such a system is not now widely used. The reason was the further development of a huge transporting complex for the whole quarry at the base of the belt-car conveyor. After successful industrial trials from 1971 through 1973, which demonstrated the systems engineering feasibility, the State Planning Committee of the USSR included the development of the belt-car conveyor in its plan for the development of the national economy. However, mistakes were made. First, a single organization was not in charge of the development. Second, a plant that was not specialized in belt conveyors was put in charge of the design and manufacturing of the conveyor system. In addition, the crusher was installed before the stacker, which negated the major advantages of the belt-car conveyor. For loading the conveyor, a special blade feeder with pendulum suspension was developed, but it was found unreliable. The main conclusion was that, in-

Jan 1, 2003

By Rao P. K, Sahoo P. K

The main constituents of ferromanganese slags are silicates of Mn, Ca and AI. Factors affecting the recovery of manganese from a low manganese content ferromanganese slag (about 16 per cent MnO) during acid leaching were studied. These included time, temperature, agitation, sulphuric acid addition, solid:liquid ratio and particle size. Agitation rates greater than 300 rev/min. leaching periods greater than 30 min and temperatures above ambient were found to have no effect on Mn recovery. Dissolution of Mn was found to be highly dependent on the amount of acid added.About 90 per cent of the Mn was recovered when 5·5 times the stoichiometric amount of acid was used. About 28 per cent of the Mn was recovered when the stoichiometric quantity of acid (with respect to Mn alone) was used. However, the recovery increased to about 75 per cent when the total stoichiometric requirement of acid with respect to Ca, Al, Mg and Fe as well as Mn was used for leaching. The extent of Mn dissolution also depended on the particle size of the slag. The percentage of Mn recovery (using 5·5 times the stoichiometric amount of acid) increased from about 60 per cent to about 92 per cent when particle size decreased from -36 +52 to -150 +200 mesh (B.S.S.). When the results of this study were compared with those in a previous study involv,ing the leaching of a high manganese content slag (containing about 40 per cent MnO) results were similar except that there was a gr-eater consumption of acid in the present case (i.e. low manganese content slag).

Jan 1, 1979

A mineral grain finder is described which is easily constructed to fit onto the stage of a standard reflected light ore microscope.The device is most useful in relocating particular grains or mineral associations on 30 mm diameter polished sections. The use of the grain finder in the teaching of ore microscopy is outlined.

Jan 1, 1988

This technical note describes a problem with WANG82, a ventilation network analysis programme. The problem was highlighted by Renison Ltd when using the programme on large, complex networks. Under certain circumstances the programme produced incorrect results or failed to converge to a solution.

Jan 1, 1986

By D. P. Penswick

The Palabora open pit is scheduled to cease operations in 2002. While the ore body continues below the bottom of the final pit shell, the stripping ratio precludes further economic open pit mining. Palabora Mining Company has investigated various means of continuing copper production, and has determined that an underground mine is the best solution. Board approval to commence construction of the mine has been granted and shaft sinking is underway. First production is planned for the year 2000 and full production of 30 000 t/d will be achieved by the end of the year 2002. [ ] Mechanised block caving will be the mining method employed at Palabora. The cave will be initiated by excavating a thin horizontal slice known as the undercut. Removal of the undercut will induce stresses which cause the rockmass overhead to fracture. Fractured rock will gravitate through drawbells to drawpoints on the production level, and be loaded by LHDs for transport to crushers.

Jan 1, 1997

By Robert Maddin

crystal prior to, polishing in order to eliminate coring. This treatment may be accomplished by wrapping the single crystal tightly in very thin, dead soft, brass foil and annealing in the presence of air for 20 hr at 800°C. Since the wrapping encircles the sptcimen three to four times, only a very slight amount of oxidation occurs on the specimen surface. On unwrapping one of these cylindrical single crystals. in. in diam by ro in. long (72.75 pct cu, 27.23 pct Zn, 0.01 pct P11, 0.01 pct re), mall light-gray depnrrits in the form of circular arcs werenoted on the part nf the foil which had been in contact with the single crystal, Fig r. (By superim- approximatetl). These deposits, which, from their color, suggest the appearance of sublimated zinc, were found to coincide roughly with a set of octahedral planes nearly perpendicular to the rod axis. The pattern shorn in the figure held no relation to the profle of the sample since the markin~s on the crystal More annealing werc attributed to traces of cube planes. It seems very likely that the deposits were formed by sutllimation of zinc diffusing from octahrdral planes since diffusian would Eogically take place along planes of maximum atomic spacing. However, it is difficult to understand why a continuous sublimation of zinc should occur from a single crystat in contact with a wrapping roil OF the same composition, and why diffusion would take place along specific octahedral planes and in a regular pattern.

Jan 1, 1949

By W. R. Hibbard

It has been proposed1 on the basis of slip and flow that the ideal deformation texture of drawn wire for face-centered cubic metals is a (111) direction parallel to the wire axis. Under these considerations, an intermediate [loo] texture is permissible but should eventually change to the stable [Ill] orientation. This theory does not explain why copper and its alloys containing up to about 30 pct nickel, 5 pct zinc and 1 pct aluminum were found to have a double [Ill], [100] texture, while alloys with at least 8 pct zinc and 2 pct aluminum developed essentially a single [Ill] texture.1,2 It does suggest, however, that the [loo] component of the former alloys should disappear with additional deformation.3 Some evidence exists to support this suggestion. Howald4 reported that annealed copper wire previously drawn 93.8 pct and 98.5 pct developed a single [Ill] texture. Since, in wire, the drawn and annealed textures are similar, these wires probably had a single [Ill] deformation texture before annealing. In addition, although cold rolled polycrystalline copper and 80-20 brass were found to form different types of pole figures,5,6 single crystals of these metals when rolled from the stable (110) [112] orientation were found to produce essentially the same polo figure.7.8 It may be, therefore, that while the addition of solute elements changes the path by which the final texture is obtained, the final texture is not changed. Experimental Results The wires remaining from the previous investigation1 already drawn about 50 pct reduction in diameter were further drawn to 86 pct and then to 96.4 pct total reduction in diameter. The textures were determined after these stages by transmission X ray photograms taken with a copper K-alpha beam rotated 0 degrees toward the wire axis. It was found that the ratio of the [111].] and [100] intensities of the double texture in copper and its alloys containing 0.94 pct aluminum, 30.70 pct nickel, 2.61 pct zinc and 4.99 pct zinc increased from about 3:l for the 50 pct reduction to about 9:l for the 86 pct reduction. After 96.4 pct reduction, these wires exhibited essentially a single [lll] texture. Summary Thus, the drawn wire deformation texture of copper and its alpha solid solution alloys containing aluminum, nickel or zinc is essentially a single [Ill] texture as predicted by theoretical considerations of slip and flow.' For copper and its alloys containing up to about 1 pct aluminum, 5 pct zinc and at least 30 pct nickel, an intermediate [loo] component is found after about 50 pct reduction in diameter, but disappears after about 95 pct reduction in diameter. For alpha solid solution alloys containing at least about 2 pct aluminum and 8 pct zinc the single [Ill] texture is developed considerably more easily and is found after about 50 pct reduction in diameter. No explanation of this compositional effect is apparent. Similar work is contemplated for cold rolled and cold compressed alloys. References 1. w. R. Hibbard, Jr. and M. K. Yen: Trans. AIME 175, 126. Metals Tech., Feb. 1948, TP 2334. 2. W. R. Hibbard, Jr. and D. E. Trout, 11: Trans. AIME 185, 620. Jnl. of Melals, Sept. 1949, TN 18. 3. W. R. Hibbard. Jr.: Disc. of R. M. Brick's paper on Deformation Textures, ASM Symp. on Cold Working of Metals, Oct. 1948. 4. T. S. Howald: Disc. of Ref. 1. Trans. AIME, 175, 126. Melals Tech. Aug. 1948, TP 2449. 5. R. M. Brick, D. L. Martin and R. P. Angier: Trans. ASM (1943) 31, 675. 6. 0. Dahl and F. Pawlek: Zlsch. Melall. (1936) 28, 266. 7. C. S. Barrett and F. W. Steadman: Trans. AIME (1942) 147, 57. 8. J. E. Burke and C. S. Barrett: Trans. AIME 175, 106. Melals Tech., Feb. 1948. TP 2327.

Jan 1, 1950

By H. R. Skewes

IN the course of small seale experiments on the electrodeposition, of copper, extremely brittle deposits were obtained from electrolytes prepared by leaching calcined chalcopyrite with aqueous sulfuric acid. It was not possible to strip the metal without fracture after it had been deposited from such electrolytes onto smooth oiled copper sheets, the usual plant procedure for the production of so-called starting sheets. The embrittlement did not occur with electrolytes made either by leaching the calcine with water or by treating an acid leachate to remove iron as hydrous ferric oxide. The electrolytes which produced brittle deposits were found to contain molybdenum in concentrations of 10 to 25 mg per 1, whereas those which produced ductile deposits contained <0.5 mg per 1. Synthetic electrolytes having the composition: Cu", 40 gpl; Fe", 0.5 to 1.0 gpl; Fe3+, 0.5 to 1.0 gpl; and H,SO,, 10 to 50 gpl, were prepared from reagent-grade salts; by adding ammonium molybdate, the embrittling effect of the higher concentrations of molybdenum (VI) was strikingly confirmed. The brittle deposits contained up to 0.03 pct Mo. The importance of oxidation state of the molybdenum was demonstrated when the electrolyte containing it was circulated continuously through a bed of fine copper metal during deposi- tion. Under these reducing conditions, the cathode deposit was ductile and molybdenum could not be detected. Molybdenum has not been recognized as one of the metals causing embrittlement of copper nor is it listed among the usual impurities. In most elec-trowinning plants there is a purification step which removes iron from the leachate before electrolysis. In these cases molybdenum would be coprecipitated with hydrous ferric oxide. In the case of the large leaching plant at Chuquicamata, Chile, where the leachate is reported to contain considerable molybdenum, it would be reduced to a lower oxidation state during removal of chlorine by means of cement copper. This may explain why the embrittling effect of molybdenum has not been reported previously. Moreover, in copper refining plants where soluble anodes have been prepared by a high temperature smelting process, it is most unlikely that any molybdenum would remain with the copper, whereas the calcines in this work were prepared in a fluidized bed reactor at a temperature not exceeding 720°C. Acknowledgment This work is part of an investigation on the roasting and extraction of copper from sulfide ores sponsored jointly by Mt. Morgan Ltd., Queensland, and the Mt. Lyell Mining and Railway Co. Ltd., Tasmania.

Jan 1, 1958

By Y. Oka, H. Majima

When a rock particle is subjected to an external force, internal stresses and deformations are experienced by the particle. Assuming that the breakage of a rock is mainly due to tensile stresses generated by the action of a pair of concentrated loads, F, directed in compression towards the loading points at the shortest distance, as illustrated in Fig. 1, the stress and deformation experienced by a particle of irregular shape can be determined with the aid of the theory of elasticity. According to the photoelastic experiments made by one of the present authors,&apos; the stress states in a rock particle of irregular shape are quite similar to that of an inscribed sphere of diameter x, as indicated in Fig. 1, but accompanied by the faint stresses, in the vicinity of the particle outside of the inscribed sphere. Therefore, the stress components in an irregularly shaped particle can be estimated by referring to stress components in a sphere. Applying polar spherical coordinates to an elastic spherical body, as shown in Fig. 1, the stress components are all expressed as multiples of F /x2 and more or less influenced by the loading angle and Poisson&apos;s number m. In general, the energy w, acting on a rock particle is defined as the product of loading compression F

Jan 1, 1970

By K. Takahashi, I. Iwasaki

it is well known1 that racemic mixtures of optical isomers can be separated by passing their solutions through a column packed with r- or 1-quartz powder so that one of the isomers becomes adsorbed selectively on the asymmetric quartz surfaces. Although the natural occurrence of r- and 1-quartz is more or less equally distributed, some localities show enough deviations toward a higher proportion of l-quartz2 to suggest that optical isomerism might influence quartz flotation. Beta-amines have an asymmetric carbon atom, and therefore optical activity may be expected. Beta-amines are reported to behave quite differently from alpha-amines in the flotation upgrading of certain oxidized iron ores.3 It is of interest, for both practical and theoretical reasons, to determine whether or not optical isomerism plays a role in the amine flotation of quartz. In this article the results of Hallimond tube flotation tests and of adsorption measurements using d-beta-phenylisopropylamine on both r- and 1-quartz are compared. D-beta-phenylisopropylamine was chosen for the tests because it is commercially available in optical isomers. MATERIALS AND METHODS Brazilian quartz crystals were hand-sorted according to the difference in trigonal trapezohedral faces, and each crystal was further checked by the Airy&apos;s spiral.4 The respective crystals were then crushed, and the -150 + 200-mesh fractions were screened out for the Hallimond tube tests. The samples were cleaned by brief leaching with warm, dilute hydrochloric acid, and then by repeated rinsing with distilled water. In preparation for the adsorption measurements, they were then dry-ground in a pebble mill for several hours, washed a few times with distilled water, and finally dried in a vacuum desiccator. By means of the Krypton gas adsorption method, the specific surfaces of r- and 1-quartz samples were determined to be 27,700 and 19,800 sq cm per gm respectively, the difference being due mainly to the decantation procedure rather than to the inherent difference in their grindability. D-beta-phenylisopropylamine was the only collector used in the study. It was solubilized by neutralizing with 110% of the stoichiometric requirement of 0.1 N hydrochloric acid. The specific rotation of the d-beta-phenylisopropylamine was determined with a polari-meter using sodium D line to be, Although the d-beta-phenylis~prop~lamine showed absorption maxima in the wave length region of 250 to 270 millimicrons, due presumably to the phenyl group, these peaks were too sensitive to be used for colorimetric determination of the residual concentration in the adsorption measurements. The amine-picrate method, used in the colorimetric analysis of dodecylammonium chloride,&apos; was found to work satisfactorily for the d-beta-phenylisopropylamine. The adsorption densities were thus determined after equilibrating 40 gm of the ground quartz sample with 300 ml of solution by tumbling in separate glass-stoppered Erlenmeyer flasks for one hour. EXPERIMENTAL RESULTS Fig. 1 presents the adsorption densities of d-beta-phenylisopropylamine on the r- and 1-quarts in the pH range of 6 to 7.5. In agreement with data reported in the literature, the adsorption density of d-beta-phenylisopropylamine was slightly higher on the r-quartz than on the 1-quartz, although the difference was not as pronounced as one might expect from the capacity of r-quartz and 1-quartz to separate racemic

Jan 1, 1969

By T. G. Sieber, T. D. Tiemann

The extraction of quartz from siliceous iron ores by dissolution in sodium hydroxide solution has been described in detail in AIME Transactions. l923 data reported covered the temperature range from 230-416°F, where a continuous increase in the amount of silica extracted with increase in temperature was found. It is the purpose of this paper to describe some unexpected results of more recent work exploring principally the range of 500600°F where higher rates and greater amounts of silica extraction were antici-p ted. In brief, the experimental procedure consists in digesting the ore under pressure in solutions of sodium hydroxide, filtering the suspension and weighing and analyzing the dried residue for iron content. The amount of extraction is calculated from the weight loss or from the iron analysis of the residue and that of the original ore.

Jan 1, 1969

By W. D. Bennett

AN interesting effect has been observed in the vacuum etching of titanium in the high temperature ß phase. Using a high vacuum annealing furnace, operating at less than 2x10-6 mm with a tubular titanium liner, it has been found possible to etch polished metallographic specimens at different temperatures between room temperature and 1000°C without contamination or increase in hardness.&apos; Heat etching of titanium has been reported by other workers,&apos; but the following example is of interest as an experiment under high vacuum in the absence of any contamination. Two polished specimens of iodide-processed titanium are placed at different positions along the axis of the furnace corresponding to temperatures of 900" and 800°C above and below the a-ß transus. The specimens are then raised to these temperatures and annealed simultaneously for 3 hr under the same high vacuum conditions. After cooling and withdrawing the specimens, their surfaces are photographed without further treatment. Figs. 1 and 2 show the results for the 800" and 900°C specimens, respectively. Fig. 1, corresponding to a vacuum etch in the a region, shows a typical equiaxed structure with what appears to be a slight shift of grain boundaries. Fig. 2, corresponding to a vacuum etch in the ß region, shows an equiaxed type of structure with the growth of striations in certain grains. The striations are only superficial, as a light polish and chemical etch restores the clean equiaxed structure. The vacuum etch, occurring as it does above the a-ß transus, records the state of the metal in the ß phase by means of the surface relief produced by the selective evaporation of metal from different grains; the metal itself reverts to the equiaxed a on cooling. The nature of the ß etch" (Fig. 2) suggests that, in transforming from the close-packed-hexagonal a to the body-centered-cubic ß lenticular-shaped laminae are formed parallel to common planes of the two structures. This would explain why some grains appear to be unaffected by the etch. The technique has interesting possibilities in the investigation of the mechanics of high temperature transformation. Acknowledgment This note is published by permission of the Deputy Minister, Dept. of Mines and Technical Surveys, Ottawa, Ont., Canada.

Jan 1, 1956

By R. B. Rosene, G. L. Foster, A. R. Hendrickson

he properties of some of the common fracturing oils, such as sand-falling rate, fluid loss and viscasity, are a function of the three major constituents of the oil. These are: asphaltic material, parafin waxes and a base oil. The base oil can be either high or low viscosity. Asphaltic material increases viscosity by thickening the oil, decreasing the rate of fall of sand through the oil. at temperatures up to 200" F. When large arnorrnts of parafin wax are present, much of the wax i.s not dissolved, but is present in the form of rnicroscopic crystals. 7&apos;his, of course is limited to temperatures below the melting points of waxe.s. As a result, parafin waxes clo not function primarily as thickener.7, but rother as bullting materials. The functiori of wax, without asphaltic material, in a low viscosity base oil is uniquely unlike that of wax with asphalt coexistent in the oil. The resulting difierence in wax crystal size governs the sand-falling rate to a large extent. An ideal type of fracturing oil is one containing neither asphalt nor waxes. In such cases, the viscosity and resulting low sand-falling rate are apparently due to soluble resin- ous hydrocarbons, which are compatible with formation oils. INTRODUCTION Since the introduction of hydraulic fracturing as a method of stimulating production from oil and gas wells, a variety of fluids have been employed to open the fractures and carry the propping agent. Such fluids include gels, emulsions, and oils. In the latter category, the use of refined oils has increased tremendously, and it is probably safe to assume that such oils represent more than one-half of the total fluid used in fracturing. The general acceptance of refined oils for fracturing can be accounted for on the basis of their relatively low cost and general applicability. To minimize transportation costs, such refined oils are generally obtained within the local areas of operation. As a result there are several kinds of oil used in different areas, with a wide variation in the basic composition. These types may vary from a fair grade of lubricating stock to a highly viscous cut-back asphalt. or road oil. Originally, little attention was paid to the composition of the oils used for fracturing, and any oil which would carry sand was considered satisfactory. Recently, however, service companies and well operators have become more concerned with the type of oils used for fracturing. With this in mind, the present work was undertaken to evaluate and compare many widely used fracturing oils to determine which constituents were most desirable for fracturing purposes. Some of the important properties of fracturing fluids are sand-falling rate, viscosity, and fluid loss. Other properties, that are actually of no less importance, include flash point, pour point, emulsifying tendencies with formation brines, and compatability with the formation oils. This discussion has been limited, however, to the first mentioned properties in order to give some idea of the general composition of the refined oils, how they function, and why. PROPERTIES OF FRACTURING OILS The properties of fracturing oils are a function of the three major constituents of the oil. These may be designated as: (1) asphaltic material, (2) paraffin waxes and (3) a base oil, which may be of either high or low viscosity. The asphaltic material clas-

Jan 1, 1956

By F. D. Wright, H. D. Fara

The solution to the plastic and elastic stresses around a circular shaft in a hydrostatic stress field that has appeared in two editions of a widely used book on rock mechanics1 is in error. Although this is a relatively minor matter, the correct solution was not found by a literature survey, so it appears worthwhile to present it. For a homogeneous, isotropic, rigid plastic-elastic body in plane strain which obeys Tresca&apos;s yield criterion the following equations must be satisfied:&apos;," In the plastic zone,

Jan 1, 1963

By L. D. Jaffe, R. K. Pitler

IT would clearly be advantageous to produce molten titanium, suitable for alloying and casting, directly from the relatively inexpensive tetra-chloride, without using a metallic reducing agent. Accordingly, a preliminary investigation has been made of the production of titanium by hydrogen reduction of the tetrachloride in an electric arc furnace. For the reaction: TiCl4(g) + 2H2(g) ? Ti(s) + 4HCl(g), Lockhart and his colleagues&apos; have calculated equilibrium constants at 800" to 1500°K, based on tables of Brewer.&apos; Extrapolating these data on the assumption that the heat of reaction varies linearly with temperature, and using Brewer&apos;s value for the heat of fusion, there is obtained for the reaction: TiCl4(g) + 2H2(g) ? Ti(l) + 4HCl(g) an equilibrium constant at 2100°K (100" above the melting point) Kp = (PHCl)4/pTlcl4 (Ph2)2 = 0.167 atm. If this is correct, starting with hydrogen saturated with TiC14 at 25°C, where the vapor pressure of the latter3 is 12.6 mm, and maintaining the overall pressure at 1 atm, 99 1/4 pct of the TiC14 would be reduced to Ti at equilibrium. An arc furnace designed for the melting of titanium and lined with water-cooled copper was used for the preliminary experimental check. Its inside diameter was 2 7/16 in. and height 6 in. The water-cooled electrode was tipped with 3/4 in. diam tung-sten. In the one run carried out, the furnace was charged with a starting batch of 293.35 g of scrap titanium,&apos; analyzing 99.24 pct Ti. After the system was twice pumped out and flushed with argon to remove air, the arc was struck in argon and kept at 400 amp dc, electrode negative, for 1 min to melt the starting batch. Commercial tank hydrogen, dried by passing over silica gel and bubbled through technical grade TiC14 at room temperature, was then admitted to the furnace. The inlet tube directed this gas downward toward the arc and melt; the gas outlet was at the top of the furnace. The quantity of gas passed through was not measured accurately but is estimated to be about 50 liters per min at a few mm of mercury above atmospheric pressure. The arc was held in the H2-TiC14 mixture at 400 amp with little difficulty. After 10 min the arc burned through the copper lining above the melt, admitting water and ending the run. (This had happened frequently in straight melting runs under argon, and is not thought due to the atmosphere used.) In the furnace were found an ingot, several small pieces, and a little metallic powder, evidently formed when water entered the hot furnace. Some titanium also clung to the electrode. The portions were weighed and separately analyzed for titanium. Their total weight was 321.76 g of 94.82 pct overall purity. Much of the impurity consisted of tungsten broken off when the titanium was removed from the electrode. No detailed impurity analysis was made because the starting materials were impure and flooding the furnace introduced further contamination. Thus, the metal recovered contained 305.08 g Ti, as compared to 291.12 g in the starting batch. Titanium could not have been carried over from previous melting runs in the furnace, as the interior was sandblasted and the electrode ground clean before the run. Evidently at least 13.96 g of Ti were produced from TiCl4. Since this would require complete reduction of 430 liters of TiCl, gas at 12.6 mm of Hg, the efficiency of the process must have been rather high. Experimental work is continuing. No reason is seen why the process could not be scaled up to the size of a 30-ton steel-melting arc furnace. In a large unit there would be a large molten pool from which liquid metal could be withdrawn for alloying and casting. The problems of electrodes and power supply are similar to those arising in arc furnaces for melting titanium. Unreacted TiC14 and the HC1 in the exhaust gases could be recovered; unreacted H2 could be dried and re-used. The melt would be saturated with hydrogen, whose solubility in liquid titanium is unknown. Small amounts of hydrogen seem to have little effect on the properties of titanium.5 If the amount introduced was so large as to impair properties or cause casting difficulties, it could be reduced by holding the melt under an inert gas or by pumping on it, prior to casting. Acknowledgment The authors would like to thank I. Preble and M. Goldman for their valuable aid in the experimental work and the thermodynamic calculations, respectively. References 1R. J. Lockhart, J. J. Ward, M. J. Hussey, and J. W. Clegg: In unpublished report, "U. S. Air Force Project Rand. Titanium and Titanium Base Alloys." Battelle Memorial Institute (1949) 37-44. 2 L. Brewer et al: Chemistry and Metallurgy of Miscellaneous Materials—Thermodynamics. Ed. by L. L. Quill. pp 13-39, 60-192. (1950). McGraw-Hill Book Co. 3 K. Arii: Scientific Reports. Tohoku Imp. Univ. (1933) 22, 182. 4 R. S. Dean, J. R. Long, F. S. Wartman, and E. L. Anderson: Transactions AIME (1946) 166, 369-381; Metals Technology (Feb. 1946) TP 1961E. * R. I. Jaffee and I. E. Campbell: Transactions AIME (1949) 185, 646-654; Journal of Metals (Sept. 1949) TP 26813.

Jan 1, 1951

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By J. Gordon Parr, D. H. Polonis

IN a previous study of hypereutectoid Ti-Ni alloys&apos; a substructure was observed in quenched powder specimens when the constitution was 100 pet retained ß body-centered-cubic phase. The alloy powders were quenched from 1000°C by a blast of helium gas and precautions already described were observed throughout the work, to minimize contamination. Ogden et al.2 have previously observed subboundaries in the ß phase of a Ti-Mn-N alloy; but this structure was attributed to nitrogen-rich a precipitation. The nitrogen content of the Ti-Ni alloys does not exceed 0.02 pet and the quenching rate was sufficiently rapid to suppress precipitation reactions. Since X-ray diffraction results have confirmed the absence of any second phase which might account for this phenomenon, it seems unlikely that this substructure is explicable in terms of nitrogen content. Fig. 1 shows the substructure in adjacent grains of 100 pet ß phase in a quenched 6 atomic pet Ni alloy. Fig. 2 shows adjacent ß grains in a similarly treated alloy; one grain contains marked intracrys-talline boundaries and the other is completely free from any substructure. The suberystals appear to have fairly regular shapes, suggesting a regular orientation relationship among them. Tempering the retained ß structure at temperatures below the eutectoid eliminates the substructure at an early stage of ß decomposition. At the present time it is possible only to guess at an explanation for this subboundary phenomenon, since very little work has been reported on substructures resulting from phase changes. It is believed that the present phenomenon is due to poly-gonization resulting from unrelieved stresses set up

Jan 1, 1957