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By R. M. S. B. Horta, W. T. Roberts, D. V. Wilson

Evaluation of results obtained by the Harris method for inverse pole figures is discussed. Two existing analyses and a new approach are compared. In the most frequently used analysis, different reflections are accorded equal weight. A second method involves area-weighting of reflections, mainly to take account of nonuniformity of Pole distribution. In the new method, reflections are weighted according to their multiplicity factors. Intensity ratios obtained from a sample of steel sheet by the three methods are compared. INVERSE pole figures offer a convenient method of depicting the proportions of material with various orientations referred to a unique specimen axis. The technique was first applied to fiber textures, but it is now frequently used as a description of texture in sheet metal, the unique axis in this case usually being the sheet normal. The Harris method' for the determination of inverse pole figures has the great merit of simplicity. It suffers certain intrinsic limitations, but provided that these are borne in mind, the results allow useful conclusions to be drawn regarding the effects of texture components on certain mechanical properties. Much thought has been given to alternative methods of texture description, aimed at eliminating the ambiguity in the simpler methods.2"6 Refinements in the method of description are obtained at the price of increasing complexity, and it seems clear that a simple method, such as that of Harris, will continue to find application. The original derivation by Harris1 has been corrected by Morris7 and later by Mueller, Chernock, and Beck.2 Since the latter reference is more accessible, it is referred to more frequently than the work of Morris. Most users of the inverse pole figure method present their results on the basis of the treatment by Mueller et al., and it is the purpose of the present communication to comment on this treatment and to suggest a simple modification to the method of presentation which enhances the meaningfulness of the results. It will be convenient first to summarize the Mueller analysis as follows: The intensity Ihkl of a hkl reflection from a textured specimen is: Ihkl=CI0AL\Fhkl\2NhklPhkl [1] where C is a constant for a given sample I, is the intensity of the incident beam A is an absorption factor. With usual diffrac-tometer geometry and a flat specimen, A is inversely proportional to the density of the specimen. L is the Lorenz polarization factor Fhkl is the structure factor for the hkl reflection Nhkl is the multiplicity factor phkl is the fraction of crystals in the polycrystal-line aggregate with any particular (nkl) plane parallel to the surface. The corresponding equation for a specimen with randomly oriented grains is lR,hkl=CRl°ARL\fnkl\2Nnklk [2] the subscripts R indicating the factors that are different for the random sample, which will, in general, have a density different from that of the textured one. The intensity ratio is hkl , c A Phkl [3] IR,hkl CR AR PR The constants are eliminated by summing over all the measured reflections ^iRMi °R AR PR ljPkkl and from Eqs. [3] and [4] T IR,hkl The only unknown in Eq. [5] is Yj phkl and before this can be evaluated, it is necessary to adopt some form of normalizing procedure. Mueller et al. assume that when a large number, n, of reflections is used, the average value of p as defined by Eq. [6] below will be unity ? = £j**l3l [6] and the final result of their analysis follows: hkl Pkkl = i I&Jf~ [7] ±y* Ihkl ^ in,hki The normalizing procedure used by Mueller et al. involves an unrealistic assumption since it gives equal weight to each of the hkl reflections. Other normalizing procedures can now be examined with a view to selecting a more appropriate one. For an infinite number of reflections, the function p can be averaged over a continuous range of orientations covering the complete solid angle 4p by the integral relation: p =1 jp(a)dQ = l [8] This is the only exact procedure, but in practice a

Jan 1, 1970

By Steve H. Carpenter, Henry E. Otto

The explosive welding of metals is dependent upon the production of a jetting action caused by the collapsing of one metal plate against another. Successful welds are generally accomplished if the yield strength of the metals is in the range of 10,000 to 90,000 psi and the sonic velocity of the metal is greater than the detonation velocity of the explosive if direct contact explosive is being used.' Should the detonation velocity exceed the velocity of sound in the metal it may still be possible to obtain the jetting action and a good weld. However, in most cases where a high detonation velocity is used complications arise because of reflected shock waves which tear the bond apart as fast as it is put together.' Explosive welding of lead presents several problems since its yield strength and sound velocity are very low. Various values have been published3-5 for the velocity of sound in lead ranging from 2000~ to 23004 m per sec. Most of the high-order explosives have detonation velocities on the order of 6000 to 8000 m per sec, which precludes their use. The dynamites have a lower detonation velocity of around 2800 m per sec which is still somewhat too high. Lower-order explosives such as ammonium nitrate (1070 m per sec) must be used to weld lead in the as-received condition if the explosives are used in direct contact. Rather than use low-order explo'sives it was decided to alter the sonic velocity of the lead. The sonic velocity is directly related to the modulus of the material according to the following expression: Fig 1—Interface of explosive weld of lead to steel. Lead is on top As-polished Magnification 75 times as well as the yield strength. Bolling et al. 6 show that the shear modulus of lead single crystals increases from about 0.72 X1011 dynes per sq cm at 300°K to about 0.98 X1011 dynes per sq cm at 0°K, an increase of approximately 3 5 pct. This gives an increase in the sonic velocity of around 700 m per sec. Hence, the sonic velocity of lead at cryogenic temperatures is approximately equivalent to the detonation velocity of the low-order dynamites. We have obtained high-quality lead to steel explosive welds using a 40 pct dynamite in direct contact with the lead. Prior to detonation the lead was chilled with liquid nitrogen (78°K) to increase the strength and sonic velocity. Welds were made while the lead was cold. Specimen sizes were 3 by 6 in. A preset angle of 5 deg with a 0.10-in. standoff at the base was the geometrical setup used. The amount of explosive used for optimum welding of an 1/8 -in. -thick lead sheet to a steel plate was found to be 7 g per sq in. A PETN sheet explosive line wave generator was used to insure a linear detonation front through the dynamite. A photomicrograph of a lead-steel weld is shown in Fig. 1. The typical wave effect that constitutes a good explosive weld is present. When tested in shear, the weld failed in the lead, indicating that the bond is stronger than the lead base metal. Higher-order explosives were also tried without success. We believe this indicates the importance of matching the detonation velocity and the sonic velocity for successful explosive welding. Note Added in Proof. High quality explosive welds of lead to steel have recently been obtained at ambient temperature using a low velocity (1000 M per sec) free running dynamite. The weld interface obtained is comparable to Fig. 1. 'S. H. Carpenter, R. H. Wittman, and R. J. Carlson: Proceedings of the First International Conference of the Center for High Energy Forming, Syracuse University Press, syracu.se, N. Y., in press. 'A. HI Holtzman and G. R. Cowan: Welding Risearch. Council Bull., No. 104, April, 1965. 'Metals Handbook, 8 ed., p. 1062, Metals Park, Ohlo. 'J. M. Walsh, M. H. Rice, R. G. McQueen, and F. L. Yarger: Phys. Rev., 1957, vol. 108, pp. 196-216; 'L. V. Al'tshuler, K. K. Krupnikov, B. N. Ledener, V. I. Zuchikhin,

Jan 1, 1968

By Earle C. Smith

The Chairman.—Mr. Earle Smith has kindly offered to make some remarks in connection with segregation in the product, Mr. Smith: E. C. Smith,* Cleveland, Ohio—I will start this Off by a story oF the code days of the American Iron and Steel Institute. In those days, Republic did not have a big strip mill, and the question came up of the check analysis of rimmed steel. I suggested that they let me be the chairman of the Committee on Accumulating the Information on the Variation of the Composition of the Ingots of Rimmed Steel. Somebody wanted to know why I wanted to be the chairman. I said, "we don't make any of the big ingots of rimmed steel, and no matter who makes them they are so bad that you don't dare publish the information. So if 1 collect it and hide it you can't charge me with having done anything that really disrupted the commercial situation." So, everybody furnished me with a rather complete story as to the horrible variations in big rimmed ingots. I took it out to my house and put it away, and it is still there. Now, segregation in the big ingot is no longer an "academic " matter as far as I am concerned. I am in a situation like that of the German who was told in 1956 about the coming war. He said: "until it is your throat that is going to be cut, you don't pay any attention to what is happening to the otherman." 'That is the way with the problem that we have in front of us. Recently I have been told that the 'Omptroller was questioning the payment for certain articles of stamped steel that had been made from rimmed steel, because upon check analysis of the rimmed steel it had been determined that these stamped articles were nut within the compositions that were included in the specification, and therefore he as the camptroller had no alternative. It was not meeting the specification; therefore, no payment. So I I say to all of you: You can very seriously consider this matter of segregation now and on into the future on the basis of the fact that it is actually going to cost your companies, which are making these products, money unless there is some new idea about the infallibility of quantitative , chemists who analyze some of these products or lawyers who read specifications, I don't know which man is going to be the major factor in the future. if the National Bureau of Standards could in some way show the specification writers the variation between good chemists analyzing for That they expect to be umpire eel. the writers would certainly realize that some of the to to which we have calmly signed our names as being O.K. are— well, as one man said to me, they might be filled by the devil, and they certainly could be filled by the Lord, but they could not he me by mankind. I would like to inject two or three things into a segregation study which I Want you to think about, because 1 would be a little surprised if there is very much discussion of them, In the first place, we generslly make steel in the United States in the basic open hearth, and I do not think there has bee,, nearly enough consideration given to segregation German the bath before it moves into the ladle. I am sure that any of the people who handled the 9400 series of the NE series when it contained the 0,60 per cent silicon have more respect than they had previously for the segregation that is within, the ladle; that is, before the metal reaches the ingot mold, the frozen ingots and the segregation in them. Another pint to which I think We ought to sis serious consideration is the segregation of iron oxide in the ingot-iron type of material, where the distinction between that and the steel segregation is that it is actually segregat. ing iron oxide, Normally we are segregating some form of carbon or sulphur, or something like that, with the stamping steel industry now coming down into the ranges of chemistry, where the segregation of iron oxide will be just

Jan 1, 1945

By J. Marin, H. A. B. Wiseman

This paper presents results of an experimental study dealing with the plastic stress-strain relations of aluminum alloy 14s-T6 subjected to combined biaxial tension and compression stresses. Plastic stress-strain relations for both constant and various types of variable stress ratios were determined and a comparison made with the simple flow theory of plasticity. THIS investigation was undertaken for two main purposes: 1—to obtain plastic stress-strain relations for Alcoa 14s-T6 when subjected to various combinations of biaxial stresses, and 2—to determine the validity of the flow theory in predicting plastic stress-strain relations for combined stresses. The biaxial stresses used were tension combined with compression. These stresses were produced by subjecting a thin-walled tube to axial tension and torsion. Various types of combined stress conditions were investigated. To provide control test data and information on the influence of biaxial stresses on the strength, the usual constant stress ratio type tests were made. These tests showed that the biaxial yield strength agrees approximately with the distortion energy theory. However, the Prager semi-empirical theory agrees best with the test results. For these constant stress ratio tests the plastic stress-strain relations were found to agree approximately with the flow theory. (For constant stress ratio the flow and deformation type theories are identical.) In view of the fact that the constant stress ratio tests cannot distinguish between the flow and deformation theories, a number of variable and special biaxial stress tests were made. These tests showed that the flow theory is inadequate, since large differences exist between the experimental and theoretical results. Special tests were also conducted to check the validity of the isotropic yielding assumption. This assumption is made in the linear-type flow theory. In these tests specimens were loaded in tension to predetermined values beyond the proportional limit stress. The tension load was removed from the specimen and the specimen was subsequently loaded in torsion to fracture. Other tests were applied with the order of torque and tension loading reversed. The nominal stress-strain curves for these two tests approximately coincide indicating that the assumption of isotropic yielding is valid. In addition, these tests verified the requirement by the slip theory of plasticity that prestraining below 140 pct of the proportioned limit stress in either torsion or tension did not influence the subsequent plastic stress-strain relations in tension or torsion. Another type of test was conducted to check the assumption that the axes of principal stress and strain coincide during plastic flow and variable stress conditions. These tests were conducted by applying combinations of axial tension, internal pressure, and torsional loads such that the axes of maximum principal stress could be rotated through 90" during the loading path. The results of those tests showed that the angle between the axes of principal stress and strain varied greatly and that the assumption of coincidence between axes of principal stress and strain is not valid. Introduction In various metal processes including forming of sheets, rolling of bars, and extrusion of rods, metals are subjected to stresses beyond the yield strength of the material. Often these stresses are not simple stresses acting in one direction, but are combined stresses acting in more than one direction. Structural and machine members are often subjected to combined stresses. To adequately determine the factors of safety for these members, it is necessary to know the plastic stress-strain relations of the material used for various combined stress conditions. Various theories have been proposed for predicting the plastic stress-strain relations for combined stress in terms of the simple tension plastic stress-strain relation for the material. To determine which theory might be adequate, test results must be obtained for various combined stress conditions, in order to compare the actual with the assumed theoretical behavior. Although there is considerable test data available for combined stress conditions in which the principal stress ratios are constant, relatively little test information is available for vari-

Jan 1, 1954

L.R. Bower In regard to the paper by J.B. Gwiazda, it makes a highly technical approach to show that the µ factor used by designers of lemniscate-guided roof supports has never really been confirmed as a maximum and assumes that convergence is vertical. Also, the paper does not appear to take into account deflection of structures, which occurs when the lemniscate and base members are fully loaded to their maximum stress level, nor the front to back line of the support in relation to differential roof to floor movements caused by strata movements under pressure. It is not unusual for differential movements to be slightly diagonal to the line of the support, particularly in faulted areas and on gradient faces. The paper also does not take into account consolidation of fines immediately above and below the support. Generally speaking, any differential movement is from face to waste and under these conditions the µ of 0.3, which appears to be an international standard, has worked in practice. However, if the face end of the support is lower than the waste end, then the µ of 0.3 can be considerably increased, giving rise to the damage mentioned in the paper. The ideal design should aim for a slightly forward bias in the lemniscate guide so that the last increment of setting is toward the face, tending to close any fissures that may have developed during the support advance cycle. The support should also be fitted with positive set valves to ensure that a high setting load density is attained to minimize bed separation. As far as powered supports are concerned, convergence is irresistible and all powered supports converge at their rated yield load. A similar principle can be applied to the differential roof to floor movements to drastically reduce the very high forces that would otherwise be applied to the lemniscate structures and pins and that, in turn, are transferred to the base arrangement and floor loading. Any differential movements are usually catered for by the 0.3 µ factor or deflection of structures in the lemniscate guide arrangement and consolidation of the floor. The floor loading, due to differential movement, is in addition to the support convergence load and requires additional bearing area to avoid possible floor penetration. Some seven years ago, Fletcher Sutcliffe Wild Ltd. (FSW) introduced a lemniscate-guided shield support where the lemniscate linkage is connected to the roof bar through two horizontally converging rams to allow differential movement to take place above a given rated figure. This is a known force and can be guarded against, whereas with rigid connections the forces, as yet, are unconfirmed. By careful design, a horizontal force in excess of 6 MN (60 tons) opposes differential movements for a total ram loading of only 2.5 MN (25 tons), or 1.25 MN (12% tons) each. This principle can considerably reduce the length and weight of the support in comparison with a rigid pin-type structure ; also, the yield load rating can be increased without affecting the lemniscate forces. The graph shows the tensile and compressive forces in a lemniscate linkage of a support with and without hydrostore. These forces react into both the roof beam and base members and, as can be seen from the support height to linkage load graph, a considerable reduction in these reactions is gained by the use of the FSW patented hydrostore system. Floor loading is considerably reduced under maximum µ conditions, and by allowing the roof bar to move with the strata, some degree of improvement to strata control is achieved in line with the assumptions in the paper. In practice, these movements have only been in the region of a few millimeters, which, in turn, reflects on the improvements to strata control by the addition of positive set valves. Supports to this design of both 450- and 280-t (496-and 309-st) rating have been successfully used in the United Kingdom for several years, negotiating many faulted areas without one single reported need for repair or maintenance. This includes supports left unattended during the year-long strike, proving the reliability of the system.

Jan 8, 1986

By J. W. Paul

"The economic features of coal mining must take into account the drain on the man power. Study over a recent 5-year period reveals an average yearly loss of 2,125 underground men, of whom 1,182 are killed by falls of roof and coal, and according to recent data compiled by the Bureau of Mines it is estimated that 54,000 men sustain lost—time disabling injuries from the same cause.Under normal activity of the mines approximately 50 lives are taken by falls of roof during every 10 days the mines are operated, or 5 persons are killed per day, which, at a compensation charge of $5,000 each, amounts to $25,000 per day. Add to this the similar number killed by causes other than by falls of roof and we have $50,000 as an approximate daily fatality charge for each day the mines operate. On the basis of 200 working days per year, this amounts to the alarming figure of $10,000,000 annually. An investment at 5 per cent to yield this amount would require $200,000,000, which is equivalent to a capital investment of $0.40 per ton of coal, produced annually, on the basis of 500 million tons. These figures apply only to fatalities for which a fixed or stated amount is paid for compensation and do not include the compensation and hospitalization paid for the approximately 103,000 upon whom idleness is enforced by a lost-time disability injury. In one State having an annual production equal to approximately 30 per cent of the total bituminous production of the United States, the most recent data shows that for each fatality there are eight serious injuries causing 60 days or more lost time. The frequency rate of accidents for that State is less than the average for the United States, and so a conservative comparison may be made by using the figures of that State in estimating the total serious injuries, which gives 16,000 as losing 60 days or more. The average number of underground employees in the coal mines of the United States for the past 10 years has been approximately 570,000; the annual underground fatalities amount to approximately 2,000 and non-fatalities to 108,000, or a total of 110,000, which means that one out of every 5.17 employees ,or 19.3 per cent, receives an injury which results in either a fatality or a lost-time disability; this figure in a little over five years will reach a number equivalent to 100 per cent of all underground workmen. Against this is the record of many miners who have worked 25 years or more without a lost—time disability injury, indicating that coal mining is not necessarily productive of injury or death to workers.In the matter of falls of roof, it is found that 85 to 87 per cent of all fatalities occur at the working face, face of a room or entry, or in pillar work. It is at the working face that the greatest roof hazards are encountered, and when about 75 per cent of the underground employees spend approximately 90 per cent of their working hours at the face, it is logical that there is where injury is most likely to occur.Although the roof hazards may vary in different beds of coal, experience has proved that roof hazards can be successfully controlled in all coal mines, essentially regardless of the character of the roof if constant care and attention are given by the management and employees in applying the principle of safety. In almost every mining district some companies maintain an extremely low frequency rate of injury, whereas in the same district with essentially the same roof conditions the opposite is true.A study has recently been made of a number of reports upon fatalities in one district of one of the principal coal—producing States and it showed that 50 lives had been lost at 23 mines as the result of falls of roof or sides. These reports were made by the mine officials, safety engineers, and safety committees and an attempt was made to give both the cause and the person or factor responsible for the fatality. A summary of the items of responsibility is as follows:"

Feb 1, 1932

it may be clearly seen that one of the most rapidly increasing items in mining operations is the cost of the timber alone, to say nothing of the cost of installation. Consequently, any practical means that may be used to lengthen the life of mine timber will greatly tend to decrease mining costs and result in important economies in operation. The four principal agents by which mine timbers are destroyed are, decay, insect attack, fire and mechanical abrasion. Decay and insect attack are credited with more than 50 per cent of the total amount of timber destroyed in the mines. Numerous methods may be used to conserve mine timbers, such as better selection, preparation, storage and segregation. It frequently happens that good timber goes into places where poor timber would do as well, and timber of inferior quality is sent into places where only the best grade should be used. However, the most effective method of conservation is by treatment with some standard preservative to prevent decay. Some of. the benefits to be noted from the use of preserved timbers are; the reduction in operating costs by decrease in timber purchases; cuts down interference with mining operations due to timber failures on main haulageways; prevents excessive falling of roof in entries by maintaining timber in sound condition; conserves timber supplies and makes possible the utilization of inferior woods; reduces the danger of mine accidents; improves mine ventilation; lessens fire hazard. Our experience thus far with preservatives, while not of a sufficient period of time to establish just what length of life we may obtain from timber so treated, results obtained during the past four years indicate that the intelligent use of preservatives will effect sufficient economies in mine timber costs to justify the expenditures made for this purpose. MR. BAKER (Concluding): Now, if there are any questions you gentlemen would like to ask about our particular operations, I will attempt to answer them. J. H. EMRICK (Sullivan Machinery Company, Denver, Colo.) ; I was wondering how much penetration you get. MR. BAKER: We get between one-sixteenth and one-eighth of an inch; it is a dipping process. With pressure treatment you get-a greater absorption; that is, better than one-sixteenth of an inch. As long as there is no mechanical abrasion, it seems to serve the purpose. MR. EMRICK: Does that apply to the condition of the timber before it is treated? If it is perfectly dry, will it absorb more treatment than if it is partly green? MR. BAKER: Certainly; one of the things we do is to have it thoroughly seasoned before it is put into the preservative. We put some green timber into the mine once, and the fungus went after it right away. MR. EMRICK: What was the difference in the depth reached by the preservative? MR. BAKER: It hardly penetrated at all when it was green. It has to be sound and well seasoned. MR. EMRICK: How long was the timber dipped or treated? MR. BAKER: According to the seasoning. If it was well seasoned, it was left in the hot bath for an hour; if not so well seasoned, it was left for about a couple of hours. C. M. BILLINGTON (General Superintendent, Rocky Mountain Fuel Company, Lafayette, Colo.): Have you found it necessary to treat timber that has been charred? MR. BAKER: No. However, I suppose it has the sane effect; in lots of places they char timber for the purpose of treatment. MR. BILLINGTON: Have you ever tried lime and salt? MR. BAKER: No, this is the only thing we have tried, the creosote and the Aczol; the Aczol is a foreign product. WM. LITTLEJOHN: Which I is preferable, the Aczol or the creosote? MR. BAKER: I couldn't say as to that. MR. LITTLEJOHN: Have you had any tests as to the value of either? MR. BAKER: We have had some of the Aczol timbers in service for a little over four years; we have had some creosote timbers in service

Jan 1, 1926

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By A. E. Back, S. F. Ravitz

When manganese ores are leached with sulphur dioxide, a large part of any zinc in the ore usually is extracted with the manganese.1 In the dithionate process,2,3 in which the manganese ore is leached with dilute sulphur dioxide gas and the manganese is subsequently precipitated by adding lime to the pregnant solution, the zinc is precipitated with the manganese. These facts suggested the possibility of applying the dithionate process to the recovery of zinc from oxidized ores or calcined sulphide concentrates. Accordingly, an investigation was begun, and preliminary tests were made on several ores and concentrates. The results were encouraging, but the need to devote available funds and personnel to other projects made it necessary to drop the work before the various factors involved in the process could be studied in detail. A brief mention of the process,4 however, elicited a number of inquiries, so that it appeared desirable to report the results of the preliminary work. The dithionate process as applied to zinc may be summarized briefly as follows: The ore or calcined concentrate is leached with dilute SO2 gas to dissolve the zinc, largely as zinc sulphate, in accordance with the following equation in which [ZnO] represents the "oxide zinc" in the ore or calcine: [ZnO] + SO2(g) + 1/2 O2 = Zn++SO4— [1] If, in the leaching step, the ore or calcine is suspended in calcium dithionate solution, the sulphate ion, as it is formed, is precipitated immediately as calcium sulphate, which is subsequently filtered off with the insoluble ore residue: Zn++SO4— + Ca++S2O6— = CaSO4(s) + Zn++S2O6- [2] An alternative procedure is to suspend the ore in water, filter off the insoluble ore residue after leaching, add calcium dithionate to the resulting zinc sulphate solution, and then filter off the calcium sulphate precipitate. In either event the zinc is obtained in the form of a pregnant solution of zinc dithionate, from which it can be precipitated as relatively pure zinc hydroxide by adding milk of lime: Zn++S2O6— + Ca(OH), = Zn(OH)2(s) + Ca++S2O6- [3] The zinc hydroxide precipitate is calcined to form the final zinc oxide product: Zn(OH)2 = ZnO(s) + H2O(g) [4] Theoretically the process is completely cyclic with respect to dithionate ion, the calcium dithionate required for reaction 2 being replaced by that formed in reaction 3. In practice, of course, small amounts of dithionate would be lost in the various filter cakes, depending on the economic washing limits. In the leaching step, however, some of the SO2 is oxidized to dithionale instead of sulphate, accord- ing to the following overall reaction: ZnO + 2SO2(g) + 1/2 O2(g) = Zn++S2O6-, [5] so that the dithionate losses are made up, at least in part. Ores and Concentrates Tested The analyses of the ores and concentrates tested are summarized in Table 1, which also includes the analyses of the calcines produced from the concentrates. The concentrates were roasted in a laboratory muffle furnace at the temperatures indicated until evolution of SO2 could no longer be detected; shallow clay dishes ordinarily were used; but calcines 2a and 2c were prepared in iron dishes, with the result that these two calcines were badly contaminated with iron scale. The "complex" concentrate, sample 1, consisted essentially of sphalerite grains containing inclusions of pyrite and other sulphide minerals too minute to be liberated by grinding within economic limits. In the " marmatitic" concentrate, sample 2, the iron was present largely as marmatite (that is, as iron sulphide in solid solution in zinc sulphide) rather than as pyrite inclusions. The zinc was present largely as the carbonate in the two "oxidized" ores, samples 3 and 4, and as the silicate in the "willemite" ore, sample 5. Leaching Tests The leaching cell was a 3-liter glass beaker placed in an electrically heated water bath manually controlled to maintain a temperature of 35°C in the leach slurry. The slurry was agitated by means of a flat paddle-type stirrer

Jan 1, 1950

By Harold M. Mooney

WHEN apparent resistivity data are taken with the symmetrical Wenner 4-electrode spread, a fixed center position is used and readings are taken for values of electrode separation. Basic data consist of apparent resistivity plotted against separation of adjacent electrodes . The interpreter attempts to infer geologic structure, such as the depth to discontinuities and the nature of subsurface earth materials. An earlier paper&apos; described methods for interpreting resistivity data. All of these involve a severe assumption, namely that the earth in the region of interest consists of horizontal layers, electrically homogeneous and isotropic. The actual earth never satisfies this assumption exactly and may deviate from it so much that none of the above methods can be applied. Attempts in three directions have been made to modify the assumption so that it approaches known geologic complexity more closely. First, curves have been calculated for dipping discontinuities. Stern&apos; and Aldredge hose a few widely separated dip angles. Trudu confined his attention to small dips. Berel&apos;kovskiy and Zubanov computed gradient curves for widely separated dip angles. Unz as given the most complete solution, with a brief attempt to treat the three-layer case. Second, anisotropy can be taken into account. It seems geologically probable that layered materials have different vertical and horizontal conductivities. Cagniard, Maillet, and Pirson et up methods for finding an equivalent hypothetical isotropic medium. Standard interpretation methods can be applied to this, and the actual medium can then be deduced. Belluigi&apos;" discounts the practical importance of anisotropy; Geneslay and Rouget do not agree with his conclusion. Third, the effect of variable resistivity in a layer can be considered. Keck and Colby" examine the mathematics of an exponential increase in a surface layer. Several authors, for example, Stevenson,&apos;&apos; consider a continuous variation of resistivity with depth. The present paper deals with a linear variation of resistivity in a surface layer. Geologically, surface variations should be expected. Unconsolidated materials such as glacial drift show marked irregularities over short distances. The effects of weathering change with depth. The moisture content of material above the water table may vary from a dry sand to a saturated clay, and both of these will be changed by rainfall. Figs. 1 to 6 present apparent resistivity curves to show the effect of a variable surface layer. In all cases resistivity varies linearly with depth down to a depth of one unit. Material beneath this depth has constant resistivity. Electrode separation is plotted in depth units. Insets on each figure show the corresponding cross-sections, plotting true resistivity against depth. To illustrate, consider curve A of Fig. 1. The true resistivity of material at the surface of the earth is taken as 0.4 units. Resistivity increases with depth, reaching a value of 1.0 at 0.5 depth units and 1.6 at 1.0 depth units. Below a depth of 1.0, all the material has very low resistivity (zero, for purposes of calculation). Curve A in the main part of Fig. 1 shows how apparent resistivity varies for this case as the electrode spacing is increased. To illustrate further, curve E of Fig. 4 corresponds to true resistivity of 1.2 units at the surface, 1.0 at a depth of 0.5 units, 0.8 at a depth of 1.0, and 1.5 for all depths greater than 1.0. Apparent resistivity curves have been plotted logarithmically so that the shape of the curves becomes independent of the units, giving the curves wide validity. A certain drift-covered area, for example, shows a gradual decrease of resistivity from 230 ohm-meters at the surface to 150 ohm-meters at the bedrock surface, 275 ft down; bedrock resistivity is 800 ohm-meters. Curve E of Fig. 5 indicates that true resistivity decreases from 1.2 units at the surface to 0.8 at a depth of 1.0, then increases abruptly to a constant value of 4.0 units. Since resistivity and depth ratios are the same, this can be used to predict the field curve. For Fig. 5, multiply true resistivity and apparent resistivity by

Jan 1, 1955

By Robert D. Pehlke, Robert G. Blossey

The solubility of nitrogen in liquid iron alloys containing chromium and nickel has been measured in the temperature range 1550° to 1700°C at nitrogen pressures to 1 ah. The solubility surface has been determined for the iron corner of the liquid metallic ternary to 21 pct Cr and 11 pct Ni. The nitrogen solubility increases markedly with increasing chromium concentration. The effect of nickel and the bilinear effect of chromium and nickel are less pronounced. The solubility data are presented, and interaction coefficients are determined from them. THE solubility of nitrogen has been determined in liquid Fe-Cr-Ni binary and ternary alloys. The work in this laboratory has been directed toward a relatively limited composition range, that is to 20 pct Cr and 10 pct Ni. Humbert and Elliott1 studied the entire ternary; but their investigation was, understandably, limited in this region. The region considered here is of the greatest commercial interest. Knowledge of the solubility in these alloys is important for accurate control of the nitrogen levels in various stainless alloys. Also, the solution behavior is of theoretical interest because of its deviations from ideal dilute solution rules at moderate chromium levels. The nitrogen solubility in the iron binaries has been reviewed extensively by Pehlke and Elliott,2 particularly with respect to the dilute solution interaction parameters. More recently, there has been some interest in accurate descriptions of solute interactions in non-dilute solutions. Most of the investigators have adopted a power series fit to accommodate any non-linearity of the data. The Taylor series expansion is adopted here, using Scimar&apos;s notation3 for the interaction coefficients. An alternate method, instead of requiring higher-order expansions, is to restrict the range of the composition variables. A planar solubility surface may be fitted to the data and its range of validity determined. If the axes of this region are displaced from the usual origin—the solvent pure iron—a change in standard state is required for the solution reaction. The standard state for nitrogen in iron is commonly taken as the hypothetical 1 wt pct solution of nitrogen in pure iron. However, for an alloy of appreciable solute concentration, e.g., 13 pct Cr or 18 pct Cr-8 pct Ni, it would be convenient to use that base composition as the solvent and redefine the solution reaction in terms of that particular solvent. A brief derivation follows, defining the free energy of solution in an alloy solvent. Following the treatment by Darken and Gurry,4 for a nitrogen pressure of 1 atm: N (pure component) = N (1 wt pct in solvent) [l] AG=RT ln100/ wt pct N in solvent Taking this reaction for an alloy solvent less the same reaction for a pure iron solvent the relation between nitrogen in pure iron and an alloy is: N (1 wt pct in Fe) = N (1 wt pct in alloy) [2] AG = RT[ln(wt pct N in Fe) - ln(wt pct N in alloy)] Adding ½ N2(g) to each side and subtracting N (1 wt pct in Fe) = ½N2(g), the total free energy for solution of nitrogen in an alloy, referred to nitrogen at infinite dilution, is given by: ½N2 (g) = N (wt pct in alloy) L3] AG°3 = -RT ln(wt pct N in alloy )PN =1 atm Interaction parameters have their usual meaning when ?G°/RT is differentiated with respect to the proper composition coordinate. If desired, the dilute alloy treatment may be utilized with the new reference composition as the solvent. This has. indeed, been done by Small and pehlke5 in their analysis of nitrogen solution in liquid 18-8 alloys. The Sieverts&apos; technique was used for this investigation on an apparatus previously described.6 The materials used in this program were: Ferrovac-E iron, 99.95 pct, Crucible Steel Co.: chromium, 99.95 pct, Union Carbide Metals Co.; nickel, 99.9 pct, International Nickel Co. Recrystallized alumina crucibles were used with no evidence of crucible-melt reaction. RESULTS The locations of the ternary compositions investigated are shown in Fig. 1. The data of Turnock7 and small8 have been alluded to in other papers.5&apos;6 There were no departures from Sieverts&apos; law observed for

Jan 1, 1969

By Howard Martens, Pol Duwez

XPERIMENTS were performed on a Cr-Fc alloy Econtaining 44.7 pet Cr in order to determine the heat evolved during the transformation of the a solid solution into the s phase, and the change in volume accompanying the transformation. Since previous measurements on the rate of formation of a from s indicated that the reaction was quite fast as soon as the equilibrium temperature of 820°C was exceeded by some 50°, standard thermal analysis experiments were performed on heating specimens of s at the rate of approximately 40°C per sec. A definite thermal arrest was observed at 870"C, Fig. 1. This result indicates that the reverse seaction of into a is exothermic. From the heating curve of Fig. 1, taking 15°C per sec as the heating rate in the neighborhood of the transformation, 2.4 sec as the time for transformation, and assuming that the specific heat of the alloy at 850°C is an average between iron and chromium, namely 9.5 cal per mol per "C, the latent heat of transformation is approximately 342 cal per mol. The order of magnitude of this latent heat was also obtained by comparing the heating curve of Fig. 1 with a similar curve obtained with pure iron under identical experimental conditions. It was found that the length of the thermal arrest for s was about 1.8 times as long as that for iron. Since the latent heat of the a to 7 iron transformation is 203 cal per mol1, 2 the latent heat of it to a would be 365 cal per mol, which is in relatively good agreement with the value determined from the heating curve. For the determination of volume change, thermal expansion curves were recorded using a specimen containing 44.7 pet Cr and completely transformed to cr by previous treatment. The curves were recorded at a rate of heating of about 4°C per min and at approximately 840°C a sharr, increase in length of about 0.08 pet took place. Fig. 2. It is therefore established that the specific volume of a near the transformation temperature is about 0.24 pet smaller than that of a, and consequently, when the s phase forms in an a matrix, it would tend to shrink away from the matrix. Since the s phase is known to be extremely brittle, these results offer an explanation for the microscopic cracks often observed in the a phase under the microscope. The results of this study are in qualitative agreement with previously published data on stainless steel 19-9DLa and on a Cr-Fe alloy containing 45 pet Cr.&apos; The increase in density due to the transformation from n to s given in ref. 4 is 0.90 pet. These measurements, however, were made at room temperature. whereas the presently reported 0.24 pet is the change at the temperature at which the transformation takes place during heating. In the graph of Fig. 2, the percentage change in length that would be observed at room temperature is given by the length X, which is about 0.27 pet. This would correspond to 0.81 pet in volume change. Acknowledgment This work was done at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. DA-04-495-ORD-18 with the Army Ordnance Corps, Washington, D. C. The authors wish to thank this agency for permission to publish the results of this investigation. References I H. Klinkhardt: Measurements of True Specific Heats at High Temperatures. Annalen der Physik (1927) 84, pp. 167-200. - H. Esser and W. Runghardt: Influence of the Method, of Dctcrmination on the Measured Heat Content of Iron. Archtvo ffur Dct Eisenhiittenwesen 11934) 8, pp. 37-38. J. J. Gilman, P. K. Koh, and 0. Zmeskal. Delta Ferrite Formation and its influence on the Formation of Sigma in a Wrought Heat Resisting Steel. Trans. ASM 1 1949) 11, pp. 1371-1388. 1 J. M. Thomas: Discussion of ref. 3. Trans. ASM (1949) 41, pp. 3 390-1392.

Jan 1, 1957

By A. T. Corey, C. H. Rathjens

INTRODUCTION Although the oil industry has been aware of the directional variability of permeability in porous rock, the directional variability of relative permeability has been largely ignored. Yet it is apparent that such an effect must be present in a system in which the distribution of oil and gas within the porous matrix is controlled by capillary forces. It is easy to visualize a rock composed of layers of fine and coarse material such that gas flow across the bedding planes would take place only after the average oil saturation had been reduced to a very low value. The fine layers, because of their greater capillarity, would remain saturated and act as barriers to the flow of gas after the coarse layers had been desaturated. Flow of gas parallel to the bedding planes would obviously take place at a much greater liquid saturation. Without more complete information concerning the geology of a reservoir than is generally available, it is not possible to predict exactly how such phenomena would affect the over-all performance of an oil field. It is possible, however, to predict qualitatively the effect of stratification on relative permeability measurements made on laboratory cores. In this investigation the effect of stratification was studied analytically by assuming that two porous materials with different capillary pressure-desaturation curves (but identical relative permeability curves) were in contact and in capillary equilibrium. As a qualitative check on the analytical results, cores having various degrees of visible stratification were used for relative permeability measurements made with fluids flowing both parallel and perpendicular to the bedding planes. A quantitative check was considered impractical because of the difficulty of devising models in which two materials of predetermined properties could be joined without the plane of contact becoming a discontinuity. THEORETICAL CONSIDERATIONS AND ASSUMPTIONS The assumption of capillary equilibrium in an oil-gas system implies that the difference in pressure between oil and gas is everywhere the same. This means that the curvature of the interfaces must be everywhere the same in order to satisfy the equation where PC is the pressure difference between phases, y the interfacial tension and r, and r2 are the major and minor radii of curvature. Depending on the pore size distribution of coarse and fine layers, the volumetric percentages of oil and gas in these layers will differ when equilibrium exists. The exact relationship can only be determined by obtaining the complete capillary pressure-desaturation curves for each of the porous materials in contact. It has been pointed out elsewhere&apos; that the capillary pressure-desaturation curves of sedimentary porous materials can often be approximated by the relation where C is a constant and Soe is the effective saturation to oil based on a percentage of the pore volume effective to flow. In the same paper it was indicated that, as a first approximation, the values of oil relative permeability are given by and the values of gas relative permeability by For this analysis Eqs. 2, 3, and 4 were assumed to apply to each of two components of a hypothetical porous rock in capillary equilibrium. It was also assumed that each of the components had a residual wetting phase saturation of 20 per cent so that 80 per cent of the total pore volume was effective to flow. The permeability of the coarse stratum was taken as 100, and its displacement pressure was such that C in Eq. 2 had the numerical value of 1. The corresponding values for the fine stratum were 10 for the permeability and 10 for C. Units are not specified because they do not enter into the final results. The choice of the permeabilities and displacement pressure ratios was made to expedite the calculations. Any reasonable rock properties could have been chosen without changing the results qualitatively. Several arrangements of the two components were studied. Table 1 summarizes the resultant permeabilities obtained for four types of arrangement. RELATIVE PERMEABILITY CALCULATIONS The first step in the computation of relative permeability for the composite cores was the plotting of the capillary pressure-desaturation curves and the relative permeability curves for the individual components according to Eqs. 2, 3, and 4. At arbitrary

Jan 1, 1957

By G. B. Thomas

Several methods of analyzing pressure build-up data in wells have been presented by various authors. This paper reviews the theory and method of D. R. Horner and presents example calculations performed on data obtained by testing several different types of wells. These calculations include, (1) graphical estimation of final static pressure, (2) determination of the productive capacity of the pay away from the well bore and. (3) the degree to which the formation adjacent to the well bore has been damaged by completion or other causes. The methods of testing and precautions which should be taken to assure the best data possible are discussed. Limitations and reliability of calculated results are also treated. INTRODUCTION Pressure testing of wells is generally limited to the determination of producing and static mean formation pressures. The so-called "static" pressure determination.. along with PVT, electric log and production data, enable the reservoir engineer to determine, within reasonable limits, the drive mechanism of the reservoir and in some cases. the amount of edge water encroachment. Producing pressure tests enable calculation of productivity indices and allow the engineer to plan the systematic production of a pool for optimum conservation of suhsurface energy. The radial flow formula advanced by Muskat&apos; has been based on the assumption of incompressible radial fluid flow. It has been known that reservoir fluids do not behave in an ideally incompressible manner. For example, incompressible flow theory indicates a simple logarithmic relationship between the difference of the instantaneous and static well pressures when plotted against time. &apos;The latter stages of this type of plot of pressure build-up data generally show a marked devia-, tion from the earlier straight line trend. which deviation may be shown to be due to the compressible flow of fluids toward the well bore. Shut-in times of 24, 48. 72. or at most 96 hours are currently in wide use for determining so-called "static" reservoir pressure. Due to the continuation of compressible flow of fluids into the well bore long after this arbitrarily taken shut-in time, the determination of static pressures has almost invariably resulted in lower than equilibrium values. Materials balance calculations made early in the life of a reservoir often result in a calculated reserve which later observations prove to be too low. Failure to obtain reliable "static" reservoir pressures within the prescribed 24 or 48-hour build-up period has undoubtedly been a major factor in obtaining these low estimates. Comparison of theoretical and actual productivity performance has indicated that formation damage and not being able to attain true static pressures have been partially responsible for the observed discrepancies. Research into the theory of compressible flow behavior has resulted in methods of applying these theories to the testing of wells. Application of the developed theories to pressure build-up performance indicates that in many cases the following can be estimated. 1. The static reservoir pressure. 2. The in-place effective formation permeability away from the well bore. 3. The degree or extent by which the formation has been damaged adjacent to the well bore, either through completion methods or subsequent damage due to fluid entry. REVIEW OF THEORY Horner2 has shown that the pressure build-up within a "point source" well is approximated by the following formula: Equation (1) is the approximate "point source" solution to the radial compressible flow equation advanced by Muskat. The solution assumes the following: 1. A point source well is producing at constant rate from the center of an infinite reservoir with a constant pressure at its external boundary. 2. The fluid flowing is present in one phase only. 3. The compressibility and absolute viscosity of the fluid remain essentially constant over the range of temperature and pressure variation encountered. 4. The well i.; shut-in at the sand face arid there is 110 after production into the well bore. 5. The formation permeability is homogeneous in the direction of flow. From Equation (1) it can be seen that if an ideal well were shut-in while producing from a reservoir under the conditions assumed, the pressure build-up would be a logarithmic func-

Jan 1, 1953

By Basil S. Fee

INTRODUCTION Probably the most important family of chemicals used in mineral processing today is a category of basic commodity chemicals loosely denoted as pH regulators. Typical chemicals which are referred to as pH regulators include lime, magnesium hydroxide, soda ash, caustic soda, ammonia, sulfuric acid, and hydrochloric acid. These chemicals are often used in very significant amounts in almost all of the major mineral processing operations such as flotation, hydrometallurgy, etc. (in dosages up to ten pounds per ton of feed ore treated). While cheaper in cost per unit weight of chemical than more specific chemicals such as collectors, frothers, extractents, etc., the overall cost to the mill operator is generally higher with pH regulators per ton of ore processed than with any other given processing chemical. For example, a rough rule of thumb in sulfide mineral flotation is that the cost of lime is double that of the collector(s) used. The symbol pH is used to designate hydrogen ion concentration. When acids, salts, and bases are dissolved in water, individual molecules are dissociated into their constituent radicals or ions. The strength of an acid or a base increases with the extent of such dissociation or ionization. An alkaline solution is one in which the number of Qydroxyl ions (OH ) exceeds the hydrogen ions (H ). In an acid solution, the hydrogen ions predominate. In either case, both ions are always present as water itself ionizes to a limited extent, that is: [ ] The pH scale is logarithmic and the pH value is the negative of the logarithm (base 10) of the molar concentration of hydrogen ions per liter of solution. For example, a pH of 5 means that the molar concentration of hydrogen ions per liter is 0.00001 (1 x 10-5). Likewise, a pH of 9 means that the molar concentration of hydrogen ions per liter is 1 x 10-9. Normally, the relationship between hydrogen ion and hydroxyl ion concentration is based on the relationship: Concentration of H ion x concentration of OH- ion = constant. Eq. (1) In dilute and/or moderately concentrated solutions that are normally used in mineral procygsing processes, the constant at 25°C is 10-14. On the pH scale, the value of pH equal to 7 represents the hydrogen ion concentration of a neutral solution. pH values lower than pH 7 indicate increasing acidity and higher values than 7 indicate alkalinity. Table 1 shows the nature of the pH scale at 25°C. Temperature affects the extent of ionization of dissolved acids, salts, bases, and water so that the hydrogen ion concentration (hence pH) of a solution is also affected by temperature. As a means of demonstrating this dependency, Table 2 shows the change of the exponent of the constant (base 10) in Eq. 1 and the pH value corresponding to neutrality as a function of temperature. It is also important, for example, that alkalinity or acidity expressed by pH not be confused with total alkalinity or total acidity. For example, total alkalinity is commonly determined by titration with a standard acid solution (usually HC1). pH is a measure of the hydroxyl ion concentration of an alkaline solution, whereas titration is a measure of an alkaline solution&apos;s acid neutralizing capacity. Thus, if one takes a series of various alkaline solutions prepared using different chemicals but all of exactly the same pH (and temperature) and then subsequently carries out a titration on each solution with a standard acid, it would be observed that the various alkaline solutions would neutralize entirely different amounts of acid. As an example, 0.08 grams of caustic (NaOH) , 6.32 grams of soda ash (Na2CO3), and 8.17 grams of ammonium hydroxide (NH4OH) all have a pH of 11.3 at 25°C. One liter of each of the above solutions neutralizes 0.073, 4.348 and 8.496 grams of HC1, respectively. Therefore, depending on the specific use of any given pH regulator, special tests need to be run by the mill operator to determine factors such as: the specific technical goals to be accomplished by

Jan 1, 1986

By Strathmore R. B. Cooke

On the basis of experiments conducted on quartz using a bubble pick-up method, it was shown in an earlier paper1 that this mineral will preferentially adsorb hydrogen, calcium, or sodium ions, depending on the relative concentrations of those ions in the solution in which the quartz is immersed. For quartz particles ranging in size from 0.2 to 1 mm, it was demonstrated that the concentration of calcium in solution (assumed present as ions) necessary to completely activate quartz for flotation is given by the expression: Ca++ = [H+] X 106 + [Na+] X 10-3 In this expression, ionic concentrations are in mols per liter. It was further shown that the pick-up method is apparently more sensitive to changes in reagent concentration than the standard captive-bubble method, and that induction times are apparently much reduced. Since completing these earlier tests, a new type of cell has been constructed; this is shown in Fig 1 and 2. In Fig 1, A is a ground joint, B is a central tube reaching to within a few millimeters of the bottom of the cell, and C is a stopper which may be removed for reagent addition, and serves the further purpose of excluding carbon dioxide from the air during the test. The entire cell is constructed of Pyrex glass, and does not give the trouble experienced with the earlier cell, in which activating ions were released from the glass at high pH values. The only critical factor in the construction of the cell is the clearance between the central tube and the bottom of the cell. This clearance should be sufficiently small that the bubble can be pressed directly on the mineral grains lying on the bottom of the cell. In the pick-up tests to be described in this paper, the reagents used were all of C. P. grade, except the sodium oleate, which was Merck&apos;s "neutral powder." The quartz employed was water-clear vein quartz, sized on screens, cleaned with both hydrochloric acid and sodium hydroxide, and given a thorough final washing with distilled water. Experimental procedures were the same as described in the earlier paper. EFFECT OF SIZE OF QUARTZ ON PICK-UP To ascertain the effect of particle size on the adsorption of calcium ions, the quartz was sized from minus 14 plus 20 mesh through the intervening screen sizes to minus 270 mesh plus 400 mesh. Each size was thoroughly cleaned, and then tested in the cell at different calcium chloride and sodium hydroxide concentrations, and at a constant sodium oleate concentration of 20 mg per liter. All particles, within the size range given, exhibited complete pick-up within the curve expressed by the equation above. This presumably means, when the conditions imposed by the equation are satisfied, that this maximum is independent of particle size. However, it was found that the range through which partial particle pick-up occurred progressively broadened as particle size decreased. This is shown in Fig 3, in which curves B, C, and D show the limits at which pick-up just commences (as the pH is increased) for particles of minus 14 plus 28 mesh, minus 65 plus 100 mesh, and minus 270 plus 400 mesh size, respectively. These results indicate that for satisfactory activation, at any given pH, a lower calcium ion concentration is required for fine particles than for coarse particles. EFFECT OF HIGH ALKALINITY ON PICK-UP At calcium concentrations of between 1 and 10 mg per liter, and at high alka-linities, it was noticed that pick-up ceased as soon as calcium hydroxide commenced to precipitate. This effect was investigated at other calcium concentrations, with the same results. Solutions of calcium chloride, containing 105, 104, l03, and l02 mg of calcium per liter were made alkaline with sodium hydroxide until calcium hydroxide just started to precipitate, according to the following equation: CaCl² + NaOH -+ Ca(OH)2 + 2NaCl The beginning of precipitation was taken as that point at which either a faint opalescence appeared in the solution, or a Tyndall cone became ap-

Jan 1, 1950

By J. T. Norton, J. G. McMullin

The ternary system of gold-silver-copper is characterized by a solid solubility gap and a two phase region in which copper-poor and silver-poor phases coexist. At about 30 pct gold, the two phases become mutually soluble at temperatures below the melting temperature. As the gold content is increased, the solubility temperature of the alloys decreases until at about 80 pct gold, the two phases are soluble down to the lowest temperature at which the alloys will recrystallize. Although the general form of the two phase region is known, its boundaries do not seem to have been investigated extensively. In an X ray diffraction study, Masing and Kloiberl have outlined the boundaries of this two phase field at 400 and 750°C. Using only microscopic techniques, Pickus and Pickus2 determined a vertical section of the ternary diagram showing the 14 kt alloys (58.3 pct gold). These two reports are riot in complete agreement. It has been shown3 that some of the ternary alloys are susceptible to age hardening and that the hardening is caused by the separation of a homogeneous alloy into two phases at the aging temperature. While the gold-copper binary system is an outstanding example of super lattice formation, Hultgren4 has shown that a few per cent of silver added to gold-copper destroys the tendency for ordering. Because of the age hardening possibilities of these alloys, it seemed advisable to investigate the boundaries of the two phase field more in detail using an X ray diffraction method, so as to permit a better understanding of the aging phenomena and enable predictions as to the behavior of other alloys to be made. This is especially true for the 18 kt alloys (75.0 pct Au) at the lower temperatures since they are known to exhibit age hardening. Twelve ternary alloys were prepared having the compositions shown in Table 1 and graphically in Fig 1. The gold used was fine gold bars supplied by Handy and Harmon. The silver was a bar of high purity silver from the U. S. Bureau of Standards. The copper was a bar of vacuum-treated, high conductivity copper from the National Research Corporation. The pure metals in the form of powder were weighed out in proper proportions and melted in graphite in a high frequency induction vacuum furnace. They were heated to 1100°C and slowly cooled. The ingots were then removed from the crucible, inverted, returned to the crucible and remelted. This remelting procedure was intended to reduce segregation in the ingots. After remelting, the ingots were checked for weight loss. The weight loss in each ten gram ingot was held to less than 25 mg. The remelted ingots were cold rolled and then given a homogenizing heat treatment of 16 hr at 760°C to remove any remaining segregation. Powder specimens were prepared by cutting the ingots with a fine file, one half the required amount of powder being taken from each end of the ingots. When the X ray diffraction pattern showed any difference in lattice constant between the ends of the ingot, the ingot was remelted and given an additional homogenization treatment. All powder samples were sealed in evacuated pyrex tubes for heat treatment. Ordinary pyrex proved satisfactory for temperatures up to 650°C but above that temperature it was necessary to use a special high temperature pyrex glass. Annealing at temperatures below 500°C was done in a salt bath whereas for temperatures of 500°C and above an electric muffle furnace was used. In both furnaces the temperature control was ± 5°C. In all annealing treatments samples of cold worked powder were placed in a furnace which was already at temperature. In this manner the specimens recrystallized directly to the equilibrium structure for that temperature. Time at temperature was selected so as to allow complete recrystallization, but very little grain growth. Specimens were quenched from the annealing temperatures by breaking the pyrex tubes in cold water. X ray diffraction photograms were made of all the heat treated powders using copper radiation and a Phragmen

Jan 1, 1950

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 L. D. Jaffe

From the limited experimental data in the literature, preliminary values were derived for the thermal diffusivity of titanium alloys and for the quenching severity of various mediums used in heat treating them. The thermal diffusivity, under quenching conditions, was found to be approximately 0.006 sq in. per sec. The quenching severity H for brine is approximately 8, for water 4, for oil 0.9, for air 0.08, and for argon 0.02 in. -&apos; The quenching severity of the Jominy-Boegehold end quench water jet against titanium alloys appeared effectively infinite. Using these results, graphs were prepared showing ideal round sizes and Jominy positions having cooled conditions equivalent to those at the center and surface of titanium alloy rounds, plates, and sheets quenched in various media. THE importance of proper quenching of steel parts has long been recognized, and much quantitative work has been done on the subject. Recently, it has become evident that for titanium alloys, too, the rate of cooling from high temperature is important in obtaining high strength and hardness. Maximum hardness and strength may not be attained in the as-quenched condition but rather after a subsequent tempering or aging treatment. Nevertheless, if cooling from temperatures near the ß transus is too slow, for the hardenability of the alloy used, a soft a-ß structure will be produced which will not harden on subsequent aging.&apos;-" The quenching of parts of practical interest can usually be approximated by simple shapes, such as cylinders (rounds) and plates (or sheets) of various thickness and combinations of these. A standard that has been used extensively for comparison purposes is the center of an ideal round: a cylinder quenched in a medium that instantly cools its surface to room temperature." For steel, considerable practical use has been made of the Jominy-Boegehold end quench hardenability specimen,".&apos; and its value for titanium alloys is becoming evident. It therefore appeared worthwhile to attempt comparison of cooling conditions in titanium alloy rounds and plates of various sizes quenched in various media with cooling conditions in ideal round and Jominy quenches. These comparisons are based upon measurements reported in the literature. Quenching Severity of Jominy Water Jet and of Brine As one starting point, there were available the data of Phillips and Tobin8 for positions on a Jominy specimen having the same hardness as the centers of round bars of various size quenched in 5 pct NaOH brine, shown in Table I. The Jominy speci- men is a round bar, normally 1 in. diam and 4 in. long, quenched by a water jet at one end and air cooled on the other surfaces.&apos; After quenching, hardness is measured vs distance from the quenched end on longitudinal flats ground 0.015 to 0.10 in. deep. The data of Table I were based on a subsized specimen of 3/4 in. diam. Since the positions tested are close to the jet quenched end, cooling there may be taken as due solely to the jet, and air cooling can be neglected. These positions are then equivalent to various locations near one surface of an 8 in. plate jet quenched on both sides. Assuming that the thermal diffusivity is constant and that Newton&apos;s law of cooling holds, temperature vs time curves at corresponding positions in Jominy specimen and round bar then may be calculated for various assumed quenching severities of the water jet and of the brine. Cooling curves are generally taken to be metallurgically equivalent when they show the same time to reach a temperature halfway between the initial (heat treating) temperature and the final (quenching medium) temperature.5 On this basis, using Russell&apos;s tables,9 upplemented by heat flow tables derived in similar fashion by the author for positions near the surface of severely quenched plates, it was found that the experimentally observed equivalence, Table I, was best matched if the quenching severity H of the Jominy water jet was taken as infinite (H = co). This means that the jet quenched surface should be considered as instantly cooled to the temperature of the water

Jan 1, 1956

By L. D. Jaffe, H. C. Mann, E. L. Reed

It has been generally believed that fracture originates at a point and, if the stress is suficient, propagates across the material from this point. Evidence to the contrary is given in Fig 1. This micrograph shows an area close to the fracture of a steel containing The material had been quenched from 1675°F and tempered at 1150°F as a round about 10 in, in diam, and had a static tensile strength of 132,000 psi and a static yield strength of 105,000 psi. The steel was broken in 3000 cycles of reversed bending at a nominal max. fiber stress of 110,000 psi at a speed of 10,000 rpm. It was in the form of a standard R.R. Moore specimen with 45" V-notch, 0.015 in. radius and 0.220 in. diam at base of notch. The fractured edge in Fig 1 is part of the central portion of the specimen which broke during the final sudden fracture. Attention is directed to the short cracks which appear as dark lines within the specimen. Similar cracks were found in another specimen of the material, broken in 1,798,000 cycles at a nominal stress of 40,000 psi. The cracks were found in several areas close to the path of the final sudden fracture. This final fracture appeared microscopically to be wholly brittle and transcrystalline. Closer to the surface of the specimens, near the path of progressive fracture, which presumably advanced gradually during many cycles, there was microscopic evidence of some local deformation, but no microcracks. Neither were microcracks observed in areas distant from the main fracture path. The following explanation is offered: In the sudden fracture of the specimen, a crack propagates along a crystallo-graphic plane, with little or no plastic deformation of the adjacent material, until it reaches a grain boundary or a particle of carbide or inclusion which stops its advance. (The particle or boundary may be outside the plane of polish and not visible in the micrograph.) A stress concentration occurs about the end of the stopped crack. One or more new cracks are likely to start in the zone of this stress concentration. They may lie in the same grain as the first crack or in an adjacent grain. New cracks may occasionally start in a nearby but not adjacent grain whose orientation with respect to the stress leads to more ready fracture than does that of the grain between. Once started, these cracks propagate along crystallographic planes in their grains and the process repeats. This leads to discontinuous, branching chains of microcracks. As the process continues, microcracks probably tend to link up by fracture of intermediate material under the influence of increasing stress concentration. Occasionally, too, there may be a series of nearby grains of similar orientation so that there is a certain continuity of fracture across them. In either case the effective size of a crack is increased, resulting in greater stress concentration at its ends and a greater likelihood of further increase of size of the continuously-fractured region. When one continuous crack crosses the entire specimen, macroscopic fracture has occurred. The fractured edge of the specimen in Fig 1 represents a series of microcracks which became continuous across the entire specimen. The short, dark-appearing cracks in the figure did not become continuous over a large area. The row of microscopic stress concentrations at their ends may link up with those of the "main crack" outside the plane of polish. The above explanation does not imply that microcracks develop at the same rate in all portions of the specimen. They will develop most rapidly where the macroscopic tensile stress and macroscopic stress concentration are greatest. Viewed on a scale large compared to the grains, the fracture would appear to progress continuously across the specimen. Although Fig 1 shows a specimen broken in a fatigue test, it is believed that the microcracks discussed do not depend on the repetitive nature of the stressing used, since they are in the region where "sudden" fracture occurred, presumably in a single stress cycle. The whole process of microcrack propagation outlined above is thought to have occurred during this single cycle. It is believed that discontinuous crack propagation may be universal in brittle transgranular fracture of crystalline solids. Further experiments are under way.

Jan 1, 1950