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Executive SIDNEY J. JENNINGS, Chairman GEORGE D. BARRON J. E. JOHNSON, JR. EDWIN LUDLOW ROBERT-M. RAYMOND Membership LEWIS W. FRANCIS KARL EILERS, Chairman J. E. JOHNSON, JR. LOUIS D. HUNTOON ARTHUR L. WALKER Finance GEORGE D. BARRON, Chairman CHARLES F. RAND BENJAMIN B. THAYER Library E. GYBBON SPILSBURY.1 Chairman. ALEX C. HUMPHREYS3 GEORGE C. STONE2 J. H. JANEWAY4 BRADLEY STOUGHTON Papers and Publications BRADLEY STOUGHTON, Chairman

Jan 2, 1919

By William P. Blake

The literature of the occurrence of quicksilver-ore in the United States does not contain, so far as the writer is aware, any mention of the locality herein described. In the preliminary report * upon the resources of the transPecos region of Texas, von Streerwitz gives a long list of minerals observed as occurring there, but cinnabar is not mentioned. In the second report upon the same region † mention is made of the reported existence of cinnabarite in one of the mountain ranges north of the Sierra Carrizo and the Bofecillos, but the author adds: " In spite of my careful examination of the float, I have not yet found any traces of this metal (quicksilver) up to the present time." Prof. Dumble, also, in * Geol. Surv. of Texas, E. T. Dumble, 1889, p. 225 (first report). † Geol. Surv. of Texas, E. T. Dumble, 1890, p. 713 (second report)

Jan 1, 1896

Executive SIDNEY J. JENNINGS, Chairman GEORGE D.-BARRON J. E. JOHNSON, JR. EDWIN LUDLOW ROBERT M. RAYMOND Membership KARL EILERS, Chairman LEWIS W. FRANCIS J. E. JOHNSON, JR. LOUIS D. HUNTOON ARTHUR L. WALKER Finance GEORGE D. BARRON, Chairman. CHARLES F. RAND BENJAMIN B. THAYER Library E. GYBBON SPILSBURY,1 Chairman ALEX C. HUMPHREYS3 GEORGE C. STONE2 J. H. JANEWAY4 BRADLEY STOUGHTON Papers and Publications BRADLEY STOUGHTON, Chairman

Jan 9, 1918

Executive SIDNEY J. JENNINGS, Chairman GEORGE D. BARRON J. E. JOHNSON, JR. EDWIN LUDLOW ROBERT M. RAYMOND Membership KARL EILERS, Chairman LEWIS W. FRANCIS J. E. JOHNSON, JR. LOUIS D. HUNTOON ARTHUR L. WALKER Finance GEORGE D. BARRON, Chairman CHARLES F. RAND BENJAMIN B. THAYER Library E. GYBBON SPILSBURY,1 Chairman ALEX C. HUMPHREYS3 GEORGE C. STONE2 J. H. JANEWAY4 BRADLEY STOUGHTON Papers and Publications BRADLEY STOUGHTON, Chairman

Jan 11, 1918

By A. M. Gaudin

IT is only in recent years that substantial progress has been made in developing a physico-chemical picture of the solid state. The molecular concept, so useful in dealing with gases, was naturally carried over to the field of crystalline solids; it has resulted in the firm implanting of erroneous concepts that only now are being eradicated successfully. Two simply written and effective books on the subject are Crystal Chemistry by Stillwell1 and An Introduction to Crystal Chemistry by Evans.' A more complete treatment of the subject is available in a book by Wells.' The monograph by Hückel4 also touches on a subject most easily perceived by reference to the brief introduction by Bragg,5 that master of the field. These texts make it clear that while some solids are built of molecules, many are built of ions, others of atoms connected in the form of giant molecules, and still others of cations and electrons. The various lattices in which these entities are systematically arranged, the joint use of several of these entities, and the transitional character of some of the bonds make for the great variety of crystalline solids. The purpose of this paper is to point out a most important corollary of present views on the structure of solids. In this connection the classification of solids in Table I is helpful. Atomic crystals are those formed by the noble gases, e.g., helium and argon. They are soft, sublime at very low temperature, of very low specific gravities, and not encountered in ores. Molecular crystals are uncommon among inorganic materials, common among organic materials. Typical examples from both inorganic and organic fields are sulphur, iodine, naphthalene, benzene, and carbon tetrachloride. These crystals are soft and have low specific gravities; where the molecules are small, the sublimation temperature is low. Filament and sheet crystals are rare. They are typified by elemental selenium and elemental arsenic, respectively. Graphite and molybdenite come near being sheet crystals. These crystals are soft in some directions, tough in others, sublime at various temperatures. Diamantine crystals, typified by diamond, are very few in number, stable at high temperatures, and extremely hard. Ionic crystals are common. Most salts, acids, and alkalies belong in the two classes of ionic crystals; examples are rock salt, fluorite, calcite, and angle-site. The salts, acids, and alkalies that do not belong in these classes are more properly regarded as transitional between ionic crystals, framework crystals, and diamantine crystals, e.g., ice and quartz. Fiber crystals are relatively uncommon mineral-ogically speaking, but common in the fields of living processes. Examples are asbestos, silk, cellulose, and wool. Many fiber crystals are so little known even now that their crystallinity may be doubted. Layer crystals, among the more interesting and useful of solids, include a wide variety of substances

Jan 1, 1956

Executive SIDNEY J. JENNINGS, Chairman GEORGE D. BARRON J. E. JOHNSON, JR. EDWIN LUDLOW ROBERT M. RAYMOND Membership KARL EILERS, Chairman LEWIS W. FRANCIS J. E. JOHNSON, JR. LOUIS D. HUNTOON ARTHUR L. WALKER Finance GEORGE D. BARRON, Chairman CHARLES F. RAND BENJAMIN B. THAYER Library E. GYBBON SPILSBURY,1 Chairman ALEX C. HUMPHREYS3 GEORGE C.' STONE2 J. H. JANEWAY4 BRADLEY, STOUGHTON Papers and Publications BRADLEY STOUGHTON, Chairman

Jan 7, 1918

By L. R. Jackson, W. T. Lankford, K. F. Smith

ComMercial steel sheet is prepared by a combination of hot and cold rolling and annealing. This treatment usually results in more or less pronounced anisotropy. The anisotropy may manifest itself both as preferred orientation and in the manner in which impurities, segregations, and the like, are aligned in the sheet. The type of preferred orientation and the organization of impurities or segregations may affect the elastic moduli, the yield strength, the tensile strength, and almost always the amount of ductility in different directions. In any case, the most important directions concerned in the anisotropy are along the rolling direction, along the width direction, and along the thickness direction. Considerable data exist on the anisot-ropy of sheet steel as demonstrated by conventional tensile tests; however, few attempts have been made to measure the constants of plastic anisotropy and use them to describe the flow of anisotropic sheet under combined stresses. In this paper, evidence is presented indicating that plastic flow in anisotropic sheet can be described by the shear-strain energy flow theory provided that the anisotropy is properly taken into account. Materials Used in the Investigation Table I lists the sheet materials used in this investigation and describes the condition in which materials were tested. Direction, of Tests and Test Methods Two types of tests were run—tensile tests and hydraulic-bulge tests. Characteristic parameters of anisotropy were determined from the tension tests by methods which will be described later. In all cases, the tensile test pieces were cut from the same quarter line and adjacent to the bulge test pieces in the sheet in order to minimize

Jan 1, 1949

By D. R. Parrish, V. J. Berry

Reverse combustion is one thermal method of recovering hydrocarbons from porous undergrortnd formations containing oil or tar. In applying this method, air is introduced via an injection well and the mixture of air and hydrocarbons is ignited in the production well. A combustion zone then recedes toward the injection well, counter-current to the air flow. If the combustion-zorie temperature is sufficiently high, the oil or tar irz place is distilled arid cracked. The hydrocnrhon flows as a vapor to the production well and subsequently is condensed at the surface. Maximum temperature and velocity of morcment arc the two dependent variubles defining the progress of the combustion zone. A theoretical analysis has been made of heat flow in the reverse-comhustion process as.srtrning linear flow in a homogeneous system. The differentirll equatious, which include the oxygen-hydrocar-hon rctrction rate, have been solved numerically. Rescllts indicate that the maximum temperature reached and he cornbustion-zone relocity both increase with an incrense in air-injection rote. Heat loss to surroundings has little effect on the maximum comhustion-zone ten?perature achieved, but it is reflected in a reduced com-bustion-zorzc, velocity. It is also predicted that an increase in the oxygen-hydrocarbon reaction rate results in a reduction in the maximum temperature reached. The calculated results are in agreement with results from reverse-combustion experinments using samples of a tar sand. INTRODUCTION Reverse combustion is one thermal method of recovering hydrocarbons from porous underground forma-tions containing oil or tar.' In applying this method, air is introduced into the underground formation via an in-jection well. In one or more adjacent production wells, the mixture of air and hydrocarbons is ignited at the sand face. The combustion zone thus formed recedes toward the injection well, counter-current to the air flow (Fig. 1). Under certain conditions, the rate of recession of the combustion zone is sufficiently rapid that only a small fraction of the hydrocarbon at any point in the formation is consumed by combustion. If the combustion-zone temperature is sufficiently high, the uncon-sumed oil or tar in place may be partially distilled or cracked. This material then can flow as a vapor with the gaseous combustion products to the production well and subsequently be condensed at the surface. Under other conditions, the combustion-zone temperature may be so low that little, if any, of the hydrocarbon is vaporized. Nevertheless, the viscosity of the hydrocarbon may be reduced enough so that other recovery methods subsequently can be applied to produce oil at attractive rates. The maximum temperature achieved in the combustion zone and the velocity of movement are the two dependent variables defining the progress of the combustion zone. Presumably. knowledge of these factors will permit estimates to be made of oil recovery efficiency, oil and gas producticn rates and average amount of injection air required per barrel of oil recovered. The maximum temperature and combustion-zone vclocity are, in turn, expected to be dependent upon air flow rate, heat losses to surrounding formations, physical properties of the rock and the hydrocarbon. the extent to which the porous formation is saturated with the hydrocarbon, the rate of oxidation of the hydrocarbon and the amount of heat released. It is desirable that the relative importance of each of these factors be understood so that the results of laboratory tests of oil recovery by reverse combustion can be properly interpreted in terms of expected field performance. It is particularly desirable to assess the importance of heat lcsses because these are difficult to control or eliminate

By Thomas Read

IN speaking of immaterial problems of industry I am using the word immaterial in its original sense, not consisting of matter; not in its derived sense, unimportant. There is nothing of a paradox in saying that immaterial problems are the most important in human life, for His a matter of everyday observation that much of the news in the daily papers, and most of the world's best literature and drama, deal with human conduct that has for its motive forces that are but little concerned with material things. The engineer's preoccupation with physical forces, in extending his control over them, has not blinded him to the impor-tance of forces that, for want of a better word, I call immaterial; but he has considered that dealing with the one is his job and the other is not. All the evidence of the past decade indicates that the latter are so in-extricably interwoven with the former in modern in-dustrial life that the engineer will have to concern himself with them whether he wants to or not. Some of the most important of the problems arising from the action of these forces relate to the mental hygiene of the workers in industry. Mental hygiene in industry was concisely defined, in terms of the best present knowledge, by Dr. C. Macfie Campbell, speaking last April before the executive com-mittee of the Associated Industries of Massachusetts, and as his statement can scarcely be bettered, I quote it below: "The term mental hygiene is apt to appear vague. The actual stuff with which mental hygiene deals may be briefly reviewed.

Jan 9, 1927

By Ernest Lilley

WHILE American scientific literature contains much information upon geologic conditions controlling the production of oil in Rumania, copper in Chile, and other fuel and metallic resources in many foreign countries, it is singularly lacking in data about the nonmetallics outside of the United States. Thus, though the United States is the outstanding market for European high-quality refined kaolin, and for the chinaware, porcelain, and other products of the European ceramics industries, Amer-ican literature contains only the briefest references to the deposits from which the raw kaolin utilized is obtained. To the writer, to whom has come in the past year .the opportunity of visiting a number of these deposits personally, they have proved of extreme interest both com-mercially and geologically. It is the latter phase that is discussed in this paper. The older and now largely crystalline rock areas of France, Germany, ;end other parts of western Europe contain numerous pegmatite dikes of which the upper portions have been subjected to surface weathering and kaolinization in much the same way as those of the eastern portion of the United States. Like the latter, the European pegmatite kaolins have long been known for their freedom from iron and other impurities offensive to the china and porcelain manufacturer. Unfortunately, they are also, like the American deposits, individually of small size and noted for their high costs of production. Deposits of sedimentary clay similar in many respects to the high-quality sedimentary kaolins of Georgia and South Carolina are known and worked, notably in southern Germany and in the Newton Abbott district of Devon and Dorset. in England. In general, their relationship to the parent rock from which they were derived is more evident than in the United States and the individual deposits are of smaller areal extent and less regular in outline.

Jan 1, 1932

By P. D. Merica

ALUMINUM and its alloys have been the subject of much investigation, during recent years, in the course of which the principal features of the constitution of most of the binary alloy systems with aluminum have been determined. Except in the case of a few metals-silicon, bismuth, cadmium, lead, zinc, and tin-an aluminum-rich compound is formed in each binary system, which forms a eutectic with the aluminum or its solid solution with this compound. Thus such compounds as FeAl3, CuAl2, Mg4Al3, and NiAl3 are formed, which are found in aluminum-rich alloys of their respective series as eutectics with the aluminum solid solution. These compounds are, in all cases, hard and brittle and their presence affects profoundly the physical properties of the alloys in which they occur. Within the zinc-aluminum system a compound, Al2Zn3, is formed that decomposes at lower temperatures. Silicon and tin each form a simple eutectiferous series with aluminum; bismuth, lead, and cadmium are only partly miscible in the liquid state with it. The extent of the solubility in aluminum, in solid solution, of these compounds or of the elements themselves, in the case of those series

Jan 7, 1919

By J. N. Hummel

THE methods of electrical prospecting, which employ contact electrodes to produce an electric field in the ground, furnish information concerning the constitution of the material beneath the surface, as indicated by the distortion of this artificially produced field and anomalies therein. To reveal the distortion of such field of known character, it is only necessary to measure qualitatively the direction of the field, using sensitive compensation methods. In such a case, the survey is relatively simple, and that is an important factor from a practical point of view, The distortion of the normal field thus determined permits an easy interpretation and gives approximate information as to the subsurface conditions, without the necessity of a thorough theoretical knowledge of the electrical field. The true field of application of the equipotential lines and search-coil methods, which are based on this principle of directional determination of the electrical field in the ground, is that of search for deposits of economic minerals for the mining industry, although they can also be used in solution of other problems; for example, in the determination of the strike of anisotropic beds. The distortion of the electric field as represented by the picture of equipotential lines or other measured curves is striking only when bodies having conductivities different from that of the country rock are embedded in the underground, or when the underground is anisotropic.

Jan 1, 1931

By G. R. Countryman, G. H. Thomas, I. Fatt

Procedures are described for scaling up turbulent friction pressure drops of inelastic fluids and laminar friction pressure drops of inelastic/elastic fluids in circular ducts. The laminar scale-up calculation method does not require the use of arbitrarily defined flow models, and can be performed directly from laminar capillary viscometry data, or by means of a numerical solution of the integral equation for Poiseuille flow, inputing true shear rate-shearing stress data from other simple shearing experiments. e.g. Couette and plane Poiseuille flows. The turbulent scale up procedure, based on the Dodge-Metzner correlation for inelastic fluids, requires evaluating the characteristic rheological parameters at the existing wall stress under laminar flow conditions. Since the wall stress is the quantity sought in a pipe flow scale-up problem, a trial-and-err or solution is indicated, and therefore a calculation method has been developed and programmed for a medium-size magnetic-drum-memory digital computer. Laminar flow data from other somces may also be adapted to this turbulent scale-upmetbod for inelastic fluids. Comparisons between predicted and experimentally observed friction losses for generalized Reynolds numbers ranging from 3 — 32.000 indicate an error band width of less than 10 per cent in circular tubes ranging in size from 0.5 to 1.89 in. in diameter. INTRODUCTION Considerable effort has been devoted to the problem of establishing an accurate procedure for predicting the laminar and turbulent flow behavior of non-Newtonian materials in pipes from data obtained with small scale laboratory or pilot plant equipment, as evidenced by the variety of reviews on the subject.1-3 Although there does not appear to be a universally accepted scale-up method for laminar flow, the various methods currently employed can be divided into two principal categories depending upon whether a functional relationship between shear rate and shearing stress is assumed, or whether a generalized correlation is adopted. The methods of Hedstrom4 and of Weltmann are typical of the first category, while the generalized correlation of Metzner and Reed6 illustrates the second category. Under appropriate conditions either approach yields a reasonably satisfactory description of laminar flow behavior. In contrast, the prediction of non-Newtonian transitional and turbulent friction losses is much more complex. For example, certain types of materials have been observed to sustain laminar flow at much higher flow rates than Newtonian liquids. When turbulence does develop, the level of agitation is damped to such an extent that the friction factor is lower than that of the original low viscosity Newtonian medium. Extremely broad transition regions and "diameter effects" have also been noted in the turbulent flow of certain chemically complex materials.' Aside from the latter complications, which are attributed in part to viscoelasticity, the existence of a variety of scale-up procedures for predicting transitional and turbulent friction losses is due principally to the chioce of viscosity parameter used in the definition of the Reynolds number. In contrast, Dodge and Metzner have demonstrated that the friction factorReynolds number relationship for inelastic fluids can be satisfactorily generalized provided the fluid property parameters are evaluated at the existing wall shearing stress.* However, the quantity usually sought in a pipe flow scale-up problem is the wall stress, and hence a trial-and-error procedure is required when dealing with non-power law materials. In this report we discuss two calculation methods: (1) for determining the wall stress, and hence the friction pressure drop, for inelastic fluids under conditions of turbulent flow by means of an iterative procedure, and (2) for predicting laminar friction pressure drops without recourse to arbitrarily defined flow models.

By S. Pearson, L. Rotherham

Measurements have been made of the variation of internal friction with temperature for OFHC copper, and for a series of binary solid solutions of high purity copper with zinc, gallium, germanium, arsenic, and silicon, to investigate the effect of alloying elements in substitutional solid solution on grain boundary viscosity. The apparatus used was of the torsional pendulum type developed by KeI1 modified so that the specimen and vibrating system could be maintained in a high vacuum. The activation energy for grain boundary relaxation in copper is 33,000 cal per mol. This is considerably less than the activation energy for self-diffusion, in disagreement with Ke's theory2 that the two activation energies should be the same. All the alloying elements increase the activation energy for grain boundary relaxation to approximately 44,000 cal per mol, increasing the grain boundary viscosity at a given temperature. The results are discussed in terms of theories of grain boundary slip put forward by MottQ and by Ke.+ Experiments have also been made to investigate the effect of small amounts of oxygen on the variation of internal friction with temperature for copper. EXPERIMENTS described in this paper were designed to investigate the effect of alloying elements in substitutional solid solution on grain boundary viscosity, using the internal friction method developed by Kel for measuring grain boundary viscosity. It was considered desirable to make the system under investigation as simple as possible by making experiments on a comprehensive series of binary alloys of copper with the elements immediately following it in the periodic table, i.e., zinc, gallium, germanium, and arsenic. These elements are within the range of favorable size factor for solution in copper, and the systems have been extensively investigated by Hume-Rothery and his co-workers." Later, in order to study the effect of the relative size of the solvent and solute atoms, experiments were made on a series of Cu-Si alloys, since the apparent atomic diameter of silicon when in solution in copper—the diameter necessary to assign to the solute atoms to account for the lattice constant of the solid solutiona—is almost the same as that of the solvent atoms. Preliminary experiments were made to measure the variation of internal friction with temperature for pure copper. Ke made some experiments on copper," but found that the curves obtained were not reproducible in consecutive experiments. The copper was maintained in an argon atmosphere during the experiments but, although he took precautions to exclude oxygen, Ke came to the conclusion that the precautions were not entirely satisfactory, and that the lack of reproducibility must be due to absorption of oxygen by the copper. Experiments have therefore been made to investigate the effect of small amounts of oxygen on the variation of internal friction with temperature for copper. Previous Work Ke made extensive experiments on high purity aluminum and was able to show that the grain boundaries behave viscously at high temperatures. He found that the relative rate of movement of the grains could be expressed as Where v is the velocity of slip, A is the constant, u is the shear stress, H is the activation energy, R is the gas constant, and T is the absolute temperature. By assuming that the boundary layer was one atom thick, he obtained a value for the viscosity which, when extrapolated to the melting point, gave good agreement with the viscosity of the liquid metal at the melting point. Ke also made experiments on other high purity and commercial purity metals:, and on some alloys." " He came to the conclusion2 that the activation energy for grain boundary slip was the same as for self or volume diffusion and for steady state creep in single crystals. Rotherham, Smith, and Greenough" have shown recently that the activation energy for grain boundary slip is not the same as for self-diffusion in tin,

Jan 1, 1957

Jan 1, 1882

Discussion of the paper of BOYD DUDLEY, JR., presented at the New York meeting, February, 1915, and printed in Bulletin No. 96, December, 1914, pp. 2767 to 2782. H. 0. HOFMAN, Boston, Mass.-At the close of the paper Mr. Dudley said that his experiments in the laboratory had shown that it was possible to separate nickel from copper by means of a chloridizing roasting, but that in order to demonstrate a process of this kind, work upon a large scale would have to be carried out. I think it was in 1913, that experiments of this kind were carried out at the works of the Pennsylvania Salt Manufacturing Co., Philadelphia, in a Wedge furnace, and at Sault Ste. Marie in a Sjöstedt furnace. They showed a satisfactory separation of nickel and copper. The ore was first subjected to an oxidizing roast, then mixed with pyrite and salt, and given a chloridizing roast. A. H. Carpenter published in the Engineering and Mining Journal, vol. xcvii, p. 1085 (1914) the details of this work. The conclusion arrived at is, that if you subject sulphide ore to an oxidizing roast, finishing at the temperature at which all nickel sulphate is dissociated, i.e., 764° C., then mix it with pyrite and salt, and subject the mixture to a chloridizing roast between 600° and 700° C., you can chloridize a high percentage of the copper without chloridizing any of the nickel, and obtain thereby a satisfactory means of separating the two.

Jan 5, 1915

By H. W. Highriter

THE method developed and used in this laboratory for the production of metallic uranium of such purity that it is ductile and can be cold-worked to fine wire or thin sheet by rolling has already been described1. It consists, briefly, in the electrolysis of potassium uranous fluoride (KUF5) in a molten bath composed of equal parts of sodium and calcium chlorides. The bath is contained in a graphite crucible, electrically heated to about 775° C., the crucible serving as the anode for electrolysis. The uranium deposits in finely divided form mixed with salts upon a molybdenum cathode suspended axially in the crucible. Upon com-pletion of the electrolysis the cathode is removed and cooled, the deposit broken and leached to remove salts. The metal powder is washed with water and dilute acetic acid and dried in vacuo to reduce oxidation. Suitable amounts are then pressed into pellets and heated in vacuo by high-frequency induction, using a thoria crucible. The uranium melts and flows away from the pellet, leaving a shell, which is largely oxide. In general, this method produced a satisfactory metal, although at times the uranium was not ductile. The investigations recorded here were made to find the cause of this embrittlement. It was known that the metal generally contained carbon, derived from disintegration of the graphite crucible in which electrolysis is conducted, in amounts dependent upon the thoroughness of washing the metal powder. Accordingly, analyses of several samples, both ductile and brittle, were made by combustion and absorption of C02 in Ascarite, using air instead of oxygen to reduce the temperature and rate of oxida-tion. Several of these metals were made with special precautions to reduce carbon content. The results show no relationship between ductility and carbon content in the range investigated (Table 1).

Jan 1, 1935

By D. L. Abata

This paper discusses recent technology dealing with the use of computer graphics in the mining industry. It presents a newly developed computer software package specifically designed for use in underground mining operations. This software package, developed under a US Bureau of Mines contract, 1) displays mine ventilation schematics and other representative illustrations for a real time data acquisition system and 2) uses the Bureau-owned Minefire and Ventilation Code for display of ventilation and contamination predictions on the microprocessor system. The package uses a unique system of display indexing that provides a simple yet efficient method of recalling a series of mine schematics detailing an underground operation and an alarm acknowledgment scheme that provides an effective method of identifying problem areas that may exist in the mine network. The package was written in Fortran for a 64-kilobyte, Z80-based microprocessor computer.

Jan 1, 1986

By E. Goldin, H. J. Juretschke

THE electrical properties of porous conductors have been studied ever since such materials, usually prepared by pressing and sintering of metallic powders, obtained practical importance. In most cases, however, the results have not been easy to interpret because of the great number of independent variables such as powder size, pressure, pressing rate and temperature, subsequent thermal history, porosity, and so on, which enter into the fabrication of industrially desirable materials. In recent years an interpretation of these properties has become of interest because the electrical properties of many new substances, prepared as fine powders by crystallization from the vapor phase or by reactions in the solid state at high temperatures, have to be determined on porous samples formed from the powder. Since theoretically significant information must refer to the fully dense state of the material, it is important to relate the electrical properties measured on such porous samples to those expected for a sample of 100 per cent density. A simple theory for the porosity dependence of the electrical conductivity and the Hall effect was recently proposed by Juretschke, Landauer, and Swanson.' Their model, assuming a distribution of pores of equal size and shape, sufficiently far apart so that each pore is embedded in a region of uni-

Jan 1, 1959

By J. H. Palm

Experiments have shown12 that the formula -S = St - (St - Se')e ne [1] expresses very well the relation between the true stress S and the true form monotonic deformation of plastic metals in single tension and compression (Fig 1). St (asymptotic or final stress), Se' (threshold stress) and ne (characteristic or specific strain) are constants, the significance of which immediately follows from Fig 1. Only at the initial stages of deformation the experimental curve runs below the theoretical curve. This may be due, at least partly, to the uneven stress distribution caused by the anisotropy of the crystals. It is now obvious that a similar formula H = Ht- (Ht- He)e ne' [2] might be valid for the relation between the hardness and the strain. The hardness can be only a function of the strain and must therefore be independent on the hydrostatic tension present in the neck during straining. Hence, if Eq 2 is correct it will also represent the relation between hardness and strain in the middle section of the neck, the strain of which is generally assumed to be almost or fully homogeneous. For aluminum, copper, and several copper alloys it is indeed observed that Eq 2 agrees very well with the experimental Vickers hardness-strain relation from zero strain on up to the strain at fracture. Moreover nc' is, for several metals fairly equal to nc- Hence H = C1 + C2S [3] C1 and C2 are constants during uniform uniaxial tension. Eq 3 was also obtained for copper by Voce.3 According to Hencky's theory4 the ratio of the Brinell or Vickers hardness and the yieldstress (expressed in kg per mm2) of a non-strainhardening metal is approximately equal to 2.8. If Eq 1, 2 and 3 are correct the ratio Ht/S, must accordingly be the same for all plastic metals and be equal to 2.8. It is now experimentally established that this ratio varies between 2.7 and 3.1 with a mean value of 2.9. Taking into account that Ht and especially St can be obtained only by extrapolation from the range of rather low strains, the agreement with the theory is very satisfactory. References 1. J. H. Palm: Appl. Sci. Res. Al (1948) 198. 2. E. Voce: Jnl. Inst. of Met. (1948) 74, II, 537. 3. E. Voce: Metal Treatment (1948) 15, 53. 4. H. Hencky: Zlsch. f. angew. Math. and Mech. (1923) 3, 241.

Jan 1, 1950