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The Climax design is for the human being and his needs. Climax President Arthur Bunker has likened the high mountain operation to a giant, 250 million tons in weight, and 12 thousand feet high. No matter how huge or complicated the plant, the design must assure efficient operation by its human operators. By the same token, living and playing facilities must be designed for fullest satisfaction in use-else the capital investment is not justified. Even the product, molybdenum, finds its application through the ever growing demands of a highly industrialized society of humans. Research in Climax Laboratories, in tune with our technical age, helps guide molybdenum to its maximum use for society.

Aug 1, 1955

By Mark Malamphy

MOST igneous rocks, and particularly those of the basic type, con-tain relatively high percentages of magnetite and other iron oxides, which give them moderately high magnetic susceptibilities and make them responsible for an important percentage of the magnetic anom-alies observed during the course of geophysical surveys by the mag-netic method. The irregular form and high susceptibility of the igneous rocks make them readily polarizable and the position and strength of the magnetic poles formed are not always explicable by theoretical calculations of anomalies due to certain assumed forms in the normal magnetic field of the area under study. During the last four years our field work has permitted us to make detailed observations of anomalies due to igneous rocks in all the states of south Brazil. The form and position of the igneous rock at some places were fairly accurately known, which made it possible to calculate theoretical anomalies and compare them with the observed data. Some of the data we obtained have been published and additional cases are now awaiting publication. In this paper, we will present a few specific cases where the geology is moderately well known and which we believe to be of considerable value as representing typical magnetic anomalies in the south magnetic hemisphere, where the inclination of the magnetic field is very low. Although the vertical intensity is negative in the Southern Hemis-phere, we have adopted the convention of plotting increase in intensity (negative) as a positive anomaly; i.e., above the x axis. This conven-tion facilitates comparison with anomalies in the north.

Jan 1, 1936

By P. W. George

This paper presents geological data regarding deposits of over 7,500,000 tons of fine-grained sulphide ore in barite gangue. A series of pyroclastics and arkoses was intruded by sills of quartz porphyry in connection with batholithic intrusions of granite 3 miles from Buchans. Gentle folding, with fracturing and shearing of tuff beds and intruded quartz porphyry, accompanied and followed the intrusion of granite and porphyry. The sulphide-barite mineralization is localized primarily in fractured and sheared tuff beds, but also in the sheared quartz porphyry. Two structures have proved particularly favorable for mineralization—one, the center of an anticline; the other, a series of weak, incompetent tuff beds intruded by thin sills of quartz porphyry and located between strong beds of arkose. During the folding the weak tuff with intruded quartz porphyry was intensely sheared and contorted and subsequently mineralized by sulphides and barite. Introduction Buchans is 5 miles north of Red Indian Lake, in Central Newfoundland, at an elevation of 900 ft. above sea level and 400 ft. above Red Indian Lake, and is reached by a 37-mile private railway from Miller-town Junction. The first ore body found at Buchans was discovered some 30 years ago in the bed of Buchans River, by Matty Mitchell, an Indian woodsman employed by the Anglo-Newfoundland Development Co. Ltd. In the years following the discovery the ore was developed by shaft-sinking and drifting, with results indicating a lenticular ore body in a shear zone, containing about 100,000 tons of extremely fine-grained sulphide ore in barite gangue averaging about 0.05 oz. Au, 4 oz. Ag, 1.5 per cent Cu, 10 per cent Pb, 18 per cent Zn. Because a profitable metallurgical treatment for the ore was not found, the mine was closed down in 1911. In 1915, Mr. H. A. Guess, Vice President of the American Smelting & Refining Co., learned of the Buchans River ore body, and after metallurgical tests had been carried on from time to time in his company's testing plant a satisfactory separation of the sulphides by selective flotation was finally effected in 1925. Prospecting for additional ore bodies was begun in 1926, utilizing geophysical methods under the direction of Hans Lund-

Jan 1, 1937

By F. L. Ransome

The following paper aims to present in a much condensed form the salient results of a detailed geological study of the Bisbee quadrangle, Arizona, carried on during the latter part of the year 1902. It is essentially an abstract of the final official report which will shortly appear in the series of professional papers of the U. S. Geological Survey, accompanied by maps, sections and illustrations. I. Geography. The Bisbee quadrangle, which includes the Warren mining district, lies in Cochise county in the southeastern part of Arizona. It is inclosed between the meridians 109" 45' and 110" 00' and the parallels 31" 30' and 31" 201, the latter being locally the Mexican boundarg line. The area of the quadrangle is about 170 square miles, and includes the southeastern half of the Mule Mountains, one of the smaller of the isolated ranges characteristic of this part of Arizona. The Mule Mountains, while less markedly linear than the Dragoon, Huachuca, Chiricahua, and other neighboring ranges, have a general NW-SE. trend. They may be considered as extending from the old mining town of Tombstone to the Mexican border, a distance of about 30 miles. On the northwest they are separated by the broad, flat floor of Sulphur Spring Valley from the Chiricahua Range, and on the southeast by the similar broad valley of the Rio San Pedro from the Huachuca Range. The maximum width of the range is about 12 miles, and its greatest elevation attained by Mt. Ballard, west of Bisbee, is 7,400 ft. above sea-level. An index-map, showing the geographical position of the Bisbee quadrangle, is shown in Fig. 1. The town of Bisbee (Fig. 2), with an estimated population of 6,000, is crowded into a few narrow confluent ravines near the

Jan 1, 1904

By A. G. H. Andersen

A FEW years ago, while the writers worked on the constitution of ternary and quaternary alloys consisting mainly of iron, chromium and silicon1,2 some information on microstructures and hardness, not incor-porated in the published work, was obtained. It has not been possible to do any further work on the properties of the alloys. The information possessed is hereby presented for the interest it. may have in connection with the constitution of the alloys.

Jan 1, 1937

By William Fink

SINCE so many different curves have been published for the solid solubility of zinc in aluminum, it seems desirable to definitely establish the correct curve by two or more independent methods. The curve published in part I1 was based entirely upon X-ray measurements because the other methods employed at that time were not satisfactory. The present paper (the seventeenth of this series on high-purity aluminum alloys) describes the determination of the solid solubility of zinc in aluminum by the measurement of electrical resistivity at temperature and by microscopic examination. Since the publication of our part I in 1932, an investigation of the solubility relations in the aluminum-zinc system has been reported by Schmid and Wassermann2, who obtained their solubility results from lattice-parameter measurements on heat-treated and quenched speci-mens. The diagram that they published is shown in Fig. 1. In this investigation they also found by X-ray measurements that the parameter of the gamma phase changed continuously with zinc content and at such a rate that it would be identical with that of the beta phase at 60 atomic per cent zinc. It was concluded therefore that the beta and gamma phases, from the point of view of structural relationship, are one single phase. They also suggested a gap of immiscibility between 270° and 350° C. The complete boundary in this region could not be deter-mined satisfactorily by the method employed and therefore was not shown in their diagram.

Jan 1, 1936

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By E. A. Holbrook

The art of ore dressing is as old as civilization itself. Jason's search for the golden fleece was perhaps only the use of sheepskins for catching gold from gold-bearing sands washed over them. From Hoover's translation of Agricola we gather that in the middle ages ore dressing had advanced through the stage of hand sorting to water concentration by jigging. German methods and apparatus continued in the lead until the closing years of the past century; indeed, it is little more than a generation ago that many ore-dressing plants in this country were designed and operated by German-trained ore-dressing specialists. Meanwhile the development of the ore deposits in this country during the nineteenth century brought forth new inventions and methods. Blake's invention of the rock breaker in 1858 and the coming of the Wilfley table about 1896 are random examples of the improvements caused by our expanding needs. Yet ore dressing remained an art developed and practiced more or less by cut and try methods. The publication of the volumes on Ore Dressing by Dr. Robert H. Richards in 1903 marks the beginning of American ore-dressing practice as a science. Previously we had as guides only a few incomplete books based on foreign practice, or scattered references and articles in our own Transactions. Dr. Richards set down all the developments that had gone before, and outlined the ways for a scientific approach to the subject. He gave us a starting point. Since then ore-dressing practice and technique in this country have set the pace for the world. Coal preparation has been called "ore dressing upside down,'' because in ore dressing we generally save a small percentage of the heavy valuable mineral and discard the lighter gangue, whereas in coal preparation we save the larger quantity of light mineral and discard the smaller percentage of heavy waste. By comparison with ore dressing the history of coal preparation is brief, extending backwards hardly 100 years, for although coal had been dug and used locally for centuries it became an important article of commerce only with the coming of the industrial revolution 150 years ago. In new mines it was to he expected that the thickest and purest seams should be worked first. So long as these lasted there was little thought of coal preparation other than hand picking of the larger impurities and simple sizing to supply the real or fancied need

Jan 1, 1934

By H. H. Rachford

Numerical solutions of immiscible flow problems in which dispersive effects of capillarity are dominated by convection require excessively fine grid spacing with attendant high computing costs. The use of coarser spacing reduces cost but often produces oscillation or undue dispersion associated with displacement fronts, A numerical formulation is proposed here which should be applicable to two-dimensional flow problems. it is in part analogous to an approach previously tested for miscible systems. The convective transport is approximated using a change of variables to yield a coordinate system moving approximately with the local characteristic velocity. The capillarity-induced dispersive terms in the differential system describing the process are approximated with respect to a fixed coordinate system by the usual implicit formulation. One-dimensional tests of the procedure yielded results in which the saturation profiles tended smoothly to the zero-capillary pressure solution as the ratio of viscous to capillary forces was successively increased in a sequence of calculations. This contrasted favorably with solutions by other numerical procedures which would require attendant grid refinements to approach the zero capillary pressure results. INTRODUCTION Numerical solution of displacement problems has until recently relied on applying methods developed primarily for transient heat-flow problems. Such problems are classified as parabolic in type, and where the heat transport is purely by diffusion their solutions are characterized by a high degree of smoothness. It is not surprising, therefore, that for approximating these solutions available finite difference methods are quite adequate. In flow problems the transport is partly by diffusion, partly by convection or flow. Although the problem remains of parabolic type because the dispersive effects of capillary forces or diffusion play some role in every displacement, at high flow rates the problem is dominated by convection, and solutions tend toward those of equations of the hyperbolic type. Solutions of hyperbolic problems are characterized by the translation of fronts, or discontinuities, that may progressively increase in sharpness. Numerical methods for treating parabolic problems become less and less satisfactory as displacement rates increase and the role of dispersion due to concentration or capillary pressure gradients becomes small relative to transport due to flow. In computation the difficulty manifests itself as an error associated with the grid size chosen. 1-6 In summary, if the heat-flow type approximations are to include the terms arising due to convection, one of several choices may be made: (1) an upstream (to the direction of flow) approximation for the convection terms may be used; (2) a centered-in-distance (CID) approximation may be used; or (3) a recently developed approximation based on the theory of oscillation matrices may be chosen.6 The last appears to have significant promise for one-dimensional flow problems; its extendibility to two or three dimensions is an open question. In either of the first two approaches, a suitably small ratio of v&/D must be maintained, where v is the velocity, & is the grid spacing and D the effective dispersivity in the direction of flow. In the first choice, the approximation of the convective part is only first-order correct and errors introduced appear as a numerically induced dispersivity of magnitude proportional to v?x. In the CID choice, the approximation can be second-order correct, but the difference formulation fails to satisfy the maximum principle unless a condition on v?x/D is met. Practically, this means that for high flow rates oscillatory solutions may result in the neighborhood of a front unless exceedingly small grid intervals are taken. While the procedure proposed by Stone and Brian4 permits a less severe limitation to be placed on this ratio, ultimately the flow rates increase relative to the dispersivity the oscillation obtains. Further, extensions of their approach to higher dimensional systems may be attended by considerable

Jan 1, 1967

By S. B. Twiss, P. R. Basford

The relationship between areas of iron powders, briquettes, and sintered compacts and tensile strength has been determined. It has been found necessary to distinguish between two types of areas which exist in such powders—a macroscopic area due to the shape and size of particles and a microscopic area due to pores and cracks in the surface. Only the macroscopic area, specifically the area due to particle irregularity, contributes to tensile strength; the microscopic area cannot be forced into contact with adjacent particles ond does not participate in bond formation. Of the two methods of area measurement employed in this study—permeability to liquids and gas-phase adsorption—only the former is useful for determining the roughness factor. A measure of this roughness, (area measured by permeability to liquid) -f- (orea of powder with the same size distribution, but made up of spherical particles), is shown to be uniquely related to tensile strength at constant density. The other important factors in determining the strength of sintered-metal compacts are the density and presence or absence of surface oxide. THE manufacture of metal parts by the process of powder metallurgy is an important and rapidly growing industry. Progress has been rapid and continuous, largely because of the excellent research in the field. Nevertheless, the process remains inherently complex and empirical. Several investigators have shown that the properties of the final compact must depend on many variables; namely, shape,' size distribution,"-" nd compositiona of the original particles, the pressure necessary to compress to the desired density, the density of the compact, the time and temperature of sintering, and so on. Through the application of some new techniques to the study of powders and compacts, and the correlation of a number of observations of known variables, the present paper attempts to clarify and simplify the underlying theory of the powder-metallurgy process. Any theory must start with the obvious fact that the strength of a compact, its most useful property, is due to the formation of welded areas between adjacent particles, and attempt to deduce what effect other variables will have on (a) the area and (b) the intrinsic strength of these welds. Such welded areas can be demonstrated by electron micrographs, as in Fig. 1. It was believed that (a) could be most directly studied by means of surface-area measurements on the original powders and on the compacts made from them; the area decrease should be related closely to the welded area. A representative group of eleven iron powders from commercial sources, and made by a variety of processes, was chosen for this study. In addition to the surface-area measurements, correlations were established between the tensile strength and all the known variables which might possibly affect it. The results are quite unexpected. They indicate that the situation is much simpler than the authors had anticipated. The strength of the sintered compact is determined, indeed, by no more than three variables; viz., the irregularity of the original particles, the density of the compact and, in exceptional cases, the amount of surface oxide. All three had been recognized previously as having some effect on the tensile strength, but in the absence of the special techniques and interpretations to be developed here, there could be no suspicion that they were the only relevant variables. Materials and Methods Material—All the iron powders were commercial products obtained from the Amplex Division of Chrysler Corporation. Powders A, B, C, and J were very pure electrolytic iron. Powder D was made from oxidized scrap reduced by heating with an excess of cast iron. Powder E was a high-grade iron ore reduced by hydrogen. Powder I was prepared by atomizing molten cast iron in an air blast, quenching the droplets in cold water, and crushing the coarse powder. Mill scale (oxide) is added and the mixture heated to reduce the high carbon content. The other powders were all prepared by reduction of iron oxides, such as mill scale. They

Jan 1, 1959

By Clarence A. Seyler

The technical difficulties of cutting thin sections of coal for examination by transmitted light have hitherto restricted the investigation of the important subject of the microstructure of coal to the few possessed of the requisite skill and time. Apart from this, the method fails with anthracites and other coals rich in carbon, owing to the opacity of the material. Occasional use of the method of polishing a surface, with or without etching, has been made, but it was not until Winter' published an account of his results that attention was seriously directed to the method. In May, 1923, a specimen of dull anthracite came into my hands; I tried Winter's method on it and the presence of megaspores and other vegetable structures became clearly visible. A preliminary notice was published by me;2 but I soon abandoned the use of Schulze's solution, having found that a mixture of chromic and sulfuric acids gave far better results. In the meantime Turner and Randall, in America, had independently developed the method of flame etching, as applied to anthracite, with great success. I have spent a year studying the method of chromic etching, which gives excellent results with bituminous coals and camels, as well as with anthracite. For anthracites, I have used the chromic method and Turner's method of flame etching, whichever was the more convenient or as a check one on the other. The polishing is done, according to metallurgical practice, by the use of a polishing machine and successively finer emery paper, followed by polishing on cloth moistened with a suspension of levigated green oxide of chromium, and a final rubbing on "selvyt" (a cotton velvet polishing cloth) moistened with alcohol. The polished sample is examined by reflected light with a 2/3 and 1/6 in. objective. Bituminous coals usually show considerable structure, and even anthracites show it faintly in places. The sample is then etched by immersion in a boiling solution made by adding 10 c.c. of concentrated sulfuric acid to 30 C.C. of a saturated solution of chromic acid; enough water is then added to dissolve

Jan 1, 1925

By Oswald J. Heinrich

During the last twenty years much has been done to investigate and define the Mesozoic formatibn of the United States along the Atlantic States, as well as in' the Territories. The investigations of Professors Hitchcock, Emmons, Hayden, H. D. Rogers, and those now in progress in connection with the geologicd surveys of Penn-

Jan 1, 1879

By R. S. Lewis

The Utah field to which the name Book Cliffs is applied runs in a northeast direction from Mt. Hilgarde, in Sevier county…

Jan 1, 1915

By William C. Alden

A great landslide occurred on June 23, 1925, in the valley of Gros Ventre River, about 35 miles south of Yellowstone National Park (Fig. 1). The relations of the north-easterly dipping rock formations of the slide scarp and of the dam formed by the slide are shown in the diagrammatic cross-section of the valley (Fig. 2). This generalized section is based on unpublished maps and notes by Eliot Rlackwelder, in the files of the IT. S. Geological Survey. Heavy rains and melting snow in the Gros Ventre Mountains had saturated clay layers in the Carboniferous strata, which dip toward the valley at angles of 18" to 21°, consequently an enormous mass of rock at the end of the north spur of Sheep Mountain became loosened and, on the afternoon of June 23, slid suddenly down into the valley. Within a few minutes this mass of debris—estimated as 50,000,000 cu. yd.—carrying

Jan 1, 1928

Jan 1, 1893

By W. P. Sykes

RECENT investigations of the molybdenum-carbon alloys have been reported by Becker and Ebert1,? Westgren and Phragmén2, T. Takei3, and H. Tutiya4. Takei3 studied the Mo-C system by employing metal-lographic and X-ray methods, and the other publications described the determination of the crystal structure of the molybdenum carbides. In exploring this system by a technique previously applied to the tungsten-carbon series5, the results of Takei were confirmed with two definite exceptions; i.e., first the composition of the eutectic, and second the nature of the carbon-rich intermediate phase. Consequently, a more thorough examination of the molybdenum-carbon constitution was initiated in an effort to correlate the data supplied by the microstructures, diffraction patterns and chemical analyses.

Jan 1, 1935

By George Enos

As the coating formed affects the corrosion rate, duplicate samples of eight non-ferrous alloys were placed in flowing mine water. The alloys tested were as-cast or as-rolled and machined or polished. The paper describes the tests and gives the corrosion losses and the appearance of the samples at the end of the test. AN IMPORTANT factor affecting the rate and nature of corrosion of metals and alloys is the film, or coating, formed on the surface; and this may accelerate or retard corrosive action once started. The formation of films and coatings is intimately associated with the chemical composition and physical constitution of both the metal and the corroding medium. A film or coating may be either the corrosion product resulting from oxidation; that is, an oxide or salt, or a deposition of suspended matter from the corroding media upon the surface of the metal, or a mixture of both. The coating may adhere tightly or loosely to the surface of the corroded metal. In short, a film or coating is the reaction product of the corroding medium and the metal, which adheres to the surface of the metal and with which may be intermingled material from the attacking media not concerned in the chemical reactions. As the, terms film and coating are used by different writers for very different things, distinction is made between the two, by the present writers, on the basis of thickness. Thus, a film is defined as a corrosion product or deposition, on the surface of a corroded metal, that is of such thickness that it cannot be measured by the metallurgical microscope. A coating, on the other hand, is of such thickness that it can be measured. If the resolving power of the 2 mm. (equivalent focal length) apochromatic oil immersion objective (N.A. 1.4) is taken as the limit of the microscope, the limiting resolution is two lines that are 0.0002-0.0004 mm. apart. It is thus possible to measure coatings that are greater than 0.0002-0.0004 mm. thick. This thickness is equivalent to 200,000-

Jan 7, 1924

ALABAMA Aldrich -Thomas, D A Altoona -Cain, J Anniston -Cowie, L K Walmsley, W N White, H E Ashland -Sturdevant, J C Bankhead -Connaway, M B Bessemer-Ball, E M McKenzie, W C, Jr Mitchell, F R Morgan, C Thompson, N E Birmingham -Abbott, C E Adams, J H

Jan 1, 1923

By J. J. Lander, L. H. Germer

Molybdenum and tungsten have desirable corrosion and temperature resistant properties, but the metals in bulk are expensive and their fabrication is difficult. Such considerations led to a search for a method of plating them upon base metals. This search was successful and led furthermore to a number of developments which could not have been foreseen. Neither pure tungsten nor pure molybdenum has been electroplated successfully, although the literature of electroplating is liberally sprinkled with the description of unsuccessful attempts. The process of plating these metals by thermal reduction of their halides has achieved onlv limited usefulness because of technical limitations and because of limited range of product quality. Plating by thermal decomposition of the carbonyls does not suffer from limitations of the same sort and the properties of the plate are readily controllable. This paper describes the plating of molybdenum and tungsten, and of compounds and alloys of these metals, by pyrolysis of their carbonyl vapors. Chromium also has been plated in this manner, but the experiments upon chromium have been less extensive and the results much less satisfactory. Probably the most important of the products which we have obtained are the alloys with carbon, and the carbides of the metals. Either molybdenum or tungsten can be deposited upon a base metal as a coherent and adherent coating. By adjusting the plating condition the carbon content of the coating can be made to have any value from substantially zero to about 35 atomic pct. The hardness is dependent primarily upon the amount of carbon in the plate and can be regulated over a very wide range, some coatings containing considerable carbon being harder than sapphire. In addition to products already known this method of plating has yielded new carbides of molybdenum and tungsten and alloys supersaturated with carbon. These new products are possible because, in the process of plating, carbonyl can be decomposed at temperatures as low as about 150°C, and thus in the presence of other substances reactions occur which could perhaps not be produced in any other way. In addition to carbides and alloys with carbon, sulphides and oxides of molybdenum and tungsten have been produced and studied. There are certain other advantages of the carbonyl method of plating. It is not required that the base have good electrical conductivity as in electrochemical processes, and the base need not have the temperature stability required in plating from a halide. Thus low melting glasses, as well as other ceramics, can be plated almost as readily as metals. In particular, the plating of glass with

Jan 1, 1949

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967