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By P. S. Bagga, P. T. Luckie

Liberation (the process of destroying the interlock between unwanted materials, such as mineral matter and pyrite, and coal) is one of the most important precursors to the benefication of raw coal in order to produce high grade marketable coals at economical recovery levels. Liberation is achieved usually by comminuting the raw coal. However, because of the significant interaction between the production of fine particles to achieve liberation and the cost of separating fine particles, the coal industry needs a method projecting the change in washability with size reduction. Such a projection can be combined with size reduction and separation simulators in order to examine completely beneficiation circuitry to produce coals of stringent specification. This paper presents the development of an appropriate liberation model for coal and its solution by Monte Carlo simulation to predict the expected washability of the raw coal as a function of comminution. It includes model validation with a known binary mixture as well as with a known teritary mixture.

Jan 1, 1983

By A. S. Odeh

During the last few years, several authors1-6 have advanced mathematical solutions, both exact and approximate, to the pressure behavior of a well producing from a region bounded by a circular discontinuity. The most recent solutions were reported by Carter, and by Bixel and van Poollen. Varter solved the appropriate equations analytically. Bixel and van Poollen reported a numerical solution and provided correlation charts for the interpretation of flow tests; their method uses an overlay technique and is valid for wide ranges of mobility and storage capacity ratios. The mobility ratio is defined as the ratio between k/p of the two zones, and the capacity ratio is defined as the ratio between $c of the two zones. We have developed independently an analytic solution, programmed for the CDC 1604, that agreed with Carter's.'1 The same differential equation, assumptions, boundary, and initial conditions were used. We ran 30 drawdowns and 30 buildups of a unit capacity ratio and of varied mobility ratios. We also varied the radial distances to the discontinuity, and the radii of drainage. We examined the results and obtained correlations that were simple to apply and useful in flow test interpretation. The results and the correlations reported here in graphical form allow the determination of the mobility of the two zones and the radial distance to the discontinuity. They eliminate the need to fit field data to a curve as is required in the overlay technique.6 Thus, the advantages of the present correlations are that they require less effort and they provide a unique answer. They also provide guidelines for selecting the parts of the flow test plot to be used in the interpretations. Moreover, the results obtained from the programmed analytic solution define the time intervals where the approximate solution reported by Hurstl and discussed by Larkin2 are applicable. Normal buildup and drawdown plots resulted in an early straight line, a long transition zone and a late (second) straight line. However, the second straight line will not occur if the drainage radius is not at least 10 times the radial distance to the discontinuity. The mobility of the imer and outer zones can be calculated from the slopes of the first and second straight lines, respectively, by the normal methods of the flow test analysis. We found that the radial distance to the discontinuity may be determined from the abscissa value for the point of intersection of the extensions of the two straight lines. Results similar to some of these were reported by Adams et aL7 The approximate solution compared favorably with the exact one during the first and second straight-line periods. However, during the transition zone, deviation occurred between the two solutions. Discussion of Figures Figs. 1 through 7 summarize the results of this investigation. On Figs. 3 through 7 there appears the equation of each respective plot. In this paper the mobility ratio M is defined as klp2/kzpl, where subscripts 1 and 2 refer respectively to the inner and outer zones, and dimensionless time = t, = 6.32 X In the investigation, M ranged from 0.25 to 50;

Jan 1, 1970

By R. F. Mehl, J. T. Ransom

For many years the Metals Research Laboratory of Carnegie Institute of Technology has been concerned with the statistical nature of the engineering properties of steel from an experimental viewpoint, particularly those properties representing ductility.' In the past three years new work has been directed toward evaluating the statistical nature of the endurance properties. It has been shown that both the fracture curve and the endurance limit in fatigue are markedly statistical in nature. The S-N curve (and the endurance limit) of ferrous materials is often determined with specimens which number as few as ten. The common procedure is to test the first specimen at a stress well above the expected endurance hmit. Each succeeding specimen is then tested at a progressively lower stress, until, after five or six tests, a specimen runs ten million or so cycles without failing. Two or three more specimens are then used to find the highest stress at which failure will not occur; the limiting stress determined in this way is called the endurance limit. It has now been found, however, that the variability in the fracture curve and in the endurance limit in heat-treated alloy forging steels is so great that S-N curves must be drawn on the basis of distribution curves which can be appraised only by statistical methods. Two methods have been adopted in this study: (1) straightforward statistical studies of cycles to fracture of a number of specimens at each of a series of stress levels, and (2) a new abbreviated statistical method, known as "staircase testing."2 The latter corisists in testing a series of specimens, one by one, with the test stress for any given specimen automatically

Jan 1, 1950

By C. E. MACQUICC

WITHIN a period considerably less than two decades, the engineering view of alloy steels has greatly changed-both as to their composition, and applications. Inasmuch as the elements used in manufacturing alloy steels are substantially the same as those which have been used for the past two or three generations, a statement like the foregoing may reasonably call for some explanation. The first commercial use of alloy steels in this country dates back to the sixties of the last century, when one of the earliest alloy steel patents, covering the use of chromium, was taken out by Bauer. About ten years later, German and French toolmakers began to introduce tungsten into tool steels. Developments along this line were more or less static for 25 years or more, the tool steel, compositions progressing along lines worked out by Mushet and one or two others in Europe. The next step in advance, made by Taylor and White inn the late nineties, consisted of heat-treating the alloy steels to enable much higher cutting speeds, thus introducing what soon became known as "rapid" or "high-speed" steels. All these developments being aimed toward the improvement of cutting tools, the compositions made were essentially of a hard, brittle nature. Following a different line of development started in the seventies, naval ordnance material began to embrace the nickel steels. These were rapidly popularized, became, and still are, with the addition of one or more elements, as chromium, molybdenum, vanadium, standard for heat-treated armor plate. During that period, however, no notable uses were made of alloy steels for engine parts or other high-stress parts where they are now considered indispensable; moreover, the present-day use of metals in the chemical industries was probably not even imagined. After the turn of the century, the necessity for making heavy-duty. machine parts, and especially the develop¬ment of the automobile, caused alloy steels to rapidly supplant plain carbon steels for engineering purposes.

Jan 1, 1930

By Edward J. Felten

THE oxidation resistance of chromium and Fe-Cr alloys is increased by small additions of yttrium or other rare earth metals.1,2 In addition, the presence of the additives increases the resistance of these alloys to spalling of the external oxide above 1000°C. This ability to prevent spalling appears to be related to the formation of an internal oxide in alloys containing yttrium or the other rare earth metals. The internal oxide is found in the form of a filamentary growth concentrated in the grain boundaries of the unoxidized metal. In alloys containing yttrium this internal oxide was found to be either Y2O3 Or YCrO3.' In an earlier report,' the growth of the external oxide was found to be controlled by diffusion through the oxide layer. Thermal balance studies were used to establish the kinetics of external oxide formation. In this related study the rate of growth of the internal filamentary oxide has also been studied. The results obtained indicate that the growth of the internal oxide is also diffusion controlled. Internal oxidation appears to occur in at least two ways. Using copper alloys containing small amounts of silicon, Rhines 3 found that between 600" and 1000oC a subscale was formed which consisted of particles of silica dispersed in the metallic matrix. The conditions requisite to internal oxidation as suggested by Rhines are: 1) a solubility of oxygen in the alloy, 2) the ability of oxygen to diffuse at an appreciable rate into the alloy, 3) the possibility of the formation by the alloying element of an oxide more stable than the oxide of the host metal, and 4) a relatively low solubility of this oxide in the metal. These conditions are fulfilled for a number of other copper alloys.3-5 Furthermore, the relationship between the depth to which the internal oxide is formed and the oxidation time follows the simple parabolic law.6 The activation energy for copper containing small amounts of silicon, germanium, iron, or manganese as calculated from Rhines data6 is about 48 kcal per mole. In some cases the internal oxide is found segregated at the grain boundaries, especially near the the surface. Observations of this type of oxide formation have been reported by stead,7 Rhines,* and Lustman. Evans" cites these cases as examples of the simultaneous movement of anions and cations during oxidation. Furthermore, Evans states that the presence of a minor constituent with a high

Jan 1, 1962

By J. Handin, S. J. Bauer, M. Friedman

Deformation mechanisms in room-dry and water-saturated specimens of Charcoal Granodiorite, shortened at 10-4s-1, at effective pressures (Pe) to 100 MPa and temperatures to partial melting (?1050°C) are documented with a view toward providing criteria to recognize and characterize the deformation for geological and engineering applications. Above 800°C strength decreases dramatically at effective pressures ? 50 MPa and water-weakening reduces strength an additional 30 to 40% at Pe = 100 MPa. Strains at failure are only 0.1 to 2.2 percent with macroscopic ductility (within this range) increasing as the effective pressures are increased and in wet versus dry tests. Shattering (multiple faulting) gives way to faulting along a single zone to failure without macroscopic faulting as ductility increases. Microscopically, cataclasis (extension microfracturing and thermal cracking with rigid-body motions) predominates at all conditions. Dislocation gliding contributes little to the strain. Precursive extension microfractures coalesce to produce the throughgoing faults with gouge zones exhibiting possible Riedel shears. Incipient melting, particularly in wet tests, produces a distinctive texture along feldspar grain boundaries that suggests a grain-boundary-softening effect contributes to the weakening. In addition, it is demonstrated that the presence of water does not lead to more microfractures, but to a reduction in the stresses required to initiate and propagate them.

Jan 1, 1982

By R. G. Aspden, D. A. Colling

THE {120}(001) texture has been reported in near 50 pct Ni-Fe alloys <0.004 in. thick1,2 and in copper 0.014 in. thick.3 This texture is one of two types of secondary recrystallization textures observed to replace a cube texture matrix and is desirable in Fe-Ni alloys because of its unique magnetic characteristics.1,2 However, the conditions for and mechanism of the {120}(001) formation are not well understood.3 During an investigation of the influence of alloying elements on the magnetic characteristics of 49 pct Ni-Fe alloys with a sheet thickness of 0.014 in., we have observed the growth of {120}(001) secondaries when strong deoxidizers such as aluminum and calcium were present. It is believed that this observation in unique and provides additional insight with regard to the mechanism for {120}(001) texture formation. Three alloys were prepared with electrolytic iron and nickel and contained a nominal 49 wt pct Ni. Alloy A was a straight binary Fe-Ni alloy, whereas intentional additions of 0.013 wt pct Ca to alloy B and of 0.59 wt pct A1 to alloy C were made. Ingots were forged at 1100 C, hot-rolled to 0.150 in. gage, pickled, and cold-rolled to 0.014 in. Standard U-shaped magnetic test specimens were punched, deburred, sprayed with MgO, and annealed in ~50°C dew point hydrogen. Textures were identified with the aid of etch pits, the

Jan 1, 1970

By Scott Turner

PRESIDENT SCOTT TURNER officiated as chairman of the opening session on mining methods, Monday morning, Feb. 15. The first paper was that of Max H. Barber on open-pit mining in the Lake Superior district, read by C. F. Jackson. W. L. Taylor stated that liquid-oxygen explosive had been tried but that the operators are satisfied with the explosives used; lb. of dynamite breaks one ton of rock. Although black powder is considered the most effective explosive, the factor of safety has decided in favor of high explosives. Lucien Eaton told of the Michigan Lime and Chemical Co.&apos;s large L. 0. X. plant at Rogers City, Mich. Mr. Turner referred to this plant, also said that the Bureau of Mines is shortly to issue Bulletin 349 completely covering the use of L. 0. X. from its inception. W. D. B. Motter, Jr., gave some items concerning Chuquicamata, Chile. Twelve years ago the blasts moved 850,000 to 1,000,000 tons, but average shots now move 250,000 to 300,000 tons. One pound of L. 0. X. breaks 3.7 tons, against 3.1 tons by dynamite. Another speaker told of some large dynamite blasts in open pits, one of 360,000 Ib. in March, 1931, and another of 430,000 lb. to be shot in 1932. Tests have been made to determine the effect of large shots on the surrounding country. Mr. Taylor said that 4- and 5-yd. shovels were preferable to those of 8 yd.; their performance is better and cost is lower.

Jan 1, 1932

By R. M. Goldhoff, J. W. Spretnak, R. Speiser

IT has been observed by Grange and Garvey&apos; that the homogenization of boron-treated steels could lead to complete elimination of the hardenability effect caused by boron. The experimental conditions leading to this conclusion involved the heating of steel specimens with and without boron at 2350°F for 24 hr. To prevent oxidation and decarburization, the specimens were encapsulated under vacuum in silica tubes. This observation of permanent deterioration of boron effect was noted in both a 0.63 pct plain carbon steel and a 0.25 pct C low alloy steel, both of which had been treated with ferroboron and homogenized at 2350°F for 24 hr. In another series of boron-treated steels which had been homogenized for shorter times, the effect was to reduce, but not completely eliminate, the boron effect. Under these circumstances, it was presumed that longer heating times would cause permanent deterioration of the boron effect in this series of steels also. Since the characteristic grain boundary constituent could not be formed in any of these steels after homogenization, it was concluded that possibly boron was being converted into an ineffective form through chemical combination resulting from prolonged heating at high temperatures. Assuming the validity of this observation, a series of experiments to establish the relationship between temperature of homogenization and kinetics of deterioration was contemplated. Initially an attempt was made to reproduce the results just described. For this purpose commercial lots of AISI 8640 and AISI 86B40 steels were used. The analyses of these steels appear in Table I. Hardenability evaluation was on the basis of the hardness of normalized sections. Grange and Garvey&apos; pointed out that these steels are air hardening to some extent and such a technique can be used. For these tests the specimens were held for 20 min in a salt bath at 1600°F and then cooled in still air. Several evacuated silica capsules containing pairs of the test steels were made up and heated for 24 hr at 2350°F. A number of failures occurred among these capsules, but evaluation of the specimens successfully treated indicated a complete deterioration of the boron effect. However, examination of the surface of the treated specimens showed that some reaction, probably with the silica tube, had taken place, since none of the specimens was bright. One further test was made at 2350°F for 12 hr, using a pair of specimens wrapped in tantalum foil prior to encapsulation. These specimens appeared bright after treatment, and their hardenability evaluation showed that no deterioration had taken place. Since these steels are extremely sensitive to de-boronization at high temperatures and particularly at long times of holding, the experimental observations raised some doubt as to the real occurrence of the permanent deterioration effect. To resolve this question an experiment was undertaken in which the high temperature portion of the treatment was completed in vacuum. For this purpose a molybdenum wound resistance furnace capable of maintaining good vacuum was used. All the pertinent accessories to this furnace were machined from molybdenum stock in order to withstand the high temperature involved in the experiment. With this equipment a temperature of 2400 °F was obtained and held under a pressure of 5x10-" mm Hg for 24 hr. A specimen of each of the two test steels was suspended in the furnace and both were heated simultaneously. Temperature was measured with a standardized Pt—Pt-13 pct Rh thermocouple, whose millivoltage at 2400°F was extrapolated from the standardization equation, good up to 2200°F. The complete evaluation of these specimens is shown in Table 11. The hardness values attained by each steel after normalizing, both before and after the prolonged high temperature treatment, remain the same. A microscopic study of the decomposition products present in the microstructures of specimens at various points in the heat treatment correlated with the hardness values observed. It seems that no permanent loss of boron hardenability effect occurs, at least in these Grainal-treated steels, when deboronization is circumvented. Acknowledgments This work was conducted under the sponsorship of the Aeronautical Research Laboratory, Wright Air Development Center, under Contract No. AF 18(600)-94, and their support and permission to publish is gratefully acknowledged. A note of thanks is also extended to the Republic Steel Corp. for supplying the materials used in the work. References &apos; R. A. Grange and T. M. Garvey: Factors Affecting the Harden-ability of Boron Treated Steels. Tro.ns. ASM, 1946, vol. 37, p. 136.

Jan 1, 1957

By Paul T. Benson

MOST important of the various departments of a custom smelter, so far as the financial welfare of the plant and the confidence of shippers are concerned, is that responsible for correct weights, accurate moisture sampling, and the obtaining of control samples that are strictly representative of the lot of ore from which they come. Treatment rate schedules are based on the metal content of ores received, reduced to dry weight. These rates must be low enough to keep the ship- per from taking his business else- where and still must allow the smelter a profit. Assay results, likewise, must satisfy the shipper, but if they show too high a metal content for the ore they represent, the smelter will actually lose money. It is always considered, and constant checks through umpire assays prove, that laboratory results are closely correct, so the bur- den of the plant profit and loss and the satisfaction of the shipper rest squarely upon the sampling department.

Jan 1, 1936

By A. T. Miesch, L. B. Riley

Distribution of minor elements in sandstone-type uranium deposits of the Colorado Plateau is being studied by the USGS on behalf of the A EC. A primary objective has been to provide basic data which could be useful in geo-chemical exploration for new deposits. The basic statistical measures — similar to those used in sedimentary petrology—are described. The underlying principle is that the frequency distributions fit or approach the log-normal form. Since 1952 the U. S. Geological Survey on behalf of the U. S. Atomic Energy Commission has conducted a study of the distribution of minor elements in sands tone-type uranium deposits of the Colorado Plateau. A primary objective in this study has been to provide basic data which could be useful in geo-chemical exploration for new deposits. Among the basic data considered important are estimates of the abundance and habit of each element in the ore and in the host rocks. It has been found that a few basic statistical techniques, and variations of these techniques, are useful in this type of study. Some of the basic techniques have been used to advantage by researchers in geochemistry and in other fields of geology, especially sedimentary petrology; others have been used to only a limited extent. Among the latter is the linear correlation coefficient, which has proved useful in assessing the element associations in a particular rock type without analysing individual mineral separates. In computing the basic statistical measures a scale has been used which is, in some ways, similar to the phi ($) scale used by sedimentary petrol-ogists in grain-size studies.&apos; FREQUENCY DISTRIBUTIONS It has been recognized for some time that the results of analyses for a given minor element in a suite of samples of rocks or ores yield frequency distribution curves which are approximately normal when the curves are plotted on logarithmic or geometric scales. In other words, the analytical results give an approximate lognormal frequency distribution. A classical example is given by D. G. Krige2 in the study of the distribution of gold values from a mine on the Witwatersrand. Another example is shown in Fig. 1, the distribution of barium concentrations in samples of uranium ore from the Chinle formation. The geochemical data are analogous to grain-size data gathered by the sedimentary petrologist. Both types of data, after simple logarithmic transformations, may be treated by conventional statistical methods based on the normal distribution. This is not to say that other types of transformations may not serve equally well or better for particular element distributions.3 Spectrographers and other analysts are quite aware of the dependence of their precision on the concentration of the element present.4 For example, in the part per million range the variation may

Jan 1, 1961

By Carl Henrich

Jan 1, 1893

Jan 1, 1969

By Steven Mitchell

BACKGROUND Homestake Mining Company began milling operations at the Bulldog Mountain Mine near Creede, Colorado in 1969. The Bulldog Mill, rated at 350 tpd, produces a bulk flotation condentrate assaying about 180 oz/T Ag and 20% Pb, from heads of about 16 oz/T Ag and 2% Pb. The circuit is straightforward with two-stage grinding to 1-5% plus 65 mesh, followed by rougher and cleaner flotation. Reagents used are Z-6, Z-11, Aerofloat 242 and Aero Promoter 404, with an Aerofroth 65-MIBC mixture for a frother. Additional information on the geology, mine and mill are available in references (1) and (2). A flow sheet for the mill and CIP plant together is attached as Figure 1. Final flotation tailings normally vary from 1.5 - 2.0 oz/T Ag. These tailings are cycloned to produce sand for underground backfill. After cycloning, the sands are repulped and given a final scavenger float. This sand scavenger recovers a small additional amount of silver which recycles back to the main flotation circuit. The tailings are recycloned and pumped to the mine or, if the mine cannot accept sand, to tailings. The majority of the silver in the flotation tailings exists in the fine fractions; cycloning upgrades the slimes and lowers the assay of the sand. The sand, after scavenging, typically assays 0.5 oz/T Ag, and the slimes assay about 3.0-3.5 oz/T Ag. From 1969 to 1976 all of the slime tailings and the sand tailings not used underground were impounded in a tailings pond located about

Jan 1, 1983

By T. C. M. Pillay, John Chipman

The Si-0 equilibrium in liquid iron was investigated in some detail by Gokcen and Chipman1 who reported equilibrium constants of the following reactions: In each case the thermodynamic equilibrium constant K was obtained by extrapolating K&apos; to infinite dilution. Their results on reaction [I] were consistent with those of earlier observers, and there seems to be little doubt as to the approximate validity of the equilibrium product determined. On the other hand, the results on reactions [2] and [3] indicated unusual curvilinear relationships between the activity coefficients of silicon and of oxygen and the silicon concentration. Since a linear relation is observed in all other similar instances, it was concluded that some source of error had affected the gas-metal equilibrium relationships. Recently the authors undertook a restudy of these equilibria with the view especially to establishing the equilibrium constant of reaction [2]. Their experiments, however, were discontinued before a tbroughly satisfactory answer had been obtained and consequently have remained unpublished until the present time. Quite recently Matoba, Gunji, and Kuwana2 published the results of a very thorough study of these equilibria. It is the purpose of the present note to Compare these three sets of experimental data, a comparison which leads to Confirmation of the results of Matoba and coworkers. The experimental arrangements described by Dutilloy and Chipman were employed. A controlled mixture of Hz, H,0, and argon was led into the induction furnace over the surface of the Fe-Si melt contained in a silica crucible. On account of the slow approach to equilibrium, runs were continued for at least 8 hr and, in some cases, as much as 12 hr. Samples were taken by means of silica tubes at the start and during the final 4-hr period of each run. Out of twelve runs only seven appeared to have approached equilibrium with sufficient certainty to be reported here. The results of these experiments, all at 1600°c, are shown by the triangles in Fig. 1. Equilibrium was approached from both oxidizing and reducing conditions and the direction of approach is indicated by the shape of the triangle. Attempts to extend the study to higher silicon concentrations were unsuccessful on account of the transfer of silica from the metal bath to the upper portions of the crucible by means of a silicon-monoxide mechanism. Matoba, Gunji, and Kuwana used similar methods and approached equilibrium from both sides. Their results at three temperatures are shown by the solid lines of Fig. 1. A line corresponding to 1600 deg is interpolated from their equations and is shown by the dotted line. The results of Gokcen and Chipman at 1600 deg in the range 0.02 to 2.0 pct Si are also shown. At concentrations up to about 0.6 pct Si, these investigators approached equilibrium from both directions, and their results in this range appear to be trustworthy. Above 1 pct Si, however, all of their experiments involved oxidation only, as shown by a decrease in the silicon content of the bath. It now seems certain that they failed to reach equilibrium at these higher silicon concentrations and that the curvilinear relation shown by their results is incorrect. It is evident that their results in the lower silicon range are in good agreement with those of Matoba and coworkers. In fact, a straight line drawn through their results would parallel the dotted line and would differ from it by only 0.05 in log K. The new data also lie close to that line. It may thus be concluded that the three sets of data are in good agreement and that the equations proposed by Matoba and coworkers for reaction [2] are satisfactory . They take the limiting value of log K&apos;, at 0 pct Si as log K ,. The slope of each line gives the value

Jan 1, 1962

By G. Y. Chin, W. L. Mammel

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain has been analyzed by Taylor and by Bishop and Hill. The Taylor analysis is based on a principle of&apos; virtual work, and involves finding, among numerous cotnbinalions of slip systems that satisfy the imposed strain, the combination in which the sum of the glide shears is a minimum. Previously, Taylor has treated the case of axisymmetric flow when slip occurs on (111)(110) (or {110)(111)) systems only. His analysis has now been extended by computer methods to the cases of slip on {112}(111) and {123)(111) systerns and of mixed slip on {110), {1 12), and (123) planes with a common (111) slip direction, all of which are important in the deformation of bcc crystals. The results are computer-plotted as contours of the ratio of the floe strength to the critical resolved slzea-r stress for slip, for axial orientations distributed throughout the standard stereographic triangle. Implications of the computer results to texture develop,merit, texture hardening, and dislocation theories oj work hardening are discussed. WhEN a single crystal is extended in the usual tension test, the lateral dimensions can change relatively freely. In this case, the glide shear produced by slip on a single slip system is sufficient to accommodate the (tensile) deformation. Since slip is governed by a critical resolved shear stress law (the Schmid law&apos;), the single active slip system is one for which the stress, resolved on the slip plane and in the slip direction, is the highest among the several equivalent slip systems. This amounts to saying that a value M = U/t = y/~ is a minimum among the equivalent systems, where M is the inverse of the familiar Schmid factor (a and E refer to tensile stress and strain, and T and y refer to resolved shear stress and shear strain). A grain embedded in a polycrystalline aggregate, on the other hand, cannot freely change its shape due to constraint from its neighbors. In this case, slip from five independent slip systems (to accommodate five independent strains) is generally required.&apos; Based on the principle of virtual work and assuming that the critical resolved shear stress for slip is the same for all systems, Taylor hypothesized that, among all combinations of (five) slip systems which are capable of accommodating the imposed strain, the active combination is that one for which the sum of the absolute values of the glide shears is a minimum. Again, this is equivalent to saying that the value of M = CjlyjI/ is a minimum, in analogy to the single slip case. Taylor aminimum,analyzed the case of {111)(110) slip for fcc metals, and applied the analysis to crystals undergoing axisymmetric flow, that is, the same macroscopic shape change as the poly crystalline aggregate under uniaxial tension (or compression). For the twelve equivalent {111}( 110) slip systems, there are 384 independent combinations of selecting five systems to satisfy the five independent linear equations of imposed strain.4 Taylor calculated the value of M for each combination* and obtained the active com- *A number of the independent combinations were omitted from consideration in Taylor&apos;s original work (see Ref. 5). bination (minimum M) for a number of axial orientations distributed throughout the standard stereographic triangle. Later work by Bishop and Hill*&apos;8 showed that Taylor&apos;s least-shear hypothesis was equivalent to a maximum work principle which they advanced. Using the simplified Bishop and Hill method for {111)(110) slip, Hosford and Backofen&apos; obtained detailed contours of constant minimum M for the same axisymmetric flow case. In contrast to {111}(110) slip in fcc metals, slip in bcc metals is generally described as occurring on {ll~)(lll), {112)(111), {123) (111) systems as well as mixed slip composed of all three. Since the direction cosines of the slip plane normal and the slip direction enter as a product in the Taylor analysis, the Taylor solutions of ,M for {110)(111) slip are identical to those for { 111} 110) slip. The other three cases of slip, however, have not been solved. In view of the numerous combinations of slip systems involved in the calculations, the Taylor analysis is clearly oriented toward computerized solutions. THE TAYLOR ANALYSIS In order to obtain the active combination of (five) slip systems by solving for the minimum value of M = we first express the (small) strain components E,, with respect to the cubic axes 1, 2, 3 ([loo], [010], [001], respectively) of the crystal, in terms of the sum of the glide shears yj from slip systems j: where n, and n,j refer to direction cosines of the slip plane normal, and dri and dsi to direction cosines of the slip direction, of slip system j, all referred to the cubic axes. In practice, the strain components are given with respect to the specimen axes X, y, 2. These components are readily converted to ers through the tensor transformation where irk and 1,~ are the direction cosines between the two sets of coordinate axes.

Jan 1, 1968

Jan 1, 1968

By RUSSELL C. FLEMING

GILSONITE is a brilliant black, tarry-like bitumen, classed technically with glance pitch and graharnite as an asphaltite. As found it is brittle, breaking much like ice, and has a conchoidal fracture. Purest forms are used in the manufacture of paints, varnishes, electrical irisulatiorl, and inks for rotogravure; molded articles such as switch handles, telephone mouthpieces, and but- tons are made from the intermediate grades, and the poorer grades are used for the saturation of felt. According to the U. S. Bureau of Mines figures, production grew from about 4000 tons mined in 1904 to 55,000 tons in 1929. This asphaltic substance is found only in the Uintah basin in northeastern Utah, in veins over a wide area. Veins in the vicinity of Fort nuchesne were first discovered about 18G2, on what was then the Uintah Indian reservation, and the vein matter was originally called Uintaite because of that fact, In the early days, S. H. Gilson. of Salt Lake City, was so persistent and zealous in his efforts to develop the deposits and find a market that the name gilsonite was given to the material. Later, the wider and more renowned wins near Wayson and Dragon, in extreme eastern Utah, became the main supply.

Jan 1, 1932

By C. W. Spencer, J. T. Smith

GRAIN-BOUNDARY surfaces are penetrated by a liquid phase when the liquid-solid interfacial tension is less than one-half the tension of the grain-boundary surfaces. Grain growth may occur in the presence of this liquid phase. burke1 reports that grain growth of this nature has been observed in two-phase ceramic systems. He suggests that the presence of a grain-boundary liquid may accelerate or decelerate the

Jan 1, 1963

By J. H. Frye, J. W. Caum, R. M. Treco

IT has been suggested that: "Insofar as the hardening due to a solute depends upon the increase of lattice parameter produced by it, it is reasonable to suppose that this hardening might be related to the resistance which the pure solvent would offer to increase in its parameter."&apos; It was further suggested that this hypothesis might be examined by comparing the hardnesses of analogous silver and copper alloys, since the stress necessary to produce a given lattice expansion is quite different in the two metals. Suitable data2,3,4 are now available on these alloys, and we shall proceed to an examination of the hypothesis quoted above. Hardness, Lattice Parameter and Ionic Overlap Increase in ultimate Meyer hardness has been plotted against increase in lattice parameter in Figs. I and 2. It is believed that most of the values are accurate within the limits indicated by the rectangles. These data are also presented in Table I. Ultimate Meyer hardness, P u, is defined by the equation: where L = load, D = diametei of an impression having the same diameter as the testing ball, which in this case is 4 mm. Increase in lattice parameter is defined as the difference between the lattice parameter of the solid solution and that of the pure solvent. The curves in Figs. I and 2 are based on equal solute concentration and an equal degree of plastic deformation pro duced by the testing ball. Hardnesses are corrected to a constant grain size for copper and silver alloys, respectively, and these two grain sizes are approximately equal. Furthermore, all solutes are from the same period of the B subgroup of the periodic table as their solvent. The question arises as to whether Or not lattice parameter is the only factor controlling the hardness of these alloys. There

Jan 1, 1943