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By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By Axel Hultgren

In ingots of silicon-killed carbon steel-made without addition of aluminum, transparent spherical or nearly spherical inclusions, up to about 0.15-mm diameter, are generally present. They may be glassy or crystallized, wholly or partially In steels of high carbon contents they consist of silica,4,12 in steels of lower carbon contents and, in consequence, higher oxygen contents, of iron-manganese-silicate with higher iron and manganese contents the lower the carbon content. Small silicate inclusions, about 0.01 mm or smaller, may occur, just as sulphide inclusions do, in portions that have been the last or nearly the last to freeze,l0,12,17 this location being verified by primary etching.10 Hence, it may be concluded that they have separated from liquid steel that has become enriched in oxygen through segregation during freezing. Silicate inclusions with a diameter larger than about 0.02 mm appear, at least in ingots of moderate size, to be distributed at random in relation to the primary structure and therefore may be assumed to have existed as droplets in the liquid steel before freezing started at the point in question. The average size of such large inclusions has been found to increase toward the axis1' and their amount to increase from the top downward in the axial region.2,10 It has been assumed that this accumulation is a result of the droplets being brought down by the slowly settling metal crystals.2 It has been suggested that large silicate inclusions generally form,6 or may form,'' by coagulation of smaller ones, or by small drops being caught by larger ones during the rising of the latter.9 The occasional occurrence of a large inclusion surrounded by a swarm of small ones has been taken as a proof of this mechanism but, as suggested later, may be explained in another way. It has been pointed out that an inclusion droplet in the liquid steel may grow at the expense of an adjacent one, which implies diffusion of soluble inclusion-forming elements in the liquid steel.'= Further, it has been pointed out that, on cooling in ladle or mold, the metal-silicate equilibrium is displaced in the direction of separation of silicate. Thus inclusions may grow in size and amount.2,3,8,12,13,17,19,20 The exposure of the liquid steel to the oxygen of the air during tapping and pouring, and the consequent reaction, has been mentioned as a source of the formation of inclusions19.20 but this possibility has not received particular attention. Further, the admixture of furnace slag during tapping1 or of refractory material from various sourcesl,20 has been considered. The inclusions due to the latter may be recognized, however, through their resistamce to hydrofluoric acid, imparted by the alumina content. Silicate inclusions are often referred to as the natural and inevitable product of reaction on adding silicon or silicon

Jan 1, 1949

By Axel Hultgren

In ingots of silicon-killed carbon steel-made without addition of aluminum, transparent spherical or nearly spherical inclusions, up to about 0.15-mm diameter, are generally present. They may be glassy or crystallized, wholly or partially In steels of high carbon contents they consist of silica,4,12 in steels of lower carbon contents and, in consequence, higher oxygen contents, of iron-manganese-silicate with higher iron and manganese contents the lower the carbon content. Small silicate inclusions, about 0.01 mm or smaller, may occur, just as sulphide inclusions do, in portions that have been the last or nearly the last to freeze,l0,12,17 this location being verified by primary etching.10 Hence, it may be concluded that they have separated from liquid steel that has become enriched in oxygen through segregation during freezing. Silicate inclusions with a diameter larger than about 0.02 mm appear, at least in ingots of moderate size, to be distributed at random in relation to the primary structure and therefore may be assumed to have existed as droplets in the liquid steel before freezing started at the point in question. The average size of such large inclusions has been found to increase toward the axis1' and their amount to increase from the top downward in the axial region.2,10 It has been assumed that this accumulation is a result of the droplets being brought down by the slowly settling metal crystals.2 It has been suggested that large silicate inclusions generally form,6 or may form,'' by coagulation of smaller ones, or by small drops being caught by larger ones during the rising of the latter.9 The occasional occurrence of a large inclusion surrounded by a swarm of small ones has been taken as a proof of this mechanism but, as suggested later, may be explained in another way. It has been pointed out that an inclusion droplet in the liquid steel may grow at the expense of an adjacent one, which implies diffusion of soluble inclusion-forming elements in the liquid steel.'= Further, it has been pointed out that, on cooling in ladle or mold, the metal-silicate equilibrium is displaced in the direction of separation of silicate. Thus inclusions may grow in size and amount.2,3,8,12,13,17,19,20 The exposure of the liquid steel to the oxygen of the air during tapping and pouring, and the consequent reaction, has been mentioned as a source of the formation of inclusions19.20 but this possibility has not received particular attention. Further, the admixture of furnace slag during tapping1 or of refractory material from various sourcesl,20 has been considered. The inclusions due to the latter may be recognized, however, through their resistamce to hydrofluoric acid, imparted by the alumina content. Silicate inclusions are often referred to as the natural and inevitable product of reaction on adding silicon or silicon

Jan 1, 1949

By A. G. McGregor

IN THE Southwest a number of large steel chimneys discharge the gases from the copper smelting furnaces. Some of these chimneys show no deterioration after twenty years, others show serious deterioration after tour years service. A steel stack 20 ft. 7 ½ in. (6.3 m.) in diameter by 279 ft. (85 m.) high, Fig. 1, used for roaster gases only at the Calumet & Arizona Mining Co.'s plant at Douglas, Ariz., was lined to the top of the bell, 40 ft. (12 m.) from the base, with common brick placed on end, lime and cement mortar being used. Above the bell, the stack was lined with 4 by 4 by 8 in. (10 by 10 by 20 cm.) building tile, placed on end, making a lining 4 in. thick. The tiles were supported on angle-iron rings, riveted to the inside of the chimney shell about 15 ft. apart. The chimney was put into use in the latter part of 1913. Four years later, considerable of the tile lining had fallen out of place and mixed with the flue dust at the bottom of the chimney. About a year later, several . flattened and distorted sheets were noticed about 70 ft. below the top. An investigation showed that the thickness of these distorted sheets, which was originally ¼ in., had been reduced one half. One year later, or six years after the chimney went into use, several holes, a square foot and smaller in area, appeared near the flat spots mentioned. Soon afterwards, when the chimney was shut down for repairs, it was found that most of the tile lining for 125 ft. from the top had fallen out and that the steel shell was badly corroded; but where the lining remained in place the shell was undamaged. Many of the tile which had fallen out of place had become soft or flaky and crumbling, others were as hard as when placed. An analysis of the hard and soft tile is shown on p. 2. These tile were of a fireclay mixture, and were used instead of common brick on account of lower cost. The steel forming the upper 125 ft. (38 m.) was replaced, and a 4 ¼ -in. (11-cm.) lining of firebrick was laid from the bell to the top of the chimney. The brick were placed on end, wedges and keys being used. After each 8-in. course was set, keyed, and wedged tight, thin mortar -water, sodium silicate, and finely ground silica-was worked into the joints. The brick are supported on angle-iron rings, every 15 ft., in the same way as the tile.

Jan 1, 1921

By J. L. Keats

IN THE literature on the elimination of metalloids in basic open-hearth practice, there are a great many heats recorded in which excellent data on changes in slag and metal composition during refining are given, but in almost all of these heats either temperature data or weights and analysis of charge are unrecorded and observations on the physical characteristics of the slag are almost always lacking. With these points in mind, a test heat was made in which as complete as data possible on all the factors that affect the elimination of metalloids were obtained. THE TEST HEAT The test heat was made in a standard 100 ton stationary furnace at the Lackawanna Steel Co., Lackawanna, N. Y. on January 17, 1922. The Charge-Scrap.-The scrap consisted entirely of rail-heat butts, selected from a number of heats made, the week before the test. The average analysis of the scrap was calculated from the analysis of these heats-and from the weight of scrap from each heat. Pig Iron.-Two ladles of pig iron were used in the charge and two samples were taken from each ladle as it was poured into the furnace. These four samples were composited for the average pig-iron sample.

Jan 2, 1926

By W. Chubb

By measuring the hardness of metals at temperatures just above and just below their allotropic change point, it has been established that crystal structure has a real effect upon the strength of metals. The DPH of cobalt, iron, titanium, uranium, and zirconium have been measured at temperatures up to 1000°C. It was found that the body-centered-cubic crystal structure is always the softer structure when it is involved in an allotropic transformation. The close-packed and more complex structures are inherently harder, and may be expected, therefore, to be better base materials for high strength alloys. IT has been observed that for metals with nearly the same melting point (i.e., tin and lead, magnesium and aluminum) the metal with the more complex crystal structure has a higher tensile strength and hardness. It might be asked whether this effect is really caused by the difference in crystal structure; and, if so, just what is the contribution of crystal structure to the strength of these metals. A qualitative answer to these questions can be obtained by measuring the change in hardness produced by the change in structure in metals exhibiting allotropic forms. The evidence for changes in mechanical properties during allotropic transformations is rather meager. In 1909, Rosenhain and Humfrey' observed that "ß" iron showed much less deformation at the transformation temperature than a iron. By means of a torsion test, Lee found that iron bars were "critically plastic" at the a-7 transformation temperature. Sauerwald and Knehans have shown that the dynamic hardness of iron increases between 900" and 1000°C. In 1930, Albert Sauveur' presented data on the hardness, tensile strength, and torsional strength of pui-e iron up to 1000°C. He concluded, "At 900°C, the a iron transforms into y iron, and this is accompanied by increased strength and stiffness and decreased ductility." The same year, Schischokin" obtained data on the hardness of thallium at temperatures above and below its transformation temperature. His data are replotted on semilogarithmic coordinates as Fig. 1. The fact that his data fall on straight lines in this type of plot is believed to attest to the purity of his metal and the accuracy of his results. In 1941, Nadai and Manjoine" obtained tensile data on pure iron with an indicated increase in strength at about 900°C. These experiments make it quite evident that changes in mechanical properties occur when a metal transforms from one crystal structure to another; but, except for Schischokin's data on thallium, none of the measurements seem accurate enough to determine the relative magnitude of the mechanical property change. Materials The metals that have been examined for changes in hardness during transformation include l—as- deposited commercial electrolytic cobalt about 99.7 pct pure, 2—Armco ingot iron, 3—are-melted iodide titanium of a purity in excess of 99.8 pct, 4—uranium of a purity in excess of 99.5 pct, 5—are-melted iodide zirconium of a purity in excess of 99.8 pct, 6—annealed, 0.08 pct C, rimmed steel, and 7—commercially pure RC55 titanium. While the purity of the first five of these materials leaves something to be desired, it will be noted that the observed hardness discontinuities occurred at the accepted transformation temperatures. (These temperatures are indicated by vertical arrows in Figs. 1 and 3 through 7.) The last two materials are commercial alloys introduced to show the effect of minor alloying elements upon the hot hardness curve. Apparatus Hardnesses at elevated temperatures were determined by means of a vacuum hot hardness machine. A diagram showing the basic features of this machine appears as Fig. 2. This machine is essentially a deadweight hardness .machine in a furnace within a vacuum chamber. The sapphire-tipped indentor

Jan 1, 1956

By W. F. Mullen, C. W. Stickler

WITH few exceptions, unit operations in the Pennsylvania slate industry in 1950 did not differ appreciably from production methods described by Behrel and Bowles2-4 several decades ago. Many traditionally picturesque but relatively inefficient hand operations continued to contribute to high operating costs in an industry in which the margin of profit, for various reasons, was admittedly low. As part of a general program in which the Pennsylvania State College has been assisting the slate industry to solve some of its problems, time and method studies were used in an effort to determine the bottlenecks of production flow. The results are as applicable to other stone industries as they are to slate. A study of the basic elements in the production of roofing slate, structural slate, and slate blackboards among selected slate producers revealed comparatively few refinements. Any marked difference in operating method was characterized largely by the available equipment, a noticeable difference in the working properties of the rock quarried by a particular company, and by either the habit thinking or ingenuity of the individual operators. With the hope that significant economies in manufacture might result, all the unit operations were broken down into elements for study and analysis. The greater part of the study encompassed those operations from the quarry rim to the finished product; however, to obtain a reasonable synthesis of time allotments per operation, several analyses of quarrying from the finish of the wire saw cut are included for reference. The complete study of quarrying made by Bowles several years ago resulted in the introduction of the wire saw into the operation; there appears to be a need for as fundamental a change in the processing of finished slate as the wire saw was in the quarrying process. Fig. 1 illustrates the flowsheet of quarried rock from the parent bed to the quarry rim with the basic elements which contribute to the difficulty of removing slate from the ground. In Pennsylvania roofing slate is produced by one of three procedures, many operations of which are quite similar. In the traditional or classical method the quarried rock is reduced by sculping and auxiliary manual treatment to workable size and then is split and dressed (trimmed to size) in the conventional shanty. Archaic as this method might appear, there are several elements that result in substantial savings over more mechanized operations. In a modified version of this method, the block is reduced by sawing and gouging preparatory to splitting and dressing in indoor stations. This method is particularly adaptable to rock which fractures unevenly by conventional sculping methods. In the third and more modern method, reduced block received from the block maker is diamond-sawed to length and finished on a production line. Fig. 2 illustrates the flow pattern in each case. In the modified and more modern plans, dressing is done on mechanically-operated trimming machines, which appreciably reduce the fatigue factor of the operator. However, it should be noted that it is advantageous for the operator to be able to control the speed of the knife to prevent breakage of certain classes of stock. In the classical plan the splitter and dresser normally act as blockmakers also and carry their eighter slabs (equivalent in thickness to eight shingles) into the shanties themselves, all of which adds to fatigue and reduced efficiency. The extremely low investment and operating expense of the classical method has undoubtedly been of paramount importance in its continuation. Production of Mill Stock The production of mill stock is accomplished by less picturesque methods than enter into the production of roofing slate but it is, in the main, relatively more efficient because of the increased use of machinery for handling and for finishing. Mill stock can be classified into two categories as far as difference in production method is concerned: structural slate and blackboards. The significant difference in operation is caused largely by the nature of the rock used for each product with the best and easiest cleaved rock being reserved for blackboards to permit the splitting of large slabs to as little as 1/2 in. in thickness. Structural stock, on the other hand, is split into panels no thinner than 11/2 in. and

Jan 1, 1952

By J. B. Fisken

(Butte Meeting, August, 1913.) BEFORE touching upon the immediate subject of this paper a few facts of a historical nature as to the general application of electricity to mining might be of interest. As to what was actually the first application of electricity to mining, opinions will no doubt always differ. My experience does not go back far enough, nor are the records to which I have had access of any value as covering this point. Sydney F. Walker, a man whose pioneer experience in the application of electricity to mining purposes dates back as far as 1876, ,gave an interesting resume of the subject in an address before the South Wales branch of the Association of Mining Electrical Engineers at its 1.913 session, and, unless his statements are shown to be wrong, they should be accepted as facts. According to Mr. Walker, the ignition of charges of blasting powder was the first operation in mining to be accomplished with the aid of electricity. Very frequently this energy was furnished by a static machine and occasionally by a magneto generator. Later, this was followed by the application of electricity to bell signals, and we are told that this application was looked upon skeptically and regarded as an expensive experiment by the mining managers of those early days. At the Paris Exposition of 1878, there was exhibited an electric lamp, which suggested future possibilities to the mining engineers of those days. The first successful application of electric lighting to underground excavations that I have been able to find any record of is that of M. Blavier. In the year 1879' he installed two Serrin lamps and successfully illuminated one of the large underground chambers in the Angers slate quarries. Another early application of electricity to the lighting of mines is that in the large chambers in the salt mines of Maros-Ujvár, in Hungary; these have been regularly and successfully lighted elec-

Jan 6, 1913

By Walter B. Devereux

Metallic copper is a product of native metallurgy in various parts of Mexico, and by somewhat varied processes. While recently examining copper mines in the State of Jalisko, I had an opportunity of witnessing Mexican copper smelting by a process which I have not seen described, and which is interesting from the fact, that a fine quality of copper is produced from sulphurous ores in three metallurgical operations, and apparently without excessive loss. The process was carried on in buildings which were part of a plant erected by an American more than twenty-five years ago for the purpose of smelting and working copper. After a few years this man met with accidental death, and the works have been but little used since. Located in the centre of a high range of mountains, far from any town or seaport, and inaccessible except over difficult mule trails, these substantial buildings, filled with furnaces and heavy machinery,

Jan 1, 1883

By N. Brown

From the theories of flow and fracture it is shown that the difference in reciprocals of the transition temperatures (OK) is a quantitative measure of temper ernbrittlement. Experimental data are given which support this conclusion. STUDIES of temper embrittlement have been made with various viewpoints; some involved a study of the kinetics of the reaction,',2'" others were concerned with changes in the mechanical properties," . and still others investigated the structural differences between the embrittled and unembrittled states by means of the microscope," -ray ,' measurements of electrode potential," and electrical resistivity." In all these studies, the difference in impact properties was the criterion for distinguishing between the embrittled and unembrittled states. By common agreement the difference in transition temperatures is now taken as a measure of the degree of embrittlement, and this measure is used as the quantitative measure upon which studies of the phenomenon are based. Vidal and Jolivet"' suggested that the degree of embrittlement was the same whether measured by impact or by a slow bend test. Their conclusion was based on tests at constant temperature. Jaffe and Buffum" using the impact and slow bend test showed that, for a given degree of embrittlement, the difference in transition temperatures varied with the method of testing. Hultgren and Chang" showed that the difference in transition temperature produced by the V-notched Charpy impact test was not the same as the value produced by the keyhole-notched impact test. This is a very fundamental point because there can be no true measure of temper embrittlement unless it is invariant with respect to the test method. Theory The purpose of this analysis is to show how the transition temperature depends on the stress distribution and the state of the material. The criterion for fracture may be stated as follws: where iF is some function of the principle stresses and F is a critical condition depending on the state of the metal. Similarly yielding occurs when Where is another function of the prin-ciple stresses and Y is a critical value depending on the state of the material. There is some controversy as to the exact form of the function f,.(u,, u,, us) but most experimental data give the following criterion:= where 8, and 6, = 21 or 0. Combinations of 6, and 8, give the various criteria such as the normal stress, the hydrostatic tension, and the maximum shear stress laws. Agreement is general that the octahedral shear stress law adequately describes the yield condition. where the bracketed factor will be called the design factor and depends on the stress distribution. Whether the metal decides to yield or fracture is given by the condition that The effect of temperature and strain rate upon Y has been studied by various investigators, It has been shown by MacGregor and Fisher" that

Jan 1, 1955

By B. D. Cullity

A distribution of residual stress after plastic elongation is proposed, in which the bulk of the material is strained in compression and a very small portion in tension, This distribution is shown to account both for the X-ray observations and for the effect of plastic straining on magnetic losses in silicon steel. The regions left in compression are tentatively identified with the interiors of the sub-grains revealed by the electron microscope. THIS paper is concerned with the general problem of the nature of the residual stress which is produced in metals by plastic elongation. A particular stress distribution will be suggested which accounts for the main X-ray diffraction observations which have been made. It will also be shown that certain magnetic measurements made on silicon steel can be understood in terms of this stress distribution. X-RAY OBSERVATIONS Uniform straining of a crystal lattice (macro-strain) causes a diffracted X-ray beam to shift its position, and nonuniform straining (microstrain) causes line broadening. If a bar of metal is plastically elongated in the longitudinal x direction and then unloaded, diffracted X-ray lines are observed to be both shifted and broadened.'-= Although the observed line shift indicates the presence of macro-strain, experiments have shown that no macrostrain, in the usual engineering sense of the term, exists.5"7 For example, removal of a layer from one surface of a stretched and unloaded bar does not produce curvature in the remainder of the bar 5'7 Fig. 1 shows the variation of lattice strain in the x direction, as determined from X-ray line shifts, with the applied stress in the same direction. The curve ABC is the normal stress-strain curve of the material, AB being the elastic portion and BC the plastic. In the elastic region AB, the strain measured by X-rays, called the lattice strain, and the strain measured mechanically are both proportional to the applied stress, and both return to zero when the applied stress is removed. Above the elastic limit the lattice strain would be expected to continue to increase along the line BD. Actually, it increases less rapidly with respect to stress, or even decreases, as shown by BE. If the applied stress is then decreased, the lattice strain decreases along EF, which is parallel to AB. As a result, there is a compressive residual lattice strain FA after unloading. STRESS DISTRIBUTION. Since a stretched and unloaded bar does not contain macrostress, it follows that the observed line shift must be due to a special distribution of mi-crostress. Such a distribution is shown in Fig. 2, which shows the variation of the stress u, across a stretched and unloaded bar. The material is assumed to consist of two kinds of regions: regions C, stressed more or less uniformly in compression, comprising the bulk of the volume of the material and responsible for the observed diffrac-

Jan 1, 1963

By N. A. Gokcen, John Chipman

D. C. Hilty (Union Carbide and Carbon Research Laboratories, Niagara Falls, N. Y.)—This paper is a very nicely detailed analysis of a difficult problem. I would like to point out that the results that Mr. Crafts and I published a few years ago had no reference to activity, or anything else of a similar nature; our results were strictly empirical. It is quite gratifying that we now have a case where results involving activity coefficients and results derived from direct observations on actual steel melts are practically identical. When two different laboratories, working from two entirely different approaches, come out with results in such good agreement in their major significance, that is an achievement. It is something that was not possible 15 or 20 years ago. There is one question I would like to ask Dr. Chip-man. It has to do with a very minor point of disagreement in these results. When we reported the kink in the Si-O solubility curve I think you may recall that it came at the different temperature levels at about the order of 0.015 to 0.03 pct 0 and 0.03 to 0.07 pct Si—we also pointed out that we had difficulty in obtaining data at that level, although we finally did get some. I note in going through the data for the present paper, that there are no samples in those particular silicon and oxygen ranges. I wonder if that was purely accidental or was there a reason for it. D. E. Babcock (Republic Steel Corp., Youngstown, Ohio)—Mr. Hilty, do you have any explanation for that discrepancy between Dr. Chipman's curve and your own Mr. Hilty—Our explanation for it at that time was that for some reason our system probably was not in true equilibrium with SiO, that is, in equilibrium with the silica crucible at that level. We did observe, however, that that was the level at which both the metal and the slag became saturated with SiO,. On the average, in studying inclusion formation in small ingots permitted to solidify normally from the molten state, we observed pure silica inclusions at silicon contents over about 0.05 pct and FeO type inclusions at silicon

Jan 1, 1953

By Barry S. Epstein

Financing the acquisition of a going coal mine operation has not had the exposure other finance-oriented projects have had. Therefore, C.I.T. feels that coal mining people and financial people should improve their understanding of the factors involved in this important type of acquisition. The discussion consists of two major subjects: analysis of the acquisition of the property, and sources and terms of funding the acquisition. Source and Terms of Funding There is a need to keep the competent medium-sized independent operator in the coal business, especially in these times of energy shortage. The creation of a resale market for coal mines encourages new investment in the coal mining business by medium-sized operators and their financial backers. Who provides debt and equity financing to acquire going coal mine operations and on what terms?

Jan 9, 1975

By A. H. Daane, R. L. Myklebust

The yttrium-manganese system has been investigated by thermal, metallographic, and X-ray diffraction methods. There are three intermetallic compounds present: YMn2 which melts congruently, YMn4, which undergoes syntectic decomposition, and YMn,, which undergoes peritectic decomposition. The compound YMn4 is ferromagnetic at room temperature with a Curie temperature of 214°C. There are eutectics at 25.2, 60.9, and 82.0 wt pct Mn which melt at 878°, 1100°, and 1075°C, respectively. Crys-tallographic data are given for YMn4, and YMn12 . The terminal solid solubilities are low. In a general program of study of yttrium metal in this laboratory some alloy systems of this metal with elements of the first transition period have been examined. This work was originally instigated by experiences in cladding yttrium with jackets of some protective metals such as Inconel for high-temperature service in air.' In some cases a low-melting phase was observed to form between the Inconel and the yttrium resulting in failure of the samples. In characterizing this reaction, a survey was made of the systems of yttrium with chromium, manganese, iron and nickel,, and it was found that a eutectic was formed between these metals and yttrium on the yttrium-rich side of the system. This present study of the Y-Mn system was carried out to examine in more detail the alloying nature of yttrium, and to correlate trends that have been observed in previous related studies. It was observed by Voge13 that in the systems of lanthanum, cerium, and praseodymium with each of the metals in the first transition series, the tendency to form compounds diminished in the order nickel, cobalt, and iron while no compounds were formed with manganese, chromium, or titanium. Beaudry and Daane4 observed a similar behavior in the systems of yttrium with some members of the first transition series except that the tendency for compound formation was greater. Both the Y-Ti5 and Y-Cra systems consist of simple eutectics, while in the Y-Fe,7 Y-CO, and Y-Ni4 systems, there are four, eight, and nine compounds, respectively. In addition to the above trends, the similar atomic radii and electronegativities of yttrium and thorium invite a comparison between their alloying behaviors with a common element such as manganese. In crys- tallographic studies, Florio et al.' have identified three intermediate phases in this system which are ThMn2, Th6Mn23, and ThMn,,. Gschneidner and Waber10 have examined published information on alloy systems of the rare-earth metals and have correlated this information with current alloying theory. From their study, they predicted that the Y-Mn system would contain one intermetallic compound. On the basis of this prediction, the trend in the alloying behavior of yttrium with the elements of the first transition series and the alloying behavior of thorium with manganese, one might expect from one to three intermetallic compounds to form in the Y-Mn system. A consideration of Hume-Rothery's rules of alloying based on size-factor, electronegativity, and valency suggested a small terminal solubility and possible compound formation. The present study was undertaken to confirm these predictions of low terminal solid solubility and compound formation and to establish the general alloying behavior of yttrium with manganese. EXPERIMENTAL Materials. The manganese used in this investigation was obtained from the Foote Mineral Co. as electrolytic plates of 99.9 pct stated purity; the yttrium metal was prepared in this laboratory. Table I gives the analyses of these materials. For the solubility studies at the yttrium-rich end of the alloy system, distilled yttrium, whose major impurity was 200 ppm Ti, was used. Preparation of Alloys. The alloys were formed by comelting the two metals in an are-melting furnace under an atmosphere of argon. The buttons thus formed were inverted and remelted three to five times to promote homogeneity. Due to the high vapor pressure of manganese, it was assumed that the weight lost during are-melting was all manganese. This assumption was based on the very good agreement observed between calculated compositions and chemical analyses of several alloys. The compositions of the dilute alloys used for solid solu-

Jan 1, 1962

By P. B. Liebermann

THE resistance to motion offered by mine cars is caused principally by: Rolling friction, flange friction, bending rails, bearing friction and wind resistance. With proper construction and with a fair amount of attention and care, that is, under favorable conditions, the first three items cannot be greatly improved. The wind resistance ordinarily is negligible on account of the slow speeds commonly used. The bearing friction, however, is a variable item, depending upon the design, the bearing material, the lubrication, the location (whether in wheel-hub or on car-body) and the alignment. Under the most favorable conditions the bearing friction will reach a lowest possible value. By the development of a successful anti-friction mine-car bearing this lowest value has been improved to such an extent as to affect the whole system of mine haulage. After being satisfied of their durability and certainty of operation, any investigation into the advantages of anti-friction bearings for mine cars will have to be based upon reliable information as to the saving in power of such bearings. While numerous tests have been made in this direction, the results have not always been convincing, principally because of the rather crude methods that were employed. These crude methods are the main cause of the wide variations existing in regard to the exact amount of the frictional resistance. Frequently an ordinary spring balance is used and the pull necessary to move a certain car or train of cars is obtained by a number of readings. Such spring balances necessarily have a coarse graduation and the continuous vibration and fluctuations to which they are subjected make them highly dependent upon the individual observer. Further, they must be frequently calibrated. Sometimes these tests were made without regard to acceleration, speed or even grade.

Jan 6, 1916

The following discussion occurred on the afternoon of Sept,. 22, 1930, as part of the fall meeting of the Iron and Steel Division at Chicago. About seventy-five men attended this session. C. B. Murray opened the meeting, as follows: C. B. Murray, Cleveland, Ohio.—It is very encouraging to see so many here this afternoon to discuss this important matter of beneficiation. The producers of ore, I am sure, are anxious to furnish the grade of ore that the consumer wants. The consumer sometimes wants that which cannot be economically produced and often the producer cannot understand why the consumer wants certain things. It was to bring together these two interested parties that this meeting was proposed. I was appointed the chairman of the meeting, chiefly because I happened to be the chairman of the Iron Ore Committee of the Institute. I know a little about iron ore but have not perhaps kept up with the times in blast-furnace practice. I am asking Mr. Sweetser, who is well informed from both sides, to take over the meeting and carry on the discussion. R. H. Sweetser, Columbus, Ohio.—We want to have a free discussion between the iron-ore men and the blast-furnace men as to just what we are trying to reach in the beneficiation of iron ores. Many of those present have had a great deal of experience. There are men here from the ranges who have been passing through the experimental stage of beneficiation of iron ores, and there are some who have already gone on to commercial production. We have reached the point where the beneficiation of iron ore is important to the whole iron and steel industry. The connection between iron-ore beneficiation and the cleaning of coal is so close that I think we can profit by working very close to the coal people. Some Aspects of the Iron-ore Situation W. G. Swart, Babbitt, Minn.—I was very much interested in Mr. Richards'* paper on tonnages and the 20-year life. There is one interesting thing about the ore reserves; that is, the irregular distribution of that tonnage. On the Mesabi Range, for example, the United States Steel Corpn. owns between 70 and 75 per cent. of the reserve tonnage. They ship bctween 40 and 50 per cent. of the annual Lake Superior

Jan 1, 1930

By J. L. Walter, W. R. Hibbard

A GREAT deal of work has been done on the rolling of single crystals of iron. Barrett and evensoon studied end orientations of heavily cold-rolled iron crystals and found that some crystals maintained a sharp single orientation during rolling. Others rotated into two or more orientations, and some fragmented and approached the entire polycrystalline texture depending on the original orientation of both the normal and rolling directions. Barrett, Ansel, and Mehl2 studied iron-silicon alloys and found that the addition of silicon to the iron had little effect on heavily rolled polycrystalline material. Dunn3 has extensively studied the cold-rolling and recrystallization of silicon-iron single crystals. Dunn found that for single crystals having initial orientation between (110) [001] and (111) [112], the principalcomponent of the cold-rolled texture is (111) [112]. Koh and Dunn4 studied the cold-rolled textures of single crystals having initial orientations in the range (001) [110] to (111) [IT01 and found that these are stable end orientations. They also found that all orientations having a [110] direction parallel to the transverse direction rotate to either the (001) [110] or the (111) [112] stable end orientation except for orientations near (112) [11], which divide and produce a final texture consisting of (001) [110]and (111) [112] components. Crystals having a (111) <112>-type texture re-crystallized to a (120) [001] or (110) [001]-type texture. Crystals having orientations with a range of (001) to (335) in the rolling plane and [110] in the rolling direction recrystallized5 to a wide spread of the initial orientations resulting from a multiplicity of 30-deg rotations about several (110) poles. The present study was undertaken to relate other orientations of crystals of silicon-iron to their cold-rolling and recrystallization textures, so that one might rationalize polycrystalline recrystallization data on the basis of the known deformation texture and the behavior of single crystals in these orientations. PROCEDURE Samples were obtained from a cylindrical ingot of 3 pct silicon iron prepared as follows: Armco iron was melted with high-purity silicon flakes under an atmosphere of argon to minimize oxidation. The alloy was poured into a special mold to form an ingot which consisted partially of large columnar crystals. Plates were cut from the columnar portions of the ingot with the longitudinal direction parallel to the columnar axes and ground to 0.040 in. thick. The plates were heavily etched to a thickness of 0.032 in. to remove the cold-worked surface. Orientations of seventeen crystals were determined by Laue back-reflection techniques keeping the mean columnar axis as the reference direction. The plate was then cut in two, parallel to the columnar axis. One portion of the plate was rolled at room temperature parallel to the columnar axis to a reduction in thickness of 84 pct. The remaining portion of the plate was rolled also at room temperature across the columnar axis to a reduction of 66 pct, at which point the crystals began to separate at the boundaries. After rolling, nine individual crystals were removed from the strip by cutting along the crystal boundaries with a jeweler&apos;s saw. Fig. 1 shows the original orientations of the six crystals that were straight-rolled and of the three crystals (4, 7, and 8) that were cross-rolled. Each rolled crystal was carefully etched to approximately 0.002 in. thick. Textures of the cold-rolled crystals were determined by use of the diffractometer with a non-integrating sample holder. The pole figures were made for the (200) poles using molybdenum Ka radiation and were plotted by an automatic stereographic projection recorder.&apos; Spurious poles were determined by rerunning portions of the pole figures using strontium oxide to filter out the Ka radiation. The central portions of the pole figures have not been determined. The pole figures were completed to about 55 deg from the periphery at which point the sample holder interfered with passage of the beam. Following the determination of the cold-rolled

Jan 1, 1959

By W. T. Allan

RAW bituminous coal has been in general use as a blast-furnace fuel in Scotland for the last century, and although its use has now been largely abandoned and it has been replaced by coke in the majority of the few furnaces which are at, present in blast in this country, coal-smelted pig iron is not yet a thing of the past; it is still being produced and mar-keted in competition with the more cheaply smelted product of the coke-fired furnace. Various factors have influenced this change in practice; the once plentiful deposits of coal of a suitable nature for the blast furnace are now not so easily obtainable; native blackband and clayband ironstones which are easily smelted in the coal-fired blast furnace, although still far from being exhausted, are not available except at a. cost that is somewhat higher than that of imported ores, making them unattractive to the ironmaster that is compelled by circumstances to smelt his iron at the lowest possible cost. Within the last 15 years overproduction of synthetic nitrogen has led to progressive reductions in the price of sulphate of ammonia, the recovery of which together with the other by-products before that time materially assisted in reducing the working costs of the coal-fired furnace. Now the sale of the by-products recovered yields a diminished profit. When the cost of the product is the only consideration the small, slow-smelting, coal-fired blast furnace cannot compare with its large, modern, coke-fired competitor. Other `considerations do not by any means all support the same side of the argument. In the smelting of pig iron to be used in the manufacture of steel where the quality of the final product depends so largely upon the control of the conversion process and so much less upon the physical quality of the pig iron used, the physical properties of the pig iron do not exert any appreciable influence upon the quality of the steel produced, therefore the methods employed in the smelting of the pig iron matter but little so long as the requisite chemical composi-tion is reached. On the other hand, in ironfounding where the simple melting of the pig iron, which is the only treatment it receives before being cast into its final form, does little or nothing to modify its original charac-

Jan 1, 1937

By Thomas J. O’Neil

During the past five years, the mining industry has been subjected to new operating constraints that are unprecedented in number, scope, and urgency. The industry must operate in a safer, cleaner manner, yet produce more without large price increases. Compliance with any new sweeping legislation is always difficult-and particularly so in today&apos;s adverse economic climate, which is being aggravated by the steady stream of environmental control and tax-reform programs. In effect, while government is unwittingly but surely undercutting the country&apos;s productive capabilities, it blames industry for the resulting failure to meet consumer demand. Any such real or alleged failure then brings heightened bitterness from Congress. During the recent energy shortage, for instance, threats of nationalization were ventilated in public along with proposals to abolish the mineral depletion allowance.

Jan 11, 1974