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By Carl Pierce

The writer of this article has not attempted to write a technical paper; on the contrary, he has tried to express in "steel-plant English," for steel men, a viewpoint drawn from his practice and experience. It is not his thought that it shall be taken as the "last word" in the making of this class of steel, or that good rimming steel cannot be made by any other practice. The paper was written to serve as the basis of a discussion from which it is hoped much benefit may be derived. The paper deals only with rimming steel made by the open-hearth process, and with the lower carbon steels, such as sheet and tin bar, rivet stock, skelp, etc., although good rimming steel as high as 40 to 50 carbon can be made by having good open slags and giving proper attention to working and tapping temperatures. Definition of Rimmed Steel Rimmed steel is sometimes called open or effervescing steel to differentiate it from killed or partly killed steel. It is steel made by a process which permits the free escape of gases from the metal in the molds. In passing up through the metal, the gases keep it in a rolling action from the walls of the mold inward. The top of the ingot rims in as the metal chills and the walls of the ingot get thicker, the center part remaining fluid until it reaches a pasty condition when it is covered with a cast-iron cap. The Charge In making up a charge for rimming steel, clean stock of a known composition must be selected, special attention being given to the analysis of the materials. The silicon in good rimming steel must be eliminated to a trace, therefore it is advisable to have a uniform amount going into the charge. Too much silicon gives a raw melting heat from which rimming steel is unlikely to result. For this reason a charge containing not to exceed 40 per cent. pig iron and 60 per cent. scrap, with no iron ore, is preferred to the Monell type of charge in which as high as 65 to 70 per cent. pig iron is used with a proportional amount of iron ore for the removal of the excess silicon and carbon. The silicon content of pig iron varies so much from day to day in the average blast-furnace practice that there is danger of getting too much of this element in the latter mixture when

Jan 1, 1926

By Clarence Zener

IT is customary to regard the stress-strain relation as consisting of two parts, the elastic region and the plastic region. The essential attribute of the plastic region is the presence of a permanent set, which remains upon removal of all stresses. The essential attribute of the elastic region is the absence of such a permanent set. Absence of a permanent set does not imply a linear relation between stress and strain, nor even a single valued relation. In fact, in no real metal is stress a single valued function of strain in the elastic region. The property of a solid in virtue of which stress and strain are not uniquely related in the elastic range will be called "anelasticity." The purpose of the present article is to review and correlate the past work upon the anelasticity of metals. The following paper by W. A. West124 describes investigations upon anelastic properties of iron. Many manifestations of anelasticity have been observed, the first as early as 1835 by Weber.1,2 In his experiments Weber subjected a specimen to a constant load (or deformation) for a given time, and then suddenly removed the load. He observed that most of the deformation suddenly disappeared, but that there remained a residual deformation, which disappeared only gradually with time, as is illustrated in Fig. I. The occurrence of a residual deformation which only gradually disappeared, Weber called the elastic after-effect (Elastische Nackwirkung). An extensive review of the early work upon elastic after-effects has been given by Auerbach.3 Another manifestation of anelasticity is the dependence of the elastic constants-e.g., Young's modulus upon the method of measurement. Thus, if dynamic methods are used, the measured value will depend upon the frequency of oscillation. Still another manifestation is dissipation of energy attending vibration, called damping or internal friction. One objective of metallurgical science is the understanding of the plastic and fracture properties of metals in terms of their microstructure. Through such an understanding will come the ability to design microstructure to give the desired mechanical properties. A study of an elasticity will furnish an invaluable aid in the attainment of this objective. Such studies, when properly guided, yield information regarding the relation between stress and strain in the individual components of the microstructure. In order, however, that this type of information may be obtained, it is necessary that the experimental studies of anelasticity be interpreted by the appropriate mathematical analysis. This article, therefore, starts with the mathematical formulation of anelasticity.

Jan 1, 1946

By Clarence Zener

It is customary to regard the stress-strain relation as consisting of two parts, thc elastic region and the plastic region. The essential attribute of the plastic region is the presence of a permanent set, which remains upon removal of all stresses. The essential attribute of the elastic region is the absence of such a permanent set. Absence of a permanent set does not imply a linear relation between stress and strain, nor even a single valued relation. In fact, in no real metal is stress a single valued function of strain in the elastic region. The property of a solid in virtue of which stress and strain are not uniquely related in the elastic range will be called "anelasticity." The purpose of the present article is to review and correlate the past work upon the anelasticity of metals. The following paper by W. A. West124 describes investigations upon anelastic properties of iron. Many manifestations of anelasticity have been observed, the first as early as 1835 by Weber.l,2 In his experiments Weber subjected a specimen to a constant load (or deformation) for a given time, and then suddenly removed the load. He observed that most of the deformation suddenly disappeared, but that there remained a residual deformation, which disappeared only gradually with time, as is illustrated in Fig. I. The occurrence of a residual deformation which only gradually disappeared, Weber called the elastic after-effect (Elastische Nackwir-kung). An extensive review of the early work upon elastic after-effects has been given by Auerbach.3 Another manifestation of anelasticity is the dependence of the elastic constants---e.g., Young's modulus— upon the method of measurement. Thus, if dynamic methods are used, the measured value will depend upon the frequency of oscillation. Still another manifestation is dissipation of energy attending vibration, called damping or internal friction. One objective. of metallurgical science is the understanding of the plastic and fracture properties of metals in terms of their microstructure. Through such an understanding will come the ability to design microstructure to give the desired mechanical properties. A study of anelasticity will furnish an invaluable aid in the attainment of this objective. Such studies, when properly guided, yield information regarding the relation between stress and strain in the individual components of the microstructure. In order, however, that this type of information may be obtained, it is necessary that the experimental studies of anelasticity be interpreted by the appropriate mathematical analysis. This article, therefore, starts with the mathematical formulation of anelasticity.

Jan 1, 1947

By Clarence Zener

It is customary to regard the stress-strain relation as consisting of two parts, thc elastic region and the plastic region. The essential attribute of the plastic region is the presence of a permanent set, which remains upon removal of all stresses. The essential attribute of the elastic region is the absence of such a permanent set. Absence of a permanent set does not imply a linear relation between stress and strain, nor even a single valued relation. In fact, in no real metal is stress a single valued function of strain in the elastic region. The property of a solid in virtue of which stress and strain are not uniquely related in the elastic range will be called "anelasticity." The purpose of the present article is to review and correlate the past work upon the anelasticity of metals. The following paper by W. A. West124 describes investigations upon anelastic properties of iron. Many manifestations of anelasticity have been observed, the first as early as 1835 by Weber.l,2 In his experiments Weber subjected a specimen to a constant load (or deformation) for a given time, and then suddenly removed the load. He observed that most of the deformation suddenly disappeared, but that there remained a residual deformation, which disappeared only gradually with time, as is illustrated in Fig. I. The occurrence of a residual deformation which only gradually disappeared, Weber called the elastic after-effect (Elastische Nackwir-kung). An extensive review of the early work upon elastic after-effects has been given by Auerbach.3 Another manifestation of anelasticity is the dependence of the elastic constants---e.g., Young's modulus— upon the method of measurement. Thus, if dynamic methods are used, the measured value will depend upon the frequency of oscillation. Still another manifestation is dissipation of energy attending vibration, called damping or internal friction. One objective. of metallurgical science is the understanding of the plastic and fracture properties of metals in terms of their microstructure. Through such an understanding will come the ability to design microstructure to give the desired mechanical properties. A study of anelasticity will furnish an invaluable aid in the attainment of this objective. Such studies, when properly guided, yield information regarding the relation between stress and strain in the individual components of the microstructure. In order, however, that this type of information may be obtained, it is necessary that the experimental studies of anelasticity be interpreted by the appropriate mathematical analysis. This article, therefore, starts with the mathematical formulation of anelasticity.

Jan 1, 1947

By B. Chalmers

THE practical importance of the phenomena of melting and freezing must have been recognized for a very long time. The difference between ice and water, for example, has had a profound influence on the history of mankind and the evolution of society. The possibility of melting a metal and allowing it to freeze in a mold of chosen shape has been an essential ingredient in our mastery of the art of shaping metals, and therefore in the evolution of the: machine age in which we find ourselves. The importance of melting and freezing, as applied to metals and alloys, has been so great, in fact, that empirical solutions have been found for the multitude of practical problems that have arisen. This approach has been so successful that relatively little attention has been directed to arriving at an understanding of the fundamentals of the processes. But metallurgy has come to a stage at which we may expect that some, at least, of the more complex problems that have not yet been solved (or perhaps even recognized) may be handled more effectively by scientific study, theoretical understanding, and logical experimentation than by trial and error. In this lecture, therefore, I propose to describe in outline what I think really happens when a metal freezes. In doing so I hope to explain many of the phenomena which have been observed, and in particular to account for the structures that are obtained in actual ingots and castings. The basic problem, to which this lecture represents a tentative partial answer, is this: a mass of metal, containing known proportions of various elements, is melted, heated to a given temperature, and then allowed to freeze under specified conditions. What will be the "structure" of the resulting metal? The term structure includes: 1—crystal size, shape, and orientations, 2—distribution of chemical elements, and 3-—shape, including cracks, cavities, pores, etc. The Solid-Liquid Interface We will first consider what takes place if a single crystal of a metal in the form of a rod is heated, not uniformly, but so that one end is hotter than the other. If this heating process is continued long enough, the hotter end will eventually melt; we will suppose that the rod is in a containing vessel so that the molten metal does not run away, Fig. 1. When some of the metal has melted, we have some solid, some liquid, and an interface or surface of contact between them. If the source of heat is now removed, the interface will move so that some of the liquid freezes, and if the supply of heat is suitably adjusted the interface will remain at rest. This very simple arrangement allows us to study the basic processes of melting and freezing, and if we fully understand this simple case, we may be able to account for what takes place under practical conditions where the heat does not all flow in the same direction, and where the heat flow is determined not by a controllable source of heat but by the heat capacity and temperature of metal and mold, and by the heat loss from the mold surface. The solid-liquid interface is evidently the region of the greatest interest to us; on one side of it there is crystalline solid, and on the other, liquid. In the solid, each atom has a well defined position, around which it vibrates as a result of thermal agitation. It only leaves this position in the relatively rare event of a "diffusion jump." The liquid is much less systematically organized. The atoms are about as far from their neighbors as in the solid, but the arrangement is much less systematic and is continuously changing. The solid and the liquid are represented diagrammatically in Fig. 2. The average energy of the atoms in the liquid is greater than in the solid by an amount that corresponds to the latent heat of fusion, i.e., the amount of heat that has to be supplied to convert unit mass of solid into liquid at the same temperature. The Two Processes As has recently been shown by Jackson and Chalmers,3 many of the features of the processes of freezing and melting can be understood if it is assumed that a continuous and rapid interchange of atoms between solid and liquid always takes place at a solid-liquid interface." It is necessary to con- sider two distinct processes, that of melting, in which atoms leave the surface of the solid and become part of the liquid, and the converse process,

Jan 1, 1955

By J. C. Williams

The operations described in this paper are those of the flotation plant of the Valley Forge Cement Co. at Conshohocken, Pa., and concern the use of a particular cationic reagent—namely, DP-243. The role of this reagent in this plant may be better understood by first considering the purpose of beneficiating cement rock in general and the specific problems at the Valley Forge plant. The ultimate purpose of beneficiating cement rock is to obtain a kiln feed of the desired chemical composition in a form suitable for the most efficient kiln operation. The chemical composition is governed by the type of cement to be made. Before government restrictions (the purpose of which is to simplify operations during wartime) limited the types of portland cement a manufacturer is permitted to produce, five principal types of cement were generally recognized by the industry. They are based upon chemical and physical specifications proposed by the American Society for Testing Materials, federal and other governmental agencies, state highway departments, water boards and other users of large quantities of cement. The physical as well as chemical specifications for any particular type of cement necessitate proper proportioning of the major components—that is, the silica, alumina, iron and lime—and it is necessary to establish and maintain definite limits for each in the raw mix. The manufacturer must then prepare a kiln feed of a composition that will yield a final product that will fulfill the desired specification. This step is further complicated for kilns using coal as fuel, by the amount and analysis of the ash introduced. The amount and nature of the dust lost during burning will also affect the composition of the kiln feed. The problem of preparing a kiln feed of the desired chemical composition is not a simple one, and it is the final product that governs the methods used to obtain such a feed. For example, in starting with a material deficient in lime for the mix sought, it may not be sufficient to raise it to the required lime content. The other constituents must also be present in the proper proportions. In some cases, it may be necessary to raise the lime content to a point greatly exceeding that of the final mix, then, by addition of one or more other materials lower in lime, obtain the mix. The rock used at the Valley Forge plant is a metamorphosed argillaceous limestone of the Jacksonburg formation, the same formation as that of the Lehigh Valley cement rock (which occurs approximately 50 miles north), and its oxide composition is similar to that of the latter. The only practical differences between the two are that, as a result of metamorphosis, crystallization of the Valley Forge rock is considerably coarser and it contains less carbon than the Lehigh Valley rock as well as slightly more magnesia in the form of magnesian mica. The calcium carbonate content of the various strata in the Valley Forge quarry ranges from about 65 per cent to over 85 per cent, the average for the entire quarry being somewhat under the requirement for manufacture of cement, which usually is from 75 to 76 per

Jan 1, 1947

By J. C. Williams

The operations described in this paper are those of the flotation plant of the Valley Forge Cement Co. at Conshohocken, Pa., and concern the use of a particular cationic reagent—namely, DP-243. The role of this reagent in this plant may be better understood by first considering the purpose of beneficiating cement rock in general and the specific problems at the Valley Forge plant. The ultimate purpose of beneficiating cement rock is to obtain a kiln feed of the desired chemical composition in a form suitable for the most efficient kiln operation. The chemical composition is governed by the type of cement to be made. Before government restrictions (the purpose of which is to simplify operations during wartime) limited the types of portland cement a manufacturer is permitted to produce, five principal types of cement were generally recognized by the industry. They are based upon chemical and physical specifications proposed by the American Society for Testing Materials, federal and other governmental agencies, state highway departments, water boards and other users of large quantities of cement. The physical as well as chemical specifications for any particular type of cement necessitate proper proportioning of the major components—that is, the silica, alumina, iron and lime—and it is necessary to establish and maintain definite limits for each in the raw mix. The manufacturer must then prepare a kiln feed of a composition that will yield a final product that will fulfill the desired specification. This step is further complicated for kilns using coal as fuel, by the amount and analysis of the ash introduced. The amount and nature of the dust lost during burning will also affect the composition of the kiln feed. The problem of preparing a kiln feed of the desired chemical composition is not a simple one, and it is the final product that governs the methods used to obtain such a feed. For example, in starting with a material deficient in lime for the mix sought, it may not be sufficient to raise it to the required lime content. The other constituents must also be present in the proper proportions. In some cases, it may be necessary to raise the lime content to a point greatly exceeding that of the final mix, then, by addition of one or more other materials lower in lime, obtain the mix. The rock used at the Valley Forge plant is a metamorphosed argillaceous limestone of the Jacksonburg formation, the same formation as that of the Lehigh Valley cement rock (which occurs approximately 50 miles north), and its oxide composition is similar to that of the latter. The only practical differences between the two are that, as a result of metamorphosis, crystallization of the Valley Forge rock is considerably coarser and it contains less carbon than the Lehigh Valley rock as well as slightly more magnesia in the form of magnesian mica. The calcium carbonate content of the various strata in the Valley Forge quarry ranges from about 65 per cent to over 85 per cent, the average for the entire quarry being somewhat under the requirement for manufacture of cement, which usually is from 75 to 76 per

Jan 1, 1947

By J. C. Williams

THE operations described in this paper are those of the flotation plant of the Valley Forge Cement Co. at Conshohocken, Pa., and concern the use of a particular cationic reagent-namely, DP-243. The role of this reagent in this plant may be better understood by first considering the purpose of beneficiating cement rock in general and the specific problems at the Valley Forge plant. The ultimate purpose of beneficiating cement rock is to obtain a kiln feed of the desired chemical composition in a form suitable for the most efficient kiln operation. The chemical composition is governed by the type of cement to be made. Before government restrictions (the purpose of which is to simplify operations during wartime) limited the types of portland cement a manufacturer is permitted to produce, five principal types of cement were generally recognized by the industry. They are based upon chemical and physical specifications proposed by the American Society for Testing Materials, federal and other governmental agencies, state highway departments, water boards and other users of large quantities of cement. The physical as well as chemical specifications for any particular type of cement necessitate proper proportioning of the major components-that is, the silica, alumina, iron and lime-and it is necessary to establish and maintain definite limits for each in the raw mix. The manufacturer must then prepare a kiln feed of a composition that will yield a final product that will fulfill the desired specification. This step is further complicated for kilns using coal as fuel, by the amount and analysis of the ash introduced. The amount and nature of the dust lost during burning will also affect the composition of the kiln feed. The problem of preparing a kiln feed of the desired chemical composition is not a simple one, and it is the final product that governs the methods used to obtain such a feed. For example, in starting with a material deficient in lime for the mix sought, it may not be sufficient to raise it to the required lime content. The other constituents must also be present in the proper proportions. In some cases, it may be necessary to raise the lime content to a point greatly exceeding that of the final mix, then, by addition of one or more other materials lower in lime, obtain the mix. The rock used at the Valley Forge plant is a metamorphosed argillaceous limestone of the Jacksonburg formation, the same formation as that of the Lehigh Valley cement rock (which occurs approximately 50 miles north), and its oxide composition is similar to that of the latter. The only practical differences between the two are that, as a result of metamorphosis, crystallization of the Valley Forge rock is considerably coarser and it contains less carbon than the Lehigh Valley rock as well as slightly more magnesia in the form of magnesian mica. The calcium carbonate content of the various strata in the Valley Forge quarry ranges from about 65 per cent to over 85 per cent, the average for the entire quarry being somewhat under the requirement for manufacture of cement, which usually is from 75 to 76 per

Jan 1, 1946

By Richards R. Vandervoot

T HE creep behavior of many polycrystalline metals at moderate stresses can be described by the empirical relationship: where Em is the minimum creep rate, A is a constant, a is the applied stress, E is the average elastic modulus at the test temperature, and D is the self-diffusion coefficient.&apos; This equation is generally applicable for strain rates of less than around 10-5 per sec and temperatures greater than about one-half the melting point in absolute units. Under these conditions atomic mobility plays an important role in the deformation process, and steady-state creep occurs when a dynamic equilibrium is reached between the generation and recovery of dislocation substructure. Although several theoretical mechanisms have been proposed to explain the creep of polycrystalline solids,2"4 the dislocation climb model2 is in accord with most experimental observations. The majority of creep data used to develop Eq. [1] came from metals with either the fcc or hcp crystal structures. However, on the basis of results for a and 7 iron as well as those for a and a thallium, Sherby concluded that the high-temperature deformation behavior of close-packed metals and bcc metals is probably the same.&apos; The greater creep resistance of fcc and hcp metals and alloys on a relative temperature scale was attributed to lower diffusivities in the close-packed structures. To further compare the creep properties of fcc, hcp, and bcc metals, creep data for all six bcc refractory metals were analyzed according to Eq. [I]. The results are shown in Fig. 1. The sources of information for the quantities used to prepare this figure are listed in Table I, except for high-temperature elastic moduli. The latter data were obtained from Refs. 28 and 29. The dashed lines in the figure represent the range and breadth of data analyzed by Sherby for fcc and hcp metals. In general, the deformation behavior of all of the refractory metals, ex- cept possibly that of tungsten, can be represented by Eq. [1]. This correlation is strong evidence of the similarity that exists between creep of pure close-packed metals and creep of pure bcc metals. At (Em/D) < 108, the results of Flagella and Tarr on tungsten (W-1 in Fig. 1) agree with the five-power stress law, while those of Green (W-5 in Fig. 1) show a seven-power stress dependence. Where (Em/D) > 108, the stress exponents for other data on tungsten were in the range 10 to 15. It is possible that the creep rate dependence on stress in this region is not a power law but exponential (i.e., Em - eßo). However, it was not feasible to differentiate between these two cases because of the steep slope and scatter in the data. Note the inflection point in the curve for the data of Flagella and Tarr (W-1 in Fig. 1). The slope of the line changes from 5 to around 10 at Em/D = 108. The breakdown of the fifty-power stress law at high stresses is not uncommon in other metals, and this phenomenon may result from nonequilibrium conditions in the material such as excess lattice vacancies produced by rapid straining.30 The mechanical strength of a polycrystalline metal is related to its microstructure. Attempts to establish the influence of grain size on the creep rate of metals and alloys have led to a wide variety of results. For example, the following effects have been observed: creep rate decreases as grain size increases;31&apos;32 creep rate decreases as grain size decreases;&apos;,33 creep rate is a minimum at some critical grain size and increases with either an increase or decrease in

Jan 1, 1969

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By T. P. Meloy

The behavior of slime-sized particles in a flotation cell is neither well documented nor well understood. In general, slimes (or &apos;fines&apos; as they will be alternatively called in this chapter) have been either ignored, eliminated, or treated empirically. Recently, however, some good experimental and theoretical work has been done that leads qualitatively to a clearer understanding of the problems involved. Fines are small particles that, owing to their smallness, behave differently from larger particles of the same material. The smaller the particle, the larger is its surface-to-mass ratio. The difference in the surface-to-mass ratio for a micron-sized particle and a centimeter-sized particle is 10,000 to 1. For our purposes we shall arbitrarily define any particle less than 10 µ 10-3 cm) as being a fine. This is generally considered the upper limit of colloidal-sized particles. Recently, the field of colloidal chemistry has successfully used the concept of the double layer to explain dispersion and flocculation of fine particles in a static system. Flotation, however, is a dynamic system due both to the turbulence of the liquid and to the coursing of the bubbles through the cell. Further more, a flotation system is a heterogeneous system in which there are a number of different types of particles which interact with one another. A further difficulty is that no two flotation systems are the same for minute quantities of a variety of common chemicals will alter the behavior of the system. These reasons make reproducible experimental results that can ex- plain fine-particle behavior difficult to obtain. In spite of these experimental difficulties, millions of tons of ore containing a large amount of fines are successfully floated every year. For example, at the Morning mill of American Smelting and Refining Co., a galena concentrate that was 42% -6 µ and a sphalerite concentrate that was 33% -9 µ were floated leaving a tailing that was 27% - 9 µ.l Ores that contain fines can generally be divided into two classes. In the first are those in which the valuable mineral tends to slime, such as galena and hematite. In the other class, one or more of the gangue minerals forms the slime; a typical example is barite. Though the problems due to the presence of fines are often the same in handling the two classes of ore, the method of handling them is different because of economic considerations. Nonmetallic mineral flotation is particularly affected by slimes, by either slime-coating effects or excessive reagent consumption. Though a given gangue mineral may not float under the conditions prevailing in the flotation cell, it may still be able to adsorb the collector. I£ it also slimes, a significant

Jan 1, 1962

By Thomas C. Atchison

An understanding of the physical processes involved in breaking rock with explosives will lead to better blasting techniques. In this chapter known rock breakage principles will be outlined, some conjectural ideas will be discussed, and areas needing further study will be pointed out. The principles outlined will serve as a basis for the design of blasting rounds described in the following chapter. 7.2-1. Factors Important to Rock Fragmentation. The efficacy of explosives as tools for rock fragmentation lies in their ability to deliver almost instantaneously large amounts of energy to a limited portion of the rock. When an explosive charge is detonated in a drill hole, its energy is released in a very small fraction of a second in the form of gas at extremely high pressure and temperature. The mechanics of the transfer of this energy to the rock and the resulting breakage are complex and not completely understood. Factors that have been identified as important to the fragmentation process may be grouped in three categories: explosive parameters, charge loading parameters, and rock parameters. EXPLOSIVE PARAMETERS. Explosive parameters known to influence breakage are density, detonation velocity, detonation impedance, detonation pressure, gas volume, and available energy. Detonation pressure is probably the best indicator of an explosive&apos;s ability to break solid hard rock. Detonation pressure is roughly proportional to the product of density and the square of the detonation velocity. The relative ability of different explosives to transmit their pressure to stress in a given rock is function of their detonation impedances. Detonation impedance is the product of density and detonation velocity. The volume of gas released in the explosive detonation undoubtedly is of importance, at least in the later stages of breakage, and is probably

Jan 1, 1968

By H. D. Outmans

The author applies the theory of hydrodynamic stability to fluid flow in porous media and concludes that the displacement of miscible liquids is stable if the stability coefficient, as defined by Eq. 19.2 or Eq. 27.0, is positive. The conclusion is invalid, however, since it is based on a faulty argument. To demonstrate this, the reader is referred to Eqs. 4.1 through 4.5 of the paper which describe, in differential form, the first-order disturbances c, u, v, w and p. In these same equations, cx, cz, gl, g3 and are functions of the stable concentration c. This concentration c is known and depends on x, z and t (the author assumes cy = 0). It follows that cx, cz, gl, g3 and µ are also functions of x, z and t. With this in mind, we turn to Eqs. 8.1 through 8.5 which were derived from Eqs. 4.1 through 4.5 by substituting Eq. 6.0. The significance of this substitution is that the author thereby limits the solutions of Eqs. 4.1 through 4.5 to equations of the form of Eq. 6.0. Eqs. 8.1 through 8.5 represent an infinite linear system with five unknowns: c, u, v, w and p. The coefficients cx, cz, gl, g3 and µ in this system are known at each point and at each instant; the coefficients containing derivatives of f are unknown. If this infinite linear system in c, u, v, w and p is to have a nontrivial solution, then it is indeed necessary (as the author states) that the determinant of the coefficient matrix of Eqs. 8.1 through 8.5, i.e., ( A 1, be equal to zero. This condition, however, is not sufficient. A non-trivial solution exists if, and only if, the rank of the coefficient matrix of the entire infinite system is smaller than five. In other words. all minors of order five must vanish and only if all the coefficients in Eqs. 8.1 through 8.5 are constant is this equivalent to the condition |A| =0. Constant coefficients means that gl, g3 and µ, for instance, are constant; and, since they depend on c it follows that c must be constant. We conclude that the condition I A I = 0, on which the author bases his calculations, is necessary and sufficient for a nontrivial solution only if the concentration c is constant. In other words, the author does not investigate the stability of a miscible displacement but, rather, only the stability of the flow of a homogeneous liquid. Using the initial condition and the fact that the coefficients are constant, we find

By Ernest Darby

WHEN bronze is melted in open-flame furnaces a considerable amount of slag is formed during the melting operation. This slag may be incidental to the melting practice or it may be formed intentionally by slag-forming constituents added to the furnace charge to provide a covering for the melted metal. When this slag is removed from the furnace, it contains, in addition to the free metal carried with it by the skimming operation, a considerable amount of metal as oxide either combined or mechanically mixed with it. By the usual crushing and washing methods this metallic oxide generally goes to the tailings pile, so diluted by other foundry waste that its recovery is economically impossible. If this furnace slag is not mixed with other foundry waste, practically all of the metal oxide as well as the free metal may be recovered by some form of smelting operation. The first side of the problem to be considered is the amount of slag produced. It may not be true that the majority of foundries have no record of the amount of slag made, but it is certainly true that a very great many either have no record or pay little attention to it. Usually the collection of furnace slag for one normal week&apos;s run will be sufficient to determine the advisability of its being handled in a different manner from the crushing and concentrating generally employed. If a large representative sample of the accumulation is crushed and concentrated and the recovery compared with the results of a careful assay, it will be found that a large percentage of the total metal content was lost in the washing process. The percentage of loss will be greater than the metallic oxide content, as some free metal in extremely fine particles always is carried away in grains of slag: From such a comparison, it may be determined whether or not the slag should be melted, sold or treated as before. An example of an actual test of this kind is given below.

Jan 1, 1928

By Ernest Darby

WHEN bronze is melted in open-flame furnaces a considerable amount of slag is formed during the melting operation. This slag may be incidental to the melting practice or it may be formed intentionally by slag-forming constituents added to the furnace charge to provide a covering for the melted metal. When this slag is removed from the furnace, it contains, in addition to the free metal carried with it by the skimming operation, a considerable amount of metal as oxide either combined or mechanically mixed with it. By the usual crushing and washing methods this metallic oxide generally goes to the tailings pile, so diluted by other foundry waste that its recovery is economically impossible. If this furnace slag is not mixed with other foundry waste, practically all of the metal oxide as well as the free metal may be recovered by some form of smelting operation. The first side of the problem to be considered is the amount of slag produced. It may not be true that the majority of foundries have no record of the amount of slag made, but it is certainly true that a very great many either have no record or pay little attention to it. Usually the collection of furnace slag for one normal week&apos;s run will be sufficient to determine the advisability of its being handled in a different manner from the crushing and concentrating generally employed. If a large representative sample of the accumulation is crushed and concentrated and the recovery compared with the results of a careful assay, it will be found that a large percentage of the total metal content was lost in the washing process. The percentage of loss will be greater than the metallic oxide content, as some free metal in extremely fine particles always is carried away in grains of slag. From such a comparison, it may be determined whether or not the slag should be melted, sold or treated as before. An example of an actual test of this kind is given below.

Jan 1, 1928

By W. D. Forgeng, D. Beregekoff

In the routine examinatlion of a wide variety of metal specimens it is sometimes necessary to have special methods of polishing in order to retain and reveal certain details in each specimen. Among such special cases is the retention of graphite in malleable and gray cast irons, the preservation of all types of non metallic inclusions in both hard and soft steels, obtaining a scratch-frec surface with soft metals, and avoiding the usual relief effects with very hard specimen. such as tool metals c3o1ltaining various carbide and nitride phases. It, is the purpose of this paper to give an account of some of these special polishing methods in use at the Union Carbide and Carbon Research Laboratories. The polishing procedures outlined have been found to give uniform results. It is obvious that only general rules and the most important working details can be given here. Following these rules, the polisher can obtain satisfactory results if he possesses the necessary patience and has a sincere desire to give as nearly perfect a finish as possible to his work. Procedure The specimen is flattened with considerablecare on a file or sharp cutting sanding belt, since the initial production of a flat surfacc greatly facilitatcs subscqucnt polishing. The polishing motors have two speed., 600 and 1200 r.p.111. ,It higher speeds specimens arc likely to he over-Ileated, therefore the high speed is used only when a saving of time is important. The following abrasive papers are used consecutively: Yo. 2, So. 1, No. 0, No. 00 and No. 000. The final wet polishing is done oil a cloth-covercd metal disk. Woolen broadcloth of the best quality and capable of resisting severe pressure is most commonly used on the last lap. . polishing felt of the type used for polishing optical glass has been found equally satisfactory and is much stronger than broadcloth. For retaining inclusions and graphite, a hard cloth with very little residence, such as

Jan 1, 1939

By D. Beregekoff, W. D. Forgeng

In the routine examinatlion of a wide variety of metal specimens it is sometimes necessary to have special methods of polishing in order to retain and reveal certain details in each specimen. Among such special cases is the retention of graphite in malleable and gray cast irons, the preservation of all types of non metallic inclusions in both hard and soft steels, obtaining a scratch-frec surface with soft metals, and avoiding the usual relief effects with very hard specimen. such as tool metals c3o1ltaining various carbide and nitride phases. It, is the purpose of this paper to give an account of some of these special polishing methods in use at the Union Carbide and Carbon Research Laboratories. The polishing procedures outlined have been found to give uniform results. It is obvious that only general rules and the most important working details can be given here. Following these rules, the polisher can obtain satisfactory results if he possesses the necessary patience and has a sincere desire to give as nearly perfect a finish as possible to his work. Procedure The specimen is flattened with considerablecare on a file or sharp cutting sanding belt, since the initial production of a flat surfacc greatly facilitatcs subscqucnt polishing. The polishing motors have two speed., 600 and 1200 r.p.111. ,It higher speeds specimens arc likely to he over-Ileated, therefore the high speed is used only when a saving of time is important. The following abrasive papers are used consecutively: Yo. 2, So. 1, No. 0, No. 00 and No. 000. The final wet polishing is done oil a cloth-covercd metal disk. Woolen broadcloth of the best quality and capable of resisting severe pressure is most commonly used on the last lap. . polishing felt of the type used for polishing optical glass has been found equally satisfactory and is much stronger than broadcloth. For retaining inclusions and graphite, a hard cloth with very little residence, such as

Jan 1, 1939

By C. G. Dunn

The measurement of interfacial teusions or grain boundary energies in metals is an important metallurgical problem, especially since it bears on growth and nucleation processes. Statistical methods of measuring equilibrium grain boundary angles, which relate interfacial tensions, have been used by some investigators1&apos;2 but more direct methods would be preferred. A direct way, based on a simple extension of a successful method of growing single crystals of silicon ferrite to predetermined orientations in flat specimens,3 is to produce three-grain specimens in such a way that the equilibrium common grain boundary will be perpendicular to the surface of the specimen. The angles to be measured then appear as the grain boundary angles in the surface of the specimen. The method of producing a single crystal specimen with a predetermined orientation is basically the same as that employed by Yoshida and Fuji-wara4 in their work on aluminum wires. The specimen, prior to any single crystal transformation, must have a matrix which will support the growth of a crystal of the desired orientation. Growth may occur through exaggerated grain growth or, if the matrix is strained a critical amount. by normal recrystallization. In either case the matrix must have stability at the temperature used to effect the transformation, this stability appearing as a long induction period for exaggerated grain growth or for the formation of recrystallization nuclei. Additional control is gained by using a high temperature gradient through which the specimen is moved at a suitable rate. To obtain the desired orientation, the specimen is fed a short way into the furnace producing one or more crystals in the hot end. After the specimen is removed from the furnace, the orientation of a crystal is determined, so that this crystal may be reoriented by properly deforming a narrow piece of the matrix between the end crystal and the rest of the specimen. This part of the specimen in the case of silicon ferrite is preferably held at red heat during the reorienting process. Fig 1 shows a specimen which is ready to be transformed into a single crystal through growth of a reoriented "seed" crystal. When the method just described is applied to the production of a three-grain specimen two crystals are grown first side by side in one end, the specimen is then reversed and the third grain grown from the opposite end. A suitable group of grains each of different orientation is one where all three grains have the same crystallo-graphic plane in the plane of the specimen. Fig 2 shows a photograph of a three-grain group prepared as described. The notches are introduced in the open ends of the grain boundaries to anchor them during the final annealing operations which ultimately should bring the grain boundaries to the lowest energy configuration. Two-grain groups with different crystallographic planes in the plane of the specimen can be similarly prepared and treated. If the two grains have different surface (gas to metal) energies per unit area, the equilibrium condition leads to a curved grain boundary.* * This feature of the problem was pointed out by J. c. Fisher. References 1. Cyril Stanley Smith: Grains. Phases and Interfaces: An Interpretation of Microstructure. Trans. AIME 175, 15. Met. Tech. TP 2387, June 1948. 2. D. Harker and E. Parker: Grain Shape and Grain Growth. Trans. A.S.M. (194,5) 34, 156-195. 3. C. G. Dunn, A. Seddon, and R. Wylie: Unpublished Work, 1946-1947. 4. Takeo Fujiwara: A Method of Producing A Long Single-Crystal Wire of Aluminum with any Desired Crystallographic Axis. Jnl. of Sci. Horoshima Univ. A, (1939) 9, No. 3, 227.

Jan 1, 1950

By Isaac H. Odell, Arthur W. Hixson, Lincoln T. Work

Although a few engineers have recognized the problem of the mechanism of filtration it has never been studied in a quantitative way. A background for a better understanding will be afforded by a survey of certain fundamental principles of filtration. In recent years, authorities have become practically unanimous in saying that the actual filtering should be done, not by the cloth itself, but by a layer of solid particles deposited upon it. Thus, a cloth may be used in which the openings are considerably larger than the particles to be filtered, provided that groups of particles form an arch or bridge over each opening. This can be accomplished if the initial pressure is so low that the arch will not be broken while it is still thin. According to Wright,&apos; the chief advantage of this method of filtration is that the open-weave cloth does not become clogged as easily as does one of closer weave, where the fine particles often work their way into the interior of the cloth and become caught there. If the character of the material to be filtered is such that it will not form a good film, then it becomes advantageous to use "filter aids" for pre-coating the cloth with a desirable layer of solids, and the coating need be only of a very slight thickness for good results. Until the film is formed, the first runnings of the filtrate may be cloudy, often necessitating refiltering this portion. A factor which has considerable effect on the performance of filters is the concentration of solids in the pulp. According to Wright, a high concentration of solids gives a porous cake, since the flow is then slower than with a thin pulp. The porosity of the cake is also affected by the pressure: a high initial pressure tends to compact the cake, and the same effect results from fluctuations of pressure. In his studies of the relation between pore size and particle size, Hatschek2 observed that the particles in a pulp tend to arrange themselves with maximum cross-section parallel to the direction of flow and that this is more marked at the higher vclocfiies. Thus, at high pressure and high velocity, a certain pulp

Jan 1, 1926