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By C. Richard Tinsley

INTRODUCTION The economic analysis (Chapter 3), the engineering studies (Chapter 10), the credit structure (and the consequential funding sources) - Chapter 11, and the overall feasibility structure for any venture are all directed to determining one major decision element: How much and how certain is the reward for taking these risks? Risk assessment is a surprisingly weak area of analysis and is usually addressed in a checklist fashion. It is much preferable to deal within a risk system so that the inevitable tradeoffs among risks are correctly made. DEFINITION The first step toward risk definition must be to ascertain all of the risks to which a project or a company is exposed; otherwise one will remain ignorant of the possibility of a financially crippling loss until it occurs. (Carter and Crockford, 1974). However, simply stating what "risk" is can lead to debate. For example, risk could be (adapted from Vaughan, 1982): -the chance of a loss - uncertainty of loss -possibility of loss - uncertainty -dispersion of actual from expected results - probability of an outcome different from the one expected - possibility of an occurrence of an undesirable contingency -a condition in which a possibility of a loss exists. For the minerals industry financier, the last definition is probably the most appropriate. However, from a mineral company's point of view the definition might well include the possibility of not achieving the expected financial return. RISK CLASSIFICATION Risk identification will be readily agreed as the all-important first step. There are five major "branches" of risk classification. These are: -Statistical -Modellers -Checklist -Project Financing -Insurance The Statistical set discovered probability theory and any risk discussion soon deteriorates into a mathematical jungle (Megill, 1977; Hartman, 1976; Reutlinger, 1970; and Pouliquen, 1970).Their use of terminology tells its own story: coin toss (binomial distribution), gamblers' ruin, delphi (oracle) techniques, monte-carlo simulations, random walks, etcetera. These techniques inadequately represent the judgements necessary in an increasingly complicated and interrelated world. The risk Modellers have turned to the computer to handle these inter-relationships but soon find barriers because of "simultaneity". Certainly the computer has its uses to conduct various analyses (marketed as "sensitivity" analyses) but very often one finds that this involves changing one or two variables at a time, all other things being equal. Unfortunately, in a modern and complex world all other things do not remain equal. The statisticians will, no doubt, jump to their own defence by citing this

Jan 1, 1985

By J. C. Shyne, T. D. Gulden

The steady-state creep behavior, in compression, of indium containing a dispersion of atomized glass particles was studzed over a range of temperature, stress, and composition. The observed behavior was not consistent with a simple model of dislocation climb over dispersed particles. From room temperature to about 100°C the temperature dependence could be described by an activation energy about one and a half times that of self-dijfusion in indium while at higher temperatures a much higher ternperature dependence was observed. THE value of dispersion-hardened and precipitation-hardened alloys has long been recognized. The mechanism of hardening, however, is not completely understood, especially at elevated temperatures where dispersed particles increase creep resistance. Following the suggestion of Schoeck1 that the rate of creep in dispersion-hardened materials is controlled by dislocation climb over second-phase particles, Ansel and weertman2 derived steady-state creep equations for dispersion-hardened materials. Their derivation was based on dislocation climb over non-deformable spherical particles in a metallic matrix. For low stresses they predicted a linear relation between applied stress and steady-state creep rate. For stresses large enough to cause dislocations to pinch off around the precipitate particles, the theoretical creep rate was shown to be proportional to the fourth power of stress. For very high stresses an exponential stress dependence was predicted. In all cases the theoretical creep rate is linearly proportional to the diffusion coefficient. This provided the primary temperature-dependent factor. Subsequently, Ansel and Lenel3 reported some experimental data on SAP, a composite of aluminum and aluminum oxide, that was in good qualitative agreement with the above theories. Their experimental creep rates, however, were four orders of magnitude less than the theory predicts. This was attributed to a low density of active dislocation sources in the material; somehow the dispersed particles inactivated the dislocation sources instead of merely interferring with dislocation motion. Meyers and sherby4 have recently reported on the creep behavior of SAP. Their results were inconsistent with a simple dispersion-strengthening model and led them to conclude that a continuous network of oxide controls the high-temperature mechanical characteristics of SAP. Because of the rather complex mechanical behavior of SAP and the lack of agreement about the morphology of its oxide phase, it appeared desirable to study the creep of a dispersion-strengthened material of controlled morphology. For the present work a dispersion of spherical glass particles imbedded in a matrix of indium was chosen. The microstructure of this material was similar to the idealized uniform dispersion of hard spheres in a deforming matrix assumed by Ansel and Weertman in their theoretical treatment. SPECIMEN PREPARATION For experimental convenience, it was decided to use a low melting-point metal in this investigation. It was necessary that the metal not be oxidized readily up to its melting temperature and that it wet the second-phase particles. It was desired that the material chosen for the dispersed phase be available as a fine powder with closely controlled size and shape. The material chosen to satisfy these requirements consisted of a matrix of indium metal containing a dispersion of atomized particles of a soft soda-lime-silica glass ranging from 5 to 30 µ in diam. The glass particles had a highly regular spherical shape. The composite was made by stirring the glass powder into liquid indium maintained at a temperature just above the melting point of indium, 156°C. The creep specimens were prepared by a hot pressing operation. Five to ten g of the mixture were placed in a steel die and pressed at 125°C for 5 min under a pressure of 30,000 psi. The resulting specimens were cylinders about 3/8 in. in diam and ranged from 0.4 to 0.7 in. high. By following this procedure a uniform dispersion was obtained in the creep specimens. Typical microstructures of specimens containing twenty and forty volume percent glass powder are shown in Figs. 1 and 2. Unfortunately, grain size could not be determined by the metallo-graphic techniques used. CREEP TESTING PROCEDURE Creep tests were performed in compression under constant stress. The specimens were placed in

Jan 1, 1963

By Ralph H. Sweetser

MUCH progress in -blast-furnace construction and in the manufacture of firebrick for furnace linings has been made since the publication of Bulletin 130 of the U. S. Bureau of Mines on "Blast-Furnace Breakouts, Explosions and Slips, and Methods of Prevention," by F. H. Willcox in 1917. At the time of publishing this report comparatively little information was available to blast-furnace men as to the fundamental facts relating to the character of blast-furnace refractories. Some of the accepted theories of only a few years ago have been completely reversed. The mortality of blast-furnace linings used to be so great that nearly every furnace plant had one or more complete linings in the brick shed ready for use in case of a lining suddenly "going out"; it was generally accepted that a furnace could not "keep her lines" more than two or three years at best, and often a hot spot in the shell would develop, or a breakout occur in the hearth or bosh within a year or two after blowing in on a new lining. In some respects these frequent relinings were not so detrimental as to he a complete loss because they afforded opportunities to take advantage of advances in blast-furnace practice. At present the cost of relining has greatly increased, but the life of a lining has also increased. Anything less than five years on a lining is now considered a short blast.

Jan 1, 1932

O. S. GARRETSON, Buffalo, N. Y.: If I may judge from the half-tone illustration engraved from a photograph of this medal and accompanying Dr. Prazer's paper, I do not think the cast ing is exceptionally fine. I have often made castings of simi lar character which I think were equally good. For instance, I have taken a coin, moulded it directly in fine sand, and cast from it in Scotch (or the equally good, if not better, Ameri can Scotch ") foundry-iron a copy quite as sharp and smooth as the original. The secret is in using very fine sifted sand. In fact, I have used for this purpose the dust which had accumulated on the beams overhead in my foundry, riddling it with a very fine sieve before using it. ['NOTE BY THE SECRETARY.—After the session at which these remarks were made by him, Mr. Garretson cast at his Buffalo foundry, in the presence of a number of members of the Institute, copies of the bronze pin furnished to visiting members by the Local Committee of the Buffalo meeting. The accom panying illustration, Fig. I, has been reproduced from a photograph of such a casting, made in green sand, under the conditions of ordinary foundry-practice, and not subsequently polished in any .way. I can also certify that the photo graphic negative was not touched, to improve its clearness of definition, before the production of the " half-tone" plate from which Fig. 1 has been printed. As, in the case of the Kytchtym medal, it was the thin, ribbon-like sprue, rather than the low-relief features of the medal itself, which indicated the fluidity of the metal and the sharpness of the casting, so in this work of Mr. Garretson it is the long and slender pin which offers the strongest evidence of these qualities. It is scarcely neccssary to point out that the filling in the mould of a long and nar row opening, such as this pin presents, is the severest test that could be imposed upon the casting, and that the sharpness of the point of the pin in the casting is striking evidence of the success with which this test has been met. The Pittsburgh Testing Laboratory .has made for the American Manufacturer measurements of this casting and an analysis of the sprue. The thickness of the main casting is from 0.049 to 0.068 inch. That of the tag bearing the stamped number is 0.024 inch. The analysis, which represents the iron ordinarily employed by Mr. Garretson for thin castings, is as follows :

Jan 1, 1899

By Edward Steidle

NOTHING stands still. We go forward or backward. As a distinct group of educators, our immediate concern is with the preparation of young men and women for participation in the mineral industries on a professional basis. I am going to have the temerity to state emphatically that for a long time as a whole we have remained in a static position. We are now confronted with the choice of advancement or retrogression. We are still in a position to make a choice and our ultimate fate will depend upon the course of action we elect to follow. Wars always have been great catalysts and social and scientific advancements mature under military stimulus in a fraction of the time normally consumed. We are now in the midst of a conflict whose duration or final effects cannot be estimated. However, the record already demonstrates that this war as never before is a mineral war in which incentive, strategy, and outcome are directly related to the distribution and utilization of minerals. The inevitable result is a drain upon our resources now reflected in our record production and a growing public consciousness of the importance of minerals in the role of human affairs. It is evident that we must seek new mineral frontiers beyond the borders of the United States and take every other precaution to forestall a "have-not" position in the world.

Jan 1, 1943

By S. A., Taylor

IT is very difficult to arrive at exact figures for the cost of maintaining excess capacity of coal mines, but we can approximate the various items. To do this, I will take the Pittsburgh district of Pennsylvania and the other districts can be compared to this one. I believe we can take the depreciation item of plant ac- count as a whole and discount it over a period of 20 years; while this is high for some items it is low for others and I believe it is not far from a safe basis. This equals 5 per cent per year, and this depreciation will take place about as rapidly when not in use as when in operation. A fair value in the Pittsburgh district to- day for plant and houses is close to $4 per ton per annum. At 5 per cent this will equal 20 cents per ton per year. The item of keeping the mine in condition, free from water, etc., will be close to an average of 2y2 cents per ton per annum.

Jan 1, 1928

ANNUAL meeting of the Woman's Auxiliary of the American Institute of Mining and Metal-lurgical Engineers convened on Tuesday morn-ing, Feb. 20, the president, Mrs. H. W. Hardinge, presiding. President Hardinge, in opening the meet-ing, said: "I have the honor and great pleasure to welcome you to our seventh annual meeting. It has been a happy year, though I started in fear and trembling. My fear is partly gone and my trembling becomes less as time goes on. Never has a chairman had such splendid cooperation and harmony in her work; no. matter how much was asked nor what the task, I have always received the same answer, `We are with you, of course we can do it.' Often the road has been untried and the way full of snares, but we have all pulled together. Is it any wonder we have had a prosperous year? I cannot thank the governing -board and officers enough for their help." Mrs. Hardinge described her trip through the West last summer, during which she visited many of the local sections of the Auxiliary. She also spoke of the work of the Rossiter Raymond memorial library which has been started as an activity of the Woman's Auxiliary. Mrs. Reynders read the minutes of the last annual meeting, and Mrs. Kemp read the treasurer's report. The latter showed that on Feb. 1, 1922, there was a bank balance of $683.61 and on Feb. 10, 1923, the bal-ance was $947.93. Mrs. Westervelt expressed the sorrow of the Auxiliary for the death -of Mrs. Florence Howe Hall and of Mrs. Levi P. Holbrook.

Jan 4, 1923

By Max Roesler

I. INTRODUCTION THE following article concerns the geological occurrence of the iron-ore deposits on the south coast of Cuba. The article is based on a detailed field study, made in the hope that some information would I gained which might be of value in the search for further orebodies, Or in the economic development of the ore already found. LOCATION The iron-ore deposits of the Firmeza district lie near the coast, in the southeastern part of Cuba, in the Province of Oriente. The orebodies of this district form part of a belt of deposits that extends from Sigua, 25 miles east of Santiago, to Sevilla, 5 miles east of Santiago, and lies on the seaward slope of the Sierra Maestra range of mountains.

Jan 10, 1916

By JOHN JERMAIN

In my opinion, the explanation of the fuel-requirements involving the conception of heat available and necessary above a critical temperature, as advanced by Johnson 1 and elaborated by Howe, Raymond and others,2 affords a theoretically correct basis for such an accounting. It is the purpose of this paper to set forth a first crude attempt to construct a formula which shall show quantitatively the relation between the various factors affecting fuel-economy, and afford a means of comparing the enormous amount of data on the fuel-consumption of various blast-furnaces, at various times and under various conditions of operation. I have also applied this formula to a large number. of individual cases, and have, by its means, compared the furnace-practice of several important iron-making districts. II. DERIVATION OF FORMULA FOR FUEL-REQUIREMENTS. The general expression for the fuel-requirements of the blast-furnace, which I believe to be theoretically correct as to form, is as follows Carbon per ton of iron = Heat per ton of iron necessary in hearth above Tc./Heat per pound of carbon available in hearth above Tc. XFactor of rate of driving. +Carbon dissolved by CO2 of flux. +Carbon dissolved incidental to reduction of ore. + Carbon dissolved in pig-iron. (NOTE.-Tc = critical temperature.) Since, according to Johnson's theory, fuel-economy is usually limited by heat available and necessary in the hearth, rather than by the total heat supplied and necessary, we may write Carbon needed in hearth = Hn/Ha in which Hn is the heat per ton of iron necessary in the hearth above some critical temperature, and Ha is the heat per pound of carbon available in the hearth above this same critical tem¬perature. 1 Trans., xxxvi., 454 (1906). 2 Trans, xxxvi., 792 to 798 (1906) ; Trans, xxxvii., 216 to 237 (1907).

May 1, 1911

By A. L. Marshall, F. J. Norton

THE object of this investigation was to make a comprehensive study of the degassing of molybdenum in order to determine how rigorous a treatment was necessary to completely remove sorbed gases from molybdenum electrodes in vacuum tubes. Some work has also been done with tungsten, nickel, iron and carbon. As a logical development of this work it has been shown that the gas is present throughout the body of the metal and a study has been made of the solubility of nitrogen in molybdenum and tungsten and the rate of diffusion of nitrogen through molybdenum has been calculated. Tests were made on molybdenum from all the commercial sources and no difference was discovered in the nature of the gases present, the amounts or the ease of removal. The reason for this was apparent when a study was made of the manner in which gases are absorbed by gas-free molybdenum. It is necessary to heat molybdenum to 1760°C.oin a vacuum of the order of 0.001 micron for a time which varies lineally with the thickness, in order to obtain a condition in which no further gas is evolved by the sample. A sample so degassed can be handled and subsequently assembled in a tube and then degassed readily. The gases obtained from molybdenum are carbon monoxide and nitrogen, the nitrogen being the more difficult to remove. APPARATUS AND TECHNIQUE The apparatus is shown in Figs. I and 2. It consisted of two units, a degassing system and an analytical system. Each had a bake-out oven, as shown surrounding the systems in the sketches. The system will be traced, starting from the sample in the degassing system. A water-cooled quartz chamber surrounded the sample. The high-frequency coil, which heated the sample, extended only around this chamber and was cooled by an air blast. High-frequency power of 0800-meter wave length was obtained from a self-rectifying oscillator circuit with a maximum power input of 20 kw. A graded seal connected the quartz to the rest of the apparatus, which was of hard' glass. The temperature of the molybdenum sample was observed by an optical pyrometer through an optical window about 40 cm. distant from the sample. Since the object viewed under these conditions was not 'a black body, true temperature was not observed, but the so-called "brightness temperature." The correction of this to true temperature is discussed in a later section. The apparatus was taken apart just above the graded seal; the quartz chamber was slipped off, washed with nitric acid, water and alcohol, and dried by an air stream. The old sample was removed by

Jan 1, 1944

By David, Levinger

THESE observations of the metal-working industries of Europe are based on a three months' tour of eight countries of Europe, in which 75 industrial establishments were visited in England, France, Germany, Belgium, Holland, Italy, Austria and Switzerland during the summer of 1927. Since the Western Electric Co. is a large consumer of copper and brass, these industries were of particular interest and differences in practices were of keen interest to us.

Jan 1, 1928

By Franklin H. Sharp, Kenneth L. Clifford

During the last few years the New Lead Belt of Southeastern Missouri has become the main source of lead in the United States. It also produces significant amounts of zinc, copper and silver. The mines are located on a narrow, mineralized trend extending southward from Viburnum, MG. for about 35 miles. The ore occurs as replacement deposits in the Bonneterre lime- stone formation which is about 1000 ft below the surface. In most of the mines, enough water is produced to supply the milling requirements without any reuse. There are dry areas, however, and at least two mills must rely on water reclaimed from their tailings lake to augment the mine water. These mills have no choice but to utilize recycled mill water.

Jan 7, 1973

By A. M. Beebee

IN the present century the coal and manufactured gas industries have been eclipsed in public interest by oil, natural gas, and hydro- electric energy, which have had the benefit of rapid development and novelty. I sometimes wish that our social- order were such that hydro power had been developed first, that the use of gas from coal had never been seriously considered, and that our domestic energy requirements were supplied by other fuels. Sup- pose the manufacture of gas from coal should then come on the scene at the present time with the current plight of the railroads, coal regions, and labor generally, presenting the fact that it could increase the amount of coal mined and shipped by the railroads by some 16,000,000 tons, and increase the coal used at existing u plants five times. Imagine the great public interest that would be manifested; it would supply the cooking and water-heating requirements of a community with a superior character of service at a cost to the customer approximately half that which had obtained previously. Would not such a situation be heralded as the salvation of our country and all help be given it?

Jan 1, 1940

By P. Somasundaran, D. W. Fuerstenau

This article presents the results of an analysis of grinding of 1:1 mixtures of 4x8-mesh quartz and limestone in laboratory ball and rod mills. From these experiments, the amount of energy consumed in grinding each component of the mixture was determined. In the ball mill, limestone consumes slightly more energy than quartz in the initial stages of grinding, but as the grinding proceeds quartz begins to consume a slightly greater fraction of the energy. The postulate that the fraction of energy consumed by any material in a ball mill is proportional to its volume fraction has been shown to be approximately true. On the other hand, in a rod mill energy consumption by quartz and limestone is equal only in the initial stages of grinding, with energy consumption by quartz greatly exceeding that by limestone as rod milling proceeds. Preferential energy consumption in tumbling mills has been discussed in a number of papers. For example, from an analysis of the kinetics of comminu- tion in ball mills, Arbiter and Bhrany' obtained rate equations based on the postulate that only coarse particles are ground, indicating that fine particles are protected from the action of the balls by coarser particles. In rod mills this protective action is much more pronounced than in ball mills. Recent studies on the rod milling of limestone-quartz mixtures have shown that this protective action causes the mineral with the lowest grindability (quartz in this instance) to consume the greater fraction of energy. 2 However, in the ball milling of mixtures it has been postulated that the consumption of energy by one of the constituents is determined by its volume fraction within the mill. 3 Possibly this hypothesis may be a simplification of the ball milling of mixtures since the protective action suggested by Arbiter and Bhrany may result in some preferential energy consumption by one of the constituents of a mixture. The objective of this study has been to determine preferential energy consumption in laboratory ball and rod mills by analyzing size distributions of each material in the products obtained from grinding 1:l mixtures of quartz and limestone. MATERIALS AND METHOD The procedure for carrying out the tests on wet grinding quartz-limestone mixtures has already been described.'r3 In the present investigation, 1:l mix-

Jan 1, 1963

By Russell Franks

IN recent years a considerable tonnage of the 18 per cent chromium and 8 per cent nickel steels has been used in lightweight high-strength structures that must be resistant to deterioration under atmospheric conditions. These steels are austenitic in character and their strength can best be increased by cold-working. Although a marked increase in tensile strength is obtained, claims have been made that the cold-worked steels do not possess fully satisfactory elastic properties. Under certain conditions, however, this has caused no great concern, because, as explained by Ragsdale,1,2 the cold-rolled steels have been widely applied for construction of lightweight, high-strength trains using spot welding for joining purposes. Ffield3 agrees that the ease with which thin sections of the cold-rolled 18-8 steels can be joined by spot welding is greatly in their favor, but that they would be more satisfactory if higher elastic properties and a higher modulus of elasticity could be obtained. He states that, as far as the mechanical properties are concerned, the straight chromium stainless steel is superior to the cold-worked 18-8 steel, and in order to illustrate, he presented the data of Fig. 1, which also give a stress-strain curve for a low-carbon 13 per cent Cr steel. Ffield? pro-posed that columbium-bearing or titanium-bearing cold-rolled 18-8 steels be given a heat-treatment (preferably for 1 hr.) in the range 400° to 600°C. to precipitate carbides in order to obtain better mechani-cal properties. Discussions by Sutton,4,5 de Ganahl,6,7 8 Krivobok and Lincoln,9 Knerr,10 and Thaden11 have given further information on the properties of the cold-rolled 18-8 steels compared with other materials used in light-weight, high-strength structures. These investigators and others point out that the ultimate tensile strength of the cold-rolled 18-8 steel can be increased to 200,000 lb, per sq. in. or higher; Krivobok et al. indicate that

Jan 1, 1940

By Russell Franks, W. O. Binder

In recent years a considerable tonnage of the 18 per cent chromium and 8 per cent nickel steels has been used in lightweight high-strength structures that must be resistant to deterioration under atmospheric conditions. These steels are austenitic in character and their strength can best be increased by cold-working. Although a marked increase in tensile strength is obtained, claims have been made that the cold-worked steels do not possess fully satisfactory elastic propertics. Under certain conditions, however, this has caused no great concern, because, as explained by Ragsdale,1,2 he cold-rolled steels have been widely applied for construction of lightweight, high-strength trains using spot welding for joining purposes. Ffield3 agrees that the ease with which thin sections of the cold-rolled 18-8 steels can be joined by spot welding is greatly in their favor, but that they would be more satisfactory if higher elastic properties and a higher modulus of elasticity could be obtained. He states that, as far as the mechanical properties are concerned, the straight chromium stainless steel is superior to the cold-worked 18-8 steel, and in order to illustrate, he prcsented the data of Fig. 1, which also give a stress-strain curve for a low-carbon 13 per cent Cr steel. Ffield† proposed that columbium-bearing or titanium-bearing cold-rolled 18-8 steels be given a heat-treatment (preferably for 1 hr.) in the range 400" to 600°C. to precipitate carbides in order to obtain better mechanical properties. Discussions by Sutton,4,5 de Ganahl,6,7,8 Krivobok and Lincoln,' Knerr,l0 and Thaden11 have given further information on the properties of the cold-rolled 18-8 steels compared with other materials used in lightweight, high-strength structures. These investigators and others point out that the ultimate tensile strength of the cold-rolled 18-8 steel can be increased to 200,000 lb. per sq. in. or higher; Krivobok et al. indicate that

Jan 1, 1940

By Russell Franks, W. O. Binder

In recent years a considerable tonnage of the 18 per cent chromium and 8 per cent nickel steels has been used in lightweight high-strength structures that must be resistant to deterioration under atmospheric conditions. These steels are austenitic in character and their strength can best be increased by cold-working. Although a marked increase in tensile strength is obtained, claims have been made that the cold-worked steels do not possess fully satisfactory elastic propertics. Under certain conditions, however, this has caused no great concern, because, as explained by Ragsdale,1,2 he cold-rolled steels have been widely applied for construction of lightweight, high-strength trains using spot welding for joining purposes. Ffield3 agrees that the ease with which thin sections of the cold-rolled 18-8 steels can be joined by spot welding is greatly in their favor, but that they would be more satisfactory if higher elastic properties and a higher modulus of elasticity could be obtained. He states that, as far as the mechanical properties are concerned, the straight chromium stainless steel is superior to the cold-worked 18-8 steel, and in order to illustrate, he prcsented the data of Fig. 1, which also give a stress-strain curve for a low-carbon 13 per cent Cr steel. Ffield† proposed that columbium-bearing or titanium-bearing cold-rolled 18-8 steels be given a heat-treatment (preferably for 1 hr.) in the range 400" to 600°C. to precipitate carbides in order to obtain better mechanical properties. Discussions by Sutton,4,5 de Ganahl,6,7,8 Krivobok and Lincoln,' Knerr,l0 and Thaden11 have given further information on the properties of the cold-rolled 18-8 steels compared with other materials used in lightweight, high-strength structures. These investigators and others point out that the ultimate tensile strength of the cold-rolled 18-8 steel can be increased to 200,000 lb. per sq. in. or higher; Krivobok et al. indicate that

Jan 1, 1940

By Gordon MacVean

THE adoption of rock dusting, as a safety measure, has made notable progress in the West Virginia coal mines since May, 1925. At that time there were but two mines in the State that were thoroughly rock dusted, mines No. 2 and No. 12 of the Boone County Coal Corp., at Sharpless. Since then it is probable that 75 per cent of the coal operators in the State have given consideration at one time or another to rock dusting. This growth of interest followed the meetings of the various mining institutes all over the country, during the summer of 1925, at which papers were presented, drawing the attention of the coal mining operators to the merits of this safety measure. Yet outside of the experience with rock dusting at the Old Ben Coal Corp., of Southern Illinois, and the Carbon Fuel Co., of Rains, Utah, there had been no actual occurrence in the coal mines of the United States, which could be taken as positive evidence of the efficacy of rock dusting in the prevention of the propagation of coal dust explosions. The U. S. Bureau of Mines, however, had run innumerable tests under conditions which closely approximated actual coal mining conditions and had clearly shown that rock dusting was effective.

Jan 1, 1926

G. A. Moore—The tin-fusion method has been a very favorable possibility for many years. The authors apparently have settled the question that delayed the method for a long time by showing that no hydrogen is absorbed in the tin. This, of course, is very important. I want to make a few remarks concerning the absolute accuracy of analysis, which must be the final basis for deciding among the various methods. From the figures in the paper, there seems to be some re-maining slight discrepancy on the actual amount of hydrogen present in various samples which may be presumed essentially identical. (This is of the order of the precision of individual analyses but appears in averaged results.) From the analyst's viewpoint, the tally of hydrogen content can be regarded as occurring in three portions. First is a large portion which comes off easily and automatically during sample storage and later on heating in the apparatus. This is fairly easily analyzed. Second is an item which may be either positive or negative in the tally sheet. In warm or hot evolution, this is a portion which, in practice, can never be re-

Jan 1, 1951

By L. J. Kashar

By means of a continuum-mechanics approach, the following equation for calculuting the pressure for axisymmetric cold forging has been derived: where P is the extrusion pressure; K and n are the strength coefficient and the strain-hardening exponent of the steel, respectively; a and b are strain factors, primarily dependent on the die design; and R is the extrusion ratio. Data from compression and backward-extrusion tests performed at a crosshead speed of 0.5 in. per min on a nonwork-hardening material pure lead) and on a work-hardening material (1018 steel) indicate that the predicted extrusion pressures obtained from the derived equation agree very closely with the actual extrusion pressures. Therefore, the equation can be used to predict backward-extrusion pressures from standard mechanical-test data. The decision to cold-forge a part is based on several considerations, most of them related to economics. However, the production feasibility is usually determined by the pressure needed to extrude the part and the availability of tooling that can repeatedly sustain this pressure for over several hundred thousand cycles. A major contribution to the cold forging of steel would result from the development of steels that could be forged at reduced pressures and from the development of techniques that permit the accurate prediction of the pressure necessary to cold-forge the part. The ability to predict extrusion pressures is necessary to properly design the tooling required for the cold-forging process. Attempts to theoretically predict the cold-forging pressure, especially for work-hardening materials, have been unsuccessful in previous investigations of the cold-forging process.1-3 Many empirical relations have, therefore, been proposed relating the extrusion pressure to the chemical composition,' the extrusion ratio,2 the tensile strength,273 and hard- ness, 2 and the yield strength3 of the material being extruded. However, these empirical relations are valid only for the specific conditions used in their development, and, in some cases, the empirical relations had a scatter band greater than * 10 pct. A study of the extrusion process was undertaken with the objective of developing predictor equations for extrusion pressure by using a continuum-mechanics approach to the problem of metal flow. The derivation of such an equation is summarized in this paper, and data are presented that confirm the validity of the derived equation. DERIVATION OF THE EXTRUSION EQUATION If the extrusion of a material through a die is considered in terms of a work balance, it has been shown that it is possible to derive an equation relating the work necessary to move the material through the die to the deformation work undergone by the material. The work done, W, in moving the material is given by where F is the extrusion force, I, is the distance the material was moved, A, is the original cross-sectional area of the material, P is the extrusion pressure acting on A,, Ap is the cross-sectional area of the extrusion punch, and Pp is the punch pressure acting on Ap. The deformation work, WD, is given by where V is the volume of metal deformed, ay is the flow stress of the metal, and E is the total strain undergone in the extrusion. If there are no frictional losses, the work done, W, is equal to the deformation work, WD; therefore, Since the volume of a metal does not change during deformation,

Jan 1, 1968