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By W. L. Saunders

IMPORTANCE OF ROCK DRILLING. IT has been estimated that the value of the mineral products of the United States is about $2,000,000,000 a year; that about $25,000,000 is expended. annually for explosives and that about double this sum is paid in wages where blasting is done. The value of the mineral products does not adequately express the importance of the industry involved in the excavation of rock and ore because of the enormous sums of money expended in tunnel driving, in quarries, and in open-cut excavation generally. We know that the Catskill Aqueduct in the neighborhood of New York, which is now nearing completion, has cost some $165,000,000 and that about one-third of this may be rated as rock excavation. These illustrations are given in order to call attention to the great importance of an industry the extension and development of which in our industrial life depend so much upon the economics of rock drilling. Reference has been made to the new Catskill Aqueduct. There are three aqueducts leading into New York, each built at periods separated by some 20 years of time. 'The first one, known as the Old Aqueduct, conveys the waters of the Croton river to New York City in a manner which reminds one of the old Roman aqueducts, the ruins of which are still in evidence. The engineers who laid out these old conduits sought to direct their lines around the hills and into the valleys, at all times avoiding the rock. When it was necessary to cross a river or a deep ravine, a bridge or causeway was constructed. High Bridge, over the Harlem river, is an arched masonry viaduct differing in no essential features from the aqueducts of the Romans. When the second Croton Aqueduct was built, about the year 1890, the art of drilling rock had been so far perfected, and the use of explosives, through the invention of dynamite, had become ,so general, that this waterway was planned and executed on straight lines, following rather than avoiding the rock. The second Croton Aqueduct is a tunnel through rock, about 32 miles in length; material gneiss, almost as hard as granite. Its construction was made practicable by sinking

Jan 9, 1913

By H. M. FRENCH

ARC welding can be defined as a process whereby two A pieces of metal are brought together, heated to a molten state by the heat of an electric arc, and fused into one piece. There are several kinds of arc welding: the metallic arc, the carbon arc, the atomic hydrogen arc and the shielded arc methods. A short description of each, together with its major applications, will serve to distinguish between them. Metallic arc welding involves an arc drawn between a metal electrode and the material to be welded, called the work or the "parent metal." It may be further subdivided into hand and automatic welding, depending on whether the electrode is fed to the arc by hand or by motor drive. This form of arc welding can be applied to most welding operations. Exceptions to its use consist of applications where very thin metals are to be welded; where it is desired to join the work with- out adding metal; or where extreme ductility may be required:

Jan 1, 1930

By James M. Barker

Sulfur is a nonmetallic element of great physical and economic importance to the world. It is widely but sparingly distributed throughout the hydrosphere, lithosphere, and biosphere. Sulfur is the tenth most abundant element in the universe and eighth most abundant in the sun. In the earth's crust, which is mainly igneous, it ranks 14th, but is eighth or ninth in sediments (Kaplan, 1972; Stanton, 1972). It apparently is very abundant in the core of the earth, because it is a strong chalcophile, and it is fifth in abundance in stony and iron meteorites (Field, 1972) where it occurs as trolite (FeS). In ancient times sulfur was called brimstone, literally "burning stone." Today the term brimstone is used interchangeably with the term elemental sulfur. Shelton (1979) summarized most of the common definitions of terms, grades, and specifications for the sulfur industry as follows (with minor additions): Sources of Sulfur: Combined sulfur-Sulfur that occurs in nature combined with other elements. Cupriferous pyrites-Pyrite containing relatively minor amounts of copper sulfide minerals. Hydrogen sulfide-A toxic gas (H2S) occurring in natural gas and petroleum. Involuntary sulfur-Sulfur produced primarily as a result of legislative or process mandates. Native sulfur-Sulfur that occurs in nature in the elemental (uncombined) form. Nonferrous metal sulfides-Copper, lead, zinc, nickel, and molybdenum sulfides that are processed for their metal content. Organic sulfurs-Complex organic sulfur compounds occurring in petroleum, coal, oil shale, and tar sands. Pyrites-Iron sulfide minerals that include pyrite, marcasite, and pyrrhotite. Sulfate sulfurs-Sulfur in anhydrite and gypsum. Voluntary sulfur-Sulfur produced in response to market forces. Basic Sulfur Products Produced and Marketed: Acid sludge-Contaminated sulfuric acid usually returned to acid plants for reconstitution. Brimstone-Synonymous with crude sulfur. Bright sulfur-Crude sulfur free of discoloring impurities and bright yellow in color. Broken sulfur-Solid crude sulfur crushed to -8 in. Byproduct sulfuric acid--Sulfuric acid produced as a byproduct of a metallurgical or industrial process, generally relating to combined sulfur sources. Crude sulfur-Commercial nomenclature for elemental sulfur. Dark sulfur-Crude sulfur discolored by minor quantities of hydrocarbons ranging up to 0.3 % carbon content. Elemental sulfur-Processed sulfur in the elemental form produced from native sulfur or combined sulfur sources, generally with a minimum sulfur content of 99.5%. Formed sulfur-Elemental sulfur cast or pressed into particular shapes to enhance handling and to suppress dust generation and moisture retention. Frasch sulfur-Elemental sulfur produced from native sulfur sources by the Frasch mining process. Hydrogen sulfide-Associated with natural gas or petroleum and produced at refineries and coke oven plants; used to make sulfuric acid or recovered sulfur. Liquid sulfur-Synonymous with molten sulfur. Liquid sulfur dioxide-Purified sulfur dioxide compressed to the liquid phase. Molten sulfur-Crude sulfur in the molten phase.

Jan 1, 1983

By A. W. Hesse

The trend of American construction toward permanence and longevity is noticeable in the more recent coal plant installations; also, the policy of many coal operators has changed from seeking to obtain the desired tonnage from several plants of small capacities to designing a single installation to produce the whole amount. The mine openings and plant of the Nemacolin mine of The Buckeye Coal Co., are located on the Greene County side of the Monongahela River, 73 miles south of Pittsburgh. The map (Fig. 1) shows the general location, also the Lambert syncline. This syncline partly accounts for the selection of the site; the other reasons were the possibilities of rail and river shipments. Two shafts and a slope were sunk to the coal, work starting on all three in the second half of the year 1917. The air shaft was sunk to a depth of 243 ft. and completed in February, 1918; the slope was completed in November, and the skip shaft was stopped at a depth of 21 ft. below the coal, then the concrete lining was stopped 8 ft. above the coal August, 1918. Work on the skip shaft was resumed May, 1923, and sunk to a depth of 60 ft. below the coal by September, but it was not until May, 1924, that the lining was poured. Max. Min. WateR Water during after Sinking, Crouting, Depth or Cu. Yd. Cu. YD. Gal. per GaL. per Opening Size Length Excav. Conc. Min. Min. Air shaft..... 20 ft. diam. 251 ft. 8 in. 4788 1902 475 2 Slope........ 11 it. by 19 it. 1 in. 857 ft. 11500 5200 50 2 Skip shaft.... 32 ft. 8 in. by 12 it. 8 in. 296 ft. 6042 2293 300 3 Fig. 2 shows sections of these openings. The surface plan shows the relative positions of the openings. Coal was first hoisted from the air shaft May 7, 1918, and entry driving was continued; but the coal had to be stored, as the railroad had not been extended from Crucible to Nemacolin. As soon as the slope was driven to the coal and the linings concreted, the entries were driven along projected lines to connect with those advancing from the air shaft, and skip shaft. As soon as the underground connections had been made between the two shafts, the hoisting by buckets was inaugurated at the skip shaft and construction on the fan at the air shaft started.

Jan 1, 1927

By D. W. Fuerstenau

On page 1243, column 1, the first line of the author's reply should read "D. W. Fuerstenau (author's reply)---," rather than D. E., as printed. In the sentence immediately preceding the first equation (page 1243, column 2)' the word "none" was omitted. The sentence should read: "However, if enough ore is put into the mill [so] that none of the energy put into the mill is wasted on metal-to-metal impact, then the product should have size modulus determined by the relation: ..."

Jan 1, 1961

By Bruno Nordberg

THE high cost of coal in Butte and the development of large amounts of cheap electric power from the Missouri river caused the Anaconda Copper Mining Co. in 1908 to make an investigation as to the possibility of adapting this cheap electric power for the operation of their many large hoisting plants. At this time electric power had already been adopted for practically all other power purposes around the mines, such as pumping, compressing air, etc. The map (Fig. 1) shows the location of the mines of the Butte mining district. These mines are located within a circle of approximately a 1-mile

Jan 9, 1913

By E. C. Lee

THE safety of mine workers has received more attention from both State and Federal law-making bodies than any other industry, a fact that shows clearly the hazardous nature of the industry. The last, but by no means the least, of the measures adopted for the protection of mine workers, is workmen's compensation legislation. This is proving to be a powerful instrument for greater safety in the industries, from the fact that special stress is laid not on how the accident happened or who may have been responsible for it, but on how badly the employee is hurt by it. The injured person does not have to employ lawyers to prove his case, because the mere fact of his employment is proof of his right to compensation. The immediate effect of such legislation is the certainty confronting the mine operator that he must pay out large sums for every accident, regardless of its cause, thus adding materially to the cost of the production of his coal. This fact furnished to the operator the strongest incentive to reduce the causes of accidents; not that the operator has ever lacked reasonable consideration for the welfare of his employees and a proper humane interest in their safety, but his engrossment in earning his daily livelihood has been so great that he has not felt that he had the time to devote to the safety of the operation. This time he must now find because of the actual-cash value of the prevention of accidents in his mines. This agency alone proved inadequate to bring about a material improvement because operators have always been willing enough to improve safety conditions when possible to do so within reasonable limits of their financial ability. The requirement in the Workmen's Compensation Laws of several of the States, that the mine operator shall insure as a guarantee of his ability to meet his compensation obligations, has furnished the needed incentive, moral and financial, necessary to the prompt and effective dissemination of a more general knowledge of the causes and

Jan 10, 1917

By Laurence Pellier

Electron microscopical studies were made of the effect of sensitization at 1200oF on a Type-.104 stainless steel with high carbon and low nitrogen and oxygen contents, after solution annealing and after cold working. The loci of the carbide precipitates in the early stages of sensitization were followed in dry stripped plastic replicas. Some observations were made by direct electron transmission on thinned films. Intragranular dislocations showed a high degree of stability through the annealing necessary to produce sensitization. I HE present work was undertaken to determine the effect of sensitization, at 1200°F, for 1/2 hr, on the electron microstructure of a Type-304 stainless steel with high carbon, and low nitrogen and oxygen contents, after solution annealing and after cold working. Many electron microscopical studies of sensitization of 18-8 stainless steels have already been made. Most of them utilized extraction replicas, from which the morphology and composition of the precipitated carbides could be established.'-" ry stripped replicas were seldom used for such studies, although it was demonstrated that they are applicable, in general, to EurveYs of the general microstructure of many alloys' and, in particular, to the observation of precipitated carbides in austenitic stainless steels.3

Jan 1, 1963

CONTENTS PAGE Need for Research in Foundry Pig Iron. By Richard Moldenke. (With Discussion) 1 Carbon Characteristics of Copper-bearing Pig Iron. By W. B. Coleman. (With Discussion) 12 A Pig Iron, Low in Total Carbon, is in Demand for Use in Various Industries. By Enrique Touceda. (With Discussion) 24 Carbon in Pig Iron. By Ralph H. Sweetser. (With Discussion) 28 Second Session (Discussion) 37 Need for Research in Foundry Pig Iron BY RICHARD MOLDENKE,* WATCHUNG, N. J. So FAR as the quality of the product is concerned, the history of the production of pig iron for foundry purposes is one of constant retrogression. The steps in this deterioration began with cold-blast charcoal pig iron, then anthracite iron, coke iron; then gradually warm to hot-blast coke iron, with the charcoal furnaces also heating their blast to get greater tonnages, and finally the present-day hot-blast coke irons with scrap additions to the ordinary burden that, according to one European report, have gone as high as 65 per cent. Parallel with this quality retrogression is the enormous increase in furnace tonnages from about 15 to over 1000 tons per day in exceptional instances of modern practice. The key to this situation is economic pressure. The effect is a growing differentiation between furnace production for gray iron and malleable foundries and, for the

Jan 1, 1927

By Hugh Roberts

During 1916 and 1917, the E. J. Longyear Co. of Minneapolis, Minn., carried out a campaign of exploration for nickel-copper ore in the Sudbury District of Ontario. The work was initiated by W. E. Smith, a resident of Sudbury, who called the attention of W. J. Mead, Chief geologist. The E. J. Longyear Co., to the fact that explorable lands in the Sudbury District were still available. Five diamond drills were employed, and holes were drilled in the townships of Levack, Trill, Denison, Blezard; Garson, Falconbridge and MacLennan. The general map of the District, Fig. 1, shows the distribution of the lands chosen. As a result of this exploration, a large body of nickel and copper ore has been found in the western part of the Township of Falconbridge. This property lies in the eastern part of the Sudbury District, east of the Garson mine.

Jan 2, 1918

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Jan 1, 1946

By Evan Just

DIRECT subsidies for mine production in this country began as an outgrowth of wartime 'price regulation. The price-fixing authorities realized that the volume of production to be required from domestic copper, lead, and zinc mines would invoke costs of production considerably higher than the established ceiling prices. Accordingly, beginning Feb. 1, 1942 the Premium Price Plan was set up, which undertook to pay premiums to mines for production in excess of quota, of 5¢ per lb of copper and 2Y4¢ per lb of zinc or lead. Quotas, except for small mines, were initially established at the average rate of production in 1941, but were later reduced arbitrarily on an individual basis. Subsequently, additional "B" premiums were set for lead and zinc of 2Y40 per lb and a further "C" zinc premium of 2%¢. Additional copper premiums were negotiated on an individual basis, mainly with small mines. Quotas under each of these successive categories were the production obtained at the next lower premium level. In other words, under ceiling prices of 12¢ for copper, 6,14¢ for lead, and 83¢ for zinc, it was possible for high-cost operations to receive prices plus premiums of 17¢ or more for copper, 12¢ for lead, and 16% 0 for zinc on a portion of their production. On the other hand, some of the larger operators received only slight premiums and in at least one instance none at all. The average price plus premium for copper was 12.25¢ in 1942 and rose to 13.65¢ in 1945. That for lead was 6.99¢ in 1942 and 8.73¢ in 1945, and for zinc it was 9.06¢ in 1942 and 11.200 in 1945.

Jan 1, 1948

By Jack A. Simon, M. E. Hopkins

GENERAL GEOLOGY Coal is defined as a combustible rock that had its origin in the accumulation and physical and chemical alteration of vegetation. Coal can be ignited and burned like the wood that was man's earliest fuel, but coal gives more heat than the same amount of wood and has many industrial uses. Unlike wood, coal is not generally found on the surface of the ground but is mined from the solid rock of the earth. Before taking up the occurrence, formation, and the somewhat unique character of coal in the rock sequence, let us briefly consider the general character of all rocks in the crust of the earth. Relatively little is known about the very earliest history of the earth, although a number of logical theories have been developed. Manned exploration of the moon and the rocks being returned to earth will, we hope, provide some answers to questions concerning the earth's origin and history. The period of earth history with which we concern ourselves here begins after great areas of water had evolved on earth and substantial land areas of once molten (igneous) rock existed. Weathering and other processes that attacked the surface of the rocks reduced them to small particles. Water provided by rainfall transported this material, ultimately, to large bodies of water where it was deposited. Thus was initiated the geologic sequence of sedimentary rocks that lie above the once molten igneous rocks. The crust of the earth is not completely stable, and throughout the geologic past portions of the crust have moved laterally and vertically. Even today, many coastal areas are slowly rising or sinking. More sudden earth movements are recognized by the earthquakes they cause. Throughout geologic history, rises in sea level or the sinking of the land areas have many times permitted the oceans to cover much of what are now the areas of the continents. Only relatively small parts of the present continents appear to have been above sea level throughout geologic time. Great

Jan 1, 1973

By C. A. Heiland

For a long time it has been known that it is possible to deduce conclusions about the physical constitution of the interior of the earth from the records of natural earthquakes obtained by stationary seismographs. In view of this fact it is surprising how late, relatively speaking, geologic prospecting by seismic methods has been taken up, although the first suggestion was made 40 years ago- that travel-time curves of artificial explosions might be used for the study of the change of the velocity of seismic waves as depth. Further suggestions of practical applications of artificial explosions for geologic purposes were made by Belar,2 by von dem Borne,3 by Benndorf4 and by Galitzin,5 but it was not until 1919 that Mintrop obtained. a patent on the seismic prospecting method which he has applied commercially on a large scale ever since. Dr. Mintrop came to this country with his method at about 1923. Since that time, several. American oil companies have developed seismographs of the mechanical type for the vertical component similar to that of Mintrop's (Humble Oil Co., Dr. Ricker). Other consulting geophysical companies designed other types of seismic devices, the simplest of them for the recording of the first impulse being the geophone (McCollum Geophone Co.). The galvanometric recording method as first proposed by Galitzin is being used (Geophysical Research Corpn.?) and use is being made even of the piezoelectric properties of crystals for portable seismographs (F. Rieber).. There is such an enormous variety of all kinds of portable seismographs, vibrographs, accelerographs, etc., that it is difficult to decide just what kind is preferable. Unfortunately, nothing has been published as yet about American designs of portable seismographs, except the Wood Anderson torsion-seismometer. After Mintrop's design of portable seismographs, other constructions were made.

Jan 1, 1928

By R. Ehrlich, F. E. Crane

A consolidated porous medium is mathematically modeled by networks of irregularly shaped, interconnected pore channels. Mechanisms are described that form residual saturations during immiscible displacement both by entire pore channels being bypassed and by fluids being isolated by the movement of an interface within individual pore channels. This latter mechanism is shown to depend strongly on pore channel irregularity. Together, these mechanisms provide an explanation for the drainage-imbibition-hysteresis effect. The calculation of steady-state relative permeabilities, based on a pore-size distribution obtained from a Berea sandstone, is described. These relative permeability curves agree qualitatively with curves that are generally accepted to be typical for highly consolidated materials. In situations where interfacial effects predominate over viscous and gravitational effects, the following conclusions are reached. 1. Relative permeability at a given saturation is everywhere independent of flow rate. 2. Relative permeability is independent of viscosity ratio everywhere except at very low values of wetting-phase relative permeability. 3. Irreducible wetting-phase saturation following steady-state drainage decreases with increasing ratio of nonwetting- to wetting-phase viscosity. 4. lrreducible wetting-phase saturation following unsteady-state drainage is lower than fir steady-state drainage. 5. Irreducible nonwetting-phase saturation 101lowing imbibition is independent of viscosity ratio, whether or not the imbibition is carried out under steady- or unsteady-state conditions. Experiments qualithtiveIy verify the conclusions regarding unsteady-state residual wetting-phase saturation. Implications of these conclusions are discussed. INTRODUCTION Natural and artificial porous materials are generally composed of matrix substance brought together in a more or less random manner. This leads to the creation of a network of interconnected pore spaces of highly irregular shape. Since the geometry of such a network is impossible to describe, we can never obtain a complete description of its flow behavior. We can, however, abstract those properties of the porous medium pertinent to the type of flow under consideration, and thus obtain an adequate description of that flow. Thus, the Kozeny-Carmen equation, by considering a porous medium as a bundle of noninterconnecting capillary tubes, provides an adequate description of single-phase flow. With the addition of a saturation-dependent tortuosity parameter in two-phase flow to account for flow path elongation, the Kozeny-Carmen equation has been used to predict relative permeabilities for the displacement of a wetting liquid by a gas. 1-5 It has long been recognized that relative permeability depends not only on saturation but also on saturation history as we11.6,7 Naar and Henderson8 described a mathematical model in which differences between drainage and imbibition behavior are explained in terms of a bypassing mechanism by which oil is trapped during imbibition. Fatt9 proposed a model for a porous medium that consisted of regular networks of cylindrical tubes of randomly distributed radii. From this he calculated the drainage relative permeability curves. Moore and slobod,10 Rose and Witherspoon,11 and Rose and Cleary12 each considered flow in a pore doublet (a parallel arrangement of a small and large diameter cylindrical capillary tube). They concluded that, because of the different rates of flow in each tube, trapping would occur in one of the tubes; the extent of which would depend upon viscosity ratio and capillary pressure. They limited

Jan 1, 1970

By George Holderer

THE Enos Coal Mining Co. owns an area underlaid by coal, of approximately 5000 acres. This property is situated 9 miles from Oakland City, in the southern part of Indiana. The mine has been in operation 5 years, during which time some 350 acres have been stripped, and stripping is now proceeding at the rate of about 100 acres per year. TOPOGRAPHY These coal lands consist of gently-rolling agricultural fields which in times past were farmed for wheat. There is no timber and but very little brush to contend with. The overburden varies from 10 to 60 ft. in depth. A thin bed of slate overlies the coal, followed by limestone, which varies from 3 to 15 ft.; this, in turn, is followed by sandstone, slate, shale and clay. There is a very wide variation in the thickness of all of these beds. The coal has an average thickness of 5 ft., and is a good grade of high-volatile bituminous. MINING OPERATIONS Briefly, the sequence of operations is: drilling holes with churn drills; blasting with L. 0. X.; stripping overburden to, uncover coal and, finally taking up the coal, which is sent to a tipple for cleaning and sizing. In order to show what is being accomplished by the use of L. 0. X., results will be shown from May to November, 1926, inclusive, and compared to the same period in 1925. No work was done in No. 1 pit during May, 1925, hence all figures are unduly low for this month.

Jan 2, 1927

By Carl Swartz

METALLURGISTS differ considerably in their opinions regarding the effect, if any, of small amounts of iron pyrites, or other iron compounds on zinc sulfide ores during the roasting operation. As a result, the literature on this subject expresses many conflicting ideas. The ore, previously crushed to pass through a one-millimeter screen, dries in the roasting kiln, losing water up to 200° to 300° C. At 150° C. iron pyrites begin to lose sulfur. As the temperature increases, while the ore is passing to the hotter part of the furnace, the sulfur burns to sulfur dioxide, leaving the metals as zinc oxide and ferric oxide. These two substances then interact to form zinc ferrite, a compound, yellow brown in, color, having the general characteristics of a spinet Like magnetite, another spinel, zinc ferrite is insoluble in alkalis and dilute acids. As a result, when leached with 10 per cent. sulfuric acid solution zinc values tied up in this compound remain behind. HISTORY In the electrolytic recovery of zinc from its ores, the roasted ores are usually leached with a 10 per cent. sulfuric acid solution. When the zinc ore contains iron pyrites as an impurity in an appreciable amount, the actual yield of metallic zinc is much lower than a theoretical calculation would indicate. Further, losses of zinc are, in a rough way, directly proportional to the amount of iron pyrites or other iron compounds present. When the iron is present in the ore in an isomorphous relation to the zinc, as in the case of a marmatite, a greater amount of zinc remains insoluble than when present as a true pyrite or marcasite. Work on the insoluble residues obtained from leaching of the calcines shows that the zinc lost is intimately tied up in this residue. Some investigators have suggested a definite compound, such as zinc ferrite, others merely a mixture of zinc and iron compounds.

Jan 1, 1927

Sponsored by the Utah Section of AIME, the 1960 Annual Rocky Mountain Minerals Conference brought more than 500 members of the mineral industry to the conference rooms of the Newhouse Hotel in Salt Lake City during the period October 5 to October 7. Under the overall supervision of J. M. Ehrhorn, general chairman, and H. E. Wright, assistant general chairman, the Conference offered 14 papers of technical interest in four sessions during the first two days, and it culminated in the Exploration Symposium held on the morning of October 7. The opening session of the Conference, meeting on the morning of October 5, heard R. P. Work, utility engineer of the Mountain Fuel Supply Co., discuss the growth and economic factors related to the use of natural gas in Utah. In his paper entitled Natural Gas Market In Utah, Mr. Work emphasized the very good prospects of natural gas serving almost all parts of that state. He mentioned that recently the El Paso pipeline, built to serve the Pacific Northwest with gas from Texas, has permitted natural gas to be available to Eastern Utah, and a tentatively planned pipeline from Green River, Wyo. to Southern California will bring natural gas to the central and southeast areas of the state.

Jan 11, 1960

Jan 1, 1966

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