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Jan 1, 1966

By F. H. Deily, D. S. Rowley, R. J. Howe

By Arthur F. Taggart

TO all Mineral Dressers, but particularly to those in the Coal and Industrial Minerals Divisions: Ted Counselman, retiring after two years at the helm of the Milling Committee, pointed with pride to the continued growth of that committee, and sang the swan song "Why ain't we a Division of Mineral Dressing?" Our genial Secretary pointed out, handily, that, you see, the way the Institute is divided there are several blocks running across this way here, and one running all the way down here, and another running part way down here, and they all cut across each other like this, and anyway the miners want to be a Division now, so why not you Mineral Dressers be good and not upset the big Institute organizational chart? And anyway again, Divisions have vested interests, and a Division of Mineral Dressing would take something away from Coal and something from Industrial Minerals, and any good institutional man can see that a Division would never give anything up. It was all quite confusing, and apparently not too convincing, because then the Milling Committee went ahead and voted unanimously it is a good idea, let's see what the other fellows think about it as well.

Jan 1, 1944

By Harry L. Washburn, Robert L. Llewellyn, W. J. Halvorsen

Many of the problems that occur in the preparation plant originate from practices in the mine. Impurities in raw coal can be in the seam itself or from extraneous material taken in mining from the roof or bottom. In the case of underground mines, the choice of mining equipment will affect the size consist and the amount of extraneous material included with the coal. Also, governmental regulations concerning the degree of rock dusting, gobbing underground, and cleanup have increased the dirt in raw coal. Sulfur dioxide emission standards, on the other hand, are pressuring the coal industry to clean coal more thoroughly. Coal supplied for coking purposes is nearly all upgraded by washing, while for the largest market, electric power generation, a high proportion is shipped as a raw product with processing, in whole or in part, only necessary when excess impurities are mined with the coal. This chapter will deal primarily with plants that process or wash coal to some extent (Fig. 1) and only incidentally with mines shipping raw run-of-mine coal crushed to a top size of, usually, 51 to 102 mm (2 to 4 in.), with little, if any, other treatment. JUSTIFICATION FOR COAL PREPARATION During the past decade, major changes have occurred affecting the market, profit, and long-range planning of the coal industry. Mining companies have become "partners" with consumers at many new and some old mines, both for steam and metallurgical coals. Coal properties have become "assigned" tonnages at mutually agreed upon conditions and prices. Lower unit-train tariffs have been instrumental in helping coal markets to compete against oil and nuclear energy. Coal prices for power plants are still on a Btu (British thermal unit)

Jan 1, 1981

By D. J. McAdam

As shown in three recent papers by the author, in two papers by McAdam and Mebs, and in a paper by McAdam, Mebs, and Geil," the technical cohesive strength of a metal, in any particular state as regards mechanical treatment and heat-treatment, cannot be represented by a single stress value, but must be represented by a diagram with the principal stressest as coordinates. Each point on the boundary of such a diagram represents a technical cohesion limit. The technical cohesive strength thus comprises an infinite number of technical cohesion limits, each representing fracture under a specific stress combination. Moreover, neither the yield strength1 nor the ultimate strength can be represented completely by a single stress value, but must be represented by a diagram with the principal stresses as coordinates. All combinations of the principal stresses may be classified in three groups as illustrated by Fig. I. Fig. Ia shows three typical stress combinations with no two principal stresses equal. The magnitude of each principal stress is indicated qualitatively by the length of the arrow. Arrows pointing away from the cube indicate tensile stresses; arrows pointing toward the cube indicate compressive stresses. Typical stress combinations with two principal stresses equal are illustrated in Figs. rb and Ic. Such stress combinations would be produced by subjecting a cylinder to combinations of uniform axial and radial stresses. The uniform radial stress may be resolved into two equal principal stresses. with the mutually perpendicular directions rotatable around the axis of the cylinder. Fig. ib shows stress combinations with Sz equal to The greatest principal stress is in the axial direction, and the stress combination tends to cause either absolute or relative increase in length.* Fig. u shows stress combinations with S2 equal to St. The greatest principal stress is in the radial direction, and the combination tends to cause either absolute or relative decrease in length. The complete representation of either technical cohesive strength, yield strength, or ultimate strength generally requires a three-dimensional diagram. When two of the principal stresses are kept equal, however, the strength of a metal may be represented by a two-dimensional diagram with the coordinates representing the axial and radial stresses.6-II In this paper, attention will be confined almost entirely to stress combinations with two of the prin-

Jan 1, 1945

By K. A. Natarajan, S. C. Riemer, I. Iwasaki

The relative significance of corrosive and erosive wear in magnetic taconite grinding is examined. The influence of different types of aeration (nitrogen, air, and oxygen) on ball wear was established for mild steel and high carbon low alloy steel balls. Ball wear data from dry and wet grinding tests are compared with those obtained in the presence of an organic solvent that does not promote electrochemical corrosion. Marked ball grinding tests and electrochemical measurements involving ball material and magnetite electrodes indicate that contribution from oxygen toward wear (corrosive wear) is relatively small, and abrasive wear appears to be significant. Rheological properties of the slurry appear to have an important bearing on the abrasive wear of grinding balls.

Jan 1, 1985

By AIME AIME

ALL technical men who are planning to visit the Century of Progress Exposition in Chicago this summer-and all reports indicate that it will be worth visiting-should try to be there during Engineers' Week, beginning June 26. At that time most of the national engineering societies of the country will hold important meetings in that city. Engineers will thus have an opportunity not only to see the Fair at a time when special programs have been arranged for their benefit, but will have the opportunity to meet their professional brothers and to attend technical sessions of direct interest to them. The A.I.M.E. headquarters will be at the Stevens Hotel, and it will be to the interest of every Institute member who expects to attend the Fair at that time to secure his accommodations as promptly as possible. A request to the Chairman of the Chicago Section, A.I.M.E., or to the Secretary's office in New York, will bring a copy of the program as soon as it is available, together with any in- formation desired about hotel accommodations or other matters. The Chairman of the Chicago Section is J. R. Van Pelt, and his address is Museum of Science and Industry, 1525 East 53rd St., Chicago.

Jan 1, 1933

By H. Hubert

THE first attempts at direct utilization of blast-furnace gas in engines were made in 1895. For a considerable time the gas had been burnt in Cowper stoves for heating the blast for the furnace, and under the boilers which supplied steam to the blowing-engines, and others serving the furnaces. It was natural, therefore, that the idea of directly employing it in gas-engines should have occurred simultaneously to several engineers, notably to Lürmann and to Lencauchez, who had pointed out the blast-furnace as a powerful -gas-producer. Nevertheless, nowhere had any attempt been made to apply it to this purpose up to the end of 1894, when Thwaite proposed it to Mr. James Riley, of the Glasgow Iron & Steel Company. About the same time investigations were being made in Belgium and in Germany, independently of Thwaite's experiments, which were not generally known on the Continent. The industrial world, which up to that time had hardly favored the idea, had thus been gradually prepared to receive it. The gas-engine, long restricted to small sizes and dependent upon the use of an expensive fuel obtainable only in large centers, now began to make headway. At the Paris Exhibition of 1889 two engines of 100 h.p. were shown and excited much interest among engineers. One had four cylinders, and was made at the celebrated works of the Deutz Company, and the other was a single-cylinder engine, exhibited by two French designers, Messrs. Delamare-Deboutteville and Malandin. In the meanwhile the design of gas-producers had made important progress, completely freeing the new engine from its

Nov 1, 1906

By A. Gatti

Studies were made on the system iron plus alumina. Various methods of dispersing and various amounts of alumina were used. Powder metallurgy techniques were used to produce the final product. Microstructures and some mechanical properties are presented. Alloys containing up to 16 pct alumina by weight are ductile at all temperatures tested. The ivon-alumina materials have a higher yield stress and improved creep resistance over that of pure iron. SINCE the development of SAP' an A1- Al2O3 powder metallurgy product, great interest has been shown in the development of a SAP-like structure in metals and alloys other than aluminum. The outstanding properties of this class of materials are: 1) Good creep resistance at high temperature. 2) High yield strengths and high hardness at high temperatures. 3) High recrystallization temperature. However, the lack of ductility and formability has thus far limited the applications of SAP-like materials. The following report deals with methods of dispersing A12O3 in Fe, processing of powders into rod, structures produced after processing, and mechanical properties of the iron-alumina material produced. Methods of dispersing the alumina and also the volume fraction of alumina added were varied. MATERIAL Powder Processing— Four methods of obtaining dispersions of alumina in iron were studied. 1) Oxidation-reduction of a Fe + 8 pct Al alloy. .2) Coprecipitation of Fe(OH)3 + Al(OH)3 from aqueous solution. 3) Colloidal mixing of Fe,O3 and Al2O3. 4) Colloidal mixing of Fe powder and A1,O3. Fig. 1 is a processing flowsheet which outlines the processing steps taken to produce a final extruded bar 1/4 in. in diameter and about 30 in. long. The - 100 mesh iron-aluminum alloy was oxidized by placing a thin layer of powder on an alumina plaque. The reduction step was modified to include 1/2 hr at 1000°C since the powders tended to become pyro-phoric unless sintered slightly after low-temperature reduction. Compacting was done in a 1-1/8-in.-diam pressing die. The slugs produced averaged 1 in. in length. The billets were encased in low-carbon steel cans shown schematically in Fig. 2. The blank is included for structure and property comparison purposes. TESTING PROCEDURE All tests were made on as-extruded material.

Jan 1, 1960

By A. B. Parsons

LECTURE, it appears, is a discourse that is supposed to be instructive. I am quite sure that you will derive no instruction from what I have to say. I will be satisfied if my remarks provoke thought along one or two mental paths that have not been traveled so fre¬quently as to be devoid of interest. I have no particular message apropos of professional engineers or professional engineering, and any conclusions that I may seem to reach will be purely tentative and incidental. Probably at times you have wondered, in a casual way at least, why so many people who are not, never have been, and never will be engineers, want to use the title. For example, I recently received a communication from a life insurance broker or salesman, whose chaste letterhead bore the legend "Estate Engineer." He was perfectly serious about it, as is also the expert accountant who assumes the imposing name of cost-analysis engineer. Dozens of equally amazing titles might be cited. Then there is that class of individuals who have been engineers, in the true sense of the word; who have gone into some other kind of occupation; but who cling tenaciously to the name engineer, usually prefixing some word or other which at once gives them away by telling what their work really is. For example, we have such pseudomorphs as the management engineer, and the sales engineer. It is quite evident that engineer is a word to conjure with. Evidently both the man who appro¬priates the designation without any justification and the ex-engineer who persists in calling himself an engineer even after he has abandoned engineer-

Jan 1, 1933

By P. A. Beck, M. V. Nevitt

All binary and a number of ternary u alloys formed by first long period transition elements were examined and found to be ferromagnetic at low temperatures. The Curie temperatures for these alloys were measured. It was found that the correlation of the Curie temperature with composition may be described qualitatively in terms of the contributions of the various component atomic moments to the saturation moment of the alloy. Ternary Fe-Cr-Mo u phase alloys were also found to be ferromagnetic, with a Curie temperature dependent on the iron content and largely independent of the unit cell dimensions. Similar relations were found for the Co-Fe-Cr and the Co-Cr-Mo a alloys, where the Co + Fe content appears to determine the Curie temperature. RECENTLY, it has become increasingly evident that the u phase is some kind of an "electron compound." Several papers1-' discussed the empirical correlation between the composition of the various u phases in alloys of the transition elements and the distribution of electrons in the partially filled d-levels of the component atoms. However, a picture of the latter can be formed only in a more or less intuitive manner, as in the Pauling theory," and the rigorous treatment of these problems is at present prevented by lack of adequate knowledge of the electronic structure of the transition elements in the metallic state. It appeared reasonable to expect that investigation of the magnetic properties, which are related to d-shell electrons, may help in clarifying the physical nature of the foregoing empirical correlation. Qualitative tests of samples of various compositions have shown that certain u alloys become ferromagnetic at liquid nitrogen temperature." The present investigation was undertaken to determine whether or not low temperature ferromagnetism is characteristic of a large variety of u alloys and to establish how the Curie temperatures of ferromagnetic u alloys are influenced by changes in composition and in lattice parameter. In the first portion of the in- vestigation, Curie temperatures were measured for a series of u alloys containing either vanadium or chromium with one or two of the elements manganese, iron, cobalt, or nickel. In the second phase of the work, data were obtained on the Curie temperature of ternary (Fe, Co, Cr)a, (Fe, Cr, Mo)a, and (Co, Cr, MO)U alloys, as a function of composition and of interatomic spacing. Experimental Procedures High frequency vacuum melting in high purity re-crystallized alumina crucibles was employed in the preparation of the u alloys, using metals whose lot analyses are given in Table I. Approximately two-thirds of the alloys were analyzed chemically, the analytical results being in acceptable agreement with the intended compositions, as seen in Tables I1 and 111. The specimens were annealed for homogen-ization in an atmosphere of purified 92 pct He and 8 pct H, mixture or in evacuated and sealed Vycor tubes at temperatures from 780" to 1300°C, depending on the temperature range of the u phase field for the particular composition. The annealing temwerature and time for kach alloy are given in Tables 11 and 111. Curie points were determined by an induction method; the change with temperature of mutual inductance between two coils was observed when the i-u specimen was inserted into the flux path between the coils. The transformer consisted of three coils each containing 1200 turns of 0.0050 in. diam enameled copper wire. The center coil, P in Fig. 1, served as the primary coil, and was linked magnetically with each of the two secondary coils, S, and S? which were connected in series opposition. The primary coil, P, was energized by an audio-oscillator, set at a frequency of 500 cycles per sec, while the signal from the transformer secondary circuit,

Jan 1, 1956

By E. S. Moore

ALTHOUGH nickel was in use in alloys long before the Christian era, the metal was not discovered until 1751, when Cronstedt recognized it in niccolite from Sweden. The Chinese apparently used a nickel alloy, known as "pahfong" thousands of years ago and Persian coins dating farther back than 200 B.C. consist of a copper-nickel alloy similar to some of those now in use in coins. The pure metal was first prepared about 1775 and the metal was refined for commercial purposes some years later. The nickel industry did not attain much prominence until the ores in New Caledonia were discovered. Exports of ore from that country began in 1875 and since that date there has been an ever-increasing world output of nickel and a great expansion in the uses of the metal except during short periods of commercial and industrial depression. Previous to 1875, for a number of years, Norway was the chief producer, although the metal was mined also in Sweden, Finland, Italy, Germany, Austria, France, China, the United States and other countries. With the dis-covery of nickel deposits in the Sudbury district, Ontario, a new factor was introduced into the nickel industry and Sudbury has since become the overwhelmingly dominant feature in the world's nickel markets. Although nickel was first discovered in Canada as early as 1848 near the north shore of Lake Huron and nickel-copper sulfides were found in 1856 by surveyors working close to the present location of the important mine at Creighton, in the Sudbury field, it was not until 188.3 that any importance was attached to this field. In that year copper sulfide attracted attention where the main line of the Canadian Pacific railroad was being projected across Canada to the Pacific coast. Mining began near this discovery in 1889 but in the meantime operations had begun in 1886 in other parts of the field and by 1890 about 100,000 tons of ore had been raised. In the Sudbury field, as in Norway and at the old Lancaster Gap mine in Pennsylvania, the ore was first mined for its copper content and difficulty in the refining of the copper led to the discovery of the important proportions of nickel in the ore. No. 3 property of the Inter-national Nickel Co., now known as the Frood, the greatest deposit in the

Jan 1, 1932

By WILLIAM BOWIE

IN most human endeavors a knowledge of the terrain is essential to the effective carrying out of projects, but no line of work is more dependent on maps than theoretical and applied geology. Maps of a kind do exist for all of the area of the United States, but most of them are crude affairs and of little use in engineering, planning, and scientific research. Topographic mapping in the United States was initiated on a national scale by the U. S. Geological Survey and the organizations that were merged in its creation to make base maps for geologists. Their work could not be effectively done then and cannot be effectively done now without maps that accurately delineate the earth's surface. The distribution of the rock masses that contain valuable mineral bodies, or that by their intrusion brought them into existence, is the first step in a study of the mineral resources of the nation. This work requires three-dimensional maps, that is, topographic maps on which the land forms are shown by contours.

Jan 1, 1938

By C. C. Herrick

The vapor pressure of indium has been measured by the torque-effusion technique, as a function of temperature between 1102o and 1422oK. For liquid indium, the vapor pressure (in atmospheres) can be represented by the equation -R In P = 5.782 x104/T - 25.29from 1000o to 1422oK. Extrapolation yields a calculated normal boiling point of 2329°K and a heat of vaporization at 298 oK of 58.09 kcal per mole by the third-law method and of 58.39 kcal per mole by the second-law method. Calculations indicate that the free-energy functions of Hultgren are to be preferred to those of Guruich. BECAUSE of the potential uses of liquid metals, it is important that convenient experimental methods be developed which will lead to a sufficient body of thermodynamic data so that reasonable estimates of properties of liquid metals can be made. Indium is particularly well-suited to investigation, since it remains liquid over a long temperature interval, it alloys readily, suitable containers for it are easily procured, and relatively few investigations of its thermodynamic properties in the region above 1000°K have been made. PREVIOUS RESEARCH The first determination of the vapor pressure of indium was made by Anderson,' using the Knudsen method and silica-lines stainless-steel cells. Kohlmeyer and spandau2 determined the normal boiling point, and a mass-spectroscopic investigation has been made by Lyubimov and Lyubitov.3 (Unfortunately, only an equation representing the data of the latter investigators has been available to us.) Hultgren et al.4 and Gurvich5 have published discordant tables of the free-energy functions for indium. EXPERIMENTAL METHOD The torsion-effusion principle has been described amply in the literature.8,7 With this method, one observes the angular deflection induced by effusion of vapor from a multihole effusion cell which is suspended from a filament producing a small rotational restoring force. The pressure within the effusion cell can be computed from the relation ziaifiai where k is the torsion constant of the filament, 6 is the observed angular deflection, and ai, fi, and qi are the area, force factor, and moment arm of the ith effusion orifice. The force factor f is analogous to the Clausing factor,' and corrects for the reduction in effusive force attributable to the finite geometry of the effusion orifice. Schultz and Searcy' have tabulated the force factors for various tube geometries. EXPERIMENTAL APPARATUS The physical arrangement employed in this study is shown in Fig. 1. The furnace elements are six Globar heat rods with 15-in. hot zones. Temperature is maintained to * 1°K by a Beck mechanism driving two 26-amp Powerstats in parallel. A Pt (Pt, Rh 10 pct) thermocouple serves as the sensing element. Four inner tubes act as vibration isolators; the air pressure required for maximum isolation was determined empirically, and is maintained by a solenoid valve. The tungsten fiber, 9 by 0.002 in., is joined to an 0.008-in. tungsten wire or graphite rod via a machined lightweight chuck.

Jan 1, 1964

By FREDERICK C. BROWN

THE practice of fine-grinding is now being so successfully - carried on in some fields, notably in West Australia, and its advisability has been so frequently pointed out' that the matter in this paper is not put forward as being new ; its chief object being to call attention to the importance of fine-grinding in the treatment of comparatively low-grade ores. I have been engaged during the last five years in the cyanide-treatment of ores in the Ohinemuri district (North Island), New Zealand, and I consider that, in the near future, extremely fine-grinding (almost sliming) will become a very important feature of the milling-methods in this field, since it seems absolutely necessary to reduce the most of ores to a very fine state of division if a high extraction is to be obtained; and, in most cases, the extra percentage of saving will leave a good margin above the increased cost of treatment due both to the fine-grinding and to the interest on the capital spent for the grinding-machinery. The average ore of the Ohinemuri field is composed of a quartz-gangue with some calcite, carrying the gold-value in the form of an alloy of gold and silver in about equal proportions, and the silver-value in the form of mixed sulphides of silver, usually associated with a considerable amount of iron pyrites. In the upper levels, the ores are decomposed and carry large quantities of black manganese oxide and some iron oxide, but, as. depth is reached, the decomposed ore gives place to sulphides and, in some mines, rhodonite, manganese silicate, is present in fairly large quantities. The average value of the

Jan 1, 1906

"Butte originated as a placer mining camp. The first gold discovery was made in the year 1864, near what is now Main Street. Placer mining was vigorously prosecuted along Silver Bow Creek and in Missoula, Buffalo, Town and Parrot gulches for a period of five years, at the end of which time, in 1870, the camp was practically deserted. In the meantime, the quartz veins so prominently traceable over the hillsides were located, the first location being made by W. L. Farlin and called the Black Chief claim, and later restaked as the Travona. Reasoning from the presence of the gold placers, free-milling gold ores were eagerly looked for by the early prospectors. Claims covering the great Rainbow and other silver lodes were located in the sixties. The presence of valuable silver ores in these veins caused the staking out of many claims, believed to be valuable only for silver, but which later proved to be enormous copper producers.Treatment of these early discovered rich ores was first attempted in arrastres. Later, stamp mills were built. The Centennial dropping 10 stamps, was the first, and in 1875 Mr. Farlin built the Dexter 10-stamp mill, intro¬ducing chloridizing-roasting. More successful processes were soon introduced and several large mills built, among which were the Alice, Lexington, Silver Bow, Moulton and Bluebird, in all representing a total of 290 stamps. The silver mining industry reached its zenith in 1887 and declined rapidly in the early nineties, following the sudden drop in the price of silver in 1892.During this period of silver mining activity the business of copper mining was making rapid strides. Development of the veins, located as silver veins, had uncovered copper ore in many instances. There was great activity in ""claim staking'' in the years from 1871 to 1879, during which period most of the claims covering the present productive copper area were located."

Jan 1, 1913

By MARK H. LAMB

(Canal Zone Meeting, November, 1910.) THE recent growth of a sentiment among cyanide-plant designers against the use of gravity-stamps for the crushing preliminary to cyanidation may be said to date from the almost simultaneous perfection of the ribbed tube-mill liner and of the tall, air-agitation tank. The first step in the resulting change of practice was the universal adoption of the tube-mill for fine-grinding and the use of coarse screening oil the battery. This was the beginning of the surrender of supremacy by the gravity-stamp ; since merely the single fact that it was a more economical machine for crushing fine had retained it in favor as compared with ball-mills, rolls, or steam-stamps. The surrender, however, is not yet complete. It is the universal practice to use rolls where a relatively small tonnage is to be crushed coarse, as, for example, when coarse concentration is included in the plan of treatment. Power, attendance, repairs, and first-cost are smaller for the rolls, under such circumstances, than for stamps; and it is becoming daily more apparent that, with no concentration to provide for, the use of rolls and tube-mills, without the complication of trommels and elevators required by concentration, is rapidly gaining favor in the eyes of the leading designers. The next step was the use of the rapid-running Chilean mill between the gravity-stamps and the tube-mill, which again narrowed the field of operation of the gravity-stamp while radically widening its screen-aperture. Such a combination of stamps and Chilean mill offers advantages when fine concentration is necessary, since the reduction in the Chilean mill call be adjusted easily and governed by varying the screen-mesh. But even concentration is now looked at askance. One of the leaders of this metallurgy has abandoned the separation and

Jul 1, 1910

By A. K. Chakravarti, A. Lihiri, G. G. Sarkar

One primary objective of India's third Five Year Plan is the expansion of coal production. The goal: boost present output of 45 million tons to 95 million tons by 1965--an increase of more than 100 pct!

Jan 7, 1961

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