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By William White

History.—The making of iron and steel from the ores of northern Mexico was for years a favorite project of the late Don Patricio Milmo, upon whose estate large deposits of coal and iron were known to exist, and with whom Mr. Eugene Kelly, of New York, was associated. Several expert examinations of the property mere made for them; and when failing health forced Sr. Milmo to retire from active part in the matter, Mr. Kelly carried on the project and associated himself with Messrs. Vicente Ferrara, of Monterrey, Antonio Basagoiti and Leon Signoret, of the City of Mexico, and other leading citizens of Mexico, Monterrey and New York, who, in May, 1900, organized the " Compania Fundidora de Fierro y Acero de Monterrey," with a capital of $10,000,000. The main reason for locating the plant at Monterrey was, that a circle drawn with Monterrey as a center, and the distance from Monterrey to Laredo as a radius, will contain all the known Deposits of iron-ore of Bessemer quality, and the greater part of the available coal, in the Republic. Moreover, Monterrey is connected with all the Mexican trunk railwaylines, and thus with the Gulf of Mexico, and supplies, therefore, the conditions necessary for prosperous manufacturing, namely, cheapness in assembling raw materials and means for wide distribution of product. It also has a number of enterprising citizens, who have been successful in mining, smelting and manufacturing operations, and a sufficiently large population to supply the necessary labor. Iron-Ore.—The company's iron-mines are on the Carrizal mountain, on the Mexican National, and at Monclova, on the Mexican International railroad. At the former locality, two mines, Piedra Iman and the Anillo de Hierro, sufficiently large

Jan 1, 1902

By Harry H. Nowlan

A heavy development campaign progressed during the year 1936 in South Texas1, following up important discoveries made in 1935. Oil and gas wells completed during the year were 1473 against 704 in 1935. The drilling program reached its peak of operations in June in consequence of offset requirements made necessary principally in Duval County in the Seven Sisters, Loma Novio, Lopez and Cole fields. There were six new fields discovered during 1936 as follows: Rhode in McMullen County; Peters, El Mesquite and North Kohler in Duval County; Wood in Starr County and Colorado in Jim Hogg County. No discovery of unusual consequence was made during the year. The pools mentioned above are simply in the primary stages of development. The most intensive exploratory work during the year was in Duval, Webb and Zapata Counties. Considerable activity also prevailed in Starr and Brooks Counties. Much significance is attached to the California Company's discovery in the Alta Mesa field in Brooks County, which is considered to be a deep-seated salt dome. The Comitas field, in Zapata County, developed some surprisingly good production in a shallow sand at 900 ft. and is being followed by a heavy wildcat campaign throughout that area in search of like production. In Starr County an active wildcat campaign is in progress in a continued effort to find new fields northwest of the Sam Fordyce field, in Hidalgo County. This play continues in a northerly direction through Starr and Jim Hogg Counties. New Fields Rhode.—The Rhode field, in southeastern McMullen County, was opened in May by the Magnolia Petroleum Co. with a gas well in the Whitsett (Upper Jackson) sand at a depth of 1810 to 1822 ft., this test is located in the southeast corner of sec. 86 on the Rhode ranch. Four gas wells have been completed, proving up a gas area of 1000 acres, more or less. Development will be slow because of lack of market for the gas.

Jan 1, 1937

By H. M. Roche

MAGNETITE is the important iron ore of New Jersey although bog ore, limonite and red hematite were mined in sizable quantity early in the state's min-ing history. The deposits of mag-netite are found in the Highland area in the northern part of the state. These ores outcrop a broad belt 20 miles wide, extending in a northeasterly direction from Phil-lipsburg, on the Delaware River, to Greenwood Lake, at the southern boundary of the state of New York, a distance of 60 miles. The area in which the magnetite is found (see map, Fig. 1) contains 1200 square miles and the center of the area is at Dover, 40 miles west of New York City. In the general area are found 18 parallel ranges or lines of ore deposits. These ranges may be re-garded as mineralized zones in which occur orebodies that are rich enough in magnetite to war-rant mining. Usually a number of the orebodies lie one above the other in the same plane, all dipping and pitching in the same direction. Within the ranges, there may be several parallel orebodies of work-able size. The average strike of the orebodies is N.41° 30' E., with an average dip of 55° southeast and an average pitch of 15 ° to the northeast. Orebodies suitable for mining range from 6 to 100 ft. wide, as measured from foot wall to hanging wall. Their heights, as measured on the dip and normal to the long axis of the orebody, vary from 200 to 3,000 ft. The length along the pitch has never been determined by mining, al-though several of the orebodies have been worked to lengths of 10,000 ft. The grade of the ore as mined today varies from 30 to 60 per cent iron, and the gangue min-erals are chiefly silica, alumina, magnesia, lime and phosphorus.

Jan 1, 1937

By G. R. Mansfield, W. B. Lang

THE third year of Government exploration for potash by the U. S. Geological Survey and the U. S. Bureau of Mines under the authorization of the act approved June 25, 1926 (Public 424-69th Cong.) is drawing to a close. The results thus far obtained are thought to be sufficiently interesting and satisfactory to justify the presentation of a brief preliminary account of the work. Review of Earlier Exploration The general geologic similarity of the Permian basin of Texas and New Mexico to the potash field of Germany had long ago suggested the possibility of the presence of potash salts somewhere in that basin, but petroleum exploration was then making little headway there and the necessary data could not be obtained. The discovery by Udden in 1912 of potash in brine from the Spur well in Dickens County, Texas, was the first direct evidence of its presence. In 1915-17 the U. S. Geological Survey drilled a test well with standard tools at Cliffside near Amarillo, but failed to find potash. Nevertheless, an observer has been kept in the field, at first in cooperation with the Texas Bureau of Economic Geology but since 1922 by the Survey alone, to secure data and samples from oil and gas tests. Since the discovery of oil in Reagan County in 1923 exploration by drilling has been rapidly extended to many parts of western Texas and southeastern New Mexico. The identification of the potash-bearing mineral polyhalite was first announced by the Geological Survey in June, 1921, the material having come from cuttings from the Bryant well in Midland County and the Burns well in Dawson County, Texas. Successive discoveries and announcements of similar purport aroused widespread interest in potash exploration, which culminated in the action by Congress already noted. Permian Salt Basin The Permian salt basin extends generally northeastward from western Texas and southeastern New Mexico through the Panhandle sections of

Jan 1, 1929

By S. A. Ford

A SHORT and accurate method for the estimation of manganese in iron and steel is of great advantage to Bessemer works, and I think it may be of interest to some of the members of the Institute to give in detail the process in use in the laboratory of the Edgar Thomson steel works. The process is based on the reaction first described by Beilstein and Jawein.* The steel, spiegel, or iron is dissolved in strong nitric acid, sp. gr. 1.4. Evaporation to dryness is not necessary, unless the amount of silicon is large, as in the case of certain pig irons. Then, as a clogging of the filter in the subsequent filtra¬tion is apt to follow, dissolve first in a dish in hydrochloric acid, quickly evaporate to dryness, redissolve in the strong nitric acid, boil, and while boiling throw in crystals of chlorate of potash from time to time. Violent action ensues, yellow fumes are given off, and binoxide of manganese is precipitated, since it is insoluble in strong * Berichte der deutschen chemisehen Gesellschaft, vol. xii, page 1528.

Jan 1, 1881

By W. E. Crandall

The No. 4 shaft and hoist at Hecla Mining Co.'s Star mine have been in operation for seven months, and as development of new mining areas proceeds in the lower portions of the mine, the system is being depended upon more extensively for personnel and material handling requirements. The hoist plant is handling full payloads, at rated speeds, over a vertical distance of 5650 ft. One of the special features of this hoist is its precision braking control under all hoisting conditions. Tests indicate that emergency stops can be made with safe deceleration rates and minimum rope and conveyance oscillation.

Jan 1, 1971

By J. F. Wilkinson

A high degree of accuracy is often required in mine-surveying, in order that expensive mining work may not be misdirected. The making of underground connections by drifts or shafts located as the result of surveys presents a crucial test of correctness not usually involved in any other class of surveying. In view of these considerations, the present notes and description of a survey made in June, 1890, for the San Francisco shaft of the New Almaden quicksilver-mines, may be of interest to members of the Institute who are surveyors. The purpose of this survey was to locate on the surface a vertical 2-compartment shaft (3.5 by 7 ft.), to connect with another vertical shaft, of practically the same size, which had been sunk a number of years before from an adit-level about 240 ft. vertically below the surface, to a deeper, so-called 600-ft. level. It will be seen, of course, that the most important matter was to secure an exact coincidence in vertical line, so that the resulting continuous vertical shaft from the surface should have no offset or irregularity at the point of junction between its two parts. The levels were of less importance; but, as the hoisting-works were to be placed in position and the new shaft permanently timbered from the start, its correct alignment was an essential requirement. The important features of the work, therefore, were the methods used in determining with certainty : 1. That the shaft was located in the right place in a general way; 2. That the ordinary inaccuracies of linear and angular measurements were so reduced as to insure correctness of location within certain defined and allowable limits. Instruments.—Thc instruments used were: a Buff and Berger transit-theodolite, with a 6-in. horizontal plate, reading to 10 seconds; a Heller and Brightly Y-level; a Chestermán steel tape, graduated in tenths and hundredths of a foot; and New York leveling-rods, graduated to thousandths of a foot.

Jan 1, 1901

By C. H. Mathewson

MY first reflection on the subject assigned to me by the officers of this symposium was that a critical description of these lesser characters in the cast of inanimate actors now before us under the title "The Role of Metals in New Transportation" would be about as well received as the description of a horse race in terms of harness buckles and jock-ey's buttons. The word "new" in the title of this symposium seems to shout strong aluminum and stainless steel, unless we transfer our attention to transpor-tation on another planet where the strength-density ratios may require very different engineering treatment. To load a speaker with the "heavier nonferrous metals" amidst the airy consideration of flying or 20th century gliding along the earth and through water, like Hermes, the messenger of the immortals, and expect an instructive or enlivening flight into the area of current exploitation and popular interest in transportation would, of course, require the performance of a miracle or at least the exhibition of genius to which I can lay no claim. But copper and nickel, headliners in other classifications, are also indis-pensable as components of the important new structural materials of transportation, and together with lead, tin and zinc perform many minor or contributory functions in this field that may indeed be con-sidered well-nigh indispensable. A complete and well planned fabric of classification, explanation and critique of even these secondary functions would take much time, and I cannot hope in the 25 minutes or so alloted for the purpose to offer more than a rambling treatment, in which a thread of continuity will be sought by anchorage to one after another of the following attributes or appurtenances of the moving vehicle: 1. The machinery and accessories. 2. The framework and superstructure, and the line or travelway. 3. Light, heat, power, water, sanitary and housekeeping services. 4. Embellishment, or style.

Jan 1, 1936

By S. F. Shaw

IT IS generally recognized that the natural gas absorbed in petroleum plays the leading r6le in moving the oil through the sands to the well and supplies the energy that delivers the oil to the surface when the wells are flowing. It is the purpose of this paper to note the amount of oil that could be lifted by this gas if 100 per cent. efficiency were obtained and the efficiencies actually obtained in the use of this gas. An article in MINING AND METALLURGY,' stated that in a Wyoming field, with a pressure of 300 lb. per sq. in., there would be absorbed 65 cu. ft. of gas per barrel, or 1.55 cu. ft. per gal. of oil. The writer does not know if data have been obtained, by experiment, for pressures beyond those indicated in this article, therefore, for the purpose of illustration, he has projected this curve to obtain figures for pressures greater than 300 lb., although probably experiment will show that the extended line is not quite correct.

Jan 1, 1926

Improvement of drilling operations through the development of new, unconventional drill bits is a prime research target at Sandia Laboratories, Albuquerque, N.M. Sandia is currently focusing efforts on four new bit designs which its engineers believe may eventually improve penetration and reduce operating costs. The Energy Research and Development Administration (ERDA) has budgeted $500,000 in support of this program to date. Two of the drill bits-one that chips rock with high voltage spark discharges, and another which fires small projectiles into the rock ahead of a regular roller bit-are designed to increase both penetration rates and downhole bit life.

Jan 8, 1975

By A. T. Schwennesen

Every engineer has occasion to trace or copy a map, plan, or other drawing on paper too thick for the ordinary way of using tracing-cloth or tracing-paper. When the figure is small and simple a copy may be made by holding the original against a window-pane, coverin& it with the paper, and tracing direct by the aid of the strong sunlight from outside. The need of utilizing this principle on a larger scale and in a more convenient position led Dr. J. C. Branner to plan the table of which the following is a description : This table was first made in the form of an adjustable glass-top table with a mirror beneath, in 1887, while Dr. Branner was State Geologist of Arkansas. Later it was modified as experience suggested until the form as here described was evolved. The device consists essentially of a drafting-table with a plate-glass top, upon which the original drawing and the paper are laid, and a mirror mounted underneath to reflect the light of the sky up through the drawing. The glass top is hinged and fitted with two arms and thumb-screws, so that it can be raised and fixed to any position, either inclined or horizontal. The mirror is pivoted and revolves about a horizontal axis, so that it may be tilted to any angle. The hood of cardboard or black cloth prevents the reflection of light from the tracing, and may or may not be attached to the table.

Jan 1, 1912

By L. D. Godshall

The extreme difficulty of obtaining a short and, at the same time, exact method for the determination of gold and silver in copper-materials has been well illustrated in "Assays of Copper and Copper-Matte," and its discussion, by Dr. A. R. Ledoux and other leading authorities on this subject.* Two general methods were used by the numerous assayers who took part in the symposium initiated by Dr. Ledoux, and whose results are given in the paper and discussion. One of these is the dry or fire-method, consisting of scorification and cupellation, the former being repeated if the percentage of copper is very high, all slags and cupels being assayed and the results so obtained added to the ordinary assay; and the copper retained by the silver buttons being determined and deducted from the combined weight of the buttons obtained from the assay of the original material, the scorification-slag, and the cupel. The other is the wet or combination-method, which, while not involving so much work, requires a longer time. Briefly, it is as follows : The material to be assayed is dissolved in nitric acid, the solution is diluted, and the fine undissolved gold is collected by means of sulphate of lead, formed by the addition of lend acetate and sulphuric acid to the solution, After standing from 12 to 24 hours, the precipitate is filtered off, and the silver in the filtrate is precipitated as a chloride or bromide, and collected by means of sulphate or bromide of lead. The solution containing this precipitate in suspension is again allowed to stand until the precipitate has settled. It is then filtered; both precipitates, containing the gold and silver, are dried, ignited and scorified, either separately or together, and the result is cupelled in the usual way.

Jan 1, 1901

By Kenneth Cottingham

The number of completions in 1944 in Ohio was only slightly greater than completions in the preceding year, but the initial daily volumes both of oil wells and gas wells declined considerably. The dry-hole ratio was a little lower than in 1943, even though in the year under review considerable effort was made to find new production. No new areas of consequence were discovered. Thirteen new gas pools, the largest of which was 1000 acres and the average 565 acres, were opened during the year. Eleven of these pools were in the Clinton sand, one was in the Oriskany, and one was in the Berea. Approximately 15 small pools might also be rated as discoveries, but because only one or two wells have thus far been completed in each, they cannot at present be properly evaluated. The latter pools average about 120 acres each. Some extensions were made to existing gas pools. The number of oil wells drilled was only one less than in 1943, yet compared with the year 1941, when twice as many oil wells were drilled, the difference is startling. Effective Aug. I, 1944, a blanket subsidy was granted of 35¢ per barrel on all Cleveland-Chatham, Coming, and Lima grades of oil, and 75¢ per barrel on Pennsylvania grade crude. The subsidy was authorized by the Office of Price Administration, with reimbursement to purchasers of the various grades made through the Defense Supplies Corporation, a branch of Reconstruction Finance Corporation. For several years the small operator, particularly the owner of stripper wells, was in a serious position. The subsidy has been a means of real help and, in addition to aiding the operator, it has prolonged the life of many small wells that otherwise would have been abandoned, with consequent loss of daily production and unre-covered reserves. It is questionable whether the price increase is sufficient to revive production of Corning grade, which has

Jan 1, 1945

By John Birkinbine

The following data concerning the general dimensions and district-location of the blast-furnaces of the United States are intended to supplement a paper of similar title, which appears in volume xiv., pages 561 to 577, of the Transactions, and bring the record to the end of the calendar year 1886. The reasons for presenting the figures at so short an interval since the former paper are that the American Iron and Steel Association has lately issued a new directory of iron and steel works (edition of 1886) from which many of the plants which have been inactive are omitted and new industries added, to such an extent as to materially affect the figures presented in the first paper; and also that the improvement in business has encouraged a production of pig-iron in 1886 in excess of any previous outputs, and the results obtained in the industry at large as well as at individual plants form a better index of what the American furnaces can accomplish than those heretofore presented. The statement will not be extended beyond the production of pigiron, although it could well be made to include the manufactured iron and steel; and while the data given have been verified as far as possible up to the close of the year 1886, no attempt, except in special cases, has been made to note the changes which have taken place since that time—changes which within the next twelvemouth will affect some of the figures here presented. At the close of the year 1886 there were 579 blast-furnaces reported on the active list—an apparent decrease, as compared with my former paper, of 97 stacks; but this was not an actual decrease, since most of the furnaces dropped from the Directory were those which, owing to location, inefficient equipment, or fake of ore-supplies, etc., were considered likely to remain inactive, although a number of them will possibly be temporarily put into blast with iron advancing in price. On the other hand the new plants added

Jan 1, 1887

1913. FRANK DAWBON ADAMS Montreal, Canada. 1921. WILLIAM CUTHBERT BLACKETT Sacriaton, Durham. England. 1923. GELAEIIO CAETANI Rome, Italy 1920. HENRY STURQIB DRINKER Merion Station, Pa, 1922. FEDERICO GIOLITTI Torino, Italy. 1906. SIR ROBERT A. HADFIELD London, England. 1928. JOHN HAYB HAMMOND New York, N. Y. 1921. FRANK WILLIAM HARBORD London, England. 1917. HERBERT HOOVER Washington, D. C. 1905. HENRI LECHATELIER Paris, France. 1931. WALDEMAR LINDQREN Cambridge, Mass. 1929. JOHN MARKLE New York, N. Y. 1921. C. MCDERMID London, England. 1913. EZEQUIEL ORDONEZ Mexico City, Mexico. 1909. ALEXANDRE POURCEL Paris, France. 1911. ROBERT H. RICHARDS Cambridge, Mass.

Jan 1, 1932

YEAR OF ELECTION 1913. FRANK DAWSON ADAMS, Montreal, Canada. 1921. WILLIAM CUTHBERT BLACKETT Sacriston, Durham, England. 1920. HENRY STURGIS DRINKER Merion Station, Pa. 1933. KARL EIKERS NEW YORK, N. Y. 1922. FEDERICO GIOLITTI Torino, Italy. 1906. SIR ROBERT A. HADFIELD London, England. 1928. JOHN HAYS HAMMOND New York, N. Y. 1921. FRANK WILLIAM HARBORD London, England. 1917. HERBERT HOOVER Washington, D. C. 1905. HENRI LECHATELIER Paris, France. 1931. WALDEMAR LINDGREN Cambridge, Mass. 1921. C. McDERMID London, England. 1913. EZEQUIEL ORDONEZ Mexico City, Mexico. 1911. ROBERT H. RICHARDS Cambridge, Mass. 1934. T.A. RICKARD Victoria, B.C., Canada 1933. ALBERT SAUVER Cambridge, Mass.

Jan 1, 1934

Organization Place Date 1917 Mine Inspectors Institute of U. S. A Indianapolis, Ind. July 9-11 American Society of Sanitary Engineers Grand Rapids, Mich. Aug. 1-3 National Association of Stationary Engineers... Evansville, Ind. Sept. 10-15 National Exposition of Safety and Sanitation.. New York City Sept. 10-15 American Iron, Steel & Electrical Engineers.... Philadelphia, Pa. Sept. 10-14 American Institute of Metals Boston, Mass. Sept. 24-29 American Foundrymen's Association Boston, Mass. Sept. 24-29 Chemical Industries, Third National Exhibition. New York City Sept. 24-29 American Electro-Chemical Society Pittsburgh, Pa. Oct. 3-6

Jan 7, 1917

1913. FRANK DAWSON ADAMS Montreal, Canada. 1921. WILLIAM CUTHBERT BLACKETT Sacristan, Durham, England. 1923. GELASIO CAETANI Rome, Italy. 1920. HENRY STURQIS DRINKER Merion Station, Pa. 1922 FEDERICO GIOLITTI Torino, Italy. 1906. SIR ROBERT A. HADFIELD London, England 1928. JOHN HAYS HAMMOND. .New York, N. Y. 1921. FRANK WILLIAM HARBORD London, England. 1917. HERBERT HOOVER Washington, D. C. 1905. HENRI LECHATELIER Park, France. 1931. WALDEMAR LINDQREN Cambridge, Mass 1929. JOHN MARKLE. .New York, N. Y. 1921. C. MCDERMID London, England. 1913. EZEQUIEL ORDONEZ Mexico City, Mexico. 1909. ALEXANDRE POURCEL Park, France. 1911. ROBERT H. RICHARDS Cambridge, Mass.

Jan 1, 1932

By Roland de Wit

Conclusions reached in a paper by weertmanl are amplified in a mathematical and graphical way. It is shown that in a stressed crystal a straight dis-location may be in a position of unstable equilibrium with respect to helix development, and how a small perturbation may start the dislocation off on its helical path. Helix development occurs by diffision; bulk diffusion is necessary for development from a screw, but core diffision is sufficient for development from an edge dislocation. For a mixed dislocation helix development can take place by core diffusion if the helix also climbs; a diffusion reversal takes place when the slope of the helix equals the slope of the Burgers vector. The work done on a crystal by the external forces is graphically shown to be consistent with the direction of motion of the dislocation in helix development. Finally a detailed mechanism for tangle formation from helices is presented. In the course of helix development a glide situation may be reached where a segment of each helix loop lies in a slip plane in which it can expand by glide. Thus is it visualized how a helix can deteriorate into a tangle. A paper by weertmanl proposes dislocation-tangle formation by a helical dislocation mechanism. The present paper amplifies Weertman's arguments in a mathematical and graphical way and presents some further ramifications of the proposed model. The importance of dislocation tangles is discussed in Weertman's paper and the references cited therein. The mechanism of their formation is not yet understood. Weertman proposes that in cold-worked crystals conditions exist suitable for the conversion of straight dislocations into helices and subsequently into tangles. Helix formation occurs by a diffusion process and Weertman proposes that at low temperatures only core diffusion is important. The present paper necessarily repeats some of Weertman's work. Since the mathematical development and notation used are slightly different from his, this was thought necessary for clarity. GEOMETRY OF THE HELIX weertman2 has shown that the equilibrium form of any dislocation line is a helix if it is assumed that the energy per unit length (line tension) of the dis- location is constant. For the special case that no external forces act on the dislocation, the helix reduces to a straight line. We shall assume in this paper that the dislocation has a helical form even when it is not in equilibrium. The parametric equation of a helix is, see Fig. l: where a is the radius of the cylinder tangent to the helix, and 270 the pitch of the helix. The pitch is related to v, the number of turns per unit length (along the axis) by the relation: When a = 0 Eq. [I] gives a straight line in the z direction. The growth of a straight dislocation into a helix is now described mathematically by letting a vary from zero to its final value. The tangent to the helix is given by where is the path length along the helix. This gives the direction of t and since its magnitude is unity we must have So that dcp/ds = (a2 +p2)-"'. The curvature of the helix is given by where n = -(cos + sin) is a unit vector normal to the helix. Note that the vectors k and n always point toward the axis of the helix, Fig. 1. FORCE ON THE HELIX The external force which makes the straight dis-

Jan 1, 1963

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