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By Dave H. Barnett, Brij M. Moudgil

The flotation technique as employed by Florida phosphate producing companies for the beneficiation of fine phosphate particles has been standardized over the years. Lower recoveries of coarse Phosphate rock by froth flotation technique, however, led to the development of new methods based on skin flotation of phosphate agglomerates. Recent developments of floating coarse rock in large flotation machines have not yet convinced the rock Producers of their higher separation efficiency. It is interesting to note that the selection of a particular machine is still bared on equipment preference by an individual company as well as proven performance of a particular machine for upgrading a specific material. Various techniques which have been developed to beneficiate the coarse phosphate rock have been discussed. Performance of the individual techniques is presented.

Jan 3, 1979

By Finn Ouchterlony

A simple bilinear R-curve description of crack extension resistance is applied to the testing of sub-size rock core specimens. The K-curve consists of a linear sub-critical part and a flat post-critical part. Formulas for the apparent energy rate resistance quantities Gm, Jm, and [R] are developed. Experiments on notched cores of Ekeberg marble, Bohus granite, and Stripa granite are compared with these predictions. The R-curve model gives reasonable results for Gm -data but fails essentially to describe the Jm and [R]-data. Another model with a sharply increasing linear post-critical part could possibly account for the [R]-data, but direct R-curve measurements seem a better approach.

Jan 1, 1982

By D. L. Luffel

This paper presents two main developments: (1) a short, constantly accelerated centrifuge method of measuring drainage capillary pressure properties of cores, and (2) a new analytic method of treatment of centrifuge measurements to obtain saturation-capillary pressure relations. Toward the first objective, a clever experimental method is presented which is certainly more rapid than previous centrifuge methods. Toward the second objective, a new analytic method is derived to eliminate the approximate method of Hassler and runner. The derivation of this new analytic method, however, appears to be in error. The new analytic solution is developed as Eq. 5 in Appendix A. At the beginning of this derivation, the average wetting phase saturation of a core is expressed as, where is the centrifuge angular velocity. Eq. D1.2 makes explicit the dependence of S and S upon The second equation shown in Appendix A expresses the relation between the three variables Since for a given porous medium the saturation is uniquely related to capillary pressure, the functional dependence of S upon P is trivial, i.e., Pc.ri does not actually appear. Thus, the function 5 (r, ) may be expressed as a new function, S*, of PC, , alone The author transforms the variable of integration in Eq. Dl through use of Eq. D2 and writes

Jan 1, 1965

By AIME AIME

WITHOUT frills, but with an admirable program of technical papers and discussion, many opportunities for social contact, and all New York for a playground, the 142d Meeting of the Institute will make the Engineering Societies Building a lively place from Feb. 20 to 23. Prices are down, even in New York. Come and forget the depression listening to the stories of old friends. Hear at first hand what is going on in your professional world. The fare is varied, of wide appeal. The program on the opposite page has been arranged carefully to minimize conflicts between the subjects in which you are interested. If it is not possible to come for all four days, check over the sessions that are most important to you. No changes in the scheduling are likely.

Jan 1, 1933

Andrew Carnegie, America's best-known ironmaster and philanthropist, died at his home at Lenox, Mass., Monday, Aug. 11, after a three days' illness. A pioneer in the steel industry, he introduced into this .country the Bessemer process And formed the plans that have resulted in this country's supremacy in the steel markets of the world. Known throughout the world for his, gifts, he is also known to engineers as the donor of the home of their National Societies and as the founder of the Carnegie Institute of Technology, of Pittsburgh. For many years, also, he was an honorary member of the American Institute of Mining and Metallurgical Engineers, the American Society of Mechanical Engineers, and of the Engineers Club of New York. What he considered the secret, of his success is shown by the epitaph he wrote for himself, "Here lies a man who knew how to enlist in his service better men than himself." He was buried Thursday, Aug. 14, in Sleepy Hollow Cemetery, Tarry-town, N. Y., the funeral services being private, in accordance with his wish.

Jan 9, 1919

By A. H. Daane, J. J. Hanak, F. H. Spedding

IN the study of the rare earths at the authors' laboratory, methods have been devised for preparing pure rare earths and many of their properties'- have been determined. Very little information is found in the literature on the properties of europium metal, which is the scarcest of the naturally occurring rare earths. Since we have recently prepared europium in appreciable quantities, we are in a position to describe the method of preparation and some of the properties of this metal. Metallic europium was first prepared by Klemm and Bommera who heated a mixture of potassium and EuC1, in vacuo, and obtained a mixture of europium metal and KC1. Trombe4 electrolyzed a molten salt bath containing NaC1, KC1 and EuC1, and collected the europium in a molten cadmium electrode as a cadmium alloy. The cadmium was subsequently removed by distillation but the properties of the residue indicate that pure europium was not obtained. McCoy attempted to prepare europium by distilling mercury from europium amalgam, but the stability of the Eu-Hg intermetallic compounds prevented a complete separation of the two elements. The preparation of very pure europium was suggested by previous work in this laboratory1,4 in which ytterbium and samarium were prepared by heating the respective sesquioxides with lanthanum metal turnings to 1450°C in vacuo and distilling ytterbium and samarium from the mixtures. Subsequently, small test experiments showed that europium also could be prepared by this method. A more detailed version of this method was used in the work described in this paper. Klemm and Bommer3 found by X-ray analysis that the metal had a body-centered cubic (bcc) structure with a lattice constant a, = 4.582 ± 0.00A (converted from kX units), with a bulk density of 5.30 g per cu cm. They found europium to be weakly ferromagnetic. Spedding, et al,7 found a,, to be 4.606 ± 0.001A. Barrett' showed that the bcc structure persists throughout the temperature range 5 to 3000K with a, at 5, 78, and 300°K being 4.551 ± 0.003, 4.551 ± 0.004 and 4.577 ± 0.001A, respectively. Trombe1 described europium as being iron gray, malleable, about as hard as neodymium and not attacked by cold water. He estimated the melting point to be between 1100 and 1200°C. Previous work in this laboratory indicated that the pure metal corrodes rapidly in air and reacts with cold

Jan 1, 1959

By G. Abowitz, R. B. Gordon

The velocity of sound, mass density, and thermal expansion coefficient were measured in dilute lead, tin, zinc, bismuth, cadmium, indium, and potassium amalgams as a function of composition. Measurements in the Hg-TI system extended ovev the wider range of composition, 0 to 40 at. pct TI. The sonic velocity was measured as a function of temperature. The calculuted adiabatic compressibility in all cases was found to decrease much more rapidly than would be expected on the basis of a linear variation with composition. An interpretation of the results is given in terms of changes in the Debye characteris -tic temperature of mercury on alloying and a possible change in the bonding of mercury itself. If a liquid is considered as an isotropic elastic medium, the phase velocity of a longitudinal elastic wave traveling in the liquid is given by where K is the bulk modulus, G the shear modulus, and d the mass density. G can be neglected for liquids of ordinary viscosity, i.e., approximately 1CT2 poise, because the shear stress component is relaxed essentially at once. That is, for liquids of ordinary viscosity and at frequencies of the applied stress up to several hundred megacycles, the relaxation time of the shearing process is much shorter than the period of the applied stress. Eq. [I] then reduces to The adiabatic rather than the isothermal compressibility is measured at the megacycle frequencies used in ordinary ultrasonic velocity measurements. The sonic velocity and compressibility have been determined for many organic liquids and aqueous eletroltes,' and the results have been interpreted in terms of existing theories for these fluids. The velocity of sound and compressibility are important parameters in theories of the liquid state. For example, equations of state have been proposed relating the free volume of liquids to the acoustic velocity.3 Comparatively very little work has been done on the acoustic properties of liquid metals and alloys. leppa,' orddon, and several other investigators

Jan 1, 1963

By R. E. Allen, A. C. Jephson

ELECTROLYTIC zinc plants of the American Smelting and Refining Co. are located adjacent to the present city limits of Corpus Christi, Texas. The original plant commenced operations during 1942, and is designed for the production of special high grade zinc from zinc sulfide concentrates.' Subsequent changes include the erection of an additional acid plant during 1950, and additions for increased generating and production capacity during 1951. New Electrolytic Plant—The new electrolytic plant is a separate unit erected for the treatment of densified fume produced at Asarco plants located in El Paso, Texas and Chihuahua, Mexico. Construction was completed and operation commenced during June, 1953. Decision for the erection of a separate plant for the treatment of densified fume is based on several factors. One of the principal reasons is the assurance of continued production rate of the original plant, which might have been jeopardized by combined treatment of calcine and fume. Of equal importance is the advantage of locating a plant on a site with adequate space for eventual expansion. General Description—The new plant for the treatment of densified fume consists of four main buildings for the following operations: storage and grinding of fume, leaching and purification, electrolyzing and casting, and rectifier units. Auxiliary buildings include a baghouse, reagent storage, and a lunch room. Leaching of ground fume with electrolyte from the cells is a batch type operation in tanks equipped with mechanical agitators and weightometers. Completed leaches are pressure filtered, the resultant residue being recovered for shipment to El Paso by conventional use of thickeners, drum type vacuum filters, and a direct-fired dryer. Filtrates from the filter section are purified in mechanically agitated tanks, filtered after completion through plate and frame presses, and then pumped to an evaporative type cooling tower. Solution discharged from the basin of the cooling tower is collected in storage tanks for use in the cells. The cool purified solutions are pumped as required from storage to the solution circuit for circulation of electrolyte through the cells. Except for the addition of purified feed solution and withdrawal of electrolyte for leaching, the circulating system for the cells is essentially a closed continuous circuit that includes the use of evaporative cooling towers for control of solution temperatures. Aluminum cathodes and Ag-Pb anodes are used for electrolysis, which is maintained at a current density of about 82 amp per sq ft. Cathode zinc produced is melted in a gas-fired reverberatory furnace and then cast into slabs on a straight line casting machine. Unloading and Storage—Fume produced by the Chihuahua plant is shipped in box cars, and fume by the El Paso plant in hopper bottom dump cars. Shipments as received are weighed on a 7 5-ton capacity railroad scale, sampled, and then moved over one of the two unloading hoppers with a car puller. The cars are then unloaded with mechanized equipment, a car scoop being used for unloading of box cars and a car shaker for the hopper bottom cars

Jan 1, 1958

PRESIDENT L E Young', Pittsburgh, Pa PAST PRESIDENTS Clyde Williams, Columbus, Ohio W. E Wrather, Washington, D C VICE-PRESIDENTS Robert W Thomas', Ray, Ariz C Harry Benedict, Lake Linden, Mich D H McLaughlin, San Francisco, Calif A B Kinzel, New York, N Y Philip Kraft, New York, N Y VICE-PRESIDENT AND TREASURER Andrew Fletcher, New York, N Y

Jan 1, 1949

By Henry M. Howe

I wish to present to you a few thoughts on some of the phenomena and laws of iron smelting. Owing to the great complexity of the subject, to the great variety of points to be taken into consideration, many of which are very poorly understood, and to the meagreness and even conflictoriness of our information with regard to some of the most important laws which govern the subject, the fruits of such thoughts as I venture to offer you must be received as speculations, not as facts. Nevertheless, in discussing old phenomena from new standpoints, thus furnishing a metallurgical parallax, if I may say so, these theoretical speculations may have their value in helping to a clearer comprehension of the phenomena and laws we now know, and in suggesting new lines of inquiry. While an increase of height in blast furnaces is not always followed by increase in their power of production, experience proves that it tends to increase it; for while we have many cases of short furnaces producing more iron than longer ones, yet enormous productions, such as those of the Lucy and Isabella furnaces of Pittsburgh, and of the furnaces of Esch sur l'Alzette, in Luxembourg, have never been reached in short furnaces. We may safely infer that height is an element essential to great production, though of course not the only essential element, and that, in the case of high furnaces which are not capable of great production, some other essential element is wanting. Moreover, experience teaches that within limits increase of height tends to increase the producing power in a still higher ratio. Thus, in the Esch furnace, which is 19.8 meters (65 feet) high, 393 tonnes (or 387 gross tons) of 31 1/2 per cent. Ore

By H. M. Howe

I WISH to present to you a few thoughts on some of the phenomena and laws of iron smelting. Owing to the great complexity of the subject, to the great variety of points to be taken into consideration, many of which are very poorly understood, and to the meagreness and even conflictoriness of our information with regard to some of the most important laws which govern the subject, the fruits of such thoughts as I venture to offer you must be received as speculations, not as facts. Nevertheless, in discussing old phenomena from new standpoints, thus furnishing a metallurgical parallax, if I may say so, these theoretical speculations may have their value in helping to a clearer comprehension of the phenomena and laws we now know, and in suggesting new lines of inquiry. While an increase of height in blast furnaces is not always followed by increase in their power of production, experience proves that it tends to increase it; for while we have many cases of short furnaces producing more iron than longer ones, yet enormous productions, such as those of the Lucy and Isabella furnaces of Pittsburgh, and of the furnaces of Esch sur l'Alzette, in Luxembourg, have never been reached in short furnaces. We may safely infer that height is an element essential to great production, though of course not the only essential element, and that, in the case of high furnaces which are not capable of great production, some other essential element is wanting. Moreover, experience teaches that within limits increase of height tends to increase the producing power in a still higher ratio. Thus, in the Esch furnace, which is 19.8 meters (65 feet) high, 393 tonnes (or 387 gross tons) of 312 per cent. Ore

Jan 1, 1877

By E. P. Humphrey

The Lehigh Valley Coal Co. finished the rebuilding of its Drifton No. 2 breaker at Drifton, Pa., in the summer of 1917. The new construction comprises an addition and the complete remodeling of the old breaker. It is of interest to note that the old structure was the first iron breaker erected in the anthracite region. The Old Breaker This old breaker was built by the Cross Creek Coal Co., under the direction of the late Eckley B. Coxe, in 1888-89, and was fully described by him in the Transactions1. The columns were cast iron, 8, 10 and 12 in. square. The floors and partitions in pockets were cast-iron ribbed plates. The struts were cast iron of "H" section; the other members were of structural iron either rolled I-beams or built-up sections. The sizes of the rolled beams varied from 6 to 20 in. deep, while the built-up sections, made of plates and angles, varied from 6 to 63 in. in depth, so that there apparently was no rule to determine the type of section used. In the remodeling of the old structure, practically everything was taken down excepting the columns and roof, and such beams as were necessary for temporary construction purposes, and, therefore, a close inspection of the old structural members could be made and the effect of the acid water on them could be noted. The cast-iron members were but slightly attacked by the water, while the wrought-iron beams, in the wet places, were corroded almost to failure. The following are analyses of cast-iron, wrought-iron, and structural-steel samples taken from the old and the new structure.

Jan 1, 1918

Adams, Bernard, Student, South Dakota School of Mines. Rapid City, S. D. '30 Ahlskog, Harold A., Student, Washington State College Pullman, Wash. '30 Aldridge, John, Student, New Mexico School of Mines Socorro, N M. '30 Almstrom, Adne A., Student, Met. Engrg., Washington State College Pullman, Wash. '29 Ancell, Virgil F., Student, Missouri School of Mines Rolla, Mo. '30 Ankudinoff, N., Mill Draftsman, Arthur G McKee & (:o., 2422 Euclid Ave., Cleveland, Ohio. '30 Apablasa, Salvador C., Student, Univ. of California Los Angeles, Cal. '31 Armstrong, Robert H., Student, Lafayette College Easton, Pa. '31 Armstrong, Thomas E., Student, Univ. of California Los Angeles, Cal '31 Aud, Robert A., Student, Lafayette College Easton, Pa. '30 Backus, Robert Small, Student, Mass.- Inst. of Tech . Cambridge, Mass. '30 Bailey, William C., Student, Univ. of California Los Angeles, Cal '30 Banning, Lloyd H., Student, South Dakota State School of Mines Rapid City, S D. '81 Barclay, M. G., Student, Colorado School of Mines Golden, Colo. '30 Barger, Thomas, Student, Univ. of North Dakota Grand Forks, N. D. '29 Barker, C. L., Student, Colorado School of Mines Golden, Colo. '30 Barker, Edgar Morgan. Student, Univ. of Utah Salt Lake City, Utah. '31 Barnwell, Earl E., Student, Oregon State College. Corvallis, Ore. '30 Bartholomees, Geo. C Box 304, Bonne Terre, Mo. '29 Bartholomees, Louis P., Student, Colorado School of Mines Golden, Colo. '30 Bary, Robert L., Student, Univ. of Kansas Lawrence, Kans. '30 Basham, Lester G., Student, South Dakota School of Mines Rapid City, S D. '31 Bates, Walter H., Student, School of Mines, Univ. of Utah .. Salt Lake City, Utah. '30 Beardshear, George T., Student, South Dakota State School of Mines.Rapid City, S D. '31

Jan 1, 1923

By M. Hansen, C. C. Wang

THE 6 phase of the Cu-Sn system (Cu,Sn, = 32.53 pct Sn) was considered to be stable down to room temperature until Owen and Iball showed by X-ray analysis that it undergoes a eutectoid decomposition into the a and e phases at a temperature near 300°C. Their findings have been confirmed by other investigators,2-5 a11 of whom used X-ray diffraction studies of powdered specimens. The transformation temperature has been reported by various authors as lying between 300" and 380°C. To our knowledge, no microscopic evidence of the eutectoid reaction has been published, as yet. It was in connection with other work that longtime annealings at 300°C were conducted with alloys containing 22, 32.6, and 35 pct Sn (nominal compositions) prepared from electrolytic copper and electrolytic tin and cast in a small iron mold. The specimens were first annealed at 700°C for 5½ hr and quenched from 400 °C after cooling to, and annealing at, that temperature for 9½ hr. After this treatment the sample with 22 pct Sn was cold worked for 15 pct reduction in thickness; the 32.6 and 35 pct alloys were too brittle to be cold worked. The final anneal at 300°C was done in a sealed pyrex glass bulb for 63 days. Fig. 1 represents the microstructure of the annealed alloy with 22 pct Sn. It shows primary a solid-solution crystals in a matrix of the (a + 8)-eutectoid formed at 520 °C. The a crystals contain 8 inclusions which precipitated from a due to the decrease in the solubility of tin in copper with fall in temperature. The decomposition of the 8 phase into a (light) and E (dark) can clearly be seen in some areas of the (a + 8)-eutectoid matrix. However, the decomposition is far from being completed, even after the long-time anneal used. Figs. 2 and 3 depict the microstructures of the annealed 32.6 pct alloy, which was intended to consist entirely of 6 phase. Due to some loss in copper on melting, the composition is slightly higher in tin. Accordingly, the sample after quenching from 400 "C consisted of grains of the 8 phase with the e phase arranged along the grain boundaries and as a Wid-manstatten precipitate within the 6 grains. After an annealing time of 63 days, the eutectoid decomposition, 6 + a + e, is still in its early, initial state. The pearlitic type of eutectoid is nucleated at the c crystals, preferably those surrounding the grain boundaries of the 8 phase. The appearance of the (a + €)-eutectoid in the 35 pct Sn alloy was very similar to that shown in Figs. 2 and 3. Again, the eutectoid decomposition nucleated at the 6 phase and proceeded from there into the 8 areas. As is evident from Fig. 2, the rate of decomposition of the 6 phase at 300°C is extremely sluggish: In the representative area shown only about 5 pct of the 8 phase has undergone the eutectoid trans- formation after annealing for 63 days. On the other hand, Owen and Williams2 have reported that X-ray photographs of powdered samples with between 17.5 and 34 pct Sn did not show 8 lines after annealing for only five to seven days at 300°C. This is in accordance with the fact that the rate of reaction in powdered samples is higher than in massive specimens, as a result of the excess free energy of the powder (due to its greater surface area). The authors wish to express their thanks to C. A. Johnson for preparation of the micrographs.

Jan 1, 1952

By Joseph E. Pogue

The outstanding features of 1926 in the petroleum industry included the following: 1. Stocks of all oils (crude and refined) were reduced, making the first annual decline since 1918. 2. Domestic crude oil production increased steadily during the last 11 months of the year, accelerating during the fourth quarter, and ending the year at the highest level ever attained. 3. Three new major oil fields were developed—Panhandle, Spindle-top and Seminole. 4. Important advances were registered in production technique, tending to retard the declines of old wells and to maintain the flush periods of new wells. 5. The problem of gaining greater economic control of production through unit operations and gas conservation received growing recognition by the industry and the Federal Oil Conservation Board. 6. The rate of drilling was sharply increased during the second quarter of the year and suffered only a very slight retardation during the closing months. 7. The runs of crude oil to stills were maintained above normal throughout the year and underwent acceleration during the fourth quarter. 8. The gasoline situation was marked by a continuous and substantial increase in the rate of production of cracked gasoline, and by an improvement in the statistical position of the commodity. 9. Prices of both crude petroleum and its principal derivatives were characterized by more profitable levels and greater stability than for a number of years past; and, while showing declines during the fourth quarter, prices did not recede sufficiently to slow down materially either drilling or refinery operations. Change in Stocks The keynote of 1926 was a reduction in stocks of all oils to the extent of approximately 24,000,000 bbl., or 4.4 per cent., of which roundly

Jan 1, 1927

By Charles Macdonald

WROUGHT-IRON eye-bars for bridges and roofs, designed upon what is known as the pin connection system, have been successfully manufactured in this country for some years. The most approved methods employed have been the hydraulic upsetting process, and by die-forging under a hammer. In upset eyes the fibre of the iron is necessarily much distorted ; and in bars of considerable size, this disturbance seriously impairs the strength of the connection. Mr. Collingwood, in discussing my paper on "Proportions of the Heads of Eye-bars," read before the American Society of Civil Engineers, Jan. 21st, 1874, submitted sketches of certain bars intended for the anchorage of the East River bridge, which had been exposed to the action of sulphuric acid a sufficient length of time to thoroughly cleanse the surfaces, and expose the condition of the fibre. These sketches are here reproduced for the purpose of illustrating the effect of this methpd of manufacture. In Figs. 1, 2, and 3, it will be observed that the fibres at A, and E, have been folded back upon themselves and otherwise twisted and disturbed, in a manner not calculated to inspire confidence in the integrity of the connection. To compensate for this defect, a large excess of metal is thrown into the eye; but a method of manufacture which involves such a necessity, even although it be the one giving the best results thus far, all things being considered, is far from being perfect.

Jan 1, 1879

By Charles Macdonald

Wrought-iron eye-bars for bridges and roofs, designed upon what is known as the pin connection system, have been successfully manufactured in this country for some years. The most approved methods employed have been the hydraulic upsetting process, and by die-forging under a hammer. In upset eyes the fibre of the iron is necessarily much distorted ; and in bars of considerable size, this disturbance seriously impairs the strength of the connection. Mr. Collingwood, in discussing my paper on "Proportions of the Heads of Eye-bars," read before the American Society of Civil Engineers, Jan. 21st, 1874, submitted sketches of certain bars intended for the anchorage of the East River bridge, which had been exposed to the action of sulphuric acid a sufficient length of time to thoroughly cleanse the surfaces, and expose the condition of the fibre. These sketches are here reproduced for the purpose of illustrating the effect of this method of manufacture. In Figs. 1, 2, and 3, it will be observed that the fibres at A, and E, have been folded back upon: themselves and otherwise twisted and disturbed, in a manner not calculated to inspire confidence in the integrity of the connection. To compensate for this defect, a large excess of metal is thrown into the eye; but a method of manufacture which involves such a necessity, even although it be the one giving the best results thus far, all things being considered, is far from being perfect.

Jan 1, 1879

Jan 1, 1918

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

By R. H. Richman, F. Borik

A 0.3 pct C-12 pct Cr-6 pct Ni steel was rolled to 93 pct reduclion in area as austenite at 510°C, and then partially transformed as desired to ~rlartensite by qnenching to - 196°C. Pole figures for the austenitic matrix and for the martensitic product were separately determined by an X-ray transmission method. The deforitration texture of' the warm-worked austenite is characlerized by (110)(225) components, and is thus closely similar to those produced in a brasses. The pole jigure of the martensite in partially transformed material agrees well with that which can be constructed by transfortnation of the {110)(225) orientations according to either the Kuvdjuniov- Sacks or the Nishi-yatuu relatiotship. Howeuer, an important result of this construction is that me-third of the predicted orientations are missing. A graphical analysis can then be used to show that in deformed austenite certain crystallographic variants of martensite (related to the most probable austenite slip systems) are suppressed, resulting in this preferred transformation. The evidence for preferred transformation is corroborated by the measured elastic anisotropy of warm-rolled and fully transformed H-11 steel. EXTENSIVE plastic deformation of a polycrystal-line aggregate in a manner that causes flow predominantly in one direction results in a preferred orientation of the constituent crystallites. The particular orientations that are produced depend upon the crystal structure and composition of the material, as well as upon the temperature, mode, and degree of deformation; in any case, the preferred crystallo-graphic orientations, or textures, are reflected in directionality of mechanical properties. Although such anisotropy may be exploited in certain specialized applications, it is more commonly diminished or eliminated by heat treatment lest it interfere undesirably in subsequent forming operations or in structural design. In the recently developed thermomechanical treatments that significantly enhance the strength of some steels,1,2 considerable deformation of the metastable austenite prior to the martensite transformation is essential to the strengthening process. If the austenite is textured by the deformation, and if the transformation to martensite proceeds according to one of the relationships established for transformation in annealed austenite, then it must be expected that the martensite will also possess a preferred orientation even though the multiplicity of martensite orientations possible in a given austen- ite crystal will tend to restore some degree of randomness. The existence of a residual anisotropy, both mechanical 3-6 and crystallographic,' has been substantiated. In the latter crystallographic investigation, preferred orientations were determined for the martensitic structure of an SAE 4340 steel rolled 72 pct as austenite at 833°C and then quenched. However, the choice of a composition that transformed almost completely to martensite during the quench to room temperature did not permit direct measurement of the prior austenitic texture. In fact, when the "ideal orientations'' associated with well-known fcc rolling textures were converted, alone or in combination, to martensite according to the Kur-djumov-Sachs (K-s)' or Nishiyama8 relations, the agreement obtained with the observed martensite texture was only fair at best. Recently a pertinent aspect of the austenite to martensite transformation was reported by Bokros and parker,10 who found that certain habit-plane variants of martensite were suppressed by tensile deformation of Fe-31.7 Ni single crystals prior to the necessary subzero cooling. It might be anticipated that the consequences of such preferred transformation are sustained during the formation of martensite in warm-worked austenite that has a well-developed deformation texture. The present investigation was undertaken first to establish more firmly the relation between preferred orientations in plastically deformed austenite and in the resulting martensite, and second to examine the textures for evidence of deformation-induced preferred transformation. EXPERIMENTAL PROCEDURES An alloy containing 0.3 pct C, 12 pct Cr, 6 pct Ni, and the balance iron, was selected because the mar-tensite-start temperature (M,) of about -100°C allowed convenient experimental manipulation of either austenite or martensite at room temperature. Furthermore, this composition can be readily deformed as metastable austenite at moderately elevated temperatures without intervention of appreciable isothermal or athermal decomposition products. The alloy was austenitized at 1150°C, aircooled to 510°C, rolled unidirectionally at this temperature to 93 pct reduction of cross-sectional area, and finally oil-quenched to room temperature. Partial transformation to martensite was accomplished by quenching to -196°C as needed. The rolled stock was reduced in thickness from 0.067 to 0.010 in. by etching in a solution of 5 pct HC1, 45 pct HNO3, and 50 pct water, and further thinned by careful mechanical polishing to maintain the two sides of the sheet parallel within 0.0003 in. After mechanical polishing to 0.005 in., electropolishing in 1:9 perchloric-acetic acid solution produced a final thickness of 0.002 in. The preferred orientations were determined from

Jan 1, 1968