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Organization Place Date 1913 Mining and Metallurgical Society of America New York, N. Y. Jan. 8 American Institute of Electrical Engineers New York, N. Y. Jan. 11 American Society of Civil Engineers New York, N. Y. Jan. 22-25 American Society of Heating and Ventilating Engineers : New York, N. Y. Jan. 22-25 American Institute of Mining Engineers New York, N. Y. Feb. 18-21 National Society for Promotion of Industrial Educa- tion New York, N. Y. Feb.. American Institute of Architects Washington, D. C. April American Iron and Steel Institute New York, N. Y. May New York Electrical Society New York, N. Y. June National Association of Stationary Engineers Cincinnati, 0. Sept. American Chemical Society Cleveland, 0. Sept.

Jan 1, 1918

By John Griffen

THE distinguishing principle of the Tromp process is the use of a medium in the bath which is not stable, i.e., the solids will settle and the density of the medium increases with depth. A medium of uniform density can most easily be effected by agitation or by means which increase the viscosity of the medium. Either of these works against the sharpness of separation of coal from its impurities. The Tromp process grinds the medium solids to relative coarseness, allows them to settle downward in the bath without hindrance, and introduces horizontal currents of medium at intermediate levels between top and bottom of the bath. This prevents any accumulation of particles denser than the upper layer of the medium from which the clean coal is conveyed away or an accumulation of particles lighter than the bottom layer or medium whence the refuse is removed. In a relatively shallow bath making a two-product separation, the intermediate horizontal currents sweep these intermediate gravity materials away to be discharged with the refuse removed by the conveyor. Such a system provides a number of advantages. The gravity of separation can be changed simply by changing the density of the medium without changing particle size of medium solids or other conditions, as would be necessary with a system requiring uniform or stable density throughout the bath. Some installations in Europe separate at 1.40 sp gr on one shift, producing a superclean coal, and on the next shift reclean refuse from dry cleaning units and effect a separation at 1.80 sp gr. Medium solids may be much coarser in size consist, which reduces the viscosity of the medium and promotes its fluidity and in turn the sharpness of separation. Coarser medium solids with a more rapid settling rate are much more easily recoverable from the dilute medium rinsed from the products. The Tromp process is not limited to the use of medium solids having magnetic properties. Instal-

Jan 1, 1953

By John Griffen

THE distinguishing principle of the Tromp process is the use of a medium in the bath which is not stable, i.e., the solids will settle and the density of the medium increases with depth. A medium of uniform density can most easily be effected by agitation or by means which increase the viscosity of the medium. Either of these works against the sharpness of separation of coal from its impurities. The Tromp process grinds the medium solids to relative coarseness, allows them to settle downward in the bath without hindrance, and introduces horizontal currents of medium at intermediate levels between top and bottom of the bath. This prevents any accumulation of particles denser than the upper layer of the medium from which the clean coal is conveyed away or an accumulation of particles lighter than the bottom layer or medium whence the refuse is removed. In a relatively shallow bath making a two-product separation, the intermediate horizontal currents sweep these intermediate gravity materials away to be discharged with the refuse removed by the conveyor. Such a system provides a number of advantages. The gravity of separation can be changed simply by changing the density of the medium without changing particle size of medium solids or other conditions, as would be necessary with a system requiring uniform or stable density throughout the bath. Some installations in Europe separate at 1.40 sp gr on one shift, producing a superclean coal, and on the next shift reclean refuse from dry cleaning units and effect a separation at 1.80 sp gr. Medium solids may be much coarser in size consist, which reduces the viscosity of the medium and promotes its fluidity and in turn the sharpness of separation. Coarser medium solids with a more rapid settling rate are much more easily recoverable from the dilute medium rinsed from the products. The Tromp process is not limited to the use of medium solids having magnetic properties. Instal-

Jan 1, 1953

By Nicasio del Castillo

INTRODUCTION The tax structure of foreign mining investment into the United States has a significant impact on the financing and the profitability of the operation. For these reasons, it is critical for the foreign investor to develop and implement a well planned tax strategy that will enable its venture to: (1) reduce its U.S. income tax liability (2) lower U.S. withholding taxes when funds are transferred from the United States, and (3) decrease or defer home country taxation on its U.S. earnings ALTERNATIVE FORMS OF INVESTMENT A threshold business and tax consideration is the form in which the investment is to be made. The most common alternatives include: forming or acquiring a U.S. mining corporation, directly establishing a branch mining operation, or entering into a joint venture or partnership with a U.S. mining company. U.S. Corporations The most common structure through which foreign mining companies engage in business in the United States is to form a U.S. mining corporation. Forming a U.S. Corporation. If the investor decides to establish a new U.S. corporation the organization is relatively simple. No distinctions are made in the United States between "public" and "private" forms of incorporation. Minimum share capital is not usually required and share capital may consist of shares with no par value. Since corporate law is the responsibility of the individual states, the foreign investor must choose a state in which to incorporate. If appreciated mining property is transferred to a corporation solely in exchange for stock or securities in that corporation, and the transferors have control of the corporation (defined as at least 80 percent of all voting shares and at least 80 percent of all other shares) immediately after the exchange, no gain or loss will be recognized. However, if the transferors receive cash or other mining properties in addition to stock, any resulting gain may, in certain situations, be taxed to the extent of the cash and the fair market value of other property received. Acquiring an Existing U.S. Corporation. Acquiring an existing U.S. mining corporation is not as straight-forward as forming a corporation. This alternative may be accomplished through either a stock or an asset acquisition. Generally, with a stock acquisition the purchaser inherits all of the business and tax attributes of the former mining corporation. If the investor is able to acquire mining assets, however, the purchaser will usually be able to avoid any unknown or hidden liabilities that could be attached to an existing corporation. Another principal advantage in acquiring assets is that the purchase price may be directly allocated to the acquired mines or other mineral-related assets with the result that the assets' depreciable base may be increased. Assuming the domestic seller and the foreign purchaser can agree, it is generally advisable to allocate the purchase price in the sales agreement to specific individual assets. From the foreign investor's standpoint, it is preferable to allocate the purchase price to depreciable assets such as buildings and equipment versus an allocation to mineral land holdings or intangibles such as goodwill, which are generally not depreciable. It is not uncommon, however, for a seller mining company being acquired to insist for tax reasons that the investor purchase shares rather than assets. If the foreign

Jan 1, 1985

By W. L. Grose, J. E. Nealy

A device developed by the U.S. Bureau of Mines for the detection and quenching of coal mine explosions suffers from the inability to discriminate between the light emitted from hydrocarbon combustion and that emitted by electrical sparks and miner's cap lamps1. Since the quenchant device is activated by an internal explosive charge, the possibility of serious injury to nearby personnel demands a detector which can reject false signals. Described herein is a detector which can provide a rapid response signal upon the emission of radiation from hydrocarbon combustion and concurrently reject spurious signals from such sources as sparks and cap lamps. It was suggested that a detector might be developed to operate on the principle of monitoring the radiation intensity emitted from two separate spectral regions and ratioing the intensities2. A series of experiments was conducted for combustion of methane-air mixtures which demonstrate the ability of such a detector to discriminate between combustion and spurious signals. Experimental Apparatus A cylindrical (3.8 in. diam by 12 in.) stainless-steel shock tube test section was used as a combustion chamber. The test section was equipped with quartz windows (2 in. diam) on either side, a piezoelectric pressure transducer, and two steel electrodes. A 10-kv capacitor discharged across the electrodes provided a submicrosecond duration spark to ignite the gas mixture within. The desired partial pressures of methane and air were obtained by using a Wallace and Tiernan 0-800 mm Hg pressure gauge with which pressures could be determined to an accuracy of % mm Hg. All tests were conducted with a total pressure of 1 atm in the chamber. To

Jan 1, 1972

By Robert Yerkes

THE following is a brief account of the methods of measuring intelligence especially prepared for use in the U. S. Army, of typical results, and of some of their immediately practical applications. It has been prepared for the assistance of army examiners and for the information of all who are interested in the relations of scientific placement to military efficiency. PURPOSE OF THE INTELLIGENCE TESTS Under the direction of the Division of Psychology, Medical Department, and in accordance with provisions of War Department General Order No. 74, mental tests are given recruits during the 2-wk. detention period. These tests provide an immediate and reasonably dependable classification of the men according to general intelligence. Their specific purposes are to aid: 1. In the discovery of men whose superior intelligence suggests their consideration for advancement; 2. In the prompt selection and assignment to development battalions of men who are so inferior mentally that they are suited only for selected assignments; 3. In forming organizations of uniform mental strength where such uniformity is desired; 4. In forming organizations of superior mental strength where such superiority is demanded by the nature of the work to be performed; 5. In selecting suitable men for various army duties or for special training in colleges or technical schools; 6. In the early formation of training groups within regiment or battery in order that each man may receive instruction and drill according to his ability to profit thereby;

Jan 2, 1919

By C. H. Samans, G. F. Tisinai, J. K. Stanley

The addition of nitrogen (0.10 to 0.20 pct) to Fe-Cr-Ni alloys of simulated commercial purity results in a real displacement of the u phase boundaries to higher chromium contents. The effect is small for the (Y + s)? boundary, but is pronounced for the (y + a +s)/(y + a) boundary. Although there is an indication of an exceptionally large shift of the n boundaries to higher chromium contents, especially in steels with nitrogen over 0.2 pct, the major portion of this apparent shift results from the fact that carbide and nitride precipitation cause "chromium impoverishment" of the matrices. The effect of combined additions of nitrogen and silicon to the Fe-Cr-Ni phase diagram is demonstrated also. Nitrogen can nullify the effect of about 1 pct Si in shifting the (y + o)/? phase boundary to lower values of chromium at all nickel levels from 8 to 20 pct. NItrogen can nullify this U-forming effect of about 2 pct Si at the 8 pct Ni level, but not at the 20 pct Ni level. The alloys studied were in both the cast and the wrought conditions. There are indications that the u phase forms more slowly in the cast alloys than in the wrought alloys if both are in the completely austenitic state. The presence of 6 ferrite in the cast alloys accelerates the formation of U. Cold working increases the rate of o formation in both cast and wrought alloys. THE major improvement in Fe-Cr-Ni austenitic alloys in recent years has been in the addition or removal of minor alloying elements to facilitate better control of corrosion resistance, sensitization, and heat resistance. One shortcoming of the austenitic Fe-Cr-Ni alloys, which never has been completely circumvented, is their propensity toward u formation. In the AISI-type 310 (25 pct Cr-20 pct Ni) and type 309 (25 pct Cr-12 pct Ni) steels, sufficient amounts of u phase can form, if service or treatment is in a suitable temperature range, to cause severe embrittlement. Also, there is a growing conviction that this phase may be contributory to some unexpected decreases in the corrosion resistance of certain of the 18 pct Cr-8 pct Ni-type steels. The present paper discusses the effect of nitrogen additions on the location of the (r+u)/d and the (y+a+u)/(y+a) phase boundaries in the ternary Fe-Cr-Ni system, for cast and wrought alloys of simulated commercial purity, and in similar alloys containing up to about 2.5 pct Si. The objective is to define compositional limits for alloys which will not be susceptible to u formation when used near 1200°F (650°C). An excellent review of the early studies of the u phase in the Fe-Cr-Ni system has been compiled by Foley.1 Rees, Burns, and Cook2 have determined a high purity phase diagram for the ternary system, whereas Nicholson, Samans, and Shortsleeve3 are- stricted themselves to a portion of the simulated commercial-purity phase diagram. Both groups of investigators show almost an identical position for the commercially significant (y+u)/y phase boundary. Further comparison of the work of the two groups indicates that, below the 8 pct Ni level, the commercial alloys have a decidedly greater propensity toward u formation than the high purity alloys. The two groups of workers agreed that both the AISI-type 310 (25 pct Cr-20 pct Ni) and the type 309 (25 pct Cr-12 pct Ni) steels are well within the (y+~) region and that the 18 pct Cr-8 pct Ni-type alloys straddle the U-forming phase boundaries. Nicholson et al.3 showed, in addition, that these boundaries shift toward lower chromium contents if greater than nominal amounts of silicon or molybdenum are added. The effect of nitrogen on the location of the s phase boundaries in the Fe-Cr-Ni system has not been known with any certainty. In 1942, an approach to this problem was made by Krainer and Leoville-Nowak,' but at that time they apparently were unaware of the slow rate of s formation in strain-free samples and aged their samples for insufficient times, e.g., 100 hr at 650°C (1200°F) and 800°C (1470°F). For this reason, it would be expected that their (y+ u) /y boundary would be shifted toward lower chromium contents (restricted ?-field) when equilibrium conditions were approximated more closely. Procedure for Studying the Alloys The alloys used were prepared in the following way: Heats of 200 lb each were melted in an induction furnace. A 5 lb portion of each heat was poured into a ladle containing an aluminum slug for de-

Jan 1, 1955

ALABAMA Anniston.-Carrington, F. G. Auburn.-Brown, R. L. Battelle.-Green, G. G. Bessemer.-Abbott, C. E. Dobbs, G. G. Ferguson, V. Birmingham.-Adams, J. H. Aldrich, T. H. Aldrich, T. H., Jr. Allen, A. W. Bonnyman, J. Bowron, J. Bush, M. W. Crawford, G. G. Crockard, F. H. Ellis, E. E. Fairbairn, C. T. Gallacher, J. Geismer, H. S.

Jan 1, 1917

By Arnulf Muan, Carlos Landolt

Equilibria involving Cu-Pt alloys, copper oxides, and atmospheres of known ox2gen pressures have been determined at 1000' and 1200 C. The data obtained have been used to calculate activity-composition relations in the alloys. A moderate negative deviation from ideality is found. At high copper concentrations, the results of the present study are in good agreement with those of previous investigators, whereas at low copper concentrations the activities obtained in this investigation are slightly higher than those reported previously. The present study is part of a research program dealing with the determination of phase relations and thermodynamic properties of copper-containing systems at high temperatures. The information available for such systems is very scanty, particularly for copper oxides and their combinations with other oxide components. Platinum is commonly used as a container in studies of oxide equilibria. To evaluate quantitatively the extent of reaction between the oxide and the container, a knowledge of activity-composition relations in Cu-Pt alloys is necessary. Such data are not available for Cu-Pt alloys in the temperature range of particular interest in the present research program, and particularly for alloys low in copper. Studies of various aspects of the systems Cu-Pt and Cu-0 have been reported in previous literature. The system Cu-Pt is known1 to form a continuous solid-solution series above 812.C, whereas ordered phases are present in certain composition ranges at lower temperatures. Thermodynamic data for the system have been reviewed by Hultgren et al.,' who presented free energies of mixing at 65Oo C, mainly derived from electromotive force cell measurements by Weibke and Matthes.3 Enthalpies of mixing at 640°C have been obtained by Oriani and Murphy4 with liquid tin calorime-try. Their results differ considerably from those derived from the temperature dependence of the data of Weibke and Matthes. Thermodynamic data for the disordered alloys have been obtained by Assayag,5 and more recently by Schmahl and Minzl,6 by Myles and Darby,7 and by McCormack, Myers, and Saxer.8 The two latter sets of data7'' became available after the present study was completed. In the system Cu-0+ two oxides are stable at high temperatures, CuO and CuzO+ each having only minor deviations from stoichiometry. Equilibria in the liquidus temperature region of the system Cu2O-CuO have been studied by Roberts and systemsmyth,9'10CuzO-CuO by Vogel and ocher,I1 by Osterwald,12 and recently the the present authors.13 The system is of the eutectic type with a eutectic temperature of 1083.C The composition of the eutectic liquid corresponds to Xcu0 = °.44, and the oxygen pressure of the coexisting gas phase is Po2 = 0.55 atm.13 Equilibrium oxygen pressures for coexistence of solid CuO and solid Cu2O have been determined by Schmahl and Muller,l4 by Gadalla, Ford, and white,l5 by Bidwell,16 and recently by the present authors.13 There is reasonably good agreement among the various sets of data. Free energies of formation of Cu2O(s) from the elements have been derived by Tretyakov,17 by Bidwell,16 by Kiukkola and wagner,18 by Pal'guev and Neuimin," and by Steele and Alcock,20 There is particularly good agreement among the latter three1'-20 sets of data. THEORETICAL BASIS Consider a subsolidus isothermal section of the system Cu-Pt-0, as shown in Fig. 1. Two phase as-

Jan 1, 1970

BRANCH COUNCILS Mining Branch E R Price, Chairman (Coal) Howard A Meyerhoff (Industrial Minerals) J V Beall, Secretary Richard M Foose (Industrial Minerals) Carroll F Hardy (Coal) Frank A Hardlaw (Mining, Geology, and Geophysics) S J Swainson (Minerals Beneficiation) Philip J Shenon (Mining, Geology, and Geophysics) Grover J Holt (Minerals Beneficiation) A C Callen (Mineral Industry Education) C H. Behre, Jr. (Mineral Economics)

Jan 1, 1952

Executive A R LEDUC, Chairman ARTHUR S DWIGHT R V NORRIS EDWIN LUDLOW E L DEGOLYER Membership J V W REYNDERS, Chairman E L DEGOLYER R M RAYMOND EDGAR RICKARD W Y WESTERVELT Finance WALTER H ALDRIDGE, Chairman GALEN H CLEVENGER J V W REYNDERS Library Chairman JOHN H JANEWAY GEORGE C STONES ROBERT LINTON ALEXANDER C HUMPHRLYS, - BRADLEY STOUGHTON

Jan 1, 1923

By P. Sen

Frequently during the processing of minerals very fine particles are generated which are difficult to recover by conventional separation techniques and are rejected with waste water from mills. A method has been evolved for the continuous recovery of such fines by allowing the suspensions to flow through a rotating cylinder. Theoretical analysis of the trajectory of particles have shown that the efficiency of separation increases with R.P.M., tube diameter, particle diameter and density. Experiments carried out with the overflow from a hydrocyclone containing particles in the size range of 2-10 microns gave a separation efficiency of 60-70% with an R.P.M. of 3500 of the rotating tube.

Jan 1, 1980

By Dewitt T. Ring

Reliable and detailed data covering the enormous number of wells drilled and the long historical production of the state, many of which were never recorded until recent years, render it impossible to gather statistical material suitable for the Institute's standardized form. The total production of crude oil in Ohio for the year was 3,654,503 bbl., which is less than the total production in the United States for the peak day of August 1937. For a period of eight years, from 1895 to 1902 inclusive, Ohio produced more oil than any other state. During the year, 1271 tests were drilled in the state, or 114 more than in 1936. Of these, 317 were oil wells, with an initial production of 7088 bbl., an average of 22.3 bbl. per well; 503 were gas wells, with an initial open flow of approximately 222,441 M cu. ft., or 443 M cu. ft. per gas well drilled; 451 were dry holes, that is, 35 per cent of the total completions. A number of factors account for the steady decline of oil production in Ohio. In the state, at the close of thc year, there were fewer than 28,122 producing oil wells. In 1936, there were 30,150 operated oil wells with an average yearly production per well of 126 bbl. The production for 1937 averaged 130 bbl. per well. During the year, 2028 oil wells were abandoned. In other words, old wells are being abandoned more than six times faster than new ones are being drilled. Since the inception of the oil and gas industry in Ohio, between 150,000 and 160,000 wells have been drilled in the state; new potential territory, offering desirable locations for either oil or gas, is becoming increasingly more difficult to find; the dry-hole percentage will continue to increase. Prices Another factor directly affecting the crude situation during the year was the matter of price and proration of Pennsylvania grade oil. The posted price for Pennsylvania grade in Ohio on June 7 was $2.37 per barrel; at the close of the year, it was $1.70 per barrel, or a reduction of 28 per cent in price. In addition to this price cut, a 50 per cent pro-

Jan 1, 1938

INDUSTRIAL MINERALS DIVISION (Nonmetallics) Established as a Division March 15, 1935 Ian Campbell, Chairman Robert C Stephenson, Eastern Vice-Chairman Allen Cole, Southeastern Vice-Chairman David P Hale, Jr, Rocky Mountain Vice-Chairman G H Waterman, Western Vice-Chairman M F Goudge, Canadian Vice-Chairman James Norton, Secretary-Treasurer Mineral Deposits Branch U S Geological Survey Washington 25, D C.

Jan 1, 1952

Addicks, L Ambler, J O Anderson, F B Armstrong, T Allen, L M, Jr Arnold, C E Adams, C E Adams, R E Anderson, A J Booth, E L Bernhardt, D I Boyd, W S Browning, W C Blake, D E Black, T B Bergman, Julius Bowen, H P Beckett, P G Blickensdefer, F C Bond, Josiah Butler, P P Bondlas. Y

Jan 1, 1923

E. O?C. Acker Jinzoc Adachi Truman H. Aldrich Walter H. Aldridge Anson W. Allen John H. Allen William R. Appleby W. Lawrence Austin W. S. Ayres David Baker John Henry Banks Henry C. Banon Alonzo F. Bardwell Wm de L. Benedict Robert Bentley Andrew A Blair Walter M. Brodie Elwin F. Brown Fredrick Burbidge H.H. Burden Charles Butters

Jan 1, 1942

E. O?C. Acker Jinzoc Adachi Truman H. Aldrich Walter H. Aldridge Anson W. Allen John H. Allen William R. Appleby W. Lawrence Austin W. S. Ayres David Baker John Henry Banks Henry C. Banon Alonzo F. Bardwell Wm de L. Benedict Robert Bentley Andrew A Blair Walter M. Brodie Elwin F. Brown Fredrick Burbidge H.H. Burden Charles Butters

Jan 1, 1941

By Larry J. Tucker

INTRODUCTION The orebody at Pea Ridge strikes NE-SW and dips at about 800 to the SE. The ore and surrounding rocks are Pre-Cambrian in age. These rocks are usually very competent. Locally strong jointing has caused problems and toward the hangingwall dikes have caused particular problems during or after the open stoping phase of production. About 396 m of sediments lie over the ore. The shape and mineral content of the orebody has been fairly consistent so far with production areas lying from the 1375 to the 2475 levels. The deeper limits of the ore- body haven't been found yet. The ore is high grade magnetite with a strike length of over 600 m and a maximum width of over 180 m on some levels at the center of the orebody. Production at Pea Ridge for the first three years of operation came from two types of open stopes. The original stopes were recovered with horizontal production rings being drilled and blasted from vertical raises. Later a more typical sublevel stoping method using vertical production rings from one or more drilling sub- levels was used. There were a number of reasons for the selection of open stoping as the initial production method at Pea Ridge. First, it was judged that the ore was not of a block cave quality. After fifteen years of production, this assumption can be verified. There was some concern during the planning days for the potential for high flow rates of water into the mine from aquifers in the sediments lying over the orebody. Dewatering wells from surface and underground were put in as a precaution and nothing came of this potential problem. Open stoping and its resulting pillar structure put off this problem by supporting the sediments a few years longer. For a moderate investment in level development some production from open stoping was quickly realized. The first open stopes were brought in on what was then the bottom mine production level (2275), near the shaft pillar and situated on the footwall. This production practice of stoping on the heels of development from shaft pillar westward and from footwall to hangingwall continued through the open stope phases of production at Pea Ridge for many years. From the standpoint of mine efficiency and pillar stability, this would not seem to be a recommended mining practice. 74 570 w electric slushers, using 1.37 m dippers, pulled the open stope ore out into 18 ton bottom dump cars. Ordinarily five of these cars made up a train, which was pulled to the dump area by a trolley powered electric locomotive. Open stoping had the disadvantage that 100% of the recoverable portions of the orebody had to be developed in order to recover 33% of the ore. 67% of the ore was left behind in a large pillar system. For many years we had no planned method for recovery of these pillars. Mining methods are of course, limited by the existing technology. Advancing technology, coupled with the limited production capabilities of open stoping, low efficiencies and high relative cost early in the history of the operation recommended that other mining methods be looked at. In Sweden, considerable practical experience, coupled with a large amount of theoretical work had become available on sublevel caving. To Pea Ridge it offered the apparent benefits of: 1) The flexibility of diesel powered trackless haulage. 2) The efficiency of two machines to one operator on longhole drilling. 3) A multilevel production picture with a large number of drawpoints for ore recovery. 4) 100% recovery of the mineable portion of the orebody in one production pass, with no pillar recovery problems left behind. This paper outlines the experiments and experiences which Pea Ridge has gone through with sublevel caving from 1967 to this date.

Jan 1, 1981

By Lloyd R. Jackson

In the past 15 years there has been a great deal of interest in the fundamentals of plastic flow and rupture in metals and a number of papers have presented substantial advances toward a fundamental insight into the mechanism of these two processes. This paper is an appraisal of the present position with respect to the following: 1. The relative importance of shear and hydrostatic stresses in controlling the plastic flow of metals. 2. The relative importance of shear and hydrostatic stresses in determining the amount of flow before rupture in metals. 3. The use of generalized strains in determining the effect of plastic flow on the work-hardening of metals. FundamentalS Involved in Plastic Flow In attempting to devise a quantitative description of plastic flow in metals, it has been customary to assume that metals are homogeneous and isotropic. The fact that neither of these assumptions is correct complicates the experimental appraisal of relations developed. Nevertheless, as will be shown, metals are close enough '0 being isotropic and homogeneous so that considerable insight into the mechanism of plastic flow can be obtained. The assumptions of isotropy and homogeneity allow both the elastic and plastic behavior of metals to be described in terms of 12 variables—six being stress variables, and six being strain variables. From this viewpoint, it should be possible to represent the stress-strain relations in the plastic range for metals by a surface in 12 dimensions. One boundary of this surface would be the surface of transition from elastic to plastic behavior; the other would be the surface of rupture. These two surfaces would be joined by the surface of plastic flow. The shape of this composite surface would depend on the test temperature and speed of straining This paper is concerned only with results obtained at constant temperature and constant speed of straining. While such a representation is conceivable, the demonstration of such a surface would present almost insurmountable obstacles. The most fruitful simplification of this concept has been the recognition that the behavior of metals in the plastic region is primarily a result of shear stresses and strains. Based on this viewpoint, it is possible to utilize stress and strain invariants that are independent of hydrostatic components to define an effective stress and strain. In effect, this amounts to reducing the task of representing stresses and strains in 12 dimensions to one of representation in two dimensions. The two invariants (one for stresses and one for strains) that have received most attention are the following: q2 = ½[(Txx= - Tyy)2 + (Tyy - Tzz)2 + (Tzz - Txx)2 + 3(Txy2 + Tyz2 + 7xx2) [1]

Jan 1, 1947

By Lloyd R. Jackson

In the past 15 years there has been a great deal of interest in the fundamentals of plastic flow and rupture in metals and a number of papers have presented substantial advances toward a fundamental insight into the mechanism of these two processes. This paper is an appraisal of the present position with respect to the following: 1. The relative importance of shear and hydrostatic stresses in controlling the plastic flow of metals. 2. The relative importance of shear and hydrostatic stresses in determining the amount of flow before rupture in metals. 3. The use of generalized strains in determining the effect of plastic flow on the work-hardening of metals. FundamentalS Involved in Plastic Flow In attempting to devise a quantitative description of plastic flow in metals, it has been customary to assume that metals are homogeneous and isotropic. The fact that neither of these assumptions is correct complicates the experimental appraisal of relations developed. Nevertheless, as will be shown, metals are close enough '0 being isotropic and homogeneous so that considerable insight into the mechanism of plastic flow can be obtained. The assumptions of isotropy and homogeneity allow both the elastic and plastic behavior of metals to be described in terms of 12 variables—six being stress variables, and six being strain variables. From this viewpoint, it should be possible to represent the stress-strain relations in the plastic range for metals by a surface in 12 dimensions. One boundary of this surface would be the surface of transition from elastic to plastic behavior; the other would be the surface of rupture. These two surfaces would be joined by the surface of plastic flow. The shape of this composite surface would depend on the test temperature and speed of straining This paper is concerned only with results obtained at constant temperature and constant speed of straining. While such a representation is conceivable, the demonstration of such a surface would present almost insurmountable obstacles. The most fruitful simplification of this concept has been the recognition that the behavior of metals in the plastic region is primarily a result of shear stresses and strains. Based on this viewpoint, it is possible to utilize stress and strain invariants that are independent of hydrostatic components to define an effective stress and strain. In effect, this amounts to reducing the task of representing stresses and strains in 12 dimensions to one of representation in two dimensions. The two invariants (one for stresses and one for strains) that have received most attention are the following: q2 = ½[(Txx= - Tyy)2 + (Tyy - Tzz)2 + (Tzz - Txx)2 + 3(Txy2 + Tyz2 + 7xx2) [1]

Jan 1, 1947