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By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By COURTNEY DE KALB

IRON ore is the cause of the present trouble in Morocco. At least three nations are interested in the outcome and private syndicates have been active. The iron deposits are found in that mountainous northern coast line known as the Rif. This is an uplift that has been cut through, by the northward drainage, representing an ancient land surface. Erosion has produced .a fiordlike coast, which circum- stance has aided contraband' traffic to the tribes dominated by Abd-el-Krim, the chief of the clan of the Beni Urriaguel, near the center of 'the north coast, opposite Alhucemas. The iron deposits are extensive in the territory of the Beni Urriaguel. They were "located," if such a term is permissible, many years ago. The first arrangements, through direct contracts with the tribal chieftains, have been reinforced by compliance with the subsequent code under the Spanish protectorate in 1914. Under those terms, the location had to be made through the Arbitral Commission sitting in Paris. These locations, or "denouncements," were made by the I-louse of Mannesmann, of Hamburg.

Jan 1, 1925

By T. Koulomzine

The theory of the Askania magnetometer, as well as a complete discussion of all factors influencing magnetometer readings, is very ably described by J. Wallace Joyce. We will assume that the reader is thoroughly familiar with this theory and we will use whenever possible the same notations for the physical values involved in the theory. On the other hand, we believe that the principal formulas of the magnetometer can be deduced much more easily by the use of differential calculus than by the methods employed by Joyce. Consequently, we are presenting herewith a resume of the theory of the vertical magnetometer in order to determine the correct formula of the temperature coefficient which we propose to compensate.

Jan 1, 1949

By R. J. Blackwell, J. R. Rayne, J. R. Henderson, W. M. Terry, D. C. Lindley

This paper presents the results of a laboratory investigation of the efficiency of water-solvent mixtures in recovery of oil. These mixtures may have the high displacement efficiencies characteristic of solvent floods and the high sweep efficiencies characteristic of water floods. Thus, the water-solvent process may increase the number of reservoirs in which a miscible-type displacement can be used profitably. The experiments on the use of water-solvent mixtures for recovery of oil were conducted to find the general applicability of the process. These studies demonstrated that, in flowing through sands, water and solvent segregated into a solvent layer on the top and a water layer on the bottom rather than flowing through the sands as a uniform mixture. Calculations based on the simultaneous flow of the water and solvent in layers were used to predict the effective mobility of the mixtures and the optimum operation of the process in steeply dipping, homogeneous reservoirs. As most reservoirs are not suited for the operation of the process under ideal conditions, experimental studies were conducted with sand-packed models scaled to represent more realistic reservoirs. These studies included the effects on recovery of oil of rate of injection, viscosity of oil, variations of permeablity within a formation and variations in water-solvent ratio. For the range of con-ditions studied, higher recoveries of oil were obtained with water-solvent mixtures than with water or practical volumes of solvent alone. INTRODUCTION A group of intriguing—because of their great possibilities—new oil recovery methods at the disposal of the petroleum engineer are the miscible displacement processes. These processes (high-pressure gas drive, en-riched-gas drive and LPG bank driven by methane) displace all of the oil from the portions of the reservoir swept by the injection fluid. The key question confronting the engineer applying one of these techniques to a particular reservoir is, "What fraction of the reservoir can be swept by injection of a practical volume of solvent?"." Intensive laboratory studies have been made during the past several years in seeking answers to the question of the sweep efficiencies which can be expected in solvent floods.' - These studies provided the answer that low-viscosity, low-density solvents channel and by-pass oil in sands with no dip. In horizontal sands, solvent flooding becomes less efficient as the viscosity of the oil increases, the recovery of oil at solvent breakthrough decreases and larger volumes of solvent are required to achieve a given recovery. More efficient displacement of oil by solvent is observed under certain conditions in sands with dip.".' If the permeability and dip of the sand are sufficiently high, gravity segregation of low-density solvent injected updip can prevent channeling. At rates of depletion below a critical rate,"." no channeling occurs. Unfortunately, in many reservoirs, the critical rate is so low that production of oil at rates below this rate is not economically attractive. And at rates over four times the critical rate, channeling is almost as severe in sands with dip as in horizontal sands. These findings pointed out that, for solvent floods to be generally applicable in recovering oil from all types of reservoirs, new methods of improving their sweep efficiencies are needed. Simultaneous injection of water with the miscible fluid was suggested by Caudle and Dyes7 as a method for improving sweep efficiencies. They theorize that water flowing with the solvent would decrease the effective mobility of the solvent and cause it to contact more oil sand. If, indeed, the water and solvent flowed as a uniform mixture, the process should have the advantages of the high displacement efficiencies characteristic of miscible floods and the high sweep efficiencies of water floods. Thus, the method (at least in theory) would greatly increase the number of reservoirs in which miscible-type displacements would be feasible. A research program was conducted to probe the technical feasibility of the water-solvent process. It

By W. E. STOKES

COMPANIES operating airplanes have had a relatively prosperous year, permitting them gradually to re- place old types of equipment. The pre-eminence of American-made planes, engines, and accessories has been challenged, either by foreign designs or by domestic patterns that have, for one reason or another. been licensed for manufacture abroad.

Jan 1, 1938

By Burnham E. Field

TAE chemical industry is constantly looking for new materials which either are more resistant to corrosion than those now available or have improved physical properties to meet the requirements of higher temperatures and greater pressures. Attack by acids is-one of the more important forms of corrosion-and in the last few years the development of acid-resistant alloys has been quite rapid. Perhaps the most notable example is that of nitric acid, 'the problem of which has largely been solved by the chromium-iron and chromium-iron-nickel alloys. Sulfuric acid may be handled in lead, iron, or the iron-silicon alloys, depending on conditions. As to hydrochloric acid, no metal or alloy can be called entirely satisfactory for handling. this acid under plant conditions.1 The results of our investigations on the resistance of the nickel-molybdenum alloys to hydrochloric acid have been confirmed by those of Guertler, Rohn, Schulz, Jenge, and others,' but thus far only one such alloy has approached commercial production in Germany; this contains approximately 15 per cent. chromium and 7 per cent. molybdenum with the remainder chiefly nickel. Dr. S. W. Parr, as far back as 1914, developed a complex alloy known as "illium," with a nickel base and containing some molybdenum.3 Dr. Parr was primarily interested in an alloy for lining bomb calorimeters, and while illium does show good resistance to acid it is too expensive for general use. Two United States

Jan 1, 1929

By Richard H. Jahns

GRANITIC pegmatite deposits are the chief source of commercial feldspar, sheet mica, beryllium, tantalum-columbium, and lithium minerals, and certain types of kaolin. They also have yielded significant quantities of cassiterite, gems, scrap mica, molybdenite, tungsten minerals, uranium-thorium and rare-earth minerals, and zircon, either directly or as the sources of placer deposits. The output from pegmatite mines in the United States is small as compared to other mineral products in terms of bulk or value, and much of it comprises minor metals and nonmetals. Nevertheless, pegmatite minerals play a vital part in domestic industrial economy, particularly in the ceramic and electrical industries. Numerous special purpose uses also are important, even though they require small quantities of raw materials. Never was United States dependence upon pegmatite mining more clearly emphasized than during World War 11, when greatly expanded demands and uncertainties of foreign sources of supply caused much concern. Such commodities as beryl, tantalite, and sheet muscovite remained high on the critical list for months at a time, and for some minerals there was a real struggle to achieve and maintain a favorable ratio of supply to demand. Satisfactory stock piles of certain sizes and qualities of sheet mica, for example, were not built up until late in 1944, when wartime requirements already had begun to level off or even to decrease. Production of all the strategic pegmatite minerals from domestic deposits during World War I1 constituted only 10 pct or less of the total domestic consumption of these minerals, but the importance of this contribution should not be minimized. Domestic production often represented the difference between increase and further reduction of existing stocks of commodities already in seriously short supply, and in the early stages of the war it was the only assured source if imports were cut off. During the recent war period, the U. S. Geological Survey carried on a program of pegmatite studies in the New England and Southeastern States, in the Black Hills area of South Dakota, in the Rocky Mountain region of Wyoming, Colorado, and New Mexico, and in various parts of Washington, Idaho, Utah, Nevada, Arizona, and California as shown in Fig. 1. Several papers and reports already have appeared as an outgrowth of this work,'-= and others are in preparation. This paper outlines some results of data obtained by the writer during the period 1942 to 1946, when he was engaged in studies of pegmatites in the Southeastern, Southwestern, and Rocky Mountain States. Beryllium Minerals Beryl is the present commercial source of beryllium metal and beryllium compounds, which are used in ceramics, in the preparation of X-ray tubes and fluorescent lamps and screens, in special processes of paint and textile manufacture, and in the optical systems of some electrical instruments. The metal also is used in nuclear physics, chiefly as a source of neutrons. Beryllium is alloyed with aluminum for certain light-metal uses and is a constituent of some nickel and iron alloys. Currently the chief demand, however, is for copper-base alloys, which are exceptionally resistant to fatigue and wear, are responsive to hardening treatments after

Jan 1, 1952

By W. R. Ingalls

THE main objective of everybody, individually and collectively as the people of nations, is to earn their living and improve the scale thereof as much and as rapidly as possible. We are able to earn" our living only by working and producing. We I are able to rise to higher standards of comfort only by increasing our production of goods, or diminishing the waste of those that we do produce, or both. This statement is trite. It is equally trite to dwell upon the importance of increased production to be derived from increased efficiency of labor and improved manage-ment; and the good results that would accrue to every-body if employers and employees would work together to secure the maximum of production at the minimum of cost. All of this is nothing more than platitude, to which every intelligent person subscribes in the abstract; but what concerns us especially, and what is neither so easy nor so understandable, is to translate the expres-sion of the abstract principle into formulas for action. The national net income obviously may be increased in two ways, or by both together. One is to diminish the waste of the goods that we already have made available. The other is to increase the supply of goods. .Increasing the supply of goods may involve the elimina-tion of waste, but a distinction is to be drawn between the waste of things that we have and the failure to obtain those that we might have. If we limit the term "waste" to the careless and profligate use of the materials that have come into our possession, together with the absorption of labor in doing obviously unnecessary things; and if we character-ize by the term "inefficiency" the failure to accomplish in our industrial operations the best of which we are capable, we shall create a distinction that will be pro-motive of clear thinking. In this paper I am going to deal with inefficiency, not waste, observing the distinc-tion, arbitrary if you please, that I have made. Without any doubt the greatest inefficiency that exists in our economic affairs is that which causes hundreds of thousands, perhaps millions, of men to be idle a good deal of the time. The major reasons for such idleness are two-fold. One of them is the conse-quence of what for convenience may be called business cycles, although I do not hold to the hypothesis of business cycles as it is now being rather widely expounded. That hypothesis involves the idea of rhyth-mic undulations due to causes unknown, but which it is hoped may be ascertained. The movement of busi-ness in waves up and down is undeniable, but that there are recurrences of cycles every so often is purely imag-inary, I think. It is unnecessary-to digress into that subject. The extents of the rises and falls above and below a median line undoubtedly is less than is commonly supposed.

Jan 3, 1922

By P. K. Foh, C. G. Dunn

IN an investigation of the rolling and recrystalliz-ing textures obtained from single crystals of Si-Fe, Koh and Dunn included specimens in the (111) [lie] orientation.1,2 This note reports some additional results obtained on samples of this orientation set aside for further study. After, primary recrystallization longer annealing treatments at 980°C produced only normal grain growth; after 16 hr at 980°C the largest grains were approximately 0.010 to 0.020 in. in diam. The orientations of 13 of the larger grains were found by the transmission Laue method. The unidentified (110) poles of these grains have been added to the (110) pole figure obtained after primary recrystallization2 to give the plot shown in Fig. 1. When grain identifications are also included, such a plot reveals the following. Two orientations agree almost exactly with the peak pole ,density positions of component B of the primary recrystallization texture, one with component A, and one with component C. All the remaining orientations except one have (110) poles near weaker and unidentified pole density peaks. In fact, the correlation is good enough for an identification of eight components. Previously only components A, B, and C were certain. The results are perhaps even more informative when combined with the (110) pole figure of the cold-rolled crystal to give the plot shown in Fig. 2. Each of the 13 orientations is identified and uniquely determined by selecting two (110) poles per crystal, which are 90" apart. The plot shows that every grain of the 13, except grain 6, has a (110) pole in common with a (110) pole concentration of the cold-rolled crystal. The orientation relationship with the cold-rolled orientation may be expressed as approximately 25" rotations about <110> axes, which is in agreement with the results found for coarse-grained primary recrystallization.2 If primary recrystallization had occurred according to the <110> rule without preference, there would have been 12 components. Actually our limited data reveals nine of the possible 12. The integrated pole figure also shows preferences among them, since three are considerably stronger than the rest. In addition to the above direct information, the following conclusions may be drawn. Primary recrystallization of the (111) [110] cold-rolled crystal produces a limited number of weak and strong components with the larger than average primary grains from these components related to the cold-rolled crystal by 25° <110> relationships. In arriving at this conclusion of limited orientations the (111) [110] orientation has to be ruled out as a source of large primaries for two reasons. First, growth in this orientation was not observed, despite an expected high grain boundary mobility (due to its 25" <110> relationship with every component of the texture). Secondly, primary recrystallization usually produces grains in new orientations, particularly in a single orientation matrix; but (111) [110] is not new. Other orientations besides those of the <110> type may be considered unlikely, of course, because the <110> relationship holds quite well for primary recrystallization2 and should produce the large primaries. There are exceptions to this rule, but probably not enough to provide large

Jan 1, 1958

By L. O. Storey

The McDermitt mine was found as a separate mercury ore-bearing occurrence approximately 305 m (1000 ft) northeasterly and in a different geologic setting from the old Cordero mine, which had been the district&apos;s major producer. The following briefly describes the discovery of the new deposit and the Placer Amex lnc. involvement. The Cordero mining property was under lease by Sierra Mineral Management from the owner Fred H. Lenway in February 1971, when the property was brought to the attention of Placer Amex Inc. (known at that time as American Exploration and Mining Co.) by Richard F. Hewlett of Sierra Mineral Management. The property was first examined by Amex geologists in the spring of 1971, who reported favorably on the project. During that year, Sierra Minerals Management had retained Dr. Larry Walters as a consultant. He proceeded to drill test mercury soils anomalies which he had found northeast of the old Cordero mine in an area overlain by recent alluvium and gravel. An area known as the D area was subsequently blocked out and ascribed a tonnage of about 18 1 kt (200,000 st) which occurs in the vicinity of the eastern edge of the currently defined McDermitt ore body. This mineralization was found in flat lying mercury-bearing lakebeds, unlike the steep structurally controlled ore which was mined in the old Cordero mine. It became apparent to Placer Amex that since the chances of much more extensive ore were good in such a geologic environment, additional exploration was warranted. A joint venture was formed in October 1972 by American Exploration and Mining Co. and Sierra Mineral Management to further explore the Cordero property. The project exploration was fully funded and managed by Amex. Sampling began by Placer Amex in the D area where an open trench had exposed the lakebed ore. Visible cinnabar could not account for the high-grade mercury assays taken from the trench, and an unknown mercury mineral was suspected. Subsequent work established the presence of a chlorine-bearing mercury sulfide which may have enriched the lakebeds as a secondary supergene mineral. Early identification of the mercury-bearing mineral corderoite (Hg3Cl2S,) aided in the geologic concepts for the ore occurrence and was helpful in exploring for the expansion of the D area. Corderoite was found occurring with cinnabar in the lakebeds, and in places it is a major contributor. Specimens of the unique ore were given to Dr. Eugene E. Foord and Dr. Pieter Berendsen at Stanford University, who subsequently identified the chemical and crystallographic makeup of the new mineral and described it for the first time as a naturally occurring substance. Metallurgical work on mercury recovery from the newly described mineral was carried out by the Placer Development Ltd. laboratories in Vancouver, and an acceptable recovery system was worked out together with a planned mill design. Step out drilling from the D area by Placer Amex Inc. encountered extensive flat lying lakebed ore. The McDermitt ore body, as subsequently defined by drilling, was found to contain 2.7 Mt (3 million st) of open pittable ore, containing approximately 5 kg/t (10 lb per st) Hg. The ore body gently dips to the north and is found lying mainly in claybeds just above an opalite breccia blanket which overlies the earlier volcanics. Some ore is also found in the opalite breccia. The mine and mill were constructed under an operating joint venture with Placer Amex Inc. and Sterling Mineral Ventures, and production began in June 1975 at the rate of 20,000 flasks per year. The mine is currently in progress.

Jan 1, 1985

By William P. Shinn

MR. GAYLEY&apos;S admirable paper on the " Development of American Blast-Furnaces" has set forth very fully the history of the development of the Edgar Thomson furnaces since the construction of Furnaces A and B ; but it throws no light on the genesis of these furnaces. That earlier history it is the purpose of the present paper to record. Mr. Gayley truly says: "A new era in the manufacture of pigiron began in 1880 with the putting in blast of the Edgar Thomson furnaces." That era had its beginning with the construction of

Jan 1, 1891

By SME

"Comparison of Secondary Fe-Mn Oxides in Fracture Coating and Heavy-Mineral Concentrates as Sampling Media, Silver City Mining Region, New Mexico," a technical paper, appeared in the Aug. 1983 issue of the magazine. In Table 1, page 1182, the correct sequence of the first five metals in column 1 (Elements) should read: Zn, Pb, Cu, Fe, and Mn under "Central District" and Zn, Fe, Pb, Cu, and Mn under "Pinos Altos District." The published table shows the sequences transposed under the opposite districts. All other columns and sequences read correctly.

Jan 1, 1984

By G. R. St. Pierre, S. W. Gilby

The equilibrium vapors established over Fe-Cr-Ni alloys containing up to 50 pct Cr at 1600°C were determined by collecting the effusate from thoria Knud-sen cells. From these data, the activities of iron and nickel in the ternary alloys have been calculated. In a separate set of measurements, a mass spectrometer was used to determine the activities of the three components in a series of Fe-Cr-Ni alloys. In binary Ni-Cr melts, the activity coefficient of chromium referred to pure solid chromium as standard state is less than one at low chromium contents but is greater than one for melts containing more than 30 at. pct Cr. For Ni-Cr melts containing less than 10 at. pct Cr, In ?Cr = 0.15-0.92 N2. Ternary activity diagrams for Fe-Cr-Ni alloys are presented. In iron-rich alloys, the interactions between the three components are negligible; however, in nickel-rich alloys, the three principal interactions have significant positive values. THE activities of components in binary Fe-Ni alloys have been measured both in the solid solution1-3 and liquid solution4-6 temperature ranges. The determination for Fe-Ni melts have been made by three different methods: transpiration,4 Knudsen-cell effusion with analysis of an accumulated condensate,&apos; and Knudsen-cell effusion with direct measurements of relative component intensities by mass spectrometric methods.6 The results obtained by the three different methods in three different laboratories are in excellent agreement and considerable confidence is placed in the activity coefficients for Fe-Ni melts. At 1600°C, the activity coefficients in dilute solution are ?°Ni = 0.66 and ?oFe = 0.40 for the pure liquid components as standard states. Measurements made on solid solution Fe-Cr alloys7-10 indicate that the component activities are slightly greater than ideal. The measured activities in iron-rich Fe-Cr liquid alloy11-16 indicate almost ideal behavior for this system. The recommended activity coefficient of chromium in dilute solution in liquid iron at 1600o C, ?oCr, is 1.18 when referred to pure solid chromium as standard state and 1.04 when referred to pure undercooled liquid chromium as standard state." The conversion factor of 1.14 is based on a melting point of 1857°C and an enthalpy of melting of 4047 cal per g at. for chromium.21,37 The activity coefficient of iron in dilute solution in liquid chromium has not been measured. Activity measurements on solid Ni-Cr alloys have been made by several investigators.17-20 During the review of this manuscript, Fruehan12 published the results of a study on liquid Ni-Cr alloys at 1600°C. He used galvanic cells22 with ZrO2(CaO) as the electrolyte and Cr/Cr2O3 for the reference electrode. His results indicate that ?oCr in nickel at 1600°C is about 1.01 when referred to pure solid chromium and about 0.89 when referred to pure undercooled liquid chromium as standard state. The activity coefficient of nickel in liquid chromium is unknown. The compositions of vapors freely evaporating from some molten Fe-Cr-Ni alloys have been measured by Lyubimov, Granovskaya, and Berenstein.23 Their results, combined with known vapor pressures, indicate strong positive deviation for chromium in iron-rich alloys and strong negative deviation for chromium in nickel-rich alloys. EXPERIMENTAL PROCEDURES This research was undertaken to determine the activities of components in ternary Fe-Cr-Ni melts containing up to 50 at. pct Cr. At the initiation of the research, we decided to use a Knudsen-cell method wherein a portion of the effusing vapor is condensed on a cold plate.&apos; The composition of the equilibrium vapor for each alloy composition is determined in this method by holding the system under constant conditions for a period of time sufficient to collect enough condensate on the cold plate for chemical analysis. The activities of components in ternary alloys can be calculated from such vapor composition determinations by Eq. [1].24

Jan 1, 1970

By William D. Klopp, Joseph R. Stephens

Chromium alloys were coated with silicon, alumi-nuw, and boron by pack cementation. None of these simple coatings provided adequate nitridation/oxida-tion protection for a Cr -0.17pct Y alloy substrate as shown by a substantial Increase in the ductile -brittle transition temperature after air exposure for 100 hr at 2100°F. Iron-modified silicide coatings afforded good protection, holding the transition temperature of air-exposed specimens to 350° F compared to 200° F for uncoated unexposed specimens and 800°F for un-coated exposed specimens. Additional attractive cant-binations of modi-tying elements included Fe-mo, Fe-Mo-W, Fe-,Mo-W-Ti, and V-Mo-W-Ti. THE desirability of increased operating tempera-tures as a mcans of improving the performance of ad-vanced air breathing engines has resulted in emphasis on the development of materials with high operating temperature capabilities. Chromium, because of its relatively low density (7.19 g per cu cm), high melt-ing point (3410°F), and adequate strength upon alloy-ing, is a candidate material for turbine buckets and stator vanes of advanced air breathing engines. How-even, chromium is not without severe limitations, the major one being susceptibility to nitrogen embrittle-ment upon exposure to air at high temperatures.1,2 For example, a 25-hr air exposure of a Cr-5 pct W* * All compositions in wt pct. alloy at 2100°F produces a 600°F increase in the duc-tile-brittle transition temperature.&apos; Although dilute alloying with such elements as yttrium, lanthanum, arid thorium3,4 or strong nitride formers5 has been shown capable of reducing nitrogen embrittlement, it is apparent that some additional form of surface protection, such as coatings or claddings, will be required for long time service in air breathing engines. Studies of aluiminide6 and silicide7 coatings and of nickel-base claddingsl on chromium alloys to date have suggested that these protection systems are inadequate. Of the aluminidc systems Studied,6 a simple aluminum and an Fe-Al coating on a Cr-5 pct W-0.1 pct Y alloy showed the lowest air exposure weight gains. However, the air exposures raised the ductile-brittle transition temperature of the coated specimens to above 1600°F from an initial level in unexposed specimens of about 500°F. A second in-vestigation for protection of Cr-5 pct W-0.1 pct Y employed gas pressure bonded alloy foils as protective claddings.1 An aluminized Ni-20 pct Cr-20 pct W alloy plus an unalloyed tungsten barrier layer gave the best performance with air exposure lives based on appearance and weight gains of over 600 hr at 2100°F. However, the bend ductile-brittle transition tempera-ture was increased to at least 1000°F after 100 hr at

Jan 1, 1970

By E. C. van Reuth

FIFTY-three alloys have been examined in the Fe-W and Co-W alloy systems in an attempt to verify the finding of o phases in these systems as reported by Goldschmidt.&apos; The alloys were examined metallographically and by X-ray diffraction. The 10-g specimens were made by powder metallurgy techniques. Very fine, high-purity powders were compressed in a double-acting die at 120,000 psi after hydrogen reduction. All compacts were then sintered for 200 hr at 950°C in a helium atmosphere. Metallographic investigation and X-ray diffraction proved this time to be sufficient to allow complete homogenization before the subsequent high-temperature anneal. Each specimen was then sealed into an evacuated silica capsule and annealed at 1400"or 1500 C (except two) for 25 hr. (The 60 pct Fe and 55 pct Co alloys taken to 1610"and 1680°C respectively were held at these temperatures for 1hr. However, since these structures were at equilibrium before the anneal, and in view of their resultant structures, it is assumed that they reached equilib-

Jan 1, 1960

By Craig S. Hartley

An approximate expression is obtained for the energy of a closed dislocation loop in equi1ibriu)n with a constant net stress. The result obtained is valid for loops in isotropic or anisotropzc materials provided that they are suJficiently large that the energy per unit length of a segment of the loop can be approximated by that of an infinite straight dislocation tangent to the loop. It is shown that this approximation leads to very close agreement with a more rigorous calculation of the elastic energy of a circular glide loop. The Gibbs-Wulff Form, GWF, of a dislocation is the closed planar loop which has the smallest elastic self-energy of all possible loops having the same Burgers vector and enclosing a fixed area, A.&apos; The energy of such a loop is related to the net resolved shear stress* required to expand the loop and to the stress required to activate a Frank-Read source.223 In the following sectiorls the problem of determining the form of the GWF is discussed and an approximate method for calculating its elastic self-energy is presented. It is demonstrated that the approximations employed lead to no serious errors when applied to a calculation of the elastic energy of a circular glide loop. This method is then used to obtain a closed form expression for the energy of GWFs in isotropic and anisotropic materials. THEORY Burton, Frank, and cabrera4 have proved that the relationship of the equilibrium shape of a two-dimensional array of atoms under the influence of the Gibbs free energy associated with unit length of its boundary, G(O), is that the polar plot of G(0) vs 0 is proportional to the pedal of the GWF.* The angle 0 is measured "The pedal of the polar graph ofG(0) vs0 is the envelope of tangents to the eraph.relative to some crystallographic reference direction. The difficulty in applying this result to a closed dislocation loop arises from the self-interaction of the loop. For a dislocation the energy analogous to G(0) is a function of the total configurati~n.~ Consequently the relation which determines the GWF is an integro-differential equation rather than the simple differen- tial equation which results when G(8) is a function of 0 alone. Mitchell and smialek3 and Brown~ have used the self-stress concept introduced by ~rown&apos; to calculate the shapes of dislocations in equilibrium with an applied stress. In this approach the glide force on an element of the dislocation loop due to the interaction of the element with the rest of the loop is equated to the glide force exerted by the local applied stress. The shape of the loop is then adjusted so that the two forces above are equal at all points on the loop. It is possible to calculate the energies of such loops by noting that, for equilibrium with an applied stress, the energy is equal to pijbiAj (summation convention) where bi is the Burgers vector, p.. is the local net stress tensor, and Ai is a vector directed perpendicular to the plane of thd loop with magnitude equal to the area of the loop. Also Brown&apos; has calculated the energy of a hypothetical polygonal GWF using the above technique and anisotropic elasticity. However, his indicated solution for the energy in the general case of an arbitrary GWF is only slightly less involved than an iterative solution of the integrodifferential equation referred to earlier. In the present work the approximation employed by DeWit and Koehler&apos; is used to calculate the energy of a closed loop in equilibrium with an applied stress. That is, the energy of a loop segment, ds, is approximated by the product of ds and the energy per unit length of an infinite, straight dislocation in a cylinder coaxial with the tangent to the loop at the angular position of the segment. This is known as the "line tension" approximation. The inner cutoff radius of the elastic solution defines the core radius, while the outer cutoff radius is determined by some characteristic dimension of the loop. Actually, both of these radii vary with the edge-screw character of the segment. The effective core radius changes because of the orientation dependence of the Peierls width of a dislocation,8 and the outer radius should be the radial distance from the circumference of the loop to the center of symmetry of the area enclosed by the loop.g However, since the energy varies logarithmically with the ratio of these radii while depending directly on the effective elastic constants, only the effect of the latter is considered. This approximation also neglects the self-interaction of the loop segments. For small loops this will doubtless be extremely important, but for large glide loops produced by plastic deformation the self-interaction is not nearly so important in determining the energy of the loop. This point is illustrated by the following calculation of the energy of a circular loop. Consider a circular loop of radius R which lies in the XI - x, plane of an infinite isotropic continuum and whose Burgers vector makes an angle $ with xs. The first-order solution for the elastic self-energy is:&apos;

Jan 1, 1970

By Eleanor Haslem, Carl A. Zapffe

THE present investigation has three principal purposes: I. To develop a method for measuring hydrogen embrittlement that avoids certain errors complicating previously used methods. 2. To explore in a preliminary way some of the fundamental factors controlling embrittlement. 3. To apply the measurements specifically to stainless grades of steel, whose sensitivity or insensitivity to hydrogen embrittlement has never been clearly defined. SELECTING A TEST METHOD Hydrogen embrittlement is a condition of low ductility resulting from excessive absorption of hydrogen by the steel at some period in its history, and may be revealed by almost any test involving cold deformation. Tensile tests, impact tests, and bend tests are commonly used for detecting hydrogen embrittlement; although numerous other tests, such as cold-upsetting or extrusion, could be used. The simplicity of using a wire specimen for cathodic and acid pickling tests, and the especial adaptability of the bend test to wire specimens, led to selection of the bend test for the present research. Bend tests usually have been of three general types: (I) fatigue, (2) reversed bend, and (3) single bend. The first two types, though widely used, are inaccurate because their measurements are counteracted by an aging effect; and the third type has not been developed to its fullest utility. The effect of cold-working in removing hydrogen is well known. During a bend test hydrogen can be observed escaping from the convex side simply by coating the specimen with oil; and any technique employing flexing or reverse bending may therefore have its measurements masked because the mechanical action reduces the embrittlement during the test. This factor is so important that even elastic flexing of a hydrogen-charged wire specimen should be avoided before testing if accurate measurements are desired. DEVELOPING A MACHINE FOR MEASURING HYDROGEN EMBRITTLEMENT As for the single-bend test, its theory is good, and recovery caused by mechanical work is kept to a minimum. With a given degree of hydrogen embrittlement, a specimen will break at a given angle if the bending is applied unidirectionally and uniformly. The radius of the bend must be kept constant; and the rate of bending should be a constant, slow enough to allow reading of the breaking angle, and yet rapid enough to prevent significant recovery from the escape of hydrogen during bending. A simple apparatus (Fig. I) was constructed using a type H Foxboro drive unit A, which is a synchronous motor with a gear-reduction ratio of 600 to I. A cord, fixed at one end to a wooden pulley B on the drive shaft of the motor, follows the pe-

Jan 1, 1946

By G. Y. Chin, M. T. Dolan, W. L. Mammel

The least work analysis of constrained deformation, first proposed by Taylor and recently modified by Chin, Hosford, and Mendorf to include twinning, has been applied to the problem of axisynmetric flow. Calculations were made, for the case of (111}(110) slip and {111}(112) twinning applicable to fcc deformation. The solutions were obtained by linear programming techniques and with the aid of computer methods. The results show that in axisymnzetric tension the onset of twinning tends to decrease the plastic strength anisotropy as compared with the case of defortnation by slip alone. In compression, however, the strength anisotropy is increased as a result of twinning. The [100] and 11111 orientations and their vicinity are unfavorable for twinning in tension and compression, respecticely. With slight modifications, the present results may be applied to bcc metals deform ing by {110}(111j slip and (112} (111) twinning. Implications of present results to wire texture development of low stacking fault energy fcc materials arc discussed. PREVIOUSLY we&apos; have applied linear programming techniques to obtain solutions to Taylor&apos;s least work analysis2 of constrained deformation of single crystals undergoing axisymmetric flow, such as occurs in an axially loaded polycrystalline aggregate. These solutions yielded values of the parameter M = o/.r = Y/w which relates the external stress-strain (u-c) curve to the shear stress-shear strain (7-y) curve for the crystal. The value of M is dependent on crystal orientation and hence enters significantly in texture strengthening considerations.3&apos;4 Recently the Taylor hypothesis was modified by Chin, Hosford, and Mendorf&apos; to include mechanical twinning. The latter has now been applied to the problem of axisymmetric flow and the results are reported in this paper. Calculations have been made for {111 )( 110) slip and {111 )(112) twinning applicable to fcc crystals. With minor changes in the indices of the slip and twin systems, the present results are also applicable to bcc crystals which slip on (110) (111) and twin on {112)(111) systems.

Jan 1, 1970

By Edward Keller

In order to conduct intelligently the sampling of copper of various forms and grades, solid or in molten furnace-charges, a knowledge of this subject is essential. Yet figures and tests have been persistently withheld from publication, and the books at our command give us little or no information in this regard. This gap in our copper-literature has led to a series of experiments, the results of which are given below. Nearly all gold- and silver-bearing copper, destined for shipment, is cast into the form of bars or pigs. For the sampler, the question arises, Does copper, so cast, remain homogeneous ? If it does, sampling should present no difficulties; but, from experience, we know that this is not the case, and we are thus led to study the behavior of the precious metals arid impurities in copper when the latter changes from the molten to the solid state. For the purpose of the experiments here described, all available grades of copper were selected, and all of them mere subjected to the same conditions, an important requisite for proper comparison. The molten copper obtained directly from reverberatory- and blast-furnaces was cast in a cast-iron mould, the sides and bottom of which were 1 inch thick, and would, therefore, give the copper a fair length of time to chill. The inside dimensions of the mould, and, consequently, of the block of copper obtained, were: length, 10 inches; width, 9 inches; and depth, 5 inches. Fig. 1 illustrates the method employed to obtain samples from these blocks. A was cut away, and the face so produced BALTIMORE COPPER WORKS,

Jan 1, 1898

By R. J. Marcotte, C. T. Eddy, R. J. Smith

The objectives of the investigation herein reported were to determine: (I) the S-curves for certain selected cast steels, (2) whether or not the published S-curves for wrought steels are satisfactory for use on cast steels of similar composition, and (3) to prepare hardenability curves of the selected cast steels. In order to make the final comparisons between cast and wrought steel more completely tangible, it was deemed advisable not only to determine S-curves for the steels submitted in the cast condition but also to roll some of the cast-steel test bars and determine comparison S-curves on such wrought material. This procedure eliminates the composition variable and makes it possible to reveal the differences resulting from plastic deformation of the cast structure in addition to providing the comparison with published data on wrought steels. Cast Steels The cast steels selected for the preparation of S-curves, or time-temperature transformation curves, were similar to S.A.E. series 1030, 2330, 4130 and 4330. Of these the 1030 was supplied by The Crucible Steel Casting Co., Cleveland, Ohio, and the other three by The Sawbrook Steel Castings Co., Lockland, Ohio. The steels were furnished in the as-cast condition. The manufacturers supplied the chemical analyses and the properties that could be obtained in the heat-treated condition—all of which is summarized in Table I. The metallographic and dilatometric procedures and equipment were in general standard. The specific technique employed was described in a report of the Steel

Jan 1, 1945