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By Henry Schaefer

Solution by electric analogy of performance problems of reservoirs containing oil and gas has heretofore depended upon a process of successive approximations based on material-balance calculations, because of variation in fluid compressibility. By the addition or subtraction of electric condenser capacity, the analogy network can be adjusted automatically for changing compressibility due to evolution of gas in the reservoir. The addition of a condenser is accomplished by an electronic circuit, which is described; subtracting a condenser is done by merely opening the electrical circuit by means of a relay. Introduction V. Paschkis and H. D. Baker1 first developed in this country a method of applying the analogy of flow of electric current in noninductive circuits to solution of heat-flow problems and suggested its application for certain other problems, such as flow of fluids or mass transfer and chemical diffusion. Necessary details for applying the analogy to flow of fluids in porous media were developed by IV. A. Bruce;= he classified3 the types of analysis and predictions that can be made by the analogy in class I, when the reservoir contains oil but no gas for the period under consideration; in Class 2, when both oil and gas exist in the free state in the reservoir sometime during the period under consideration. Duplication of bottom-hole pressure history and predictions for class I reservoirs can be obtained directly by electric analogy. Until now, the solution of problems pertaining to reservoirs in class 2 was obtained by successive approximations along with material-balance calculations. The object of this paper is to present a method for simplifying the application of electric analogy to class 2 reservoirs, resulting in a solution of these problems as direct as is possible for class I reservoirs. This is accomplished by an electronic control circuit, which adjusts the analogy network for changing compressibilities of fluids contained in the reservoirs. Analogy Network In electrical phenomena the analogy to two-dimensional fluid flow in a porous media is that of current flow through an ideal conducting sheet. This sheet, perfectly insulated on both sides, has resistance and capacitance uniformly distributed throughout its area but is of negligible inductance. The need for having the surface boundaries perfectly insulated is that good correspondence may be had with a permeable fluid-conducting stratum bounded above and below by impermeable media. 111 actual application the ideal conducting sheet, which has distributed parameters, is replaced by a network having lumped values of resistance and capacitance—the resistances are series elements and the capacitances are shunt elements. The larger the number of lumped

Jan 1, 1947

By H. H. Uhlig

In our study of the mechanism of and the prevention of corrosion in stainless steels, it was considered of fundamental importance to obtain knowledge of the surface structure of such alloys. If corrosion resistance is due to a self-healing oxide layer, which like a paint film protects the underlying metal, it would be obviously relevant were the effort made to make the film less permeable and more adherent; for example, the surface might be expected to respond to an anodizing process, which is found successful in increasing the film thickness and corrosion resistance of aluminum. However, if passivity and corrosion resistance of stainless steels are due to another cause, the attack of the problem would follow another path. One of the most effective techniques for studying passivity and corrosion tendency is the measurement of the electrochemical potential. Not only can one determine by potential measurements whether a metal is active or passive, but also one can determine the degree of passivity and rate of transformation of passivity with time. Chemical media that build up or destroy passivity when in contact with the steel can also be classified by potential measurements. Something can be learned, too, of the effect of alloy additions such as molybdenum to 18-8, known to decrease corrosion of the alloy in chloride solutions. A study of alloys in previous investigations has sometimes included data on the electrochemical potentials. Tammann and Sotterl measured the electrochenlical potentials of alloys of iron-molybdenum and iron-chromium and reperted the critical concentration of molybdenum or chromium at which passivity initiates. Strauss2 made similar measurements for the iron-chromium system. The electrochemical potential3 has also been used to indicate carbide precipitated 18-8. In 18-8, heat-treated to precipitate carbide, active metal exists at the region of the grain boundaries, contrasted with passive metal within the grains, the active metal accounting for a resultant active potential. Several

Jan 1, 1940

By Leslie F. Tedsen, John E. Dorn, Alan E. Flanigan

It is necessary occasionally to use aluminum-alloy sheet where moderately elevated temperatures are encountered. Considerable attention has been directed toward determining the influence of "artificial aging" on the room-temperature properties of the precipitation-hardenable alloys, as testified by numerous company reports and by references I to 4. Investigations on the properties at elevated temperatures are few, however, and have not always covered the range of times and temperatures of greatest interest. The present investigation was instituted to overcome this deficiency. The work was done for the Office of Production Research and Development of the War Production Board, under the supervision of the War Metallurgy Committee, as a part of the "restricted" Project NRC-548. It has been released for publication by the Office of Production Research and Development. AS is well known, the high-strength aluminum alloys achieve their remarkable properties as a result of precipitation-hardening. In production they are subjected to a solution heat-treatment followed by quenching, to retain the supersaturated solid solution. The solution treatment is followed by "aging" (precipitation-hard- ening) either at room temperature or at a suitable elevated temperature. A considerable increase in tensile and compressive yield stresses results from precipitation at room temperature ("natural aging"). Through the elevated-temperature process ("artificial aging") it is possible to obtain values of yield stress considerably higher than those attainable by natural aging. The increase in yield stress is accompanied by a smaller gain in ultimate tensile stress and by a decrease in elongation. During the first stages of artificial aging the yield stress increases steadily until it reaches a maximum value. In this condition the material is said to be "fully aged." Further exposure results in "averaging," attended by a steady decrease in yield stress. In the production of the artificially aged materials, temperatures and times are selected to achieve full aging. The following important characteristics are associated with the process: 1. The higher the temperature, the more rapidly is the fully aged condition attained. :7

Jan 1, 1946

By Albert J. Phillips

When brasses containing from 61 to 62.5 per cent. copper are very rapidly cooled from temperatures near their melting point to below 0" C., unusual results are obtained. These results are quite unexplainable from a consideration of the old copper-zinc constitutional diagram but they can be satisfactorily explained by means of the diagram revised by Genders and Bailey1 (Fig. 1). Experiments on a 60/40 Brass If an alloy containing 60 per cent. copper is heated to any temperature between approximately 760' C. and its melting point, it will consist entirely of beta. Upon slowly cooling, alpha will start to separate just below 760" C. Since this alpha will contain nearly 65 per cent, copper, the beta will be impoverished by its separation. As the temperature decreases the composition of the separating alpha will approach approximately 61 per cent. and the beta in contact with the alpha will maintain an equilibrium composition approaching 54.5 per cent. copper. If the rate of cooling is extremely slow, especially at the lower temperatures, stable equilibrium will be established by diffusion through the alpha and beta so that eventually 85 per cent. of the alloy will consist of alpha containing 61 per cent. copper, while 15 per cent. will be beta containing 54.5 per cent. copper. With a faster cooling rate diffusion cannot keep apace and the constituents will be cored, the alpha varying from 65 to 61 per cent. copper and the beta from 60 to 54.5 copper. In this case the amount of alpha will be less than 85 per cent. and the beta will be increased correspondingly. The general structure thus obtained is illustrated in Fig. 2. When a more rapid rate of cooling is effected by quenching in water, the alloy is retained largely in the beta form. However, the crystals of beta are usually outlined with dark fringes which at high magnifications are found to be very fine alpha-beta structures almost martensitic in appearance. The separation of this fringe can be greatly suppressed

Jan 1, 1930

By Arthur Phillips

The progress made in recent years in the art of dispersion-hardening has naturally led to an intensive study of alloy systems capable of yielding supersaturated solid solutions at ordinary temperatures. In general, the investigations have been confined to rather precise determinations of solubility limits and to experimental approaches designed to furnish more complete information regarding the rate and nature of precipitation under appropriate thermal conditions. Efforts are being made to focus more sharply on the atomic changes that are a direct consequence of the instability of the supersaturated solution. Here precision X-ray methods have come to be of considerable importance because lattice parameter measurements indicate very precisely the concentration of solute atoms in the solvent lattice. In spite of the general acceptance of parameter values as a criterion for the placing of solubility limits, it may be suggested that no thorough appraisal has been made of the several factors that conceivably may affect such measurements. More specifically, little attention has been devoted to the significance of surface energy conditions, specimen size and method of preparation, with particular regard to the genesis of the grains and the surface concentration changes as a consequence of heat treatment and etching. Stenzel and Weertsl recently published the results of a detailed study of precipitation reactions in aluminum-rich copper alloys. They found that, although copper lowers the lattice constant of aluminum, a 5 per cent copper alloy quenched from 150" and 225' C. had parameter values unquestionably higher than that of pure aluminum. Their results seem to substantiate, at least qualitatively, the earlier work of von Göler and Sachs,2 who indicated a parameter value, for the same alloy annealed for 24 hr. at 200° C., some 0.0008Å. larger than that of pure aluminum. Stenzel and Weerts attributed the abnormal lattice dimension to the effect of strain induced by the precipitation of CuA12. Weerts3 later

Jan 1, 1934

By S. A. Montague

Mica can claim a considerably greater importance than would be assumed from its comparatively small dollar volume, which came to about $37,000,000 for the United States industry as a whole in 1957. Mica is one of the strategic minerals. We must depend on imports from distant sources for virtually all of our requirements of high grade block and all of our mica splittings. Mica is essential and indispensable for vacuum tubes and high-performance condensers, two electronic components which are vital military necessities besides being nearly indispensable to civilization today. Composition and Properties Mica is the general name for a group of some nine different minerals, two of which, muscovite and phlogopite, are the minerals used by the mica industry as its raw material. Several of the other varieties are commercially useful-vermiculite, * used for heat insulation in expanded form, and lepidolite, used as an ore of lithium while the others-biotite, roscoelite lepidomelane, paragonite and zinnwaldite have little or no commercial importance. Biotite frequently occurs as an undesirable impurity in muscovite. Table 1 lists various properties and other data concerning muscovite and phlogopite. Chemically, mica is a complex silicate of sodium, potassium and aluminum. Most varieties of muscovite are higher in sodium, and of phlogopite in magnesium. There are no important uses of mica where the chemical analysis is important, except that in some uses of ground mica, the content of iron oxide present as an impurity must be kept to a very low limit. Muscovite occurs in a range of color from the so-called India "ruby" which is more closely a pinkish brown, to light and dark green, with numerous other intermediate shades. Ruby color is usually preferred by industry, especially in the better qualities. When split very thin the color in most [ ] micas disappears. Muscovite mica is frequently found containing black and red "stain" as a homogeneous part of the books or sheets. In most cases this stain or impurity is magnetite

Jan 1, 1960

By Howard Scott

INVAR is the preeminent low-expansion metal by virtue of the fact that it can be prepared with a zero coefficient of expansion at atmospheric temperature. This fact suggests that there is little room for improvement in the expansion properties of the low-expansion nickel steels. The inference is true, however, only so far as the expansion at and near atmospheric temperature is concerned, because the expansivity of invar starts to increase rapidly on heating above 100° C. and soon reaches the value of copper. Guillaume1 met this situation by increasing the nickel content above that of invar. By that expedient, alloys having low expansivity under higher temperatures were obtained, but not without a large increase in minimum expansivity. The increase in minimum expansivity with increasing nickel content severely limits the technical applications of these alloys at high temperatures. Prospects of improving the expansion characteristics of the nickel steels is offered by alloying. Search for an advantageous alloying addition by analogy with other alloy systems, however, is not productive because the low-expansion characteristic is unique with that system. The rule of mixtures usually gives a fair value of the expansivity of other solid-solution alloys, but in the iron-nickel systems gives a value of 18 X 10-6 per deg. C. whereas the actual value is 1 X 10-6 per deg. C. Apparently suitable additions are not to be deduced from such ingenuous considerations. Recognition of the fact that the temperature range of low expansivity in nickel steels is terminated with loss of magnetism affords a more promising basis for the selection of an advantageous element. One may expect from that fact that additions of nonmagnetic elements to the iron-nickel alloys are detrimental to the low-expansion characteristic. Indeed, carbon, manganese, silicon, copper and chromium are detri-mental to the expansion properties and no nonmagnetic element is reported to be beneficial. From the same viewpoint, the addition of a magnetic metal offers prospects of improvement. As two of the three ferromagnetic elements are already present in the

Jan 1, 1930

By S. L. Hoyt

Some of the more important properties of finished materials are strength, ductility, toughness, resistance to alternating and repeated stresses, etc. Of these, the property that appears to have received the least consideration, at least in this country, is toughness, which is due, possibly, to our regarding toughness as a qualitative property or, at any rate, as one that parallels ductility. This arises out of our greater experience with the simple carbon steels in the rolled or forged (non-heat-treated) condition which, qualitatively, are tough if ductile and are not tough if brittle. In this way we have erroneously become accustomed to judging the toughness of a material from its behavior in the tensile or similar test. The point of view presented in the present paper is that toughness, like hardness or tensile strength, should be regarded as an independent property and of sufficient importance to require, in so far as that may be possible, quantitative determinations. If such be true, it becomes at once necessary to devise experimental means for measuring or valuating toughness, and the notched-bar impact test (the Charpy test) is advanced as the most logical test that has so far been developed for this purpose. It is further advanced, with particular emphasis, that we have two kinds of toughness to deal with and, accordingly, they will be dealt with independently. Classification of Materials According to Toughness Toughness has been defined somewhat as follows: Tough materials are those that offer considerable resistance to permanent deformation but which, once such resistance has been overcome, may be deformed plastically, but only by the expenditure of considerable energy. In other words, tough materials may be deformed plastically but they absorb a considerable amount of work in the process. This kind of toughness may be called "static" toughness when the rate of loading is reasonably slow or "dynamic" toughness when the rate of loading is comparatively rapid, as in impact testing, but in all cases the stress distribution is essentially uniform. However, static toughness does not

Jan 1, 1920

By Chester T. Sims, Robert I. Jaffee

The thermoelectric behavior of the Pt—Pt-Re thermocouple and the resistance of rhenium to attack by certain molten metals is discussed. In addition, data are presented on the stress-rupture behavior of drawn wire, the tensile characteristics of rolled sheet, the variation of Young's modulus with temperature, and the effect of specimen size and fabrication method on the work harden ability. Mechanical properties of thoriated rhenium are discussed. This includes data on the effect of thoria in rhenium on tensile properties, ductility, work hardening, and recrystallization. RECENT work by the authors', has described methods of fabrication and some of the physical and mechanical properties of rhenium. Rhenium was established as a high melting, dense, refractory-type metal with favorable mechanical properties. In addition, Todd and co-workers' and others" have studied such properties of rhenium as the work function, specific heat, and the resistance of rhenium to the water cycle. Revelation of these and other properties has led to serious consideration for application as electrical contacts, high temperature thermocouples, and wear resistant materials. chanical properties reported previously,' several additional examinations have been conducted. The stress-rupture behavior and the Young's modulus of rhenium have been investigated at elevated temperatures. Tensile data have been obtained for rolled sheet, and a study of the relative work hardening characteristics of rod, wire, and sheet has been conducted. Variation of Modulus of Elasticity With Temperature—The Young's modulus of a % in. diam annealed rhenium rod was determined from room temperature to 880"C (1620OF). The rod, approximately 6 in. in length, was activated in a transverse vibration apparatus suspended in a furnace. The resonance frequencies of the rod were measured and used to calculate the moduli values. The driven frequency was 569 cycles per sec, and a protective helium atmosphere was used. The data, plotted in Fig. 1, show that the modulus decreases in an approximately linear manner with temperature over the range tested.

Jan 1, 1957

By A. B. Kinzel

THE demands of the petroleum and chemical industries for steels to be used in pressure vessels and similar structures at artificially low tempera-tures are continually increasing, and the writing of proper specifications with suitable tests becomes increasingly important. Likewise, the selec-tion of suitable steels for such applications is of increasing concern to the metallurgist. It is generally recognized that highly alloyed steels of the austenitic stainless type retain their properties even at very low tempera-tures and represent the best technological solution of the low-temperature steel problem. However, in many instances less expensive carbon or low-alloy steels suitable for service within limited temperature ranges are available. The problem thus becomes one of defining the various factors involved in the production and fabrication of these less expensive steels and determining the temperature ranges in which their properties justify engineering application. Most of the applications involve welded structures, and the heat effect of welding as well as the nature of the weld metal are matters of prime concern. The first problem that the metallurgist faces is the determination of the type of test to be used as a criterion of the performance of the steel in low-temperature service. It has been generally recognized that the static properties of steel as determined in the ordinary tensile test undergo a gradual and relatively slight change as the temperature of test is lowered in the range of current interest; i.e., from room temperature to minus 120° C. It is further generally recognized that the behavior of steel under impact involving notch sensitivity is definitely affected at the lower temperatures. While the major subject of this paper is the effect of grain-refining deoxidizers, of low-alloy additions and of welding on the low-temperature notched-bar impact properties, an inquiry into the general behavior of steel under low-temperature impact testing is included. This is a pertinent portion of the investigation and the results thereof are

Jan 1, 1937

By C. B. Post, D. G. Schoffstall

A determinatioil of the hydrogen content of molten steel by means of the Vacuum-extraction method, as reported here, consists in first casting a sample of the bath in a bomb, so that the gases evolved during solidification are trapped for analysis. A portion of the cast steel sample is then prepared and heated at a temperature of 600" to 800°C. under high vacuum, and the gaser given off during this vacuum extraction (which are shown to be hydrogen), are collected and measured. Analysis of the gases evolved on solidification and the gases in the solid sample enables an accurate determination of hydrogen in the molten steel. Fig. I shows the bomb and accessories that have been found suitable for trapping the gases evolved on solidification. The bomb is made of scamless steel pipe, approximately 7 in. long by 136 in. i.d., and welded at the bottom. An ordinary pipe cap has a vacuuni-type metal stopcock threaded and brazed in its upper end. This pipe cap fits onto the bomb by means of machined threads. A flange is brazed to the pipe at the point where the cap starts to tighten up, and a rubber gasket is placed between the flange and cap. Heavy vacuum grease is used between the flange and gasket and the gasket and cap. The weight of the complete bomb and it? interval volume is known before the sample is cast. In practice, a sample of about 400 grams of steel is poured into the bomb, the funnel quickly swung out of the way, the bomb cap spun down the threads and tightened against the gasket, and the bomb set in a pail of water to keep the gasket and vacuum grease cool. It is estimated that at least 80 per cent 01 the gases evolved from the liquid sample during solidification are trapped in the bomb."

Jan 1, 1945

By Albert Sauveur

AT the New York meeting of the Institute, February, 1914, Professor Hopkinson and Sir Robert Hadfield presented an important paper entitled Research with Regard to the Non-Magnetic and Magnetic Conditions of Manganese Steel.1 Any contribution on manganese steel by its discoverer necessarily carries with it much weight and is entitled to serious and close consideration. The momentous discovery of that alloy by Sir Robert Hadfield some 30 years ago was the signal for great activity in the field of alloy steels; and the remarkable results obtained in the last two decades probably constitute the most important modern advance in the metallurgy of steel. The authors of the paper referred to above are unable to reconcile with the allotropic theory the interesting results obtained by them in heat treating manganese steel. When they speak of the allotropic theory, however, I understand that they have more especially in mind the existence of beta iron. It is not my understanding that they question the occurrence of iron in the two allotropic varieties known as gamma and alpha. If I am wrong, I trust they will correct me. A careful consideration of the experimental results reported and discussed by the authors leads me to believe that on the contrary they can be very satisfactorily explained in terms of allotropy and that, in the light of our present knowledge, they cannot be accounted for in any other way. The physical properties of non-magnetic manganese steel described by the authors are those pertaining to iron-carbon alloys in which iron is present in the gamma condition, or, in other words, to austenite. The metal is then characterized by great tenacity and ductility and low elastic limit, while its hardness, mineralogically speaking, is not excessive, but of a special kind termed "tough hardness" by the authors. Even when subjected to the restraining influence of a large amount of manganese and of considerable carbon, however, relatively rapid cooling

Jan 9, 1914

By Leslie F. Tedsen, Alan E. Flanigan, John E. Dorn

It is necessary occasionally to use aluminum-alloy sheet where moderately elevated temperatures are encountered. Considerable attention has been directed toward determining the influence of "artificial aging" on the room-temperature properties of the precipitation-hardenable alloys, as testified by numerous company reports and by references I to 4. Investigations on the properties at elevated temperatures are few, however, and have not always covered the range of times and temperatures of greatest interest. The present investigation was instituted to overcome this deficiency. The work was done for the Office of Production Research and Development of the War Production Board, under the supervision of the War Metallurgy Committee, as a part of the "restricted" Project NRC-548. It has been released for publication by the Office of Production Research and Development. AS is well known, the high-strength aluminum alloys achieve their remarkable properties as a result of precipitation-hardening. In production they are subjected to a solution heat-treatment followed by quenching, to retain the supersaturated solid solution. The solution treatment is followed by "aging" (precipitation-hard- ening) either at room temperature or at a suitable elevated temperature. A considerable increase in tensile and compressive yield stresses results from precipitation at room temperature ("natural aging"). Through the elevated-temperature process ("artificial aging") it is possible to obtain values of yield stress considerably higher than those attainable by natural aging. The increase in yield stress is accompanied by a smaller gain in ultimate tensile stress and by a decrease in elongation. During the first stages of artificial aging the yield stress increases steadily until it reaches a maximum value. In this condition the material is said to be "fully aged." Further exposure results in "averaging," attended by a steady decrease in yield stress. In the production of the artificially aged materials, temperatures and times are selected to achieve full aging. The following important characteristics are associated with the process: 1. The higher the temperature, the more rapidly is the fully aged condition attained. :7

Jan 1, 1946

By H. H. Uhlig

In our study of the mechanism of and the prevention of corrosion in stainless steels, it was considered of fundamental importance to obtain knowledge of the surface structure of such alloys. If corrosion resistance is due to a self-healing oxide layer, which like a paint film protects the underlying metal, it would be obviously relevant were the effort made to make the film less permeable and more adherent; for example, the surface might be expected to respond to an anodizing process, which is found successful in increasing the film thickness and corrosion resistance of aluminum. However, if passivity and corrosion resistance of stainless steels are due to another cause, the attack of the problem would follow another path. One of the most effective techniques for studying passivity and corrosion tendency is the measurement of the electrochemical potential. Not only can one determine by potential measurements whether a metal is active or passive, but also one can determine the degree of passivity and rate of transformation of passivity with time. Chemical media that build up or destroy passivity when in contact with the steel can also be classified by potential measurements. Something can be learned, too, of the effect of alloy additions such as molybdenum to 18-8, known to decrease corrosion of the alloy in chloride solutions. A study of alloys in previous investigations has sometimes included data on the electrochemical potentials. Tammann and Sotterl measured the electrochenlical potentials of alloys of iron-molybdenum and iron-chromium and reperted the critical concentration of molybdenum or chromium at which passivity initiates. Strauss2 made similar measurements for the iron-chromium system. The electrochemical potential3 has also been used to indicate carbide precipitated 18-8. In 18-8, heat-treated to precipitate carbide, active metal exists at the region of the grain boundaries, contrasted with passive metal within the grains, the active metal accounting for a resultant active potential. Several

Jan 1, 1940

By Howard Scott

Invar is the preeminent low-expansion metal by virtue of the fact that it can be prepared with a zero coefficient of expansion at atmospheric temperature. This fact suggests that there is little room for improvement in the expansion properties of the low-expansion nickel steels. The inference is true, however, only so far as the expansion at and near atmospheric temperature is concerned, because the expansivity of invar starts to increase rapidly on heating above 100" C. and soon reaches the value of copper. Guillaumel met this situation by increasing the nickel content above that of invar. By that expedient, alloys having low expansivity under higher temperatures were obtained, but not without a large increase in minimum expansivity. The increase in minimum expansivity with increasing nickel content severely limits the technical applications of these alloys at high temperatures. Prospects of improving the expansion characteristics of the nickel steels is offered by alloying. Search for an advantageous alloying addition by analogy with other alloy systems, however, is not productive because the low-expansion characteristic is unique with that system. The rule of mixtures usually gives a fair value of the expansivity of other solid-solution alloys, but in the iron-nickel systems gives a value of 18 X 10-6 per deg. C. whereas the actual value is 1 X 10-6 per deg. C. Apparently suitable additions are not to be deduced from such ingenuous considerations. Recognition of the fact that the temperature range of low expansivity in nickel steels is terminated with loss of magnetism affords a more promising basis for the selection of an advantageous element. One may expect from that fact that additions of nonmagnetic elements to the iron-nickel alloys are detrimental to the low-expansion characteristic. Indeed, carbon, manganese, silicon, copper and chromium are detrimental to the expansion properties and no nonmagnetic element is reported to be beneficial. From the same viewpoint, the addition of a magnetic metal offers prospects of improvement. As two of the three ferromagnetic elements are already present in the

Jan 1, 1930

By G. R. Speich, L. Zwell, H. A. Wriedt

HORNBOGEN1 has recently shown that it is possible to measure the degree of segregation accompanying cellular precipitation in ferritic Fe-Zn alloys by measuring the lattice parameter of the ferrite phase within the cell. In extending this work to study a wider range of composition and to evaluate the free-energy change accompanying the growth of the cells, the lattice parameter and the boundary of the a! phase in Fe-Zn alloys were redetermined to check the earlier work of Schramm.2 This appeared to be necessary since the Fe-Zn diagram has been drastically revised since the work of Schramm. Stadelmaier and Bridgers3 have recently shown that, contrary to prior belief: the y iron field is closed and the a phase boundary extends to an a + T + L peritectic at 782°C where peritectic a contains 42 at, pet Zn. The phase T in equilibrium with the a solid solution has a composition near Fe3Zn10 and a cubic 081 type structure.' The alloys were prepared by two different methods. In the first method carbonyl iron powder (400 mesh, 99.8 pet pure) and high-purity zinc powder (200 mesh, 99.99 pet pure) were mixed in a ball mill and then pressed in a die at 40,000 psi pressure to make compacts with a diameter of 5/8 in. and a thickness of l/4 in. These were sealed in evacuated quartz capsules, gradually heated to 1100°C over a period of 1 week (3 days at 600°C) 3 days at 800°C, 1 day at (1100°C), and then quenched in iced brine. For the alloys containing 23.4 and 30.1 at. pet Zn, the final homogenization anneals were performed at 1000" and 850°C) respectively, to prevent melting. In the second method, alloys were prepared by saturating high-purity iron millings (0.001 in. thick, 99.9 pet pure) in zinc vapor. For each alloy the impregnation was conducted at a fixed vapor pressure of zinc and a fixed temperature between 750' and 800°C. When saturated, the millings were quenched in water. The compositions of the alloys prepared by both methods are shown in Table I. The lattice parameters of the ferritic solid solutions were determined by comparing the 26 values of their 310, peaks (using Co Ka) or of their 211 , peaks (using Cr Ka) with those of corresponding peaks for high-purity a iron. The 20 values were measured at room temperature with an X-ray dif-fractometer (G.E.-XRD5). By using a fiducial value of 2.8664Å for the lattice parameter of pure a iron at 25oC,5 the lattice parameters of the zinc-bearing

Jan 1, 1964

By K. S. Krishnam, A. G. Guy

VOLUME 6 of the Transactions of the Baikov Institute of Metallurgy, Moscow, is devoted to the subject of "the experimental and theoretical study of the physical characteristics of dilute solid solutions,11 and summarizes work that has been done largely in the years 1958-9. In view of the attention that Soviet investigators have given to this subject, it seemed useful to carry out an independent experimental investigation in an effort to judge the scientific basis and practical significance of this field of study. The present note is a preliminary report of this investigation. The first property studied by the Soviet group was X-ray spectra of solid-solution alloys.' An anomaly observed at low concentrations (--0.05 at. pct) of the alloying element led to the theory that each impurity atom in a transition-metal base alloy is the center of a "block" of affected atoms with a radius of about 10"7 cm. This theory was further developed in a later paper.2 By this time similar anomalies had been found in diffusion coefficients3 and in thermal expansion.4 The entire development up to 1959 was reviewed in a comprehensive paper, and further theoretical ideas were also published at this time. Finally, the volume mentioned above was published in 19607 giving new experimental data on anomalies in optical properties and Hall constant, and a new theoretical treatment also appeared.' Although western scientists have done both theoretical work, summarized recently by Friedel,9 and considerable experimental work on dilute solid solutions, there is little support for the marked anomalies reported in the Soviet papers. Of the physical properties studied by the Soviet investigators, thermal expansion was chosen for the present investigation because of the relative ease of obtaining the necessary precision of measurement. A Leitz dilatometer was used for this purpose, and a special technique involving interchanging of the two specimens being compared permitted a precision of 0.05 x X in average thermal expansion over the range 27° to 600°C. The specimens were heated and cooled in vacuum or in a protective atmosphere at a rate of 50 °C per hr. Ferrovac E iron was used as the comparison specimen and in every case had a coefficient of expansion higher than (or equal to) that of the alloy. Since unintentional impurities are an important factor in studies of dilute alloys, special attention was given to the purity of the iron and the alloys used. The alloys were the same of those used by Abrahamson10 and by Michalak," and their preparation is described in these references. Chemical analyses of the Ferrovac E iron and of typical Fe-W and Fe-Mo alloys are given in Table I. The purity of the iron and alloys is undoubtedly higher than in the

Jan 1, 1962

By B. Wilshire, W. J. Evans

W. J. Evans and 8. Wilshire SEVERAL recent investigations1-6 have shown that the strain, c, during transient and steady-state creep is well-represented by the expression: € = e0 + et(l - e-mt) + Esl [l] where Eo is the instantaneous strain on loading, ET the total transient strain, C, the steady creep rate! and m a constant relating to the rate of exhaustion of transient creep. However, it has been noted6 that deviations from this equation occur over the first 10 to 15 pct of the transient stage, when the creep rate, (. decreases more rapidly than is predicted by this equation. This rapid decrease has been attributed to a large change in work-hardening coefficient. It 1s widely accepted that steady-state creep results from a balance between the rate of strain hardcning h and the rate of recovery r (=-s(st) as: dE/dt = Es = r/h [2] Comparison of values obtained for h at the end of the initial extension and during steady creep suggests that h increases several fold during the transient stage. which has the effect of reducing the creep rate proportionally.7 To examine the dependence, on r and h, of the deformation behavior during transient and steady-state creep. a series of constant-stress creep tests was carried out at 413°C at 6000 psi using 70-30 a brass. Prelinlinary investigation showed that. with this material. the transient stage constituted a significant portion of the total creep life (-0.4tf. where tf is the time to fracture). The alloy. obtained from Metals Research Limited. was made from high-purity copper, 99.999 pct. and zinc. 99.99 pct. Heat treatment at 675°C for 4 1/2 gave a uniform grain size of 5 mm-1. Details of specimen preparation and creep testing procedures have been given previously.6 Values of h (?s/?E) were determined by measuring the instantaneous strain. ?E. which occurred on increasing the stress during creep by a small amount. ?s. Similarly. v (= -?s/ ?t) was derived from the incubation period. At, after a small decrease in stress.' Several values of v and h were obtained throughout duplicate creep tests. using different stress increments in the range 300 to 800 psi. The accuracy with which Eq. [I] represents the present creep curves was established by determining the best value of the constants Es, Et, m , and 6, using a digital computer program based essentially on the graphical solution for this equation devised by Conway and Mullikan.9 About 40 strain/time readings were taken during transient and steady-state creep. Over most of the creep curve, the average difference between the measured reading and the calculated strain at the appropriate time was less than 0.0001. However.

Jan 1, 1969

By R. D. Vaughn

The limiting cases of non- Newtonian fluids flowing inside a concentric annular duct are developed without using a model of the fluid behavior. The solutions provide limits with which to test the various models of fluid behavior such as the power law and Bingham plastic models. The results of previous theoretical work are discussed in terms of limiting cases. This limiting case study also shows that experimental work on flow of non-Newtonian fluids in annular ducts should be confined to ducts for which the ratio of the radius of the inner wall to that of the outer wall is less than 0.3 and preferably less than 0.2. INTRODUCTION During the last 10 years the problem of laminar flow of non-Newtonian fluids in concentric annuli has received much attention large1y because of its application to the hydrodynamics of the wellbore. Recently solutions utilizing the power law1,2 and Bingham plasticl,3,4 models have been published. In this paper the method of limiting cases, which has been successfully applied to laminar-flow heat transfer516 will be applied to the problem of flow of non-time dependent, non-Newtonian fluids through annuli. This method permits solutions for the limiting cases to be made without using a model of unknown validity. The solutions, therefore, provide limits with which to test the various models which have been or will be proposed. A pertinent conclusion concerning the region of experimental work is also provided. DEVELOPMENT OF LIMITING CASES The limiting cases for the axial flow of fluids in concentric annuli may be defined with reference to Fig. 1. It is possible to define two limiting cases which pertain to the physical dimensions of the annulus. First, the annulus must degenerate to a circular pipe as the radius of the inner wall decreases or, as k = (k R/R) ? 0. Second, the annulus must approach the limit of parallel plates of infinite extent as the spacing between the inner and outer tubes becomes small in comparison with the radius R of the annulus, or as k?1. It is also possible to ascertain three limiting cases which pertain to fluid behavior. With reference to Fig. 2, as a fluid becomes progressively more pseudoplastic, the shear stress-shear rate relationship progressively approaches the indicated horizontal line more closely. At this limit the shear stress becomes independent of the shear rate. At the other extreme of increasingly dilatant behavior, the vertical asymptote is approached. Intermediate between these two limiting cases lies the case of the Newtonian fluid. Fluids which exhibit a yield shear stress also approach the limiting case of "infinite" pseudoplastic behavior. The remainder of the theoretical development is concerned with the description of and the solutions

By E. A. Peretti

BEFORE embarking on a detailed investigation of the system indium-antimony-bismuth, experiments were carried out to determine the existence of quasi-binary sections. The bordering binary systems are known1 and show the occurrence of three intermetallic binary species corresponding closely to InSb, InBi and In2Bi. Attention was focused on the low-indium end of the ternary diagram where the possible quasi-binary sections, excluding ternary compound formation, would involve the pairs: InSb-Bi, InBi-Sb and InSb-InBi. The latter pair revealed itself as a true quasi-binary, so it was investigated fully by thermal analysis, x-ray and microscopic examinations. All compositions were made by proper combination of three elements involved. The indium had a guaranteed purity of 99.97 pet; the antimony contained 99.99 pet Sb, and the bismuth had a purity of 99.99 pet. Alloys were made by melting together antimony, bismuth and indium in evacuated, sealed pyrex-glass tubes at a temperature of 600°C with vigorous agitation. The melts, weighing about 80 grams, were allowed to freeze in the sealed tubes and finally were transferred to glass tubes for the taking of cooling and heating curves. A protective atmosphere of helium was used, and the melts were stirred mechanically while cooling at rates of from 0.5 to 3°C per min. Temperatures were measured with a calibrated chromel-alumel thermocouple and were recorded graphically on a Minneapolis-Honeywell extended-range recorder working in conjunction with a Leeds and Northrup type K-2 potentiometer. Conventional polishing techniques gave satisfactory results in preparing specimens for microscopic examination. Etching was carried out with Vilella's reagent or aqueous mixtures of chromic oxide with either nitric acid or sulfuric acid plus dichromate. Conclusions deduced from the thermal analysis and microscopic examinations were confirmed by X-ray photograms using Co-K alpha radiation. The phase diagram is shown in Fig. 1. The liqui-dus consists of an uninterrupted line running from the freezing point of InSb (525°C) to a eutectic point experimentally indistinguishable from the freezing point of InBi (110°C). X-ray patterns of the InSb show a slight expansion of the lattice with the addition of InBi, and microscopic work indicated the solid solubility of InBi in InSb to be less than 0.5 pet at room temperature. Acknowledgment We wish to thank the Indium Corporation of America for the loan of the indium used in this investigation. References 1 E. A. Peretti and S. C. Carapella, Jr.: Trans. ASM., 1949, vol. 41, P. 947. T. S. Liu and E. A. Peretti: Trans. ASM, 1952, vol. 44, p. 539. Metals Reference Book, vol. 1, 2nd ed., AIME, p. 345.

Jan 1, 1959