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By W. F. Carew, F. A. Crossley

IT has been reported that the Ti-8 pct A1 alloy is ductile as water quenched from 800°C but brittle as annealed at 650 °C." The present, somewhat limited, investigation was undertaken to discover the cause of the embrittlement. In order to evaluate to some extent the continuity of the embrittling phenomenon, alloys of 6, 8, and 10 pct A1 were studied. Subsequent to the completion of most of this work, Ence and Margolin reported that a Ti,A1 phase exists and that two or more unidentified compounds may exist in the Ti-A1 system.' Materials, Equipment, and Techniques The alloys were prepared using Kroll process sponge of 124 Bhn hardness. In addition, some 8 pct A1 material was made with iodide titanium. The sponge-base alloys were prepared as melts of 4 lb or more by double arc melting. The iodide Ti-8 pct A1 alloy was prepared as 200-g buttons. The alloys were forged at temperatures of 980" to 1150°C. Results of chemical analyses are given in Table I. A Baldwin-Southwark 60,000-lb capacity tensile machine, equipped with an autographic stress-strain recorder, was used for the tensile tests. Standard tensile test specimens, 0.252 in. diam, were used. Standard Charwy V-notch impact specimens were tested using a -kiehle machine. specimens were sealed in evacuated Vycor bulbs for heat treatment. Powder samples for Debye-Sherrer anal- ysis were prepared by filing and screening through 325 mesh. The —325 mesh fraction was taken in an effort to concentrate a microstructural constituent assumed to be less ductile than the a phase. The powder samples were stress relieve2 by annealing

Jan 1, 1958

By Claus Guenter Goetzeil

(New York Meeting, February, 1937) The object of this investigation was to determine whether silver alloys could be used instead of the currently employed insert of high-expansion Average Coefficient per Deg. C. over Range 20° to 200° C. Pure aluminum..................................... 24.6 X 10-6 Cast low-expansion Si-Cu-Ni-A1 piston alloy............ 20.0 X 10-6 High-expansion austenitic Cu-Ni cast iron.............. 19.3 X 10-6 Cast steel (0.25-0.35 C, 0.40-1.0 Mn).................. 12.6 X 10-6 Cast iron (3.15 total C, 2.16 Si)....................... 12.8 X 10-6 Pure silver.......................................... 18.9 X 10-6 austenitic ferronickel alloy, to reduce the wear of ring grooves in light metal pistons. A typical example of a piston containing a ferronickel insert is shown in Fig. 1. The high coefficient of expansion of silver made it worthy of consideration, while the small size of the insert would render its use feasible in Germany as an emergency measure. The coefficients of linear expansion of several metals and ailoys are as shown in the table above. Obviously the melting point of the insert must be high enough to prevent it from melting when the light alloy is cast around it. This imposes a lower limit of about 850" C. for the solidus of the silver alloy. Pure silver melts at about 961" C., so that the tolerable depression in the solidus is rather small. To avoid deformation of the insert during use a Brinell hardness number of at least 60 appears necessary.

Jan 1, 1937

By Henry F. Adams, Guy H. Ruggles

In this paper the authors aim to chronicle the experience and salient points brought out in changing flotation reagents at a concentrator which had probably been using a minimum amount of oil at a minimum cost per ton, to a more complicated system requiring a partial chemical control. The original oils were coal tar and pine oil. The new reagents are lime, xanthate and pine oil. It was found that there were no insurmountable difficulties and eventually the cost of the new reagents per ton of ore proved to be very little more than that of the old. Lime Plant When the question of handling lime came up there were two propositions open: (1) to handle the lime dry; (2) to handle it wet in the form of an emulsion. Granting that a dry lime feeder would function properly, delivering lime uniformly, the chief objection was the dust that would be raised when these feeders were being charged or operated, as the only possible location was on a gallery beneath which men were working. With this objection the handling of lime as an emulsion seemed to be the better scheme. The lime plant which was first installed was for experimental work on one section. This was gradually changed and developed until it was of sufficient size to accommodate 20 sections. The various changes will not be discussed and the following description deals only with the fully developed plant. Crude as it is, and perhaps somewhat expensive to operate, the lime-handling plant has been quite successful. Much has been learned which will pave the way for a better installation in the future. Burnt lime is received loose in standard gage box cars. This is the product of the kilns and has had no screening or sorting. A grab sample is taken from each car as it is unloaded. An average of the analyses of samples from 44 cars gave the following: Available CaO Total CaO, Oxide and Hy- MgO, Fe²O³ + Al²O³, Insoluble, Per Cent. drate, Per Cent. Per Cent. Per Cent. Pek Cent. 88.3 79.2 1.6 ' 1.3 2.2

Jan 1, 1928

By D. H. Desy, L. C. Fincher

The magnesium-rich end of the Mg-Ti phase diagram was investigated. The liquidus, solidus, and solvus boundaries to 1 pct Ti were established. All alloys were prepared by saturating molten magnesium with titanium in a consumable titanium crucible under inert gas maintained at 230 psig. The liquidus of the Mg- Ti system was determined by analysis of dip samples taken from 700° to 1300°C under equilibrium conditions in a pressurized inert atmosphere furnace and by analysis of small ingots rapidly poured and quenched from 1400° to 1500°C. The solubility of titanium in magnesium ranged from 0.018 wt pet Ti at 700°C (0.012 wt pet at 650°C by extrapolation) to 1.035 wt pet Ti at 1500°C. The solidus for compositions ranging from 0.03 to 1.00 wt pet Ti was determined to be 650° ± 1°C by thermal analysis. The titanium solid solubility values ranged from 0.08 wt pet at 350°C to 0.19 wt pet by extrapolation to 650°C. The freezing reaction is peritectic. No intermetallic compounds were found in the system; the phase in equilibrium with molten magnesium saturated with titanium was found to be titanium with magnesium in solid solution. Solid titanium will dissolve at least 1.32 wt pct Mg. PREVIOUS investigations of the Mg-Ti system have shown considerable disagreement on the solubility of titanium in liquid magnesium. Furthermore, the solid solubility of titanium in magnesium has not been well established. Liquidus curves for previous work and for the present investigation are shown in Fig. 1. Aust and Pidgeon1 used a dip-sampling method on molten magnesium held in equilibrium with solid titanium under a protective atmosphere to determine the solubility and found that it ranged from 0.0025 wt pet Ti at 651°C to 0.015 wt pet Ti at 850°C. Eisenreich2 introduced titanium into molten magnesium by means of TiCL4 adsorbed on BaCl2. Ingots were then cast at various temperatures. Making the assumption that only the titanium dissolved in magnesium at the time of casting was soluble in H2SO4, Eisenreich determined the solubility of titanium in molten magnesium to range from 0.003 wt pet at 655°C to 0.115 wt pet at 800°C. Eisenreich also determined the solid solubility of titanium in magnesium to be 0.015 wt pet at room temperature and 0.045 wt pet at 500°C. Since the solid solubility just below the freezing temperature for the bulk of the alloy was much larger than the liquid solubility just above the freezing temperature, Eisenreich concluded that the freezing reaction was peritectic. Obinata et al.3 equilibrated molten magnesium with titanium in hermetically sealed titanium containers which were then furnace-cooled. The titanium content of the magnesium was then determined and found to range from 0.170 wt pet at 700°C to 0.85 wt pet at 1200°C. No intermetallic compound was found in the system. The Armour Research Foundation4 determined two points on the solvus by electrical resistivity methods: 0.00057 wt pet at 200°C and 0.0008 wt pet at 300°C. At higher temperatures, data were meaningless with no trends observable. The authors of this report believed that the lack of significant data at the higher temperatures was due to variations in specimen geometry, although there was no positive evidence to verify this supposition. The present investigation was undertaken to clarify the uncertainty in both the liquidus and solvus of the magnesium-rich end of the Mg-Ti system. EQUIPMENT AND MATERIALS The equipment used in this investigation, with some modifications, was essentially that used by Crosby and Fowler5 in their determination of part of the Mg-Zr phase diagram. The equipment, as modified for this work, is shown in Fig. 2. It consists of a sealed furnace chamber which can be pressurized with inert gas so that melts can be made above the boiling point of magnesium at atmospheric pressure. Melts are made by induction heating in a titanium crucible which, after diffusion of sufficient magnesium into the walls of the crucible to saturate the titanium at the sampling temperature, comprises the solid phase in equilibrium with the molten magnesium. Dip samples may be taken with the sampling tube, or the entire furnace may be tilted so that ingots may be poured into a mold in the side chamber. The principal difference from the earlier apparatus is in the thermocouple, which in the present equipment is enclosed in a protection tube and immersed directly in the melt. The tips of both the thermocouple protection tube and the sampling tube, which dip into the melt, are made of high-purity titanium. The 4 1/2-in.-long titanium tip of the sampling tube is threaded into a steel tube, O in Fig. 2, which extends through the top of the furnace. To determine whether the temperature at the tip of

Jan 1, 1969

By Ralph Hultgren, Prodyot Roy

Manganese vapor pressures from 1250° to 1500°K were measured by conventional Knudsen and torsion-effusion methods in twelve Fe-Mn alloys with compositions from 9 to 80 at. pct Mn. The Knudsen re-sults agveed approximately with previous measurements found in the literature which indicated the solutions were nearly ideal. However, except for the higher manganese compositions, the initial torsion readings indicated much (up to 50 pct) higher vapor presszcres than the Knudsen method. These high readings decreased steadily with time. The results are interpreted as due to depletion of surface concentration of manganese during evaporation. Thus the initial torsion readings are the most nearly correct and Knudsen methods on alloys are to be regarded with suspicion unless it can be demonstrated that diffusion rates are rapid enough to replenish surface concentrations depleted by evaporation. For the lowest manganese contents and highest temperatures, depletion causes initial torsion readings to be too low. FEW thermodynamic data are available for alloys of the high-melting transition metals due primarily to experimental difficulties at the high temperatures involved. Measurement of vapor pressure is one of the most promising techniques to be applied to this problem. From the vapor pressure of a component of an alloy phase, its activity or its partial molar Gibbs energy can be directly calculated. From measurements over a sufficient range of temperatures and compositions the partial and integral Gibbs energies, enthalpies, and entropies may be determined through Gibbs-Duhem integration. For solid phases of variable composition, which commonly are found in alloys, measured vapor pressures are low because of depletion of the surface concentration of the more volatile component as it is selectively vaporized. Diffusion from the interior tends to restore the depleted concentration. The seriousness of the effect depends on the relative rates of diffusion and vaporization. Although depletion has been recognized as a factor,' direct measurements of its rate are lacking and quantitative estimates of its effect on measurements are uncertain. In the present work the vapor pressures above a series of Fe-Mn alloys have been measured by the torsion-effusion method. This method permits a measurement of the vapor pressure of manganese as soon as the sample comes to temperature and continuously throughout the run. The rate of decline of the apparent vapor pressure measures the rate of depletion and the torsion reading at zero time should be correct. At high manganese concentrations (70 and 80 at. pct Mn), the torsion reading remained nearly constant; surface depletion was negligible. There was a slow drop in measured pressure due to bulk loss of manganese from the sample. However, for lower manganese contents, especially at high temperatures, the depletion effect was considerable and the apparent vapor pressure decreased steadily with time. For these alloys the Knudsen method should give pressures which are too low. The measurement of pressure in the Knudsen method cannot be made until enough manganese has been vaporized to be weighable. The Knudsen result is therefore an integrated average between the initial and final vapor pressures. To verify this, conventional Knudsen measurements were also made with results in approximate agreement with previously published Knudsen measurements for these alloys. As expected, for the lower manganese contents the initial torsion readings of pressure were as much as 50 pct higher than the Knudsen. THE APPARATUS The apparatus, shown in Fig. 1, is capable of operating to temperatures up to 2000°K. A vacuum of 5 x 10"6 mm Hg can be maintained. Temperatures were measured to +3° by a W-Re thermocouple placed in the dummy cell, N. The torsion cell consisted of two alumina crucibles with holes in their covers. They were placed in the molybdenum holder shown suspended from the torsion wire. Rectangular torsion wires (1 by 4 mm) were found to have superior sensitivity and less residual distortion than circular (2-mm-diameter) wires. The precision of angular measurement was found to be *0.025 deg; the variation is no doubt due to temperature fluctuation and vibration. For the Knudsen experiments the alumina cell was set on the support, N. SAMPLE PREPARATION 800-g samples were prepared by melting together electrolytic iron and electrolytic manganese and pouring the melt into a water-cooled copper mold. Melting and pouring were done under a helium at-

Jan 1, 1965

By B. S. Gottfried

A generalized mathematical model is presented, which describes the thermal recovery of oil in linear systems with convective external heat loss. Three-phase fluid flow, conduction-convection heat transfer, chemical reaction between oxygen and oil and aqueous phase change are included, making the model applicable to a variety of thermal recovery processes. The complexity of the model requires that numerical solutions be obtained with a digital computer. The numerical approximations of the partial differential equations are presented and the algorithm is discussed in detail. The analysis is applied to the detailed simulation of a forward-combustion laboratory tube experiment. The results of the simulation exhibit with reasonable accuracy all of the principal thermal and bydrodynamic characteristics observed in the laboratory (i.e., the propagation of a combustion zone, a steam plateau, and oil and water banks). Numerical variations in the parameters appearing in the external heat-loss term, the aqueous phase-change term, and the Arrhenius combustion term are examined, and their effects on the predicted temperature profiles, oil and water production histories, and the air-oil ratio are presented. In spite of an oversimplification in the chemical reaction mechanism and the considerable computer time required to obtain solutions, the model represents a major advance in the ability to simulate the phenomena observed in thermal recovery experiments. INTRODUCTION Thermal oil recovery refers to a class of recovery processes where heat is supplied to a reservoir to provide the necessary expulsive energy. This thermal energy can be supplied externally as steam or hot water, or it can be generated in situ by forward or reverse combustion. In either case, however, thermal recovery processes are charac- terized by the simultaneous flow of two or three fluid phases in a variable - temperature field, accompanied by possible chemical reaction or phase-change effects.2-5, 7- 10, 14,16-18,20-22 Although a physical understanding of the thermal recovery processes is far from complete, it is possible to construct mathematical models which describe approximately all of the principal physical and chemical phenomena. However, attempts to solve such models, even with high-speed computers, involve formidable mathematical difficulties. Consequently, theoretical solutions have been obtained only for idealized cases in which important physical phenomena are neglected. For example, consider the process of forward in situ combustion. All such theories which have been developed consider only certain aspects of the process, such as heat transfer, 2-4,8,9,l6,l8 heat transfer with phase change,10 heat transfer with chemical reaction,7 or the hydrodynamics of three-phase flow.21 A general theory including all of the above phenomena has not been developed to date. This paper presents a unified theory of thermal recovery processes in linear systems. A mathematical model is developed which explicitly includes conduction-convection heat transfer with convective external heat loss, chemical reaction between air and oil, aqueous phase change, and the hydrodynamics of three-phase flow. A system of equations is developed which can be solved numerically on a high-speed digital computer, resulting in predicted temperature, pressure, and saturation histories in space and time. The model allows a more detailed simulation of thermal recovery tube experiments than had previously been possible. THEORETICAL DEVELOPMENT Consider the linear flow of gas, water and oil in a homogeneous porous medium. Assume that the oil will react with gaseous oxygen, and that mass is transferred between the water and gas phase by evaporation or condensation. In the absence of hydrocarbon phase change, intraphase diffusion,

Jan 1, 1966

By R. A. Wattenbarger, H. J. Ramey

A systematic study has been made of the application of the real gas pseudo-pressure m(p) to short-time gas well testing. The m(p) function can be used in real gas flow problems to account for the variation of viscosity and z-factor with pressure. A mathematical model was solved numerically to generate solutions of various real gas flow problems. The effects of turbulence, formation damage and wellbore storage were included in the model. The analysis of simulated well tests showed that the interpretation methods normally used for liquid flow are generally accurate when the m(p) is used. For practical rates without turbulence, the solutions are not rate-sensifive, and the flow capacity.. kh and skin effect can be determined accurately from either a buildup or a drawdown test. However, the kh calculated from a drawdown test can be significantly low when turbulence is present. A case was simulated in which this error wa.s 36 percent. Turbulence does not affect the determination of kh from buildup tests. The proper determination of kh from p and pa buildup and drawdown plots is developed by analyzing their relationship to the m(p) method. A simple equation is given that can be used for long-range gas well performance forecasting. This expression is compared with a method pre-sended by Russell et al." Introduction The formation flow capacity and wellbore damage condition can be determined for liquid-producing tests by means of buildup and drawdown tests. These tests make use of short-time pressure transient data rather than stabilized flow tests that are often used for gas well testing. Tracy' presented a method of gas well testing that was based on ideal gas equations and utilized p2 buildup plots. This method was shown to be good for low pressure wells. MatthewsZ suggested plotting p and using an average slope and average gas properties. This method was more successful on high pressure wells. Al-Hussainy, Ramey and Crawfordh howed that variation in gas properties could be simplified by using the real gas pseu do-pressure m(p). Some cases showed that the use of the m(p) function Original manuscript received in Society of Petroleum Engineers office Aug. 8. 1967. Revised manuscript received June 11, 1968. Paper (SPE 1835) was presented at SPE 42nd Annual Fall Meeting held in Houston Tex., Oct. 1-4. 1967, and at SPE 4th Annual Eastern Regional ~eetin$ held in Pittsburgh. Pa., Nov. 2-3. 1967. 0 Copyright 1968 American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. 'References given at end of paper. provided an accurate method of interpreting buildup and drawdown tests. Because the work of Al-Hussainy et al. included only a few actual cases, there was a need to explore the use of the m(p) method for a greater variety of flow conditions. The occurrence of turbulent flow around the wellbore often is an important factor in gas well testing. Swift and Kiel,' and Carter et a1.' treated turbulence in gas well testing, but did not consider the variation of viscosity and z-factor with pressure. This paper presents the results of an investigation of the application of the m(p) method to buildup and drawdown testing. Vhe investigation included the effects of turbulence, formation damage and wellbore storage. Gas Flow Equations To formulate the mathematical model, many of the assumptions usually used in well testing theory are applied. The system has radial geometry with a closed outer boundary and is composed of a horizontal porous formation that has uniform and isotropic rock properties and uniform thickness. Allowance is made, however, for a radial region of reduced permeability near the wellbore. This region represents formation damage. The geometry of the system is shown in Fig. 1. Darcy's law does not always apply to gas flow. A more general expression is needed for non-Darcy, or "turbulent" REGION OF DAMAGED PERMEABILITY SEALED BOUNDARIES ClRCULAR WELL BORE Fig. 1—Radial flow model. AUGUST, BT7

Jan 1, 1969

By Alexander L. Field

The rate of elimination of carbon largely controls the time required to make a heat of steel by the basic open-hearth process and to an important degree determines the cost of refining. Practical experience has led to the generally accepted belief that the use of slags relatively high in iron oxide, such as are required to bring about rapid refining, leads to a certain sacrifice of quality in the product. As a consequence, a compromise must be made between the exceedingly slow rate of carbon drop which would correspond to the ideal case and the rapid rate which would best satisfy the condition of minimum cost. An increase in rate of refining necessarily implies an increase in the concentration of iron oxide dissolved in the metal. However, even for the infinitely slow rate that corresponds to slag-metal equilibrium, the metal would contain a certain definite concentration of dissolved iron oxide. It is a matter of great practical importance, therefore, to determine the quantitative relation between the minimum or equilibrium concentration of iron oxide in the metal and the higher concentrations which must actually obtain in practice. The present paper is devoted to the development of certain equations, derived from the established laws of physical chemistry, which will enable this relation between rate of refining and the degree of oxidation of the metal bath to be computed from operating data. So attempt is made to exhaust the possibilities of this general method of treatment. In considering rate of refining, attention is mainly confined to rate of carbon elimination. However, the equations are of a more general nature and their application may readily be extended. The results of the preliminary calculations given herein indicate that increased rate of refining may have a decided effect in increasing the concentration of iron oxide dissolved in the metal. The uncertainty which attaches to the calculated value for this relationship arises in part from probable errors in experimental data on which the calculations are based, and in part from the lack of complete or favorably disposed information on basic open-hearth practice. When the relation between rate of refining and degree of oxidation of the metal has been more accurately established than has been done in the present paper, it will then become possible to consider what comprises

THE first session of the Institute was held at the Smithsonian Institution, on Tuesday evening, February 22d. The members were welcomed to Washington and to the Smithsonian by Prof. Joseph Henry. President Holley responded to the cordial welcome of Professor Henry, and then read an introductory address on the subject of Technical Education. Following the discussion on President Holley's address the following persons, duly proposed and indorsed by the Council, were elected members and associates of the Institute : MEMBERS. Emile R. Abadie, - St. Louis, Ma. R. J. Anderson, - Pittsburgh, Pa. Commander L. A. Beardslee, - Washington, D. C. Charles Bender, - New York City. Channing M. Bolton, - Richmond, Va. Thomas E. Bowman, - Silverton, Colorado. Calvin E. Brodhead, - Bethlehem, Pa. M. L. Brosius, - Lewistown, Pa. Harvey H. Brown, - Cleveland, Ohio. James A. Burden, - Troy, N. Y. J. P. Clemes, - Sonora, Mexico. N. H. Cone, - Nederland, Colorado. W. F. Durfee, - New York City. Robert Frazer, Jr., - Ashland, Pa. Joseph E. Galigher, - Bingham, Utah. William Golding, - Steel Works P. O., Pa. Samuel E. Griscom, - Pottsville, Pa. Gen. E. Burd Grubb, - Beverly, N. J. Arthur R. Guerard, - Charleston, S. C. Edward Hart, - Easton, Pa. Prof. Lewis M. Haupt, - Philadelphia. . R. S. Hawley, - Buffalo, N.Y. John W. Hoffman, - Philadelphia. Nelson P. Hulst, - Milwaukee, Wis. H. C. Humphrey, - Philadelphia. Ed. P. Jennings, - Ithaca, N. Y. B. F. Jones, - Pittsburgh, Pa.

Jan 1, 1876

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By N. L. Svensson

The model developed by Tuylor for the calculation of Polycrystalline yield strength has been applied to the case of an aggregate hawing a preferred orientation. In general this procedure requires the specification of texture by means of weighting factors applied to specific orientations. The problem to which the model has been applied is that of the yield-strength aniso-tropy of cold-rolled aluminum whose rolling texture was described as a combination of (110)[112] and (311) [112] In this case yield-strength anisotropy is defined by the rutio of yield strength measured at an angle 8 to the rolling direction to that measured along the rolling direction. The method of calculation of yield-strength ratio as a function of ? is described and the results show good agreement with experimental values. The orthotropic yield criterion suggested by Hill has been applied to the results and the strain ratio R also calculated as a function of ?. This has been compared with calculations using the method suggested by Elias, Heyer, and Smith which does not exhibit suck good agreement with observation. one deficietlcy of the method presented is that the strain ratios used by are those applying to iso-Irobic materials. The method should therefore be reg-clrded only as a first abbroximation to the prediction of anisotropy. THE problem of calculating the stress-strain characteristics of polycrystalline aggregates from the properties of single crystals has attracted attention for a number of years. The most important contributions to this study have been those due to: Sachs,' Cox and sopwith,2 Taylor,3 Kochendorfer,4 Batdorf and Budiansky,5 Calnan and Clews,6 Bishop and Hill,7,8 Kocks,9 Budiansky, Hashin, and sanders, 10 Kroner,11 Cyzak, Bow, and payne, 12 Budiansky and Wu,13 and Lin.14 While the earlier work has been largely superseded, recent developments tend to support Taylor's solution" within the restriction imposed by his assumptions. The essential features of Taylor's approach were: 1) the material is rigid-plastic; 2) each grain experiences the same strain components as the aggregate as a whole (the problem was that of uniaxial deformation with principal strain components in the ratio 3) all regions of each grain deform uniformly; 4) work hardening occurs equally on all slip systems. While Bishop and Hill7 have generally validated this approach, there has been some criticism offered. Kocks? as pointed out that since multiple slip must occur the single-crystal data must be determined from orientations arranged such that polyslip takes place. Boas and Hargreaves,15 and others, have shown experimentally that the strain distribution within grains is not uniform, the strains in the vicinity of grain boundaries being less than those in the center of the grains. Both of these criticisms can be largely offset by the suitable choice of single-crystal critical shear stress. However, for the problem analyzed below, the critical shear stress is not directly used and, consequently, these criticisms lose their importance. The more recent contributions have attempted to obtain a more complete analysis by considering an elas-toplastic material and considering interactions between grains of differing orientations. Lin14 has considered the early stages of yielding for a polycrystalline aggregate having specific regions of defined slip plane orientations. On the other hand, Budiansky and Wu13 have allowed for these interactions for randomly disposed grain orientations and have calculated the polycrystalline stress-strain curves for crystals exhibiting either elastic-ideally plastic or kinematic hardening characteristics. This work has shown that yielding commences when the macroscopic stress is 2.2 times the critical shear stress for slip in a single crystal (7,). The yield stress-strain curve then rises becoming asymptotic to a value of 3.072 7,. This is close to the value obtained by Bishop and Hill (3.06) in their confirmation of Taylor's method. This, of course, is to be expected since, at large strain values, the elastic strains are negligible and the rigid-plastic model is satisfactory. The results of Budiansky and Wu indicate that the result obtained by Taylor is 7.7 pct high at a plastic strain which is two times the elastic strain at the initiation of yield. By defining the anisotropy in terms of relative values, the ratio of yield strength at orientation ?, to that measured in the rolling direction, the effect of the discrepancy in Taylor's solution is considered to be of lesser consequence. Therefore, it is anticipated that an analysis based on Taylor's solution, which can be quite straightforward, should provide a reasonable estimation of the anisotropy of materials having a preferred orientation texture. OUTLINE OF TAYLOR'S METHOD In fee metals there are four possible slip planes (the octahedral planes) and in each there are three possible slip directions (the edges of the octahedron), that is a total of twelve possible slip systems. von Mises16 has shown that at least five independent slip systems must become operative in each grain of the polycrystalline aggregate in order to preserve continuity of strain. With this geometrical requirement as basis and the assumptions previously listed, Taylor determined the operative slip systems for a number of orientations of the tensile stress axis specified in the unit stereographic triangle. For the ith slip system, the critical shear stress

Jan 1, 1967

By E. P. Shea

The Anaconda Co.'s Geological Department at Butte, Mont., was started early in the Company's history because of litigation involving vein ownership and extralateral rights. The problems, some of which were resolved in courts, were many because of the large number of veins and lode locations. Defensive action was required to prove ownership and protect against illegal exploitation of the downward and extra-lateral extensions of the ore bodies. In many cases it was necessary to define the outcrop of the vein and to show that its apex was within the boundaries of the lode claim. Exhibits illustrating geology were needed to present the cases clearly, and these could be made only after careful inspection and mapping of the underground workings by competent geologists. Also, The Anaconda Co. was one of the first companies to recognize the worth of skilled mining geologists and the value of accurate records in the search for new ore. The department was organized in 1900 by H. V. Winchell who, with D. W. Brunton, worked out the methods. Reno Sales was Chief Geologist from 1906 until 1948 when he was succeeded by V. D. Perry, the present Chief Geologist. Under their direction, F. A. Linforth, M. H. Gidel, C. H. Steele, E. P. Shea, C. C. Goddard, Jr., and W. A. O'Brien enlarged the scope of the work and improved the technique.

Jan 3, 1961

By E. N. Silverman

Mixtures of' MnS, ZFeO-SiO,, ZMnO.SiO, FeO, and MnO were prepared synthetically and used to study the planes ZFeO. Si0,-ZMnO.SiO,-MnS, FeO-MnO-MnS, and Fe0-MnO.Si0,-MnS in the quaternary system. Because the oxides and silicates studied flux MnS, inclusions in this system are partly liquid during rolling. Also, oxygen can modify subsurface inclusions through the reaction MnS + FeO—FeS + MnO during the soaking of ingots and the reheating of blooms and billets. NONMETALLIC inclusions in steel have long been a subject of study and conjecture because the properties of many steels are known to be affected by the the kind and amount of inclusions present. In free-machining steels, the type of inclusion present has a direct bearing on their machinability; in other steels, cleanliness is important and metallurgists direct their efforts at reducing the amount of non-metallic inclusions. Thus, the accumulation of knowledge about the formation and behavior of inclusions during all stages of steelmaking and processing should aid in improving the quality of steels and decreasing the production costs resulting from rejections. Previous studies of inclusions have contributed greatly to our understanding. The investigators have generally examined inclusions in finished steel. Boulger, Moorehead, and Garvey1 found that in Bessemer steels, low silicon contents results in globular sulfide inclusions with attendant high machin- ability ratings. Van vlack2 also found that low silicon contents favor inclusion morphology that contributes to high machinability ratings. Boquist and Stoll* found that silicon content affected sulfide inclusions and machinability of blooms, billets and bars more than did the finishing temperature in the range between 1775° and 2075°F. Carney and Rudolphy3 studied the distribution of sulfur, manganese, silicon, and carbon in a commercial ingot of resulfur-ized steel and found that silicon was concentrated near the bottom. This helped to explain why bottom cuts had poorer machinability. Klinger and Koch4 developed techniques for extracting inclusions from steel, and the technique devised by Gurry, Chris-takos, and stricker5 for extracting carbides can also be adapted to the study of inclusions. A different approach to the study of inclusions in steel consists of synthesizing the constituents that form inclusions and determining the phase eauilibria in the system that contains the constituents. The resulting phase diagrams can then be used to determine the effect of the various constituents upon each other. In this way, it becomes possible to under-

Jan 1, 1962

By J. W. Wolfe

The Benedict-Webb-Rmbin equation of state was used in digital computer programs to make rapid determinations of natural gas equilibrium phase compositions. Mixture components were the nine hydrocarbons, methane through heptane. Comparative tests were made with data from field separators, plant exchangers and literature sources. For most tests made, the B-W-R equations predrcted component K-vallles, mixture enthalpies and phase aensities within tile accuracy of available correlations for rune-component mixtures: significant deviations were noted when mixtures contained components heavier than heptune. INTRODUCTION Rapid, accurate methods for calculating the properties of hydrocarbon mixtures are needed for predicting the behavior of natural gas processes. For example, because of the common use of two-phase separation methods in gas proccssing, calculations must be made for the density and composition of equilibrium vapor and liquid phases. In addition, predictions must often be made for the temperature and pressure changes associated with the flow of single- and two-phase natural gas fluids through heat exchangers, chokes and turbines. The complex nature of non-ideal mixtures makes rigorous calculations for these natural gas properties difficult and time-consuming. Natural gas properties have conventionally been determined with generalized data correlations. These correlations, such as the K-values presented in the NGAA Equilibrium Ratio Data Book, are usually based on some average property of the mixture and have proven to give satisfactory estimates for the properties of most oil and gas systems. Digital computers, however, have not only increased the utility of these correlations, but also have made practical the use of equations of state for calculating the properties of natural gases. Potentially, if basic pure component data are available, all the desired thermodynamic properties of mixtures can be derived from a single equation of state describing the mixture. Currently. the best equation of state for describing the behavior of pure, light hydrocarbons over single-and two-phase regions, both below and above critical pressure, is that of Benedict. Webb and Rubin.' The equation contains eight constants which are determined by empirically fitting the equation to pure-component PVT data. Benedict and his co-workers presented the clevelopment of their equation as early as 1940.2 The B-W-R equation is a modification of the Beattie-Bridgeman equation of state and gives better PVT predictions than the Beattie equation at densities above the critical density. Benedict et al. made the equation applicable to mixtures by relating the mixture constants to composition and the constants for pure compounds. These authors, in a serics of articles in 1951,' showed the accuracy of the B-W-R equation when applied to light hydrocarbons and their simple mixtures, and demonstrated the equation's utility for making vapor-liquid equilibria calculations. Since its inception, the B-W-R equation has been the subject of many papers. Numerous additions and modifications have been proposed,'-',"'-':' the purpose of most being to improve the equation's ability to predict PVT properties of specific mixture systems. In 1959, Opfell, Pings and Sage summarized much of the work on the B-W-R equation in their book on equations of state." Since natural gases are primarily mixtures of light hydrocarbons, the B-W-R equation is a natural choice for an equation of state to compute both phase equilibria and thermodynamic properties of natural gases. Consequent-

Jan 1, 1967

By Walter L. Maxson, Fred C. Bond

There is more information contained in a screen analysis than is ordinarily recognized, and there is an increasing need for methods of making this additional information easily available. As more comprehensive studies of crushing and grinding are made, and as the possibilities of decreased expense and increased extraction through a closer control of grinding are explored, methods of interpreting screen analyses assume an importance which they have not had heretofore. The information commonly desired, which can be determined from a complete and carefully made screen analysis, includes: (1) the size distribution of the material passing the finest screen, (2) the presence of a hard grinding fraction, (3) the location of natural grain sizes, (4) the presence of different materials with markedly different grinding characteristics, (5) the presence and amount of finely divided material such as clay, which is merely unlocked in grinding, and (6) the total surface area of the ground product. It is necessary to know the fundamental law of size distribution of a homogeneous material in order to correctly resolve a screen-analysis curve, and to understand the variations and anomalies that a sample may exhibit when compared with the ideal curve. This fundamental law was developed by Gaudin,1 who showed that when the logarithm of the per cent weight retained on any screen and passing the next larger screen in the Tyler standard screen scale was plotted against the logarithm of the screen aperture the resulting curve for the finer sizes of a homogeneous crusher or grinding-mill product would be a straight line. Gross and Zimmerley2 experimentally confirmed Rittinger's law, which states that the useful work done in crushing a homogeneous material is directly proportional to the new surface area produced; and showed that in the larger screen sizes resulting from impact crushing a

Jan 1, 1935

By Charles A. Stetefeldt

This treatise is the sequel of a paper on "Russell's Improved Process for the Lixiviation of Silver-ores," etc., read at the Chicago meeting, in May, 1884, and published in the Transactions, vol. xiii., page 47. The facts it presents are principally compiled from Mr. Russell's notes on his practical experience gained in various places where the Russell process has been introduced. For a complete understanding of this paper a perusal of my former one is desirable, as can be seen from the frequent references here made to it. All silver-ores that do not carry a large percentage of lead or copper can be treated by Russell's process with success and economy. I do not mean to create the impression that from ores containing considerable quantities of lead and copper a high percentage of the silver cannot be extracted by this process. Such ores, however, will, in many localities, be reduced to better advantage by smelting. In case lead-bearing silver-ores are suitable for concentration, it may be profitable to concentrate the ore by Krom's dry system, obtaining a smelting-product high in lead, and to lixiviate the tailings and the dust. This plan has been adopted in a mill recently erected in Cortez District, Nevada. The dry system of concentration deserves the preference because it delivers the tailings and the dust in a condition ready for chloridizing-roasting. In wet concentration the drying of the tail ings would be expensive, and there would be a considerable loss of silver in slimes. Oxidized ores, containing silver chloride and lead minerals, may be lixiviated after crushing, and the tailings may be concentrated for lead. In this case wet concentration would be most suitable. This has been done at the Old Telegraph Mine, Utah. I would give, however, the preference to dry concentration in all cases which, of course, requires that concentration should precede lixiviation. The Russell process is also adapted to the treatment of tailings resulting from ores which have been worked either by the old

Jan 1, 1887

By W. F. Chiao

With the application of dislocation damping theory an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. A ductile steel was compared with a brittle stee1 by simultaneously measuring the ultrasonic attenuation and velocity during tensile test, and the density of free dislocations and their mean loop length were then calculated as a function of strain. The results showed that in the ductile steel there was always a large generation of dislocations and great extension of loop length occurring at some stage within the early plastic region. In contrast, the brittle steel showed very little or no such sudden changes in dislocation dynamic states after the onset of plastic deformation. Furthermore, a strong temperature dependence of dislocation dynamic states was also observed in the ductile steel and a hypothesis was suggested that a thermally activated process of dislocation rearrangement could occur at higher deformation temperatures. The activation energy of dislocation rearrangement at room temperature was estimated as about 2030 cal per mole.C. DUCTILITY is an indispensible property in the application of engineering materials, especially steel. During the past two decades the theoretical and experimental approach to the understanding of flow and fracture of metals has been constantly undergoing changes and progress." while the fracture behavior of metals can be influenced by many factors such as chemical Composition,3 second-phase particle mor-phology,4 and dislocation arrangement,5 it is now a general belief that the fundamental understanding of the ductile-brittle fracture phenomena of solid materials must stem from the study of dislocation dv-namics developed under stress conditions.6,7 Most of the traditional ductility tests, such as Charpy impact test, slow bend test, and tensile fracture test, cannot by themselves reveal directly the mechanisms of ductile to brittle transition of materials. In the experimental investigation of tensile ductility it would be ideal to be able to study directly the dynamics of dis-locations in a bulk specimen during the process of deformation. Since the ultrasonic pulse technique is the only satisfactory method for studying dislocations and the fine details of deformation characteristics in metals in the course of a tensile test, it would appear that a comparative study of ultrasonic attenuation changes during tensile tests of metallic materials exhibiting different ductility might be very informative. So far no work comparable to this study has appeared in the literature. Recent progress in both theory and experiment has indicated the feasibility of studying the dislocation mechanisms of ductility behaviors by ultrasonic measurements during tensile test. Granato and Lucke8 have developed a quantitative theory that enables the calculation of dislocation density and their average loop length from the measurements of ultrasonic attenuation and velocity, and several investigators, including Chiao and Gordon,9'10 have shown that simultaneous ultrasonic measurements can be successfully made during a tensile test. Furthermore, many investigators11-13 have repeatedly proposed in the past several decades that deformation and fracture are mutually self-exclusive, and that the ability or inability of a material to deform plastically, i.e., to generate dislocations, is a major factor in determining whether the material will be ductile or brittle. Thus, in the present work an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. This article is principally concerned with the study of the relation between the propagation of ultrasonic waves and tensile deformation in a steel series which displays quite different toughness at room tempera-turk. changes in attenuation and velocity of ultrasonic waves have been measured as a function of strain during the deformation process. The results have been interpreted in terms of the vibrating string model for dislocation damping as developed by Granato and Lucke, and it has been found that some of the more subtle predications of the model are in good agreement with the experiments. This would be especially meaningful because most of the previous experiments in testfying the model were carried out with single crystals of high-purity materials and little work has been done with polycrystalline steel alloys. EXPERIMENTAL PROCEDURES AND RESULTS Specimen Materials. The tensile specimens used throughout this experiment were of two compositions selected from a series of Fe-Mo-0.77 pct Mn-0.22 pct C steels prepared for a ductile-brittle fracture transition study. One steel contains 0.21 pct Mo and the other 1.03 pct Mo. These two compositions were chosen for the present study because they possess quite different toughness properties at room temperature. The 0.21 pct Mo steel is quite ductile while the 1.03 pct Mo steel is rather brittle, as measured by the standard Charpy impact test. The alloys had been prepared by vacuum induction melting and chill casting in steel molds. The ingots were hammer-forged into 1/2-in.-sq bars from which tensile specimen blanks were cut. These blanks were first normalized under argon atmosphere at 1700°F and then reaus-tenitized and isothermally transformed at 1050°F to a bainitic microstructure. The chemical compositions, heat treatments, hardness measurements, and Charpy transition temperatures of the two steels are listed in Table I.

Jan 1, 1970

By C. W. Spencer, B. F. Addis, G. H. Bishop, C. A. Steidel

STUDIES of the inter granular attack of metals by liquids have generally been confined to polycrys-talline specimens. This note reports the results of preliminary studies of the penetration of bismuth-rich Ni-Bi liquids into oriented bicrystal specimens of nickel. It is found that isothermal penetration follows a parabolic rate law and shows a definite anisatropy with respect to direction on the grain boundary surface. Nickel bicrystals containing < 100> tilt boundaries were grown using the Czochralski method. Relative misorientation of the parent crystals was controlled to ± 1deg. The boundaries are straight in the growth direction, i.e., the common <100>, and generally straight in the transverse direction, as shown in Fig. 1. The starting material, Inco HPM grade nickel was contained in a recrystallized alumina crucible and maintained under argon. Bicrystals typically contain 30 ppm C, less than 10 ppm S, O, N, and 50 ppm residual metallics, principally iron and silicon. Specimens, as schematically illustrated in Fig. l(c),were cut from bicrystal ingots using a thin water-cooled abrasive wheel. To insure removal of all residual strain, which accelerates the penetration, specimens were round through 600 grit silicon-carbide, chemically polished, and annealed for 4 hr at 1375°C under argon. The procedure described by Cheney et al.1 for exposing specimens to

Jan 1, 1962

By W. P. Z. German

Some attention should be given to definitions. The term "unit operation " may have at least two meanings. One meaning is the merging of titles and the development and operation of the unitized area, as if it were one tract of land held under a single oil and gas lease, according to a definite program intended to accomplish a maximum recovery from the pool as a whole at a minimum of cost. It is incomplete when the royalty owners do not also merge their titles to their oil and gas rights in the area, and is complete when they do. The other meaning is not accompanied by any merger of titles, but the development and operation of the area is in accordance, as nearly as reasonably practicable, with such a program. This second conception may be nothing more than a cooperative development and operation plan, but in this paper it is regarded as more than that. If there cannot be unit operation without a merger of titles, it would seem that the state cannot require unit operation, for it cannot require a merging of titles; but if it may consist in requiring each and all of the leaseholders to develop and operate or to submit to a development and operation according to some such common plan as is referred to above without at the same time requiring a merger of titles, it would seem that unit operation may be required by the state. Whether the states have this power is the subject to be herein considered. If the state can so bind the several lessees, it also can so bind the several lessors. The writer does not know what would be an ideal plan for the development and operation of a pool; but it takes into account the fact that the accumulation of gas and oil is not uniform throughout the formation; that often free gas, highly compressed, occupies the upper portions of the reservoir, the oil with compressed gas in solution coming next in order; that at places oil is not overlain by free gas, and sometimes there are peaks where free gas is not immediately underlain by any oil; and the fact that these substances are held under a uniformly distributed pressure, generally referred to as "rock pressure." It also recognizes that the most efficient utilization of this naturally existing reservoir pressure in the recovery of the oil requires that there be no operation of wells completed into areas where gas only has accumulated, for this diminishes the

Jan 1, 1931

THE first session of this meeting was held Tuesday evening, in the chamber of the Common Council, the President, Mr. David Thomas, in the chair. Mayor Carroll, of Troy, gave a cordial welcome to the Institute, which was responded to, on behalf of the Institute, by the first Vice-President, Mr. R. W. Raymond. The Council reported the names proposed for membership with recommendation for election. The following named gentlemen were duly elected: Anthony, J., . .Williamstown, Pa. Babcock, George, . . .Troy, N. Y. Blake, Theo. A., . . . . . . Sa n Francisco, Cal. Blossom, T. M., . . . . . . New Pork. Boalt, James A., . . .San Francisco, Cal. Bowman, Amos, . . . . San Francisco, Cal. Chester, Prof. A. H., . .Clinton, N. Y. Dewey, C., . Pittsfield, Mass. Dock, Gilliard, . Shamokin, Pa. Emerson, O. D., . .New York. Endres, John J., . .Pittsburgh, Pa. Firmstone, Frank, . Easton, Pa. Fowle, W. B., . Philadelphia, Pa. Frazier, Prof. B. W., . . .Bethlehem, Pa. Gardner, George A., . New Pork. Goodyear, Watson A., . .6an Francisco, C al. Griswold, Chester, . Troy, N. P. Griswold, J. A.,* . . .Troy, N. Y. Hague, J. D., . . .San Francisco, Cal. Hahn, 0. H., . .Eureka, Nev. Harkness, T. C., . . . . . . Wilkes-Barre, Pa Harris, Samuel, . . .Hudson, N . Y. Henry, &. T., . Oxford, N. J. Holley, A. L., . .Brooklyn, N. Y. Howe, H. W., . . .Troy, N. Y. Hunt, Dr. T. Sterry, . Boston, Mass. Jannet, J., . Troy, N. Y. Knapp, John A., . .New Pork. Laughlin, Henry A., . . .Pittsburgh, Pa.