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By Leon Merker

FLAME fusion growth of strontium titanate crystals was undertaken to obtain large transparent crystals on which physical data could be gathered. The fact that strontium titanate is a cubic crystal and probably has a high index of refraction indicated that it might be useful in optics. No large boules* of strontium titanate had been synthesized previously, and none have been found as natural occurrences. The flame fusion process, invented by Verneuil in 1904,1 was first applied to grow large crystals of ruby and has since been used extensively to grow crystals of corundum and spinel on a commercial scale. Only during the past nine years has this technique been applied to the growth of large single crystals of other high melting compounds such as rutile,2 mullite,3 and ferrites4 One of several significant advantages of the flame fusion technique over more conventional methods of growing crystals from a melt is that the crystals are grown without the use of melt containers. This fact alone excludes other methods of growing crystals from a melt whenever there are compounds with a melting point near 2000°C or above. Growth of the crystal, similar to that of a stalagmite, takes place inside a circular refractory furnace that does not contact the crystal, Fig. 1. This eliminates a serious source of impurities as well as the likelihood of multi-crystalline solidification along the container walls. The flame fusion technique is particularly advantageous for research because it produces large crystals quickly and at lower cost. A corundum crystal 25 mm long and 12 mm in diam can be grown in 2 to 3 hr. Operating conditions permit observation of the growing crystal during any stage of the process. The various flame patterns and a wide range of oxidation-reduction conditions can be investigated in a relatively short time. It should be pointed out that formation of the foot of the boule is the most critical step in growing an unfractured boule. When the tip of the sintered cone is fused to initiate crystal growth, the original area of fusion should be kept as small as possible so that one crystallite can assume dominance over all the others and propagate as a single crystal. If the boule start happens to consist of several crystals, usually the entire boule also contains several crystals. In many cases these tightly cohering crystals exhibit different crystallographic orientations. Although the basic technique of the original Verneuil process has been retained, refinements in method and burner design have been developed in recent years. For example, boule growth may be initiated on a seed crystal rather than by fusion of a sintered cone. The danger of multicrystalline or twinned boule starts is thus eliminated, and this procedure may also be used to grow boules of predetermined crystallographic orientation. Prior Art: Of the many attempts to produce artificial gem crystals, most early efforts% ere directed toward synthesis of .rubies and sapphires and diamonds. None of these efforts resulted in a process that was commercially practical. Without exception only tiny crystals of corundum were obtained, and those at excessive cost. Verneuil announced his process in 1904; Ravier6 in 1934 presented a detailed description of a commercial boule production plant. Descriptions of the German synthetic stone industry, the process details, and the equipment used have been published by Barnes7 and by Merker.'

Jan 1, 1956

By N. J. Grant, C. F. Flo, F. B. Cuff

An investigation of the Ti-Cr system has shown the presence of a complete series of solid solutions in the ß phase, with a minimum in the solid us near 50 pct Cr. An intermetallic compound, TiCr2, forms during cooling from the ß solid solution. There is a eutectoid reaction at the low chromium side of the system. IN view of the recognition of the potentialities of titanium and its alloys as important structural materials there has arisen a need for a systematic investigation of various titanium binary diagrams. Of these, the Ti-Cr system was of particular interest because of the improved properties imparted to titanium by small chromium additions. A literature survey disclosed a partial constitution diagram that had been suggested by Vogel and Wenderott,¹ This diagram, shown in Fig. 1, is the result of work done on the Fe-Cr-Ti ternary system. Alloys containing less than 43 pct Cr were not investigated. In addition to this, a study of alloys in the Ti-Cr system was reported by McPherson and Fontana.² Adenstedt3 furnished a number of dilato-meter curves obtained from specimens containing 5, 10, and 15 pct Cr. Very recently, McQuillan4 submitted a proposed diagram covering the complete range of compositions between titanium and chromium. This diagram was in general agreement with the one described here. Experimental Procedure Sponge titanium (99.7 pct) and electrolytic chromium (Bureau of Mines analysis: 99.03 pct Cr, 0.40 pct Fe, 0.53 pct O2) were used for the initial determination of the system. Subsequent refinement of points, particularly for the low chromium side of the diagram, was accomplished by using iodide titanium and high purity chromium (National Research Corp. analysis: 0.050 pct C, 0.045 pct O2). The Ti-Cr alloys were prepared by melting 25 g charges in an enclosed, water-cooled copper crucible using a movable tungsten electrode. The atmosphere was helium, prepurified by first passing it through a drying agent and then through sponge titanium heated to 850°C. Particular care was taken to avoid any large scale segregation resulting from insufficient mixing of the components. Each charge was melted and kept molten for approximately 1 min, allowed to cool, inverted, remelted, and kept molten for an additional minute. In order to ascertain the amount of impurity pickup (oxygen and nitrogen) during the melting procedure, three iodide titanium specimens were melted in sequence and then checked for increased hardness. The specimens in the as-cast condition showed a relatively large hardness increase over the hardness of the as-received iodide titanium. The scattering on these readings was large. However, after the specimens had been homogenized at 840 °C for 2 hr and slowly cooled, the measured increase in hardness over the as-received titanium was small with a corresponding decrease in scatter. The reason for this hardness change is that in heat treating these specimens below the transformation temperature (885°C) there was a conversion from the as-cast structure to the more nearly equilibrium structure of the annealed specimen. The alloys were analyzed for chromium content and although the actual percentage was invariably low the deviation from the nominal composition never exceeded 0.6 pct Cr.

Jan 1, 1953

DEVELOPMENT of a chemical process for the extraction of pure metals from mill concentrates or metal scrap has progressed beyond the pilot plant stage and may prove an important adjunct to present smelting and refining methods if initial commercial operations prove economically successful. Developed by the Chemical Construction Corp., the new process involves the treatment of oxide and sulphide ore concentrates by chemical methods, instead of the usual smelting and refining techniques. Several of the many applications are now scheduled for commercial use. Refiners using the new process will prepare ore concentrates by standard flotation methods, introduce the concentrate as a slurry into an autoclave along with water and an acid or ammonia. From the resulting leach solution, recovery of individual metals is made by use of suitable reducing agents. By varying conditions during treatment, different metals in the ore are produced separately as pure powders, which may be pressed into forms ready to market, or in the case of copper, extruded as rods or pipe. The reagents are generally recovered. By manipulating the variables during reduction, selective separation of nickel, and/or cobalt, and/or copper can be made simultaneously. The separation is a continuous operation. Low metal prices are not immediately in view because of the tremendous demand at this time. However, reduced metallurgical treatment costs will allow economical mining of orebodies with lower metal content, permitting increased production to meet demand. Although the practical horizon for use of the new process appears to be limitless, one factor may enter into its employment. Just how low grade a concentrate can be economically used is unknown. In addition, for present practical considerations, only metal below zinc in the electromotive series may be processed. Each commercial application requires specific technique adaptation and pilot-plant data for engineering design. A nickel-cobalt-copper process has been researched and piloted in collaboration with Sherritt Gordon Mines, Ltd., for the firm's Lynn Lake properties. In addition, processes were tailored for cobalt concentrates of Howe Sound Mining Co., and National Lead Co., in view of the urgent need for this specific metal. Major General William N. Porter, president of Chemical Construction, says of the new process, "piloting experience has shown that production cost, from ore concentrates to pure metals should be considerably below current costs." Other savings may be realized by cutting transportation and personnel costs, and by reducing the time lag between mining and pure metal from months to a matter of hours. First commercial use of the process will start sometime this summer. Chemico is slated to finish building a $2.5 million cobalt refinery for Howe Sound Mining near Salt Lake City. The plant is expected to raise world cobalt production by 40 pct. The plant will process 35 tons of 20 pct cobalt concentrates from Howe Sound's Blackbird mine near Cobalt, Idaho, daily. Yearly production is expected to reach 2000 tons of pure metal, about one half of U. S. consumption in 1950. Steps in the Howe Sound application of the process are: 1. Acid oxidation leach. 2. Filtration (residues thrown away are insoluble compounds-gangue, iron, arsenic). 3. Cementation (for Cu removal because Cu content is too low for recovery). 4. Reduction from ammoniacal solution. 5. Separation of Co and Ni as mixed metals (95 pct Co and 5 pct Ni). 6. Recovery of ammonium sulphate. Under construction at the Fredericktown, Mo., mine of National Lead is a $5 million refinery sched- [ ]

Jan 1, 1952

By R. Stefanko

The use of strain gauges and compression pads for an underground bolt installation in a central Pennsylvania coal mine revealed that satisfactory anchorage could not be maintained in the shale stratum that constituted the immediate roof. Comprehensive laboratory tests resulted in a new shell designed with an increased area of contact and smaller surface serrations. Retightening of the bolt was also found to be beneficial for maintenance of high load values. Roof bolting in coal mines has progressed very rapidly in the last decade, and today this method of support is in general use. There are many theories concerning the functions of roof bolts, but the importance of beam building is indisputable. Proper tension in the bolts minimizes shearing along bedding planes and creates a thick, competent beam from individually weak layers. Bolting must be accomplished immediately upon exposure of the roof, and bolt tension must be maintained if roof failure is to be prevented. Seams are being mined today with roof bolt support where conventional timbering was not effective.' The widespread use of continuous mining equipment was made possible by roof bolts which permit long supported spans free of obstructions. Since adequate anchorage is the key to successful bolting, better methods for determining the efficiency of anchorage are continually being sought. Attempts have been made to measure bolt loads, thus assessing anchorage efficiency by employing sensing devices between the bolt head and roof. 3-s None of the techniques appears to be very accurate, and all have at least one serious deficiency. The greatest efforts are being directed toward the standardization of the pull test.6" Nevertheless, the author believes that the pull test is only one criterion for establishing the efficiency of anchorage and not necessarily the most important one. The conventional pull test involves the short-term application of forces, whereas the success of roof bolt installations is dependent upon the ability of anchorage to sustain relatively long-term forces. Therefore, it would appear that the time-dependent function of the anchor is the single most important parameter for the success of roof bolting in many types of rocks. UNDERGROUND TESTS Strain gauges and compression pads were employed to measure bolt loads in a central Pennsylvania coal mine.8 Bolting had been employed only sporadically in the shale top since dubious benefits were obtained with this type of support. Table I shows some typical results from this investigation. Anchorage losses were extremely variable among the bolts, but all showed a considerable degree of bleed-off. The tests indicated that anchorage efficiency was extremely low in this type of shale. The results confirmed that bolting under these conditions was practically worthless, and thus a waste of material and labor. Probably even more important, bolting constituted a hazard when reliance was placed upon it for support. Certainly the complete lack of confidence in roof bolting, which was apparent in the mine personnel, was justifiable since the bolts did not accomplish their purpose. PRELIMINARY LABORATORY BOLT TESTS The extreme losses in bolt tension that were detected in underground installations prompted a comprehensive study to assess the causes. However, preliminary studies were first made to determine the combined stresses in a roof bolt and to prove conclusively that the observed bleed-off phenomena were due to anchorage: slippage and not to some other physical manifestation. In all of the ensuing tests

Jan 1, 1962

By J. H. Henderson, R. J. Wygal, J. Naar

Experimental work is reported which shows that consolidated rocks and unconsolidated porous media exhibit different imbibition flow behavior. At a given saturation the imbibition nonwetting permeabilities for a rock are smaller than the drainage permeabilities. The contrary happens for unconsolidated aggregates — imbibition nonwetting permeabilities are larger than drainage ones. A similar difference is observed for the wetting phase. Imbibition permeabilities are larger than drainage ones for a consolidated rock but smaller than drainage permeabilities for an unconsolidated medium. The results of these differences are examined for two cases. 1. Flooding Efficiency — Craig's1 scheme for the computation of production history of a five-spot water flood is shown to agree extremely well with experimental results obtained when using a system packed with glass spheres if imbibition relative permeability curves are used. 2. Alcohol-Slug Displacement — Published theory 2 on oil displacement by alcohol slugs has been questioned despite the apparent agreement between predicted and observed results. The present work suggests that, if imbibition relative permeability curves characteristic of the unconsolidated media used in the early experiments had been available to make the predictions, the inadequacy of the theory would have been immediately evident. The experimental work shows that poorly consolidated formations tend to behave like unconsolidated media. Finally, it is shown that the difference in imbibition behavior is directly related to pore-size distribution and cementation. PART 1 — THE FLOW BEHAVIOR OF UNCONSOLIDATED AGGREGATES Experiments on scaled models of field reservoirs are useful for studying new displacement processes which are incompletely understood. Even when a mathematical description is possible, the solution might be difficult and complex. An answer obtained from a scaled model is extremely valuable in such cases. A great amount of work$-5 therefore, has been devoted to the derivation of scaling laws. Similarity groups have been defined which assume (1) that the relative Permeability curves of the prototype and the model are the same whether the displacement is an imbibition or a drainage process and (2) that there is a linear relationship between the capillary pressure of the model and the prototype. For practical reasons (simplicity in the preparation of models, duration of the experiments, etc.), the porous media of laboratory models are usually unconsolidated packs of sand or glass particles. Hence, unless the capillary and flow characteristics of unconsolidated and consolidated systems are identical, the model data are applicable only to unconsolidated formations. The usefulness of scaled-model studies may then be seriouslyrestricted since most oil-bearing sands are consolidated. Perkins and Collins6 suggested the use of model and prototype curves normalized with respect to both relative permeability and saturation to improve compliance with scaling criteria. Even this technique does not give a satisfactory model-prototype match. This paper reports an observation of two-phase flow in unconsolidated sands which shows that, for most displacements, "scaling" in the strict sense of the word is not even qualitatively feasible with a sand model. It provides, however, a firm foundation for testing a theory by matching it with observed performance of laboratory-size models. EXPERIMENTAL AS a part of a basic study of packed aggregates, the relative permeability of glass-spheres and sand-grain packs was measured with capillary control. The fluids were oil and air' The spheres were packed in plastic cylinders 1-in. in diameter;

By M. A. Selim, W. H. Somerton

Thermal expansions and heats of reaction of three typical sandstones were measured in the temperature range of 25°to 1,000°C. The significance of these data in subsurface heat-transfer calculations is discussed. Linear thermal expansions were measured both parallel and perpendicular to the bedding planes. Volume expansions are reported as the perpendicular expansion plus two times the parallel expansion. Expansion behavior of the sandstones was found to be controlled by the expansion characteristics of the quartz content. Differential expansion of the quartz grains and other minerals included in the sandstones caused permanent deformation of the heated samples after they were cooled to room temperature. Structural damage resulting from heating is probably an important cause of the reduction of thermal conductivity of heated samples. Measurements of heats of reaction were based on the known heat required for a- quartz inversion. Thermal reactions, which probably include deby-droxylation of clay minerals and decomposition of carbonate minerals contained within the samples, were found to require more than one-fourth of the amount of heat necessary to raise the temperature of the rock alone. In shales and limestones, the reaction heat could be substantially greater than that required from specific heat considerations alone. INTRODUCTION In earlier work, l-3 methods of measuring thermal properties were developed and thermal data for several sedimentary-rock types were reported. Data included thermal conductivity, specific heat and thermal diffusivity. In addition, calculations of heat transfer in subsurface formations may require data on the thermal-expansion characteristics of rock and the heats of reaction of mineral constituents. Thermal expansion of rocks is relatively small in magnitucle and, from the standpoint of change in bulk density, has only minor effects on heat-transfer cliaracteristics. Thermal-expansion behavior, however, may have significant effects on the structure of rocks. Differential expansion of different minerals and along different crystal-lographic axes may result in structural damage which could effectively reduce the thermal conductivity of the rock. Many mineral constituents of sedimentary rocks undergo phase or related changes when heated to sufficiently high temperatures. Although some of these reactions (such as the a-ß quartz inversion) are reversible and the heat absorbed is returned to the system upon cooling, many of the major reactions are irreversible. Through certain temperature ranges, the additional heat energy required to complete the reactions may be nearly as great as that necessary to raise the temperature of the rock in the absence of thermal reactions. If the heat requirements for these reactions are not considered, serious errors in heat-transfer calculations may result. Thermal-tzxpansion and thermal-reaction data have been obtained for three typical sandstones. Methods of measurement and results obtained are reported and discussed in the following. THERMAL EXPANSION OF SANDSTONES The linear expansions of three outcrop sandstones (Bandera, Berea and Boise) have been measured in the temptbratue range of 25° to 1,000° C. Expansion measurements were made in the directions parallel and perpendicular to the bedding. The differential expansion apparatus used is that described by Mitoff and Pask.4 The test sample is heated in an electric furnace with a temperature rise of 6°C/minute. The lengthening of the samples upon heating is compared with the small and known expansion of a fused silica rod. The change in length is transmitted to an X-Y recorder by means of a Statham transducer. A maximum error of ± 1.5 per cent has been obtained with this apparatus

By J. G. Richardson, K. H. Coats

During the initial growth of a gas bubble in an aquifer storage reservoir the injected gas tends to override the water. The resulting low displacement efficiency and high rate of gas travel down-structure make it difficult to maintain water-free production. This paper illustrates the use of two-dimensional, two-phase calculations to simulate this gas-water displacement. Calculations were performed for a stratified aquifer and for several homogeneous sands differing in permeability, porosity and thickness. Results are discussed and compared with performance predictions obtained from the simpler Buckley-Leuerett and Dietz formulas. This comparison indicates the necessity for the two-dimensional calculations in realistically simulating the gravity override of the water by injected gas. INTRODUCTION In recent years natural gas has been stored near markets in aquifers where insufficient storage capacity is available in depleted fields. Operators of these aquifer storage reservoirs have encountered technical problems relating to the gas-water displacement accompanying initial growth of the gas bubble. Injected gas tends to override the water, with a resultant low displacement efficiency and high rate of gas travel down-structure toward spill points. Low displacement efficiency makes if difficult to sustain water-free gas production. Sometimes the fingering of gas down-structure may be so pronounced that the injection rate must be severely curtailed, which excessively lengthens the time required for bubble growth. This paper is concerned with estimating — for given aquifer characteristics and fluid properties — the displacement efficiency, rate of gas movement down-structure and rate of gravity drainage of water behind the gas front. Several published articles relate to simulative capability necessary to handle this problem. The Dietz formula1 and Buckley-Leverett2 method have some applicability to the problem; Woods and comer3 reported one-dimensional, radial calculations which accounted for the two-phase flow of gas and water. Most recent research directed toward understanding aquifer behavior in relation to gas storage has concentrated on single-phase flow in aquifer.4 Douglas, Peaceman and Rachford5 presented a method for calculating multidimensional two-phase flow in reservoirs; their method has been applied in work reported by Nielsen and Tek,6 Blair and peaceman7 and Goddin.8 Refs. 5 and 7 show comparisons between experimental data and calculations similar to those employed here. One purpose of this paper is to illustrate the use of two-dimensional, two-phase flow calculations in simulating the difficult problem of water displacement by gas in a vertical cross-section. The pronounced fluid density and viscosity differences combine with the disparity in horizontal and vertical dimensions of the cross-section to pose one of the more difficult problems in reservoir simulation. The calculations described account for capillary and gravity forces, relative permeability and reservoir heterogeneity. An example reservoir is described and calculated results are presented for a variety of injection rates and values of permeability, reservoir thickness and dip angle. A second purpose is to compare the two-dimensional calculations with results obtained from the Buckley-Leverett and Dietz formulas. For this reason most calculations were performed for a simplified example reservoir to which the latter techniques might reasonably be applied. However, the computer program employed applies equally well to cases involving arbitrary spatial variations of permeability, porosity, reservoir thickness and dip angle.

By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.' The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod' and of von Rosenberg' are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger's6 concept of the dispersion of velocities. After a very clear description of Scheidegger's theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958

By R. A. Swalin, L. A. Neimark

The research work presented in this paper had initially a two-fold goal. First, further data concerning the low-temperature recovery of cold work was desired. Recovery phenomena have been extensively studied in face-centered-cubic metals but at the time of initiation of this research, no investigation concerning the low-temperature recovery in body-centered-cubic metals had been made. During the course of the investigation a paper by Martin on the recovery of point defects in molybdenum appeared.&apos; Comparison of our results on tungsten with Martin&apos;s results on molybdenum will be made. Secondly, knowledge concerning the influence of a particular type of impurity addition on the recovery kinetics was desired. It has been known for a long time that extremely small amounts of certain impurity additions exert a profound influence on the recrystallization behavior and the resulting microstructure of tungsten. Small amounts of potassium silicate and aluminum chloride added prior to the reduction of tungsten oxide to the metal have been found by Smithells to raise the recrystallization temperature markedly,2 and yield an ultimate microstructure in which grains several millimeters long are produced in fine wires of say 10 mil diam. If the impurities are added singly, ordinary secondary recrystallization results with none of the spectacular properties of the wire to which special additions were made. Swalin and Geisler3 and Rieck4 have studied the recrystallization behavior of such doped wire in some detail. The former workers found that small amounts of these impurities raised the recrystallization temperature over 400°C and electron microscopic examination revealed no obvious inclusions in the microstructures. In fact. chemical analysis showed that there was <0.001 pct K, <0.002 pct Al, trace of Si, and <0.0003 pct 0 in the wire studied. The possibility that the role of the special impurities is to keep the structure open by void formation and that submicroscopic porosity acts as the inhibiting agent has been discussed.2&apos;3 Meijering and Rieck5 have suggested that the impurities are strung out as second-phase particles in a direction parallel to the drawing direction. It was thought that a kinetic study of recovery could perhaps elucidate the role of the impurities to some extent. When a metal is deformed by cold work three basic types of defects are thought to be introduced into the crystal lattice, namely, interstitials, vacancies, and dislocations. Van Bueren6 has proposed that recovery of cold-worked metal is a four-stage process, each step being the result of the annealing of a primary defect or a combination of defects and having a unique activation energy. The steps in order of increasing activation energy are attributed to a) the diffusion of interstitials recombining with vacancies, b) diffusion of vacancy pairs, c) the diffusion of single vacancies, and d) climb of dislocations. In metals with relatively low- or medium-range melting points the temperatures for recovery are low enough so that the first three steps may occur during room-temperature deformation. For tungsten, because of the high melting point and subsequently high recovery temperature, it was calculated, using Nowick&apos;s approach7 that this recovery would occur in the temperature range 200" to 600°C. It is also known that recovery of X-ray line broadening, presumably due to dislocation climb, occurs at about 600°C.8 EXPERIMENTAL METHOD Two types of cold-rolled 10-mil-diam tungsten wire were used in the investigation; a) pure tungsten, (called undoped) and b) G. E. No. 218 wire (called

Jan 1, 1961

By P. S. Roller

P. S. ROLLER,*College Park, Md.-The author introduces the idea of a grind limit, or lower size limit of the particles formed directly by grinding, and this is stipulated to be 0.70 micron. I wonder where all the particles come from that lie between the resolving power of the microscope and 0.7 micron, which are seen under a microscope in examining a sample of grind? There is also introduced the idea of excess fines; this is all right in itself but the author&apos;s quantitative definition seems to be virtually impossible to justify, and, moreover, is obscure. Just why E, the excess fines, should he defined as the distance between an F line and a y line is hard to follow, and just where the distance should be measured does not appear to be stated, as it should be since the F and y lines intersect and the distance between will depend upon where that distance is measured. The basis of the presentation is the relation of log weight against log size that was "discovered" by Schuhmann. While this relation is implied to fit, the only evidence that I can see is a slightly irregular line in Fig. x between 2 per cent and 18 per cent by weight and then a precipitous drop at 18 per cent away from any sort of straight line. Some of the conclusions are rather startling. It is stated that E, the excess fines, remains constant for all the comminution products of any particular material, except that it may decrease for some coarse crusher products. No reason is given for this assertion. One would, on the contrary, expect that excess fines, if such a concept is permissible, would generally vary with different conditions instead of being constant. Again, "as much net energy is required to reduce a ton of quartz to particles of the grind-limit diameter (namely, of course, 0.7 micron) by grinding as is required to melt the quartz." This would require many data to prove, but no proof is given; any consideration would reveal the impossibility of such a result. Still further, ore samples "ground to widely different sizes, and with different circulating loads and different size distributions or product, show the same production of new surface area per revolution of the mill, when this grind limit is used." This statement is confuted by ordinary experience, which teaches that grinding efficiency varies generally with the condition of material. For example, the cushioning effect of fines is widely accepted, while the inefficiency of a ball mill when the feed is too coarse is also well known. R. SCHUHMANN, JR.," Cambridge, Mass. Contrary to Mr. Bond&apos;s stand, there is a great deal of miscellaneous experimental evidence that comminution does not stop at around 0.7 micron, nor does it cease consuming energy at that point. Comminution is in fact recognized as an important method of producing colloids., Mechanical comminution methods were used by von Weimarn6 to produce colloidal dispersions of a variety of solids, including the minerals chalcocite, galena, hematite, stibnite. Utzino7 gives average particle sizes ranging from 0.02 to 0.09 micron for colloids produced by mechanical comminution of several crystalline solids. Andreasen and Berg&apos; have ground

Jan 1, 1941

By Jean-Jacques Prompsy, J. S. Rinehart

The purpose of the present study was to arrive at a better understanding of the stress fields developed within drill bits under dynamic loading and the influence that these stress fields could have on the failure of the drill bits. Particular emphasis has been given to the influence that bit shape has on the establishment of highly localized, potentially destructive stress inhomogeneities within the bit. This paper covers one phase of a broad study involving three velocity regimes: impacts at very low velocities, 0 to 20 ft/sec, a velocity range in which dynamic effects are just beginning to be found; impacts at velocities ranging from 20 to several hundred ft/sec, arange commonly encountered in practical drilling operations; and impulsive loading through the detonation of explosives, a velocity range in which the dynamic effects are greatly exaggerated and made more identifiable. Specifically, fracturing which develops at the end of a cylindrical bar undergoing a shock produced by impact was experimentally investigated, the impacted area being the face of a truncated cone terminating the cylindrical bar. Fracture characteristics were looked at as a function of impact velocity, area of impacted face and cone angle — parameters of considerable importance in the design of drill bit. EXPERIMENTS The specimens were made of Plexiglas, which enabled the fracture pattern to be easily observed. In Plexiglas, the velocity of a longitudinal wave is about 8,700 ft/sec, and the velocity of the transverse wave about 4,200 ft/sec. The specimens were impacted by a steel cylinder whose lower face was parallel to the terminal face of the experimental bit, as shown in Fig. 1. The impacting mass was shifted up and down on two steel rods, dropping from a maximum height of 11 ft, with the velocity varied between 0 and 6.5 m/sec. The initial mass of the cylinder was 4.1 kg, which could be increased by steps up to 8.8 kg by addition of steel plates. The velocity of the steel cylinder was determined by using an electric circuit; as the cylinder dropped, it contacted two steel wires, the first one starting and the second one stopping an electronic counter. Two similar counters connected in parallel were used to corroborate each other. The velocity was checked at each drop as it had been observed to vary somewhat from drop to drop. The two contact wires were located just above the top of the specimen so as to give a value of the instantaneous velocity of the steel cylinder at impact. The distance between the wires was 40 ± 0.5 mm and the discrepancy between the counters was never more than 0.1 m/sec. Thus the velocity was known to within 3.25 per cent. This precision was sufficient with respect to the precision of the machining of the specimens. A very small lack of parallelism between the face of a specimen and that of the impacting hammer resulted in an oblique impact which required a much lower velocity to break the specimen. The experiments had a twofold purpose — (1) to observe the fracture pattern, and (2) to find relationships between the minimum velocity required to generate a fracture within a specimen and the

By G. F. Sager, B. J. Nelson

Magnesium alloy forgings offer higher and more uniform mechanical properties than heat treated magnesium alloy castings and are used principally for light weight parts that may be stressed in fatigue or subject to impact loads, or where space limitations do not permit the use of the necessarily bulkier magnesium alloy castings. Compositions and Properties of Magnesium Forging Alloys The nominal compositions and properties of the principal commercial magnesium forging alloys are given in Table 1. The two that are most commonly used are AMC58S and AM65S. The former has the highest strength and is, therefore, employed for heavy duty applications. However, the forging of this alloy and of AMC57S ordinarily requires the use of slow speed hydraulic presses. The forging alloy AM65S combines good, although somewhat lower, mechanical properties with excellent forging characteristics. This alloy can be forged on hammers, upsetters, rolls, and mechanical presses, as well as on hydraulic presses. These characteristics make it particularly useful for many applications. Manganese Segregation in AM65S The alloy AM65S contains 5 pct tin, 3 1/2 pct aluminum, and a small amount of manganese, the manganese being added to insure satisfactory resistance to corrosion. Some manganese segregation was occasionally encountered in this alloy. In many applications, such segregation is of no particular consequence, but when forgings are acid dipped prior to the application of various chemical coatings, the segregated particles of manganese constituent may stand in relief. The resultant surface roughening may impair appearance and is undesirable in forgings employed in the textile industry, where very smooth surfaces are essential to avoid the catching and breaking of fine threads. An effort was therefore made to determine the cause of manganese segregation in this alloy and find a method for its elimination. Radiographic examination of a series of cast ingot sections and extruded samples of the AM65S type having manganese contents ranging from zero to about 0.7 pct revealed no appreciable manganese segregation when the manganese was less than about 0.4 pct. A small amount was observed with a manganese content of 0.46 pct and considerable with manganese contents of 0.6 pct or higher. Attempts to eliminate the manganese segregation by variations in the melting and casting conditions were unsuccessful and it soon became apparent that the trouble was attributable to the fact that the manganese contents that caused segregation were in excess of the amounts that would remain in solution at temperatures encountered in the melting and/or casting operations prior to the complete solidification of the ingots. A knowledge of the amounts of manganese that would be soluble in molten alloys of the AM65S type at various temperatures was obviously desirable. The liquid solubilities of manganese in binary Mg-Mn alloys and in Mg-Al-Mn and Mg-Zn-Mn alloys have been determined by Tiner and others,* but no data on the solubility of manganese in molten magnesium alloys containing tin and aluminum are given in the literature. For this reason, an investigation to determine the solubility of manganese in a magnesium alloy containing 5 pct tin and 3.5 pct aluminum (AM65S type) was undertaken.

Jan 1, 1950

By C. A. Siebert, S. H. Bush

Isothermal temper-embrittlement studies were conducted on a 5140 steel at various temperatures for times as long as 3000 hr. Specimens from the embrittled steel were subjected to impact tests, metallographic examination, microhardness, and lattice-parameter measurements. SEVERAL of the steels in the low alloy group are subject to a pronounced decrease in impact energy if held within, or cooled slowly through, a range of temperatures below the lower critical. This phenomenon, known as temper embrittlement, is quite pronounced in the chromium steels of which AISI 5140 is typical. This study considered the response of one heat of 5140 steel when embrittled isothermally at various temperatures for times as long as 3000 hr. Excellent reviews of the work done in the field of temper embrittlement have been written by Hollomonl and Woodfine.&apos; Both authors list the various theories which have been advanced to explain temper embrittlement. Some of the mechanisms considered were: 1—a transformation below 700°C; 2—an allotropic modification of iron; 3—precipitation from the ferrite of such compounds as carbides, nitrides, phosphides, or chromium oxides; 4—decomposition of retained austenite; 5—modification of special carbides; 6—grain-boundary segregation; and 7—selective distribution of carbides. The present study investigated the changes in hardness, Meyer&apos;s number, impact properties, micro-structure, and lattice parameter which occurred on embrittlement. Previous studies considered the influence of microstructure and of prior austenitic grain size3 on the response of 5140 steel to temper embrittlement. Equipment and Procedure All samples were taken from one heat of 5140 steel; the chemical composition of this steel was: 0.43 pct C, 0.86 pct Mn, 0.020 pct P, 0.019 pct S, 0.27 pct Si, 0.84 pct Cr, 0.10 pct Ni, 0.06 pct Mo, 0.10 pct Cu, and the remainder Fe. The material was received as % in. rounds. This stock was cut down to blanks measuring approximately 0.425~0.425~2.196 in. Heat Treatment: The rough blanks were normalized at 1600°F (870°C) for 1 hr, then austenitized at 1600°F (870°C) for 1 1/2 hr, and quenched into an agitated oil bath. The specimens were tempered at 1275°F (690°C) for 5 hr and water quenched. These tempered specimens were designated as the toughened state. Embrittling Treatments: The tempered bars were divided into sets and subjected to the various embrittling treatments listed in Table I. Temperatures from 750" to 1050°F were investigated for times of 1 to 3000 hr. Special tests to determine the effect of heating a short time at a higher temperature after long-time embrittlement at some lower temperature were also conducted. All specimens were water quenched at the end of the embrittling cycle, then ground and notched to obtain standard Charpy V-notch specimens. Impact Tests: The bars were fractured in a 260 ft-lb Charpy impact unit; specimens were fractured at temperatures ranging from —315°F to room temperature. Fixed temperatures used consisted of —315°F with liquid nitrogen, —115°F with dry ice and acetone, and 32°F with ice and water. Intermediate temperatures were obtained by suspending the bars in a jig over the liquid nitrogen, dry ice and acetone, or ice and water.

Jan 1, 1955

By R. T. DeHoff

Saltykov&apos;s meihod for the determination of the size distribution of spherical particles from measurements made on random plane sections is extended to particle shapes which are not equiaxed. The analysis permits the deterrrzination of the size distribution of aggregates of ellipsoidol particles provided all particles have tlze same shape. V ARIOUS solutions to the problem of the determination of the size distribution of spherical particles from measurements made on random plane sections have appeared in the literature since the original solution was first published by Scheill in 1934. Solutions have been offered utilizing measurements of the diameter1y2 or area3&apos;4 of circular sections that result when a test plane is passed through an aggregate of spherical particles, and the length of intercept5y6 that results when a test line is passed through the aggregate. To the best of the knowledge of the author, no method has been proposed which permits the determination of the size distribution of particles that are not equiaxed. The purpose of this paper is to develop a method which permits the determination of the size distribution for a specific class of particle shapes which cover awide range of axial ratios; namely, ellipsoids of revolution. In the interests of simplicity, it is necessary to limit consideration to aggregates of particles which are all similar in shape; that is, the ellipses which, by rotation about one of their axes, generate the particles, all have the same axial ratio. The size distribution, which is to be determined by the analysis, is arbitrary. It is also assumed that the section, or sections, upon which the measurements are made represent the average of all possible sections through the structure. This ideal condition can be approached as nearly as may be desired by observing a sufficient area of sections taken at random positions in a randomly oriented aggregate, and in random positions and orientations in an aggregate that has one or more axes of orientation. SIZE DISTRIBUTION FOR PROLATE ELLIPSOIDS Consider an aggregate of cigar shaped, geometrically similar particles (prolate ellipsoids), dispersed in an opaque matrix. Let the size of each particle be specified by the length of its minor axis, By Fig. 1, and the shape, q, be defined by the ratio of its minor to its major axis, B/A. Let the index, j, refer to dimensions of ellipsoids in a particular size class, and the index, i, to dimensions of an ellipse resulting from the intersection of a test plane and a particle. The size of such a section is specified by the length of its minor axis, b. Let the particles be arbitrarily divided into k size classes, and let the increment of size between each class be A, where A = &,$, B,,,being the minor axis of the ellipsoids in the largest size class. Since all sections are represented on the test plane, the minor axis of the largest of the sections observed, results from the intersection of the test plane with an ellipsoid in the largest size class at its center, and is therefore equal to Bmax Thus the increment, A = The final result will consist of the k numbers which represent the number of particles in each size class per unit volume of aggregate:

Jan 1, 1962

By L. A. Roe, John Jan

Iodine is a soft, lustrous, grayish-black nonmetallic element with a density of 4.9. It is the least active of the four members of the halogen family. The other members are, in order of increasing activity, bromine, chlorine, and fluorine. Iodine is a solid at ordinary temperatures, while bromine is a liquid and chlorine and fluorine are gases. Iodine melts at 113°C and volatilizes at 184.4°C to a blue-violet gas with an irritating odor. It occurs in nature only as iodates and iodides or other combined forms. It was discovered by Bernard Courtois in France in 1811, who noticed its presence as an unknown substance in crude soda ash obtained from burning seaweed. Gay-Lussac recognized it as a new element and named it iode, from the Greek word "ioeides or iodes" for violet color (MacMillan, 1970). The world production is not known with any great certainty, but it is probably between 25 and 35 million lb per year, of which about 30% is consumed in the United States. Geology and Mineralogy Iodine compounds occur as a minor constituent as a mineral in the Chilean nitrate deposits and in solution in brines and seawater. According to the US Geological Survey, it is the 47th most abundant element in the earth&apos;s crust. The minerals lautarite, Ca (I03)3 (calcium iodate), and dietzeite, Cat (103)2 (CrO4), (calcium iodate-chromate) are found in Chilean nitrate deposits which are located in Antofagasta and Tarapaca provinces on the eastern slope of the coast range in a desert area. Various brines contain iodine compounds. Seawater contains about 0.05 ppm of iodine and some seaweeds will extract and accumulate it up to 0.45% on a dry basis. Some coals in West Germany also contain iodine compounds. The known and potential sources of iodine reported in 1968 are given in Table 1. Table 2 lists estimated world iodine reserves. Iodine has been recovered from brines in Java, Indonesia, France, England, and the USSR. Iodine has also been recovered from seaweed in Ireland, Scotland, France, Japan, Norway, and the USSR. The indicated reserves and future resources of iodine are large but have never been adequately measured. Analysis Iodine as the free element can be detected by the characteristic blue color it gives to a starch solution. Quantitatively it is determined as the free element by titration with standard thiosulfate solutions using starch as an indicator. Colorimetric methods are also applicable. Markets and Prices Iodine and its compounds are generally marketed in the form of: iodine, crude; iodine, resublimed; calcium iodates; calcium iodide; potassium iodide, sodium iodide, and numerous organic compounds. Product Specifications Crude iodine, World market: 99-99.5% 12. Crude iodine, US produced, average: 99.8% 12. Crude iodine, USP XVII Specs: not less than 99.8% percent I2. Resublimed iodine is usually 99.9% and ACS specifications call for not over 0.005% total bromine and 0.020% nonvolatile materials (Anon., 1971). Prices, c.i.f. United States, for iodine have been steadily increasing from $1.18 per lb of crude in 1967 to $6.37-7.27 in January 1981 (Anon., 1981). In 1980 the price of iodine increased by 50%.

Jan 1, 1983

By T. L. Berger, M. C. lnman, M. F. Rose

AFTER shock loading, mechanical twinning has been observed by several authors1-4 for a variety of fcc metals and alloys. It has been shown2,3 that low stacking fault energy materials deform primarily by the formation of mechanical twins and stacking faults during dynamic loading. Further, Inman, Murr, and Rose2 have shown that a correlation exists between the average hardness and the volume percent of mechanically twinned material in stainless steel. It has been observed in nickel&apos; that mechanical twins are produced during shock deformation if the peak pressure associated with the shock wave is greater than 350kbar. It is the purpose of this work to discuss shock-hardening mechanisms in nickel and to determine to what extent the initial condition influences the final response. The "flying plate technique" was used to generate planar shock waves with peak pressures as high as 710 kbar. The details of the technique5" have been discussed elsewhere and will not be repeated here. The material used in this study was polycrystalline nickel of 99.98 pct purity and had an initial grain size of 0.18 mm. Prior to any deformation, all samples were given a stress-relief anneal of 6 hr at 600°C in a vacuum furnace. After annealing, the initial condition of the samples was changed by cold rolling individual samples from 0 pct to a maximum of 80 pct reduction in thickness. This provided samples with controlled initial histories for shock deformation. Immediately after shock loading, the specimens were slowed and quenched by suitable arrangement of buffer material and water bath. This technique minimized specimen damage and the effects of shock heating on the samples. Since deformation twins in high stacking fault energy fcc metals are only produced at high stress levels, the initial defect configuration prior to mechanical twinning should greatly influence the number of twins formed. In fact, Zukas and Fowler7 have found that prestraining in iron and steel greatly suppresses the formation of mechanical twins during the shock deformation process. Following the methods of Warren and warekois8 and Cohen and Wagner,9 X-ray diffraction profile analysis was performed to determine the incidence of stacking faults and mechanical twins in the deformed nickel. Analysis was made on samples in the annealed, cold-rolled, shock-loaded, and cold-rolled—shock-loaded states. The estimated accuracy of the peak position measurements is *0.01 deg in 2?. Therefore the accuracy in the measurement of the relative peak shifts between the (400) and (222) diffraction line profiles is on the order of *0.04 deg in 2?. None of our measurements indicated peak shifts greater than 0.04 in 28. This would correspond to a fault density of -1 pct and sets the limit on the sensitivity of our instrument. Similarly, analysis of the shift in the center of gravity of the diffraction line profiles yields the minimum measurable value of the twin fault probabilitya to be -0.002. Fig. 1 shows mechanical twinning in nickel shock-loaded to 400 kbar. In this photograph, fault intersections are clearly visible. The thickness of the individual fault lamellae was determined from the image widths of their lines of intersections by the

Jan 1, 1968

By Albert G. Anderson

I&apos;m sure many of you have wondered what the term "Cross Flow Filtration" means. I shall explain it so that you more clearly understand it, and I hope you will be able to make it a useful tool for you in the future. In the simplest form of cross flow filtration contaminated fluid. or feed stream, is fed at a high velocity down the center of a porous tube, clear fluid weeps through the porous wall of the tube while the suspended solids concentrate in and are swept away by the feed stream. (See figure A). The high velocity flow of the feed stream tends to keep the inside of the tube free from a build up of contamination. By utilizing this cross flow approach to filtration, we have been able to concentrate such things as paint pigments, titanium dioxide, iron oxide, precipitated metals such as uranium yellowcake or silver, cadmium, some metal hydroxides, as well as gelatinous particles such as yeast cells. You will recognize that cross flow filtration lends itself to a recirculation loop system due to the necessity of maintaining a high velocity on the inside of the tube. This means that we generally have a storage tank from which we are recirculating, and the solids will concentrate in the storage tank. (See figure B). The storage tank design becomes an integral part of the total system and is very important to the total function of the system. The cross flow filter system requires only low pressure, and will work with centrifugal pumps, diaphram pumps or in some cases no pump at all. As an example, if we wanted to filter a 10 GPM (37.8 liters/min.) stream that contained 1% of submicronic particulate, we would flow the 10 GPM (37.8 liters/min.) into the storage tank and recirculate through the filter at a flow of anywhere from 30 GPM to 100 GPM (113.6 to 378.5 liters/min.) depending upon the filterability of the particles from the liquid. As the contaminated fluid recirculates, the solids will build up in the storage tank and loop until they reach a level, which is dependent upon the design of the tank. Then the settling rate in the tank becomes equal to the amount of the solids being fed to the tank, and as a result you reach an equilibrium in the amount of solids being presented to the inside of the porous tubing. We have in effect created a dynamic settling tank or thickener. A flow of 10 GPM (37.8 liters/min.) of clear filtrate comes off for either recycle or disposal with periodic removal of thick mud from the bottom of the tank. The thick mud can be either processed through a centrifuge, a rotary drum filter. a flat bed pressure type filter, or other means. Often the small volume of filtrate from the mud de-watering stream can be recycled back into the recirculation tank so that any fines in the feedback are again concentrated, thus closing the loop on the continuous process 100% removal system. Cross flow filtration will not do efficient molecular separation. We work primarily with discrete solids but we do separate them totally from the liquid carrier fluid. I know some of you will raise your eyebrows when I say that we remove 100% of the particulate, but in measurement tests, we have measured the filtrate cleanliness with instruments that record as low as .05 ppm and the instruments read zero, so that it is less than .05 ppm.

Jan 1, 1980

By d&apos, K. Mukherjee, C. R. Antonio, R. J. Maciag, G. J. Fischer

Tensile data indicate that over the range of strain rates 10-5 to 10-1 sec-1 and in the temperature range 298° to 743°K the flow stress at a given temperature may be expressed as: C0 = Cem where m changes abruptly at a critical strain rate of 10-2 sec-1. The Zener-Hollomon parameter was tested and found to be invalid except at temperatures exceeding 700° K. Values of AH calculated for temperatures above 700°K ranged from 30 to 47.5 kcal per g-mole. ThE flow characteristics of aluminum and aluminum alloys as a function of temperature and strain rate have been of interest to various experimenters for many years. Trozera et al.1 determined tensile flow curves for pure aluminum and concluded that the combined effect of temperature and strain rate on the flow stress could be related using the Zener-Hollomon parameter. More recently, Hockett2 proposed a relationship between compressive flow stress, temperature, and true strain rate which could be represented by a surface. Holt et al.3 studied strain rate effects on flow stress in a number of aluminum alloys at room temperature. It was determined that there is a critical strain rate above which a strain rate effect is observed. It was also reported that the strain rate sensitivity was significant in aluminum alloys in the "0" condition only. In a recent review paper McQueen4 has considered a number of mathematical expressions which have been used to describe the relationship between stress, strain rate, and temperature. These expressions have been applied to the flow characteristics of a number of different metals and alloys including aluminum. In the present work the strain rate sensitivity of 7075-0 aluminum was determined in the temperature range of 298° to 743°K. The tensile flow stress at 0.2 pct offset was obtained over a nominal strain rate range of 10-5 to 10-1 sec-1. EXPERIMENTAL Threaded tensile specimens were cut from a single heat of 7075-T6 aluminum. The composition of this heat is given in Table I. The test bars had a gage section 1.5 in. long by 0.250 in. diam and conformed to ASTM specification E-8-57T. After machining, the bars were annealed at 413° ± 10°C for 2 hr. They were then cooled to 260°C in 3 hr, and finally air cooled to room temperature. This treatment is commonly used to produce the "0" condition. Load-time curves at constant crosshead speeds were obtained at various temperatures using an Instron testing machine. Crosshead speeds ranged from 0.002 to 40 in. per min. A three-zone resistance tube furnace was used for the elevated-temperature tests. Temperatures were measured at three points along the gage length by means of suitably placed thermocouples. Each tensile bar was held at temperature for 30 min prior to testing and the maximum temperature variation along the gage length was kept below 1°C. In all, 275 samples were tested and each data point plotted is an average of at least two tests. In many cases the point represents up to six tests. RESULTS AND DISCUSSION Values of the flow stress at 0.2 pct offset at six different temperatures are plotted vs strain rate on log-log coordinates in Fig. 1. Over discrete ranges of strain rate, the data for each temperature fit the expression:

Jan 1, 1969

By Erwin Pink

It has been pointed out in a previous publication&apos; that, for a given strain rate, serrated yielding can be observed only at certain test temperatures. Fig. 1 shows the results obtained for polycrystalline and re-crystallized tantalum, Va group in the periodic table of elements, where serrations in the course of deformation match the decrease of total elongation. However, there was no evidence of repeated yielding when testing molybdenum or tungsten, VIa group, at similar conditions, i.e., annealed and air-cooled samples (serrations have been found in quenched tungsten2). The reason for the observed serrations in the stress-strain curve are dissolved impurities on interstitial sites of the lattice. Of importance is the concentration of oxygen, carbon, and nitrogen, which are in random solution. Two methods to calculate the limiting concentrations for serrated yielding have been evaluated and applied with more or less success in estimating the role of carbon and nitrogen in mild steel.3 J. Friedel4 has given two equations, which determine the upper and lower strain rates i for the appearance of serrations at a certain test temperature: W denotes the binding energy of the interstitial atom, -1 ev for refractory metals;5 e&apos; the portion of continuous strain in the discontinuous stress-strain curve, measured as -3x10-3; b the Burgers vector, c the concentration, see Table 11, in atom fractions; p the dislocation density, -2 X l09 per cm2 at an average stress ?, -15 kp per mm2 at medium strain. k stands for the Boltzmann constant, T for the absolute temperature, and D for the diffusion coefficient. Table I. Eq. [1], for a given strain rate, determines the minimum temperature, and [2] the maximum temperature, below or above which no "dynamic strain-aging" can occur. According to the calculation, which uses the given quantities, serrations should only be observed within the cross-hatched temperature regions in Fig. 1, and this is in good agreement with the experiment. The effect of varying impurity concentrations is indicated schematically in Fig. 2: only Eq. [I] is affected. Setting Eq. [I] equal to [2], one can calculate the limiting concentration cmin which first causes serrations. The second method uses the aging condition by Cottrell and Bilby6,7 \£i/ \ n. a / where n(t) is the number of impurity atoms, which segregate at a dislocation line of 1 cm length after the time t (t in our case is the time between "repeated yield drops" in the serrated curve, or, the time until the above mentioned strain E&apos; is obtained, i.e., -1 sec for medium intensity or serrations). no is the number of impurity atoms in 1 cm3 and A = Qb4ep[(1 + v)/(l - v)], derived from equations given in Ref. 7. p is the shear modulus, 18,800 kp per mm2 for tantalum, 12,200 for molybdenum, AE the tetragonal distortion caused by interstitial impurities in a bcc lattice (approximately 0.4 for both tantalum and molybdenum) and v Poisson&apos;s ratio (0.35 for tantalum, 0.30 for molybdenum). From Eq. [3], combined with the condition for a pronounced yield drop as formulated by cottrel16 (at least one impurity atom segregated at the unit length of a dislocation), again a no min, and hence the concentration Cmin can be calculated.

Jan 1, 1970

By J. L. Zakin, G. K. Patterson, J. M. Rodriguez

Correlation has been obtained between drag-reducing characteristics for turbulent flow in a pipe and measurable properties of several polymer solutions. Several concentrations of high molecular weight polymethyl methacrylate in toluene, high molecular weight polyisobutylene in both toluene and cyclohexane, medium molecular weight polyisobutylene in cyclohexane and benzene and low molecular weight polystyrene in toluene were studied. Data obtained in these nonpolar solvents and literature data for more polar solvents were successfully correlated as the ratio of measured friction factor to purely viscous friction factor vs the modified Deborah number vrl/D0.2 where 71 is the first-mode relaxation time of the solution estimated by the Zimm theory. A shift factor which is a function of intrinsic viscosity 1/(4[?] - 1) allowed all the data obtained with nonpolar solvents to be correlated as a single function. For these systems, most of the data fit a single curve to within + 5 percent of the average friction factor ratio. The shift factor did not give a unique function of the data for the more polar systems. INTRODUCTION The phenomenon of drag reduction in polymer solutions was first studied by Toms1 in dilute solutions of polymethyl methacrylate in mono-chlorobenzene. The drag ratio for flow through circular tubes has been defined2 as the ratio of the pressure. drop of the solution to the pressure drop of the solvent at the same flow rate. The drag ratio is less than 1.0 for a drag-reducing fluid. Practical use of drag reduction is being made in fracturing operations in the petroleum industry.3 A more fundamental quantity is the friction factor ratio, defined as the ratio of the observed pressure drop to that predicted for a solution of the same viscosity characteristics and density at equal flow rates using the Dodge-Metzner friction factor equation4 Viscous solutions with drag ratios greater than 1.0 can have friction factor ratios less than 1.0. For practical applications, it is drag reduction which is of interest. However, for correlation the fundamental ratio is the friction factor ratio. In recent years, drag reduction has been studied extensively. Recent studies have shown that reasonable predictions of the incipience of drag reduction in polymer solutions can be made from the properties of the solutions and the flow Variables.5 However, it has not been possible to predict accurately the amount of drag reduction to be expected for a given polymer solution without any drag-reducing turbulent flow data on the same solution.6 For flow through circular tubes it is well established that there is a concentration effect and a diameter effect on drag reduction. Toms1 observed that drag reduction increases with an increase in the concentration of the solution up to an optimum concentration beyond which, due to the increased viscosity of the solutions, the drag ratio increased with an increase in concentration. Hershey 7 observed that for dilute Newtonian polymer solutions in nonpolar hydrocarbon solvents, a normal transition region may be obtained followed by a departure from the von Karman equation (on a friction factor-generalized Reynolds number chart). The point of departure is a function of diameter: the smaller tubes depart at the lower Reynolds numbers. Concentrated solutions may show no abrupt transition region, but merely an