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By H. L. Eiselstein, F. P. Huston, B. B. Betty

An extensive program for the establishment of creep data on high-nickel alloys has been in progress during the past seven years. This paper presents the accumulated data on two solid solution alloys, cold-drawn, annealed Monel and cold-drawn, annealed Inconel. Data on these two alloys in other conditions will be published at a later date. Monel, a nickel-copper alloy, is normally considered a corrosion-resistant material, but it will be shown that it also has considerable creep strength, validating its use at temperatures up to and including 900°F. Inconel, a nickel-chromium-iron alloy, is definitely a heat-resisting alloy possessing good creep strength and oxidation resistance up to iiooOF., and because of its oxidization resistance has been used successfully at much higher temperatures for lightly stressed parts. The literature contains but meager data on the creep properties of high-nickel alloys. Howevcr, Bennett and McAdam have presented a substantial quantity of creep data for cold-drawn Monel.1 The material as tested was not representative of mill production for it was cold-drawn to a reduction of area of 40 per cent as against 13 per cent, which is the mill standard for Monel. Twenty-two individual tests were run on each alloy in the investigation described in the following pages. The data and curves presented herein represent an integration of all the tests to obtain the most accurate picture of the creep properties of these alloys. Neither of the two alloys was found to be embrittled by the combination of temperature and stress, as evaluated by room-temperature tensile and impact tests that were made following creep testing. These data indicate that no tendency toward embrittlement exists. It is recommended that 6300 lb. per sq. in. be used as a working stress for cold-drawn, annealed Monel at 900°F. and 13,200 lb. per sq. in. for cold-drawn, annealed Inconel at the same temperature. Table 8 lists recommended working stresses, based on 80 per cent of the stress to produce a minimum creep rate of 0.01 per cent per 1000 hr., for Monel and some steels. Equipment The equipment used for these tests consists of Colville creep-testing machines manufactured by the Tinius Olsen Testing Machine Co. The load is adjusted, depending on the stress level, to give an error in the stress of not more than ± 0.1 per cent. This is based on considerations of lever sensitivity and the stress used for the standard (A.S.T.M. Tentative Standard E22-38T) 0.505-in. diameter creep specimen having a 2-in. gauge length. The single-specimen furnaces are provided with primary and secondary windings, from

Jan 1, 1945

By David C. Russell

The Department of the Interior used to be a quiet, noncontroversial, almost boring agency. It, after all is the fifth oldest of the Departments, and as an old line Federal agency it has studiously performed its preservation and resource management functions in a caretaker mode--though some would say more "undertaker" than "caretaker"--locking up the body and soul of America piece-by-piece. Yes, quiet, serene. That is until Jim Watt showed up. And we have all seen that version of Mt. Vesuvius which resulted--only it was the environmentalists who blew their tops. Ronald Reagan chose Jim Watt as Secretary of this fine old agency to prove that one-third of our Nation's land and over a billion acres on the Outer Continental Shelf can work for this Nation. At the foundation of President Reagan's charge to Secretary Watt is a belief in the tenets of the free enterprise system, and in the individual freedoms upon which this country was founded. There are those who don't share this belief in democracy and free enterprise, and those who believe this 205 year experiment called the United States of America will fail. Nikita Krushchev said "we will bury you"--obviously he didn't agree with our system. An Italian sociologist, Franco Ferrorotti, said bureaucratic stagnation will kill capitalism. Certainly we have all felt the ravages of bloated bureaucracies. Perhaps one indicator in the United States is the Federal Register, that daily compilation of Government's largesse. In 1970, 20,000 pages of the Federal Register were published. A decade later, in 1980, that volume had quadrupled to 80,000 pages. The Federal bureaucracy can stagnate from excessive budgets as well. The Interior Department spent $60 million on administering Federal coal leasing in 1981. That's nearly two bits a ton for every ton of coal leased in 1981. You wouldn't stay in business very long if your administrative overhead on inventory was that outrageous. But the pessimism of our critics is apparent from more than red tape and bloated budgets. For decades America has been fasting--consuming too little of America's wealth of minerals, subsisting instead on a diet heavily reliant upon mid-east oil, with little emphasis or concern for inventorying and developing domestic energy and mineral resources. Economics--yes. But short-term, short-sighted economics. Excessively dependent upon foreign imports, of oil, cobalt, chrome and other strategic minerals, the U.S. measures its time before another embargo--or fallen Shah, or Soviet manipulation, or Saudi shift, or, as we witnessed in Egypt, assassination--an untimely loss to mankind and efforts to bring peace to the troubled mid-east. These disruptions, in addition to their tragic human tolls, impair the free world's security. Huge chunks of the United States have been locked away in dozens of single land use categories in the name of conservation, with only the foggiest idea of what resources might be denied the American people-and this at a time of unacceptable levels of energy and strategic mineral imports. More than half and perhaps two-thirds of all Government-owned lands are totally withdrawn from or severely restricted to development under the mining and leasing laws. We must continue to rid Government of the overly zealous restraints which have been keeping us from drawing upon that which can help restore our economy and national security. When we assumed responsibility, the United States was dependent on foreign sources for about 40 percent of its oil. In 1981, our oil import bill was approximately $83 billion--nearly 17 times what it was in 1972. Our reliance on foreign sources for essential minerals is even more disturbing. We must look to other countries--some unfriendly, some unstable--for 22 of 36 strategically critical minerals. Yet the energy resources on federal lands which are owned by the American people could meet our needs for centuries if properly managed. Eighty-five percent of the crude oil yet to be discovered in America is likely to come from public lands, as will 40 percent of the natural gas, 35 percent of the coal, 80 percent of the oil shale, nearly all of the tar sands, and substantial portions of uranium and geothermal energy. Our vast hardrock-mineral wealth includes untapped deposits of essential elements we now import, such as chromium, copper, platinum, and cobalt. The obvious question is, if these abundant resources can help to revitalize our economic strength and to preserve our national security, why aren't we using them to better advantage? To a large extent, the answer can be found in past decisions to restrict public access to the federal estate, thus deferring to us or our successors the tough decisions that flow from Congress' mandate to provide for environmentally responsible development of America's energy and mineral treasures. Here is the legacy this Administration inherited: In January 1981, 7 years after the onset of the Mideast oil embargo: ---Less than 15 percent of federal onshore lands were under lease for oil and gas development; ---No oil and gas leases had been issued in Alaska for 15 years;

Jan 1, 1982

By G. Meyrick, H. W. Paxton

Observations on the tensile deformation of single crystals of austenitic stainless steels as a function of composition, orientation, and temperature are described and compared with relevant data for other alloys. Crystals free from second phases show sharp yield points followed by Lüders' extensions of up to 20 pct. The critical resolved shear stress is strongly temperature-dependent increasing fourfold between 423O and 77°K. A temperature-independent low rate of hardening follows the Luders' extension and is frequently associated with overshoot. Unlike pure metals where Proficse cross slip usually occurs at the end of linear hardening, this stage is terminated either by cross slip or by slip on the conjugate system, the particular node apparently depending upon initial orientation and composition. The presence of 6 ferrite or martensite has a profound effect upon the magnitude of the yield stress and the shape of the stress-strain curve. In experiments on transgranular-stress corrosion cracking of austenitic stainless steels in boiling magnesium chloride, several workers1'2 have shown that increasing amounts of nickel tend to reduce the probability of specimen failure. Reed and paxton3 have observed in single crystals that the macroscopic crack plane changes as the nickel content is increased. For 18 pct Cr-8 pct Ni, the crack plane is sensibly perpendicular to the applied tensile stress; for 20 pct Cr-20 pct Ni the crack plane is (100). The average crack-propagation speed is much lower in the 20 pct Ni crystals. Furthermore, the possible importance of stack-ing-fault energy in nucleation and growth of cracks has been suggested by a number of workers. While the general effect of variations in stack ing-fault energy appears to be quite well-correlated with observed variations in cracking characteristics, each of the theories assigns rather different detailed reasons for these effects. Because the stack ing-fault energy of austenitic steels is believed to be increased with increasing nickel content, and because some theories of trans-granular cracking postulate a mechanical stage in the crack propagation (rather than relying entirely on electrochemical solution), it appeared to be of some interest to investigate the mechanical properties of a series of different compositions of aus-tenite single crystals. These experiments were considered of intrinsic value in view of the relative scarcity of such data on fcc alloys. This paper gives the results of some experiments carried out with this aim in mind, and suggests various 'other experiments which may be helpful in future studies. The experiments are also of interest in view of the recent interest in obtaining higher-strength steels by control of the imperfection content of austenite; although the compositions are not directly comparable, the results are still probably valuable. Comparisons with experiments on other fcc alloy crystals are made where possible to see how well the general pattern of behavior is understood. EXPERIMENTAL PROCEDURE The alloys used in this investigation were vacuum-melted heats of nominally 20 pet Cr-20 pet Ni-60 pet Fe, 20pctCr-16 pct Ni-64 pct Fe, and 20 pctCr-12 pet Ni-68 pet Fe.* Analyses of the material are

Jan 1, 1964

By J. L. Gillson

Historically, rock deposits and sand deposits of titanium minerals came into production about the same time, although there may be some argument as to what is meant by production. Beach deposits of heavy minerals in India (Figs. 1-4) and Brazil (Figs. 5) were worked for monazite about the turn of century, but as there was then no market for titanium minerals, these were thrown away. The rock rutile deposits at Roseland, Va., Fig. 6, were worked to supply rutile for titanium chemicals and for coloring ceramics long before there was a titanium pigment business. The pigment industry started about the middle twenties, both in Europe and the U. S., and almost simultaneously the rock deposits at Ponte Vedra Beach near Jacksonville, Fla., were worked for titanium content. Since those days, production from both types of deposits has continued to grow at a rapid rate; many deposits of both types have been found, and reserves have grown to very large figures. In total tonnage of reserves, there is no doubt that the rock deposits are far ahead of the sand deposits; nevertheless there is a very large tonnage of commercial sands available. It is the quality of titanium mineral in the sand and the relatively lower costs of operating sand deposits that have kept them abreast, at least in annual tonnage produced, with the rock deposits. The principal titanium mineral used is ilmenite, but as soon as that mineral began to be sought as a titanium ore, it was obvious that there are ilmenites and ilmenites. Textbook ilmenite should have the composition FeOTiO2 and should analyze 52.6 pct TiO2 and 36.8 pct iron as Fe. The Indian ilmenite, for almost a generation the standard ore for manufacturing pigment in the U. S., was found to analyze about 60 pct TiO, and only 24 pct. Fe, and most of the iron is in the ferric condition. The whole process of pigment manufacture in the U. S. was built up on the use of a raw material of that grade, and the American chemical engineers who operate the pigment plants shuddered at the thought of using a rock ilmenite with 45 pct or so of TiO, and nearly 40 pct Fe. Intensive search was made around the world to find other deposits of rich black sand, like the Indian beaches, but although a few were found, there was some objectionable feature about each. A deposit in Senegal, south of Dakar (Fig. 7), was worked for a while, but an organic coating on the grains made attack by acid difficult. Modern practice would have included a scrubbing operation, in a caustic soda bath, to eliminate the organic coating. Brazilian deposits were numerous, but individually small, and shipping from them difficult. Deposits on the east coast of Ceylon had many attractive features, but the ilmenite analyzed only 54 pct TiO2 and could have been used only with a penalty. Sand deposits with 2 pct ilmenite, like those now worked in Florida, would not have been considered commercial ore, even if they had been known at that time. Most rock ilmenites are associated or mixed with hematite or magnetite, which accounts for the lower titanium and higher iron values than in the sand ilmenites. The Norwegians, English, and Germans, with cheap Norwegian rock ore at hand, learned to install in their pigment plants adequate capacity on the black side, as it is calltd, and counterbalanced the extra cost of plant, and larger amount of acid used, by the lower cost of ore. When World War II arrived, two of the largest pigment manufacturers in the U. S. had to learn how to use the Adirondack ilmenite, but one of them very gladly went back to sand ores when the Florida deposits came into large-scale production after the war. The other continues to use Adirondack ilmenite and finds it commercially attractive to do so. Rutile is not a raw material for titanium pigment manufacture by the sulfate process, since it is insoluble in sulfuric acid. In addition to its small consumption in chemicals and ceramics it began to be used in quantity in welding rod coatings. With the outbreak of World War 11, and the tremendous need for welding rods in shipbuilding and other structural steel construction, rutile suddenly became in heavy demand. The sand deposits on the eastern shore of Australia (Fig. 8A) which had been worked in a small way since 1934 were brought into production, and some stream placers in Brazil were worked and rutile concentrates shipped to American

Jan 1, 1960

By J. A. Putnam, A. D. K. Laird

In laboratory research on the behavior of oil, gas and water in porous materials, no direct method has been devised to measure saturation without disturbing the flow. Indirect methods involving various forms of radiation have been developed for measuring one or two components. The X-ray absorption method for two components has been described previously1-3. The possibility of three component measurement has also been mentioned1. Since two component measurement still requires considerable care to insure accuracy, the fact that three components can be measured satisfactorily is not generally appreciated. The fraction of the energy of an X-ray beam of one wavelength transmitted through a material is given by the transmission factor. in which 1 is the beam's path length through the fluid. p is the fluid density, and 1,. is its mass absorption coefficient. Eq. 1 implies that all parts of the beam pass through equal amounts of the fluid. Practical applications are, therefore, limited to systems in which the fluid is distributed so that I varies negligibly over the cross-section of the beam. Typical variations of the transmission factor with X-ray tube potential arc shown in Fig. 2 from which experimental points have been omitted for clarity. The X-ray absorption of low pressure gases in a core is practically zero so it cannot he distinguished from that a vacuum by instruments that will differentiate between liquids. The transmission factor of a gas in a core is. therefore, unity. Consequently, the saturation of only one gaseous component can be found. If two fluids completely fill a core, their two saturations add to unity and, therefore, only one value of the transmission factor, T, is needed to determine both of them. When two liquids do not completely fill the core, their saturations do not add to unity and transmission factors at two wavelengths must be measured. At one of these wavelengths, 7 for one liquid must be different from T or the other liquid. The change of T for one liquid us the wavelength is changed between the two values must be different from the corresponding change of T in the other liquid. The two values of fluid saturation will also give that of the gas because the three saturations must add to unity. In Fig. 2 it can be seen that there are many large differences of T between various oil solutions and water solutions at any one potential, and between potentials for any one solution. Consequently, conditions for optimum accuracy of measurement of the saturations of a gas and two liquids can be chosen. Once the operating potentials have been selected, however. it is more convenient to cross plot the data from Fig. 2 on transmission factor-solution concentration coordinates for the chosen potentials, as shown in Fig. 3. Fig. 3 was used to plan the experimental procedure for Core N-38-1. Since the voltage control at 45 kv was good, the slopes of the curves in Fig. 2 at this potential would cause little error. At low potentials, however, the voltage control was not good, so 33 kv was chosen because the small slopes of the curves made voltage control less critical. The lowest strength beam that could be measured reasonably at 33 kv corresponded to a minimum T factor of 0.385. Fig. 3 shows that both 4.80 weight per cent of cadmium chloride in water and 24.0 per cent of iodobenzene in crystal oil had this T value, and, consequently, were indistinguishable to the X-rays at 33 kv. Thus, at 33 kv, the liquid saturation was given by the same curve regardless of the relative amounts of oil and water solutions present. This simple calibration curve from which the gas and liquid saturation can be read, is shown in Fig. 4. Fig. 3 also shows that at 45 kv, T for the aqueous solution is 0.610. and that T for the oil solution is 0.220. These values were transferred to Fig. 4 to give the triangular calibration plot from which the brine and oil saturations can be found, after the gas saturation has been determined at 33 kv.

By J. S. Bryner

In the study of metallographic specimens in the electron microscope, there is need for a method of locating the same field in both the light microscope and the electron microscope. This need arises chiefly from the fact that in the electron microscope the magnification and degree of resolution are so much higher, and the field so much smaller than in the light rnicroscope that it is often difficult, if not impossible, to identify positively what is being observed. The difficulty is increased by the fact that, because a transparent film replica of the metal surface must be used in the electron microscope, micro-constituents can be identified not by their color but only by their texture and contours. For these reasons it is desirable to obtain a series of photographs showing the same field in both microscopes in order that the appearance of common microstructures and micro-constituents in the electron microscope may be identified and catalogued for future reference. The need for a method of locating the same field in both microscopes arises also when it becomes desirable to enlarge in the electron microscope for more detailed study a particular interesting structure observed in the light microscope. Using the standard polystyrene-silicalJ replica technique, in which the silica film replica is fished from the ethyl bromide on a 1/8 in. diam zoo-mesh specimen screen, the possibilities of locating a particular area on the film in the electron microscope are rather remote. The desired structure may be obscured by the wires of the specimen screen or unrecognizable at the high magnification. A solution to the problem would be provided if a specially designed specimen screen, containing an opening which could be absolutely identified and quickly located in the electron microscope, could be fastened to the silica film replica in such a position that the desired field on the specimen would be located at the identifiable opening in the specimen screen. The design for such a specimen screen, a method for producing it, and a technique for fastening it to the silica film replica are described below. Description OF Method The Specimen Screen A simple design for a specimen screen containing an opening easy to identify and locate in the electron microscope is one with two lines of openings at right angles in the form of a cross. Such a screen is shown in Fig I. The opening at the center of the cross is identified easily and can be located quickly in the light microscope and in the objective image of the electron microscope. The specially designed specimen screens for this work were produced in quantity by electroforming. On both sides of a polished strip of copper I X 3 X 1/8 in., twenty patterns of the cross of openings were punched with a diamond point micro-hardness tester, using a load of magnitude

Jan 1, 1949

By T. N. Rhodin

There can be two types of films on solids, those which are stable in mono-layers and those which tend to aggregate into three dimensional structures. A great number of metal films formed by condensation onto a solid base are unstable in the sense that they will aggregate into crystals providing the atoms possess sufficient surface mobility. The crystalline structure of the film is strongly influenced by the base in many systems and, in some cases, a single orientation prevails when the force fields around the atoms in the supporting crystal are sufficiently strong.' Relatively little is available in the literature about the nature of these forces and the role they play in promoting a preferred orientation of the atoms arriving at the substrate surface. An understanding of their periodicity and magnitude relative to the surface forces characteristic of the film itself should provide insight into the critical dependence of film orientation on the nature and temperature of the substrate. In addition, this effect may be very useful in preparing samples for surface studies. The study of the physical and chemical characteristics of pure metal surfaces has been severely handicapped by the presence of strongly adherent foreign films. Furthermore, the randomness of the surface orientation has obscured interpretation of experimental results. Evaporation of metals in high vacuum onto carefully selected substrates under ideal conditions for preferred orientation appears suited to the preparation of flat, oxide-free, oriented films for surface reaction studies. Many factors influence their structure and some understanding of the mechanism of their formation is a necessary prerequisite for obtaining satisfactory surfaces for study. The dominant factors in defining film structure are film thickness and growth rate and the nature, condition, and temperature of the substrate. GENERAL ASSEMBLY The system was enclosed in an 18 in. bell jar which rested on an L-shaped neoprene gasket on a ground steel plate as indicated in Fig 1. Rapid evacuation of the system to 10-6 mm mercury was facilitated by a 4 in. manifold, 2 in. packless valve, and an extra large diffusion pump. Suitable arrangement of valves on a secondary manifold readily permitted introduction of purified gases

Jan 1, 1950

By William Johnson

IT is now recognized that several important types of reactions in metallic systems proceed by the formation of nuclei and the growth of these nuclei. The process, of freezing is a simple example of this, as Tammann pointed out years ago.1Tammann held that the rate of freezing is determined by a rate of nucleation, expressed as the number of nuclei formed per unit volume of unfrozen liquid per second, and a rate of growth of these nuclei, expressed as the linear rate of radial growth in units of length per second. For isothermal freezing the conception is simple; for ordinary freezing, extending over a range of temperature, it is not as simple, for the values of the two constants must change with change in temperature. There is ample evidence that the postulated mechanism is correct even though a quantitative derivation of the rate of isothermal or of ordinary freezing in terms of the two constants has been lacking. In recent years other reactions have been found to proceed in a similar fashion. It has been well established, particularly by Bain,2-8 that the formation of pearlite from the eutectoid decomposition of the solid solu-tion austenite proceeds in such a way, and Polanyi and Schmid, Tammann and Crone, Parnop and Sachs, and others'-1 have shown that the process of recrystallization proceeds in a similar way. Isothermal reaction rates have been determined for eutectoid decom-position by a number of investigators. Bain's2-8 work on the formation of pearlite from austenite is especially valuable in this respect-the type of isothermal reaction curve obtained, as illustrated in Fig. 13, showed an initial slow rate, accelerating to an intermediate maximum rate which then decelerated to the completion of the reaction; similar curves have been obtained by Wever and his collaborators.' Other eutectoid decompositions show similar behavior: for example, the decomposition of the beta eutectoid in the copper-aluminum system, studied by Smith

Jan 1, 1939

By Irving Cadoff, Richard Nolder

An analysis oj a series of samples of single -crystal silicon grown on sapphire shows that ,four distinct orientation relations exist. There are at least thirteen crystallographic planes which serve as substrates ,for epitaxial growth The model which assumes that silicon substitutes for aluminium and bonds with the oxygen atoms of the sapphire to form the first later for subsequent growth can account for the epitaxial geometry in all four cases. Multiplici-ties 01 specific orientations are found which are explained by the symmetry of both the sapphire and silicon crystal structures. It was reported in the previous paper' that single-crystal silicon films can be deposited on single-crystal a A1,03 (sapphire) with a wide variety of orientations. The silicon films, however, were found to deposit in only four different orientation relationships with respect to the sapphire substrate. The X-ray data have been analyzed to determine the plane and direction of atomic fit and an atomic model to account for the epitaxial relationships at the silicon-sapphire interface has been developed. These results are described in the present paper. EXPERIMENTAL The Laue X-ray data described in the previous paper were reduced to stereographic projections in a standard manner. These data were supplemented with X-ray reflection data obtained with -& E and A Full-Circle Goniometer (Electronics and Alloys, Inc.) mounted on a Phillips diffractometer unit. The silicon films were thin enough to result in characteristic reflections from the substrate as well as the silicon. The superimposed stereographic projections were analyzed to determine the orientation relationships. Ambiguities were resolved by referring to constructed models of various lattice planes for both silicon and sapphire. These lattice models were also used to develop the model for atom fit at the interface. DATA AND ANALYSIS 1) Crystal Structures. The crystallography of silico-n, which is of the diamond cubic class with a. = 5.4~, is straightforward. The sapphire structure is more complex and generally difficult to represent in pictorial form. It is of the rhombohedra1 class but usually referred to hexagonal axes. The transformation of indices between these two systems can lead to ambiguities which will have bearing on the analysis presented herein. Therefore, the basis used in this paper is described in the appendix. Referred to the hexagonal system, the parameters of sapphire are co = 12.95.&, a, = 4.75~, c/a = 2.73. All parameters are for room temperature. Figs. 1 and 2 illustrate schematically the hexagonal unit cell model of sapphire used for this analysis. The oxygen atoms are assumed to occupy positions in an idealized hexagonal array on basal planes. Their actual positions are in a slightly distorted hexagonal array. The aluminum-atom positions are scaled to their actual positions in the lattice with respect to the basal layers of oxygen atoms. It was found that an idealized model where the aluminum atoms are assumed to lie exactly at the octahedral interstices of the oxygen lattice, similar to that used by ~ronberg,' was not adequate for this study.

Jan 1, 1965

By B. H. Cody

THE Morenci concentrator of the Phelps Dodge Corporation is a part of the project that was completed after five years had been spent in development of the open-pit mine, equipment and process testing in the former No. 6 concentrator, and construction of the reduction works. The reduction works, of which the concentrator is a part, is about a mile and a quarter southeast of Morenci, on the highway that leads up Morenci Canyon. The concentrator has a nominal capacity for the treatment of 45,000 tons of ore daily. The original plant, which has a rated capacity of 25,000 tons of ore daily and is now in its fifth year of operation, began production on Jan. 30, 1942. The addition, to increase the capacity 8o pct, began operation on Dec. 1, 1943. The equipment of the original plant has been described in MINING AND METALLURGY (May 1942). No changes in equipment were recommended for installation in the concentrator extension and only one major change, forced by a shortage of maintenance labor, has since been made. Metallurgical treatment has been altered in some ways as experiments progressed and as labor and economic conditions dictated. No complete description of the operation of the concentrator has been published, so this paper will record such operating and equipment changes as have been necessary, the operating methods that have been developed and the metallurgical results that have been obtained. Descriptions are given in the order of the processes with a flowsheet and an equipment list of each process for convenient reference. The questions asked by engineer visitors have guided the detail in which operation and maintenance are described. During the period Jan. 30, 1942 to Sept. 1, 1946, ore milled has totaled 43,595,253 dry tons, from which 1,643,885 tons of concentrate have been made, containing an indicated production of 783,164,809 lb of copper. The principal results obtained in operation of the concentrator during the years 1942 to 1945, inclusive, and to Sept. 1, 1946 are shown in Table 1. A graphic general flowsheet of the plant is given in Fig I. ORE The Morenci ore that is now being treated is a medium-hard monzonite porphyry in which the principal sulphide minerals are chalcocite and pyrite. A minor amount of covellite is present. Chalcopyrite and bornite have been observed under the microscope. The chalcocite occurs mainly as a coating on pyrite. Some of the coatings are so thick that the pyrite presents the appearance of being an inclusion in chalcocite. Some are less than one micron thick and are barely visible at 500 diameters magnification of a polished cross section. Some chalcocite is present as a dissemination in the gangue. Various oxidized copper minerals are present as a result of oxidation in place but they represent a minor proportion of the copper minerals of the ore body. Oxidation

Jan 1, 1947

By N. S. Stoloff, R. G. Davies

A study has been made of the efject oj different dislocation-precipitate interactions upon the temperature dependence of the flow stress of aged Ni-14 at. pct A1 alloy. It is observed that when the dislocations bow between widely spaced (-20004 coherent Ni3Al particles the flow stress decreases with increasing temperature in the normal way. However, when the dislocations cut closely spaced (-5004 particles the flow stress is independent of temperature from -100 to 600°C, due to a balance between softening of the matrix and an increase in strength of the particles with increasing temperature. The retention of strength at high tempera-tures of commercial nickel-base alloys, which are strengthened by the precipitation of a phase based upon Ni3Al, is thought to be due to the unusual strength properties of Ni3Al. The flow stress of Ni3Al increases continuous1y from -196"C to a maximum at -600"C. It is concluded from a series of thermal-mechanical tests that the sevenfold increase in flow stress over this temperature interval is due to a lattice effect and is not diffusion-controlled. The flow stress of precipitation- or dispersion-hardened materials depends on the resistance to dislocation motion within the matrix and the extra energy required for dislocations to bow between or to cut particles. If the dislocations bow between the particles or if the strength of the cut particles is constant with temperature, then the flow stress of the precipitation-hardened alloy must decrease with increasing temperature due at least to the decrease in elastic modulus of the material. There will be softening also from thermally activated cross-slip or climb, offering an additional degree of freedom for dislocations to avoid particles. For example, in the case of nickel containing a dispersion of thoria,' which most probably deforms by dislocations bowing between particles, the flow stress decreases by about 50 pct between 25" and 650°C. In A1-Cu alloys2 aged to produce the 8" precipitate, dislocations cut the particles, and the flow stress decreases by about 20 pct between -269" and 25°C. However, many commercial high-temperature nickel-base alloys, for example Inconel-X and Udimet-700, exhibit little or no decrease in flow stress with increasing temperature up to about 700°C. A characteristic feature of these alloys is that they are strengthened by the precipitation of a phase based upon Ni3A1. Guard and westbrook4 and flinn' have shown that Ni3Al (and alloys in which a third element such as molybdenum or iron is substituted for part of the aluminum) is unusual in that the hardness and flow stress increase with temperature to a maximum at about 600°C. For the flow stress of a precipitation-hardened alloy to be independent of temperature we propose that the particles must be cut by dislocations moving through the matrix and that the strength of the particle must increase with increasing temperature. Theories of precipitation hardening do not take into account the flow stress of the dispersed particles that are cut during deformation; the only dissipative process usually considered7 is the creation of interface within the particle and between the precipitate and matrix. The purpose of the present investigation has been to study in detail the temperature dependence of the flow stress of a nickel-base alloy strengthened by the precipitation of Ni3Al in two structural conditions such that when deformation occurs it does so by dislocations a) bowing between the particles and b) cutting the particles, respectively. A simple binary Ni-14 at. pct A1 alloy was chosen because considerable information is already available for this system concerning phase equilibria and precipitation reactions and rates.' Dislocation-precipitate interactions in the binary alloy should be similar to those in the more complex commercial alloys. In addition, the mechanical and physical properties of NisAl were studied in detail in the hope of elucidating the mechanism by which the strength increases with increasing temperature up to 600°C. EXPERIMENTAL PROCEDURE For the study of the effect of precipitation of Ni3A1 upon the temperature dependence of the flow stress, an alloy containing 14 at. pct A1 was utilized; a Ni-8 at. pct A1 solid-solution alloy was employed as a comparison material. Vacuum-cast ingots were hot-rolled at 1000°C and cylindrical compression samples, 0.20 in. diam by 0.40 in. high, were prepared from the 1/4-in.-diam rod. Specimens were recrystallized and solution-treated at 1000°C for 1/2 hr and then water-quenched. A preliminary study revealed that, when the Ni-14 at. pct A1 alloy was aged for 1 hr at 700°C, significant precipitation hardening was obtained, and that the structure was free from grain boundary discontinuous precipitation; an overaged condition was produced by annealing the aged specimens at 850°C for 1 hr. To circumvent the difficulties involved in the hot rolling and swaging of Ni3A1, compression samples,

Jan 1, 1965

By E. H. Rose

THE present symposium on flotation machines provides a unique opportunity for group reappraisal of standard or habitual viewpoints. A symposium is by definition a trading post for observations that might prove complementary when put together, thus leading to useful thoughts that might not have been evident from the original observations individually. The present paper, pertaining to power consumption in flotation, is deliberately an experiment of that kind. Data were solicited from the operating superintendents of several of the major flotation plants on this continent. The information received, covering a total of 14 separate operations in seven plants, has been collated in terms of power intensity; that is, the total power input per cubic foot of cell volume. This departs somewhat from the conventional expression of power per ton of ore treated, though the latter figure is also given for the plants concerned. Because of wartime restrictions, particularly in Canada, identifying names of plants and machines are withheld. Not as a firm conclusion, but as a tender for symposium discussion, the following points are made: I. That flotation is a power operation in much the same sense as ball milling. 2. That contact time is the complement of power intensity and may be decreased as the latter is increased. 3. That a decrease in flotation power per ton of ore can result from an increase in power intensity. ANALOGY WITH GRINDING In grinding, it has become axiomatic that the more the power put into a given operation, the greater the work performance. The analogous view is now proposed that the effectiveness of any flotation operation will be related to the mechanical energy usefully applied to that operation. Under this view, each increment of properly directed input energy should give either an increase in unit tonnage or an improvement in the metallurgical separation (concentrate grade or tailing grade), until either the theoretical limit imposed by mineral constitution or surface condition is reached, or until further increments of power become uneconomic under the law of diminishing returns. Thus, as in grinding, there are two forms of output that greater power input or improved utilization of power can produce. As for the law of diminishing returns, lower unit cost of power through improved generating efficiency in the past decade has pushed the limit back. Over and above this, however, there is strong indication in the operationg data herein presented that higher power intensity results in an actual economy of over-all power consumption. Like crushing and grinding, flotation accomplishes a rupture of the forces of molecular attraction, by taking particles from the common environment and placing them in the two separate environments of

Jan 1, 1944

By P. E. Hildebrand, S. W. Mao, C. N. Crain

Hydrologic and economic criteria figure in many obvious ways in water resources development, but they are rarely linked quantitatively, and most of the applications are pertinent only to the case in point. In the preparation of a regional plan for the massive program of groundwater development in the Punjab, situations have arisen where the choice among two or more alternatives was made by analyzing the economic implications of critical hydrologic parameters. Two of these situations which are of more or less general interest are described herein. The first involves basic development policy, i.e., the question of whether groundwater development should be based on the demand of the economy, or the conservation concept of safe yield. The analysis demonstrated that mining of groundwater is clearly indicated for areas where alternative supplies are unavailable. The second problem involves integrating hydrologic data into an economic model to determine optimum well design. From an analysis of all pertinent factors, a simple nomograph was derived for determining well specifications on site during construction. The nomograph can be modified for use in any alluvial terrain. In the Northern Zone of the Indus Plains —the region known as the Punjab- Pakistan is proceeding with integrated development of water and land resources on a scale never before contemplated. The heart of the development plan is a massive program of groundwater development to supplement canal irrigation supplies and to provide drainage relief to the irrigated lands. By the close of 1966 about 2500 high-capacity wells were in operation and furnishing the water supply and drainage requirements for nearly two million irrigated acres. The development plan calls for the construction of a total of nearly 30,000 wells with an aggregate capacity of 120,000 cfs by 1980. This is part of an integrated program eventually affecting over 20 million acres of irrigated lands. [This development program is administered by the West Pakistan Water and Power Development Authority (WAPDA) for which the firm of Tipton and Kalm-bach, Inc. serves as regional planning consultant for the Northern Zone. The material presented herein is derived from planning studies which have been made in connection with the preparation of a regional development plan for the Northern zone.] Pakistan is proceeding with this large-scale development of land and water resources at a time when she is at the threshold of an almost calamitous population growth. Furthermore, she is attempting this development at a time when most of her usable land is already occupied and her food demands exceed current production. Here in the Northern Zone is one of the largest continuous areas of irrigated land in the world, easily irrigated, with a warm, dry climate and ample potential supplies of surface water and groundwater. Except for an abundance of land and labor, other primary resources are lacking or in very limited supply. The agriculture sector so dominates the economy that only by means of an effective development of the agricultural resources can other sectors grow and contribute to a viable economy. Because of inadequate irrigation, farming here has not effectively participated in the twentieth century revolution in agriculture, and only by means of massive development of potential supplies can Pakistan catch up. Capital for any kind of mass development must come from the outside. But the overriding restraint to development of the land and labor resources is the availability of water. ECONOMICS OF DEVELOPMENT The decision-making process in planning regional development becomes increasingly complex as the various sectors of the economy become more highly developed. Where, as in this case, one sector dominates the economy and its development can be considered the key to development of other sectors, the decision-making process is simplified and it is easier to identify alternatives and to trace the prob-

Jan 1, 1970

By F. R. Archibald, F. C. Jackson

The. prospect of winning aluvinum from clay was recorded almost a century ago at a time when the metal was no more than a curiosity.$ As the industry developed, and it has probably developed faster than that of any other metal, the expanding need for raw materials was adequately met by the ample supplies of bauxite ore. As with the other metals older in industry, however, lower grade ores have gradually entered the raw-material field through improvements in ore dressing, insufficienoy of high-grade ore supplies, favorable geographic location, or national necessity for domestic supply. So with aluminum, or alumina, which has been established as the requisite intermediate, the time may have come when a satisfactory process, with favorable location and suitable raw materials, can hold a sound place both in metallurgy and economics. It is the purpose of this paper to describe the Ancor process and its proposed application in treatment of clay in a plant now under construction at Harleyville, South Carolina, by the Defense Plant Corporation. Development of the AncoR Process The Ancor process has developed through successive stages of laboratory investigation, pilot-plant demonstration using neph-eline syenite and pilot-plant demonstration using kaolin-type clay from South Carolina, and is now in preparation for unit trial on an operating plant basis using the latter material. The laboratory studies were carried out over a number of years in the laboratory of the American Nepheline Corporation in Rochester, N. Y., and for the same company in the ore-dressing laboratory of Beattie Gold Mines, Que. Ltd. at Dupar-quet, Quebec. Both companies are associated with Ventures Ltd., Toronto, and its associated American companies. The work was originally undertaken with a view to recovery of alumina and alkalies from nepheline syenite as an adjunct to the American Nepheline Company's established business in the glass and ceramic trades, but as a process developed the possibility of application to clay and other aluminous raw materials became apparent and the laboratory studies were broadened to include these as well. Under the more pressing impetus of wartime needs and possibilities, pilot-plant operations were undertaken at the Canadian Bureau of Mines Ore Dressing Laboratories in Ottawa, and for purposes of demonstration under joint sponsorship of the Canadian Bureau of Mines, The American Nepheline Corporation, and The Aluminium company of canada Ltd. Upon completion of this program, of

Jan 1, 1944

By T. Egleston

THE manufacture of charcoal in kilns was declared many years ago, after a series of experiments made in poorly constructed furnaces, to be unprofitable, and the subject is dismissed by most writers with the remark that in order to use the method economically the products of distillation, both liquid and gaseous, must be collected. It is asserted with truth that the number of kilns required for a large production of iron would be so great that it is doubtful whether any works would be justified in making the necessary outlay for their construction, but it can also be asserted with equal truth that for any such production in a given locality the use of charcoal as fuel would be equally unjustifiable. It appears to have been forgotten that there were other manufactures besides iron in which large amounts of charcoal were used, but these consumers seem to have been guided entirely by the results of the experiments of the iron men, who necessarily made the largest quantity of it. Some authors speak in a doubtful way of the quality of the charcoal produced, and a few concede that with great care good charcoal can be made in kilns, but that most of the workmen do not like kiln charcoal. This is the real secret of the opposition to this method of manufacture. Most of these objections were written when charcoal was the most important fuel used by the iron manufacturer, and when what was a large production of iron for several furnaces was less than that produced by a single modern one, in localities where other fuels can be had. Almost all that has been written on the subject related to the use of the fuel for the manufacture of iron in the blast furnace, where very peculiar properties are required, and where the quantity produced is limited by the height of the furnace, and this in turn by the crushing resistance of the charcoal. A large production was, therefore, only possible when the best and hardest woods were used. Of all these objections there is not a single one which is not equally applicable to any method of charcoal manufacture, whether it be meilers, pits, or furnaces. Until recently, therefore, the manufacturers of charcoal iron * Read at the Pittsburgh meeting, May, 1879.

Jan 1, 1880

By C. M. Wayman, G. R. Srinivasan

A metallographic study of the isothermal products formed between 750° and 285°C was made in an Fe-7.9 wt pct Cr-1.11 wt pct C alloy, and a time-temperature-transformation diagram was determined. The study shows that the austenite decomposes into three different products: pearlite above 540°C, ferrite and carbide between 540° and 300°C, and lenticular bainite below 300°C. No upper bainite forms in this alloy. The results are discussed in terms of carbon diffusion models for upper bainite formation. AUSTENITE transforms into several products depending on the temperature, composition, and rate of cooling, and the various transformation products have been a source of controversy for a long time. Since the classical study of Davenport and ~ain' extensive work has been carried out. The present study concerns the isothermal transformations in an alloy which was used for a detailed investigation of bainite crystallography and provides information supplementary to the work of Lyman and Troiano who studied austenite decomposition in steels containing 1 pct C and varying amounts of chromium. Their work showed that increasing the amount of chromium in high-carbon steels had the effect of depressing the B, temperature and of shifting the TTT curves to longer times and lower temperatures. They further found that if the chromium content is increased in a 1 pct steel to about 9 pct no bainite would form even after a period of 100 days. However, a preliminary investigation by the present authors showed that bainite plates do form in steels containing about 8 pct Cr and 1 pct C. In view of this and some results from a thin-foil electron microscope investigation of the bainite formed in the present alloy: it was considered desirable to investigate the other isothermal products as well. EXPERIMENTAL PROCEDURE The alloy used in the present investigation was obtained from a triply vacuum-melted ingot prepared from high-purity materials. Chemical analysis for the alloy verified the composition to be Fe-7.9 wt pct Cr-1.11 wt pct C. Metallographic observations were made on i by i by « in. specimens which were aus-tenitized at 12 50°C for 50 to 60 hr in evacuated quartz capsules and then water-quenched. Since the M, temperature for this alloy is below room temperature, the homogenizing treatment produced a completely austenitic structure consisting of very coarse austenite grains (ASTM #0-1). Several samples of the austenitized specimens were metallographically prepared and observed for any proeutectoid carbide separation. It was found that all the carbon was in solution. The water-quenched specimens were upquenched and given isothermal treatments at temperatures between 285" and 750°C for varying periods in molten salt or lead baths. The specimens were then water-quenched, and those showing less than 5 pct transformation were used for plotting the beginning of the austenite decomposition. To ensure the removal of the disturbed layer, the mechanically prepared specimens were electropolished in a 1:6 HzS04, CHSOH solution for 10 to 15 sec at 20 v. Final polishing was done with a vibratory polisher using 0.05-p alumina. Various etchants including nital, ferric chloride, and hot ferricyanide (Murakami's reagent) were used to bring out details in the different transformation products. The ferricyanide etch was used whenever the preferential etching of carbides was desired.

Jan 1, 1969

By S. Stutz

COAL, like most other minerals, only exceptionally occurs in a sufficiently pure state to he directly available for general manufacturing purposes. And even where this is the case, the small coal or slack is usually more impure than the lump coal, as the slate, clay, etc., from the roof and bottom of the vein become mixed with it in the handling it undergoes. These impurities often exceed ten or more percent in addition to the impurities of the coal itself. The most common impurities of the coal are slate, or shale, clay, and sulphur. The latter occurs in different forms, but most frequently as bisulphide of iron, or iron pyrites, and as sulphate of lime, or gypsum. In both cases the impurities add greatly to the amount of ash, and where they are present in considerable quantities the raw coal, and still more the coke made from it, is unfit for the, manufacture of iron. Coke will contain on an average at least ;fifty per cent, more ash and sulphur than the raw coal from which it is, made. To the manufacturer of iron every additional per cent. of ash which his coal or .coke contains is a source of additional expense, seemingly small, and yet very important in the aggregate. In the blast-furnace, for instance, the ash must be heated up to the melting-point, and, since it is composed largely of refractory substances, the consumption of carbon in melting it will be equal to at least one-half of its weight ; that is, a certain part of the coke is consumed for the melting and fluxing of the ash and is lost. Besides this, it is well enough known to the-iron-master that coke containing less ash makes the slag or cinder more liquid and less inclined to stick to- the walls of the furnace. Fuel containing much sulphur produces generally a white iron, poor in carbon, while from the same ore and flux, with a pure fuel, a good foundry iron might be obtained. The work of separating slate, sulphur, etc:, from the coal 'has as yet only been succesafully accomplished by the washing process. This process depends for its success on the differences in the specific

Jan 1, 1881

By Richard V. Hughes, Rudolf J. Pfister

The necessity for getting more water into sands of low permeability in any secondary-recovery water-flood operation in order to recover all the available oil always has been a major problem. In the early days of water-flooding the addition of soda ash and caustic soda to fresh input waters was recommended and tried without success in the Bradford field. The most frequent difficulty was sand plugging. The use of natural and artificial brines often has been suggested for water-flooding, in the belief that laboratory observations of decreasing fresh-water throughput rates in measuring water permeabilities of consolidated sand cores might be partially explained by swelling of clays. A review of available literature bearing on the subject and related laboratory experiments are presented herein, offering an explanation for failure in use of soda ash and caustic soda waters and supporting the recent concept that every water used for input purposes in the secondary recovery of oil should possess such physical and chemical characteristics as to keep the clay content of the producing sands in a permanently flocculated condition. Produced brines meet this requirement. Their use is recommended as a means of increasing intake rates of tight sands and oil recoveries, as a solution to brine-disposal problems, and as a means of conserving a natural resource. Introduction There is a general belief among those engaged in the secondary recovery of oil by water-flooding that one of the most important requirements for the success of any such project is an adequate supply of good, fresh water. Fresh waters have the advantages of being more easily stabilized than salt waters and of being usable about the lease for all purposes. The use of brines for water-flooding never has been given much consideration in the Pennsylvania Grade area. The use of brines in Mid-Continent operations has been considered largely as a substitute for fresh waters, which were economically unobtainable for many operations. Estimated recoveries for some water-drive fields indicate that less of the original oil in place will be left upon abandonment than with the above-average practices used in Pennsylvania Grade water-flood operations. Lower residual oil saturations than 25 pct of the pore space following the water-flooding of Third Bradford sand cores in the laboratory are unusual. In comparison, water-flushed sands surrounding any virgin oil pool are found to be practically devoid of oil. Such lower natural residual oil saturations may be the result of a time factor much longer than economic under artificial water-flood operations, but neither the producer of primary oil nor the producer of oil by secondary recovery can obtain maximum recoveries unless full advantage is taken of all natural forces and

Jan 1, 1947

By Richard V. Hughes, Rudolf J. Pfister

The necessity for getting more water into sands of low permeability in any secondary-recovery water-flood operation in order to recover all the available oil always has been a major problem. In the early days of water-flooding the addition of soda ash and caustic soda to fresh input waters was recommended and tried without success in the Bradford field. The most frequent difficulty was sand plugging. The use of natural and artificial brines often has been suggested for water-flooding, in the belief that laboratory observations of decreasing fresh-water throughput rates in measuring water permeabilities of consolidated sand cores might be partially explained by swelling of clays. A review of available literature bearing on the subject and related laboratory experiments are presented herein, offering an explanation for failure in use of soda ash and caustic soda waters and supporting the recent concept that every water used for input purposes in the secondary recovery of oil should possess such physical and chemical characteristics as to keep the clay content of the producing sands in a permanently flocculated condition. Produced brines meet this requirement. Their use is recommended as a means of increasing intake rates of tight sands and oil recoveries, as a solution to brine-disposal problems, and as a means of conserving a natural resource. Introduction There is a general belief among those engaged in the secondary recovery of oil by water-flooding that one of the most important requirements for the success of any such project is an adequate supply of good, fresh water. Fresh waters have the advantages of being more easily stabilized than salt waters and of being usable about the lease for all purposes. The use of brines for water-flooding never has been given much consideration in the Pennsylvania Grade area. The use of brines in Mid-Continent operations has been considered largely as a substitute for fresh waters, which were economically unobtainable for many operations. Estimated recoveries for some water-drive fields indicate that less of the original oil in place will be left upon abandonment than with the above-average practices used in Pennsylvania Grade water-flood operations. Lower residual oil saturations than 25 pct of the pore space following the water-flooding of Third Bradford sand cores in the laboratory are unusual. In comparison, water-flushed sands surrounding any virgin oil pool are found to be practically devoid of oil. Such lower natural residual oil saturations may be the result of a time factor much longer than economic under artificial water-flood operations, but neither the producer of primary oil nor the producer of oil by secondary recovery can obtain maximum recoveries unless full advantage is taken of all natural forces and

Jan 1, 1947

By W. G. Bearden, P. P. Scott, G. C. Howard

This paper concerns the rupture or breakdown of rock formations as related to drilling, completing, and stimulating production of wells, and comprises data compiled from a study of literature and records of treatment of oil and gas wells. and from tests conducted in bores drilled into rock cores and outcrops of rock. Results of the investigation indicate that the internal pressure to rupture cylinders of rock and to breakdown rock formations surrounding a bore in the earth is dependent upon the extent of intrusion of fluids. the position of bedding planes. the ratio of internal to external diameter, the tensile strength of rock, and magnitude of confining pressure, and is independent of the size of bore, degree of fluid saturation. and temperature of rock within practical limits. It is concluded that the mathematical relationship of pressure in bores and stresses in the surrounding rock must not be limited by the simplifying assumptions of homogeneity. isotropy, and impermeability; that the incidence of lost circulation of drilling fluids to induced fractures may be reduced by preventing intrusion of fluids into the small intrinsic fractures along weak bedding planes; and that the magnitude of the breakdown pressure of wells to be treated may be lowered by removal of mud cake. INTRODUCTION The purpose of this paper is to present and discuss the results of tests which may serve to broaden the understanding of the phenomena of rupture or breakdown of rock and thus contribute to the improvement of the techniques for drilling and completing wells. including such operations as preventing lost circulation, stimulating production, and placing cement. Since the early recognition of the possibility of rupturing rock adjacent to a well by fluid pressure, the distribution and magnitude of stresses around a well and the internal pressure to cause failure have been expressed mathematically by application of the principles defining the elastic and inelastic behavior of thick-walled cylinders of a homogeneous. isotropic, impermeable material. In either the elastic or plastic state, if the conditions of homogeneity. isotropy, and impermeability were the normal characteristics of rock. there would be no reason to question the validity of the above principles when applied to rock. However. since most rock formations are characteristically permeable to some degree, contain bedding planes and small intrinsic fractures. and are heterogeneous, rendering invalid the assumptions of homogeneity, isotropy, and impermeability, the application of the thick-walled cylinder theories to the behavior of rock formations penetrated by a bore appears illogical. Also the failure to consider the effect of the properties of the drilling fluids, which certainly intrude in various degrees into most rock formations. is further cause for questioning the application of these principles. Even in the case of cylinders of hardened chrome-nickel steel, which would he considered relatively homogeneous isotropic. and impermeable, as compared to rock, it has been observed that the internal pressure capable of being withstood by the cylinders varied with the sizes of molecules comprising the rupturing fluid used. Because of these apparent weaknesses in the theories of the behavior of thick-walled cylinders when applied to bores in rock, and the importance of knowing the true behavior of rock under the influence of fluid pressure when planning drilling and completing procedures for wells, tests were undertaken to determine by observation the actual rupturing pressure of cylinders of rock and the effects of such variables as environmental conditions and characteristics of rock formations, fluid properties, and bore dimensions. It was intended that by these tests the validity of the thick-walled cylinder theories when applied to rock would be determined and, if found invalid, mathematical expressions would be derived for predicting stress and rupturing pressure of rock formations under various conditions. Since the derivation of mathematical expressions has been only partially completed, all of the results of the latter phase are not included in this paper. PROCEDURE The investigation was initialed with a study of the theories pertaining to the rupturing of thick-walled cylinders of homogeneous. isotropic, impermeable material and a study of the

Jan 1, 1953