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This issue presents the first of several articles making up the Bump Symposium, which was held at the 1958 Annual Meeting of AIME. Other Symposium papers will appear in the September issue of Mining Engineering. THE term mountain bump describes the sudden rupture of one or more coal pillars under excessive stress. These bursts occur with varying degrees of violence and sometimes include adjacent strata, especially the bottom rock. Many failures do not develop enough violence to be dangerous and are regarded as an aid to coal production, but severe occurrences are accompanied by tons of flying coal, dense clouds of dust, and excessive gas emission. Such bursts sometimes throw heavy machinery several feet. Major factors to be considered in the problem are the nature of the strata above and below the seam and the depth of cover. Bumps are classified as to their nature, extent of damage, and point of occurrence, e. g., face bump, coal bump, high side bump, low side pavement bump, and district bump. The problem is extremely complex, and it cannot be over-emphasized that preventive measures, if they are to be successful, must be based on a thorough study of conditions in the individual mine. In western Canada, for example, the McGillivray mine, operating in a 9-ft seam at 2000 ft, has experienced severe bumps, but there have been no occurrences in the International mine, which operates in the same coal seam at 2400 ft, where the coal averages 17 ft thick. Differences in conditions governing the operation of these two mines are described in one of the following articles (see page 883). Again, most bumps in coal mines take place along pillar extraction lines, but at the Sunnyside mine in Utah they also occur a long way from active workings and sometimes in virgin territory. It is usual, too, for such failures to occur under fairly deep cover. But at Sunnyside, to cite only one instance, there have been disturbances along the main fault zone under less than 500 ft of cover. All too often conditions favorable to bumps are revealed only by actual mining—at Springhill No. 2 mine, drilling in roof and pavement strata disclosed a 60-ft sandstone bed after operations had started— and where extraction has advanced too far for preventive measures to be incorporated in the mining plan, districts have had to be abandoned. But in an era when premium ores are being rapidly depleted in the face of rising demands, abandonment is not easily justified. There must be systematic planning to eliminate coal mine bumps, insofar as this is possible. As in the Gary district of West Virginia (see page 888) much has been accomplished by planned operations based on known factors in bump control. But even this is not enough. Precise instrumentation is needed to indicate where bumps are likely to occur, and in both the U. S. and Canada stress analysis studies are being carried out with this object in view. These pages reveal the progress being made.

Jan 1, 1959

By Anal J. Mehta, Theodore D. Tiemann

Growing demand for steel and increasing dependence upon foreign ore makes the need for developing the technology for treatment of low-grade iron ores greater than ever before• Representative of these added interests were the studies carried on at the University of Wisconsin• These studies included among others: anionic and cationic flotation, magnetic separation, roasting followed by magnetic separation, electrostatic separation, a hydrogen reduction process,6,7 and caustic digestion• The idea of removing silica by caustic extraction is not new•-1; The principle of concentrating siliceous iron ores by this method is based on the fact that silica is soluble in sodium hydroxide solution while iron oxides are essentially insoluble• For this process to be economically feasible, it is believed that some method of recovering silica from solution as a marketable by-product, with recycling of spent liquor is necessary. Precipitation of silica with carbon dioxide will allow subsequent causticizing of the spent liquor with lime• Caustic thus produced can be recycled for digestion• A flowsheet of the envisioned process is given in [Fig• 1] The purpose of this paper is to describe results obtained from the investigation of carbon dioxide precipitation of silica from sodium silicate solutions, which could be later applied to the caustic extraction process to treat low grade siliceous iron ores, particularly taconites.15 Theoretical Considerations The soluble silicates of sodium include sodium orthosilicate (2Na2O•SiO2), sodium metasilicate (Na20•SiO2), sodium disilicate (Na1O•2SiO2), and more highly siliceous products approaching Na2O•4SiO2• These materials have been described in detail by Vail•16 Stones has reported that the extraction of silica is not significantly affected by the amount of silica in solution until the Si02/Na20 ratio exceeds that of orthosilicate (Ratio = 1/2)• However, as the Si02/Na2O ratio exceeds that of metasilicate (Ratio = 1), silica extraction is significantly impaired• The present experimental work was confined to orthosilicate and metasilicate solutions, as to be successful the envisioned commercial process for the extraction of silica from siliceous iron ores would operate in this region. The mechanism of extraction of silica from aqueous sodium silicate solutions is complex in nature. For the carbon dioxide process-18 of core and mold making in which silica is also precipitated from sodium silicate solutions by gassing with carbon dioxide, the reaction of aqueous silicates with gaseous carbon dioxide has been represented by the equations: [ ] However, these equations are very much oversimplified• It has been shown that the reaction between aqueous sodium silicates and carbon dioxide gas is ionic in nature 18 Considering this fact and the mechanism for digestion of silica in aqueous sodium hydroxide, the overall conversion of aqueous sodium silicates to solid silica may be represented in ionic form by the following equations: [ ] Silicon in the silicate ion is shown here with a coordination number of 6• This may be in doubt, but it is known that ion (SiF°)-2 exists; it seems logical that the Si (OH) e 2 ion should be equally capable of existence•

Jan 1, 1977

By Caudle B. H., Cooper H. E. Jr., O. K. Kimbler

The results of studies of areal sweepout behavior in nine-spot injection patterns are presented in this paper. The ratio of the production rates of the two types of producing wells in a nine-spot pattern is considered in its effect on breakthrough. A model study was used to develop a method to predict the production histories of both side and corner wells and to develop the production history of the pattern or the field. INTRODUCTION The importance of areal sweepout behavior in injection operations has been recognized for a number of years. We now know that the fraction of a reservoir which will be reached by an injected fluid is a function of the geometric arrangement of the production and injection wells and of the mobility ratio of the fluids. Of these two, the mobility ratio (which is a measure of the relative ease with which the oil and the injected fluid can move through the reservoir) appears to have the greatest effect on recovery. The effect of mobility ratio on production history has been reported for most of the dispersed injection patterns (i. e., five-spot, staggered and straight-line drives).4-6 ere has been very little published on the nine-spot injection pattern. This may be because the two types of producing wells in the nine-spot pattern can—and sometimes should —be produced at different rates. This adds a second variable (the fist being mobility ratio) to be covered in a study of the nine-spot flooding network. Muskat1 has reported the sweep pattern efficiency at breakthrough for a mobility ratio of one at various ratios of producing rates for the two types of wells. For these conditions he found maximum oil production at breakthrough to occur when the corner well (the producing well farthest from the injection well) is produced 10.7 times as fast as the side well. Other investigatorsa2,3 have studied a few of the many possible operating conditions possible with this injection pattern. This paper presents the results of studies which are strictly applicable to a nine-spot injection pattern surrounded by other nine-spots in a homogeneous reservoir and which has no flowable gas present (no oil bank is formed). Although the full ranges of the variables mentioned above have not been covered, the results reported here should allow reasonable estimates of field operations to be made. EXPERIMENTAL The well spacing geometry of the nine-spot pattern is shown in Fig. 1. Here we see that each injection well is surrounded by eight production wells arranged in a square. Four of these producing wells are located at the corners of the square; the other four are in the midpoints of the four sides. These two types of producing wells are called "comer wells" and "side wells" respectively. It is the ratio of the producing rates of these two types of wells that affects the breakthrough recovery, as calculated by Muskat.' This ratio is defined as the total producing rate of a corner well divided by the total producing rate of a side well. The model used in this study represented one-eighth of a nine-spot pattern, as shown in Fig. 1. It contained the equivalent of one-fourth of a side well, one-eighth of a comer well, and one-eighth of an injection well. Because of these proportions, the actual producing rate ratios in the model were one-half of the ratios of producing rates as

Jan 1, 1965

By Hsun Hu

Direct observations were made on the recrystalli-zntion of a cold-rolled (110) [001] crystal of 3 pct Si-Fe by annealing thin sections of the specimen inside the electron microscope during examination. Subgrain formation, presumably by polygonization, occurs rapidly, followed by a slow increase in the subgrain size before recrystallization can be detected. No migration of the subgrain boundaries was observed, and the formation of recrystallization nuclei by coalescence of subgrains is suggested. Re-c~ystallization characteristics of various texture components were individually examined. AS reported in a previous paper: orientations of the various deformation texture components in a 70 pct cold-rolled (110) [0011 crystal of 3 pct Si-Fe were completely confirmed by transmission electron diffraction patterns taken at various areas of the specimen. These orientations can be summarized as follows: Over most areas of the deformed crystal (111) planes are parallel to the surface. These areas correspond to either $- the two main defor: mation textures, the (111) [112] or the (111) [112].2-5 Within a few areas, (100) planes parallel to the surface are frequently found. These areas represent the minor deformation texture component, the (100) [Oll] type, which is derived from rotated Neumann bands.2'4'5 Only in very rare instances are (110) planes found parallel to the surface. This orientation corresponds to the very weak texture component of the (110) [001] type. In a pole figure, this (110) [0011 orientation is located within the orientation spread between the two main (111) [1121 type textures. Usually the electron diffraction patterns taken at various areas of the specimen are very simple ones, i.e., for any one area the pattern consists only of sharply defined spots of a single orientation. In some areas, however, more or less continuous rings of weaker intensities are superimposed on a simple pattern, indicating the presence of a wide range of additional orientations. In order to understand in detail the recrystallization of this cold-worked crystal, the recrywtallization characteristics of each of the various deformation texture components must be examined. This can best be done by using a high-temperature stage and transmission electron microscopy techniques, whereby small areas corresponding to the various texture components can be selected individually for examination. The present paper presents results obtained by this method. MATERIAL AND METHOD Specimens were prepared from a previously studied1 single crystal of a commercial grade 3 pct Si-Fe alloy with an initial orientation (110) [00l], cold-rolled 70 pct from 0.014 in. to 0.004 in. in thickness. Thin foils were prepared by electrolytic polishing as described in the earlier paper.' Specimens of this thin foil were then mounted in a high temperature stage similar to the one designed by Whelan.6 A direct current was used as the heating source. The temperature of the heating grid was calibrated by means of a Pt vs Pt-10 pct Rh thermocouple in a vacuum chamber (0.01 to 0.02µHg). Maximum variation within the temperature range of 250o to 000°C was about ± 25°C. After the desired areas were selected for examination, the specimen was heated to a low temperature for some time while the selected area was constantly watched. When no further change in structure and orientation could be observed, a higher temperature was applied. Photomicrographs and diffraction patterns were taken from time to time during examination, with the heater temporarily turned off* while the photographs were

Jan 1, 1962

By A. O. P. Casbarian

An analytical method is developed to determine the variation of the ultimate lateral resistance of a plate in a cohesionless soil with depth. This analysis is based on a modification of Rankine's classical earth pressure theory and the theory of plasticity as applied to soils. The ultimate resistance is defined as the product of the effective stress at the midpoint of the plate, the area of the plate and a dimensionless variable termed the ultimate resistance factor. This variable has been plotted us the depth ratio: i.e., the ratio of of the depth of embedment us the height of the plate. The resistance of a plate may then be calculated using the values af the ultimate resistance factor from the chart provided or the equation may be programmed for use in an analysis of anchor systems in cohesionless soils. It is emphasized that the analysis is semitheoretical. The theory has been compared with experimental results reported in the literature and results indicate general agreement. Actual field tests are necessary to further verify this theory. INTRODUCTION With the exploration for oil offshore in waters all over the world, it is of importance to determine the behavior of the various soils in relation to their ultimate resistance to deformation. Examples of such problems are the holding capacity of anchors and the lateral resistance of piles. Very little information is available in the published literature on the design and performance of anchors, in either cohesive or cohesionless soils. The analysis developed in this report is the first step in obtaining a solution for the determination of anchor holding capacity in a cohesionless material. DISCUSSION The theory used in the analysis is based on the ultimate strength of the soil and is the maximum resistance developed by the plate against further movement. In such a state the elastic deformations are disregarded in comparison with the plastic deformations. Hence, the plate can be considered as completely rigid. The theory of plasticity determines the three unknown stresses at any point by means of two equilibrium conditions for a small earth element in combination with the failure condition. However, the exact solutions can only be carried out in a few simple cases such as, for example, when the rupture or failure lines are straight (Rankine theory) or with spiral and straight rupture lines (Prandtl theory).l Kiitter 2 derived a single equation expressing the variation of the stress in any given rupture line. To utilize this equation, it is necessary to know the stress in the rupture line at a certain point. Unfortunately, this is difficult to obtain unless the rupture line intersects the free surface at a certain angle or when the earth is cohesion-less and unloaded. A method to overcome this is to consider only the boundary conditions at both ends of a rupture line without investigating the equilibrium of the earth above the rupture line. This assumes that the rupture lines meet the surface at statically correct angles, so that boundary stresses may be determined. As Kiitter's equation furnished a relation between these stresses, the unit earth pressure may be calculated at the point where the rupture line meets the wall. Another way in which Kotter's equation may be applied is in investigating the equilibrium of a soil mass above a rupture line. This method assumes that the failure or rupture line is known and that the boundary stresses in the rupture line at the ground surface can be determined. In this case it is possible to determine the earth pressure from the equations of equilibrium.

Jan 1, 1967

By Frank Woolley, John F. Elliott

The high-temperatzrre solulion calorimeter has been modified and an extension dynamic analysis of i/s transient behavior has provided an improved basis for interpretation of the experimental data. The partial molar heats of mixing, Him, of aluminum, copper, and silicon in the corresponding binary liquid-iron alloys haz,e been measured directly at 1600°C. The resulls in kcal per g-alom are: THE high-temperature1,2 solution calorimeter was planned and designed to obtain directly the partial molar heat of solution of solute elements in a variety of liquid metals that might serve as solvents. Results obtained in the temperature range of 1000° to 1200°C were described in the two earlier publications. However, a long-term goal in the program has been to obtain measurements at 1600°C of the heats of solution of elements in liquid iron. Hence, subsequent to the work last reported,2 and based on the experience of the first two studies, the calorimeter system has been modified and operated at 1600°C to obtain measurements on the Fe-Si, Fe-A1, and Fe-Cu systems. This paper reports the results of the work. THE MODIFIED SYSTEM It was clear from the earlier results that the most precise measurements can be obtained with the high-temperature solution calorimeter when the solution time is less than approximately 30 sec. This can be achieved only when the bath temperature, Tb, is above the melting (liquidus) temperature of the solute material being dropped. A second point of importance is that the refractories used earlier liberated considerable water so that, although the oxygen potential of the atmosphere in the system was satisfactory for work with nickel and copper, it was too high for work with iron, silicon, and so forth. Third, for work at 1550" to 1650°C, an improved temperature-sensing unit is needed. The modified calorimeter in its latest form is shown schematically in Fig. 1. The refractory brick and the Kanthal-Super heating elements which formed the furnace for heating the solute addition have been replaced by a smaller resistance-heated tube furnace which is insulated with bubble-grain alumina. A more elaborate gas purification system was installed to maintain a satisfactorily low oxygen potential in the atmosphere of the calorinieter chamber and of the solute addition furnace. As was the case in the earlier work, at the beginning of a run the calorimeter chamber is evacuated and then filled with purified argon so that a total pressure slightly in excess of 1 atm is maintained during the run. When either of the furnaces within the enclosure attains a red heat, 6 pct H2 is added to the atmosphere. Throughout the run, gas from the calorimeter is circulated through a de-oxidation system at the rate of approximately 5 standard liters per min; the changeover time for the gas within the calorimeter enclosure is approximately 1 hr. The essential stages of the deoxidation system are: a copper furnace at 600°C, a drying tube of anhydrite, and a titanium furnace at 800°C. The oxygen potential of the gas stream in the purification system can be monitored at several points by a stabilized zirconia oxygen cell. This cell is invaluable in detecting the development of leaks in the container vessel and the gas circulating system. The installation of the solute-addition furnace allowed either of two types of temperature-sensing units to be mounted on a water-cooled probe. The first was a small optical device using a silicon diode that was

Jan 1, 1968

By Michael Chender

INTRODUCTION The project financing described elsewhere in this book is available to major mining companies on the basis of a strong balance sheet, a significant equity position in a project of proven feasibility, and a demonstrated ability to bring ore deposits into production. "Junior" mining companies, which are most active in Canada, Australia, the US, and South Africa, by definition do not meet these criteria. In many cases, junior companies will need to raise money simply to cover the costs of acquiring and exploring potential deposits. In what follows we will look primarily at junior financing practices in the US and Canada, although the same general principles will apply in Australia and South Africa. The principal vehicles for junior mine company financing are limited partnerships, the private placement of securities and debentures, and public offering of securities, and property deals with stronger companies, in the form of leases, earn-ins and co-ventures. The cost (in terms of dollars or equity) and, to some extent, the applicability of using these difficult approaches varies with the stage of development of the property and with the corresponding degree of risk to the investor. Much junior company fund raising is, in fact, "interim" financing in that it allows the company to improve its properties and develop its assets to the stage where more favorable financing arrangements may become available. Companies will therefore often use several of the approaches described above during the development life of a specific property. LIMITED PARTNERSHIPS Limited partnerships and syndications are a popular way of structuring the initial private financing of mine developments because of their attractive tax consequences for the well-to-do investor. Costs of exploration and development can in many countries be passed through as deductions to the limited partners, who are thus able to gamble on a possible windfall at little real cost. In addition to private Canadian funds, much German money flowed into Canadian exploration ventures on this basis, but stopped in 1982 due to economic conditions in West Germany. In the US, recent regulations have, in the great majority of cases, taken away the ability to "shelter" income in mining limited partnerships. Deductions taken by the individual investor cannot exceed the amount of money he actually has at risk. Nevertheless, the allowable deductions are still attractive and some of the major mining companies are now beginning to look at limited partnerships as a vehicle for attracting additional exploration funding. Ranchers Exploration and Development has successfully put together several drilling funds on this basis. THE PRIVATE PLACEMENT Initial funding for the acquisition and preliminary exploration of prospects is often accomplished through a private placement of unregistered securities or, where it is not a problem to carry debt on the statement, by a private placement sale of debentures. A fledgling company wishing to do a public offering may well be advised by an underwriter to accomplish a small private placement as a precondition of the larger offering. In this way, the sale of the registered securities is not inhibited by the company starting out with a debt-ridden balance sheet and no demonstrated ability to secure the additional financing generally necessary beyond the proceeds of that offering. In the US, the securities offered in a private placement are not registered with the Securities and Exchange Commission (S.E.C.) but are restricted as to their resale, and could be further restricted by a underwriting agreement

Jan 1, 1985

By Lane Mitchell

A ceramic product or processed material is a solid composed of materials which have been subjected to heat above 468.3°C (875°F). The raw materials, which are blended together (or in some cases used singly), are selected and utilized for various reasons such as ease of fabrication, aid to processing, to yield desired properties after processing, lack or controllable degree of toxicity or hazard, availability, cost, and perhaps other considerations. Almost all solid inorganic, some organic, and some liquid and gaseous materials have the potential to be used individually in some ceramic product. There are several fundamental functions to be fulfilled in every ceramic product and a number of secondary functions are desirable in specified products. These functions are generally met by the most widely occurring minerals and rocks of the earth and their debris. This fact characterizes ceramics as a field utilizing the raw materials most available to man. Of course, specified products utilize synthetics, organics, and rare inorganics to produce desired results. Any solid nonmetallic product processed by subjection to temperature above a red heat may be called a ceramic product. Widely used construction materials and units, domestic utensils and units, industrial parts to facilitate manufacture, technical components, and aesthetic creations are very often of a ceramic nature because of their durability, inertness, hardness, ease of fabrication, cost, and availability of the ingredients. Often, organics or metals cannot meet desired specifications for some of these products. The rocks and minerals and mineral debris of the earth are largely siliceous. Oxygen and silicon comprise roughly 75% of the earth's crust with aluminum, iron, calcium, and the alkalies following in abundance. Silica (SiO2) and silicates can be melted to form glasses. Alumina (A1203), present in a mineral compound, gives greater durability, hardness, and strength, but lessens the glass-forming property. Iron, calcium, and the other alkalies flux silica and reduce melting points. Thus sand, which is generally almost pure SiO2, and clay, which is generally hydrated alumina silicate, are the most widely used of all ceramic raw materials-principally because of the glass-forming propensities of silicates. In ceramic formulations, clay is generally a refractory filler or skeletal material, having in the raw state a plasticity derived from its colloidal grain size and its water-loving nature. On the other hand, silica sand is a glass former or nonplastic filler. Clay and silica sand in pure forms are quite refractory, i.e., not easily melted. Clay, although siliceous, is less of a glass former than pure silica and is more refractory. Natural contaminants, such as iron oxide or limestone, adulterate many clays and some sands. These contaminants act as fluxes and reduce the fusion points of the mineral or blends. Glass is made from silica sand by fluxing the sand with strong bases, usually soda ash and limestone. Red building bricks are hard and durable because the sand and clay have been partially fused with help of natural iron oxide serving as a flux. The iron oxide performs a dual function, serving as a pigment as well as a flux. In a blend of clay and sand and iron oxide, the sand is more susceptible to fusion than is the clay. Although silica sand and clay are the most widely used raw materials in most ceramic products, many other minerals, and some nonminerals are utilized in products where these materials can produce or aid in achieving desired results. Limestone and dolomite, feldspars, pigmentary minerals, refractory oxides or carbides, and special property producers can

Jan 1, 1983

By M. A. Dayananda

Based on the Kirkendall frame of reference, a method is proposed for the determination of atomic mobilities of all the diffusing species in a multicorn-ponent system with a single diffusion couple. The method is based on an atomic mobility model developed on the concept of negligible interactions among the intrinsic fluxes. It is shown in the model that mobilities can be obtained directly from the cumulative intrinsic fluxes past the Kirkendall interface. The proposed method replaces the need for a prior determination of interdiffusion coefficients far the calculation of mobilities. Relations between intrinsic diffusion coefficients and mobilities are derived and the mobility calculations are illustrated with diffusion data in Cu-Zn-Mn alloys at 850°C. ThE concept of "intrinsic flux" with respect to a fixed lattice was introduced "i Darken1 to explain toa Kirkendall effect2 demonstrated by the motion of inert markers during isothermal diffusion in single-phase binary solid solutions. Based on this concept, intrinsic diffusion studies have been made in various binary metallic systems3,4 employing such a lattice frame of reference, commonly referred to as the Kirkendall interface. Similar approaches, both theoretical and experimental, have been presented5"10 to study intrinsic diffusion in multicomponent systems. Based on the direct integration of Fick's law extended to multicomponent diffusion, Philibert and Guy8 proposed a method for the determination of intrinsic diffusion coefficients. For an n-component system, this procedure requires an experimental study with (n — 1) diffusion couples, all having their Kirkendall interfaces at the same compositio;, where n(n — 1) intrinsic diffusion coefficients are defined. This technique has been employed for ternary diffusion studies by Dayananda and Grace" and Guy and Leroy.11 A different approach is recommended by Ziebold and Cooper,12 who have derived relations between interdiffusion coefficients and atomic mobilities employing fluxes referred to the local center of volume. Their analysis is based on the simplifying assumption of negligible interactions among intrinsic fluxes. This assumption has been considered satisfactory for dilute solutions.5"7 The use of this analysis for the calculation of mobilities requires an initial determination of interdiffusion coefficients with a set of diffusion couples having intersecting diffusion paths. It is the purpose of this paper to propose a method that would permit a direct determination of mobilities of all components of a multicomponent system from a single diffusion couple. This method is based on a mo- bility model developed with diffusion fluxes referred directly to the Kirkendall interface, generally identified by inert markers. gen erall, like that of Ziebold and Cooper,12 employs the simplifying assumption that the flux of each component relative to a fixed lattice is caused only by the driving force of its own chemical potential gradient. THE KIRKENDALL INTERFACE Inert markers are employed in diffusion couples to locate experimentally the position of the Kirkendall interface. They are initially placed at the weld interface for "sandwich" couples, or at the original vapor-solid interface for vapor-solid couples. Studies of marker motion in binary systems3'4 with both types of couples indicate that markers remain in a plane of constant composition and move with this plane para-bolically with time. Parabolic marker movements were also observed in ternary Cu-Zn-Mn couples by Dayananda and Grace.10 It is reasonable to expect a similar marker behavior even for diffusion couples with a higher number of components.

Jan 1, 1969

By B. C. Wonsiewicz, G. Y. Chin

THE presence of deformation bands in cold-worked metals is known to influence the development of deformation textures1 but has not been considered in any theoretical treatments. At the present time the most rigorous theory of deformation textures appears to be based on Taylor's concept of homogeneous deformation of a crystal within a polycrystalline aggregate.' For each crystal the Taylor theory allows the operation of several equivalent combinations of five or more slip systems. Hence deformation bands can arise from the operation of a separate combination of slips in each of several portions within a crystal. On the other hand, a second type of band may occur as a consequence of slip on systems other than those selected on the basis on homogeneous deformation. This type appears to be associated with crystals of symmetrical orientations, such as the [loo] and [lll.] axial orientations in drawn wires of fcc single crystals studied by Ahlborn.3 In this note we propose a simple mechanism of deformation banding of the second type, and compare the theoretical results for wire drawing of [loo] and [Ill] with Ahlborn's observations. In outlini the model requires that the work to accomplish a given overall shape change by banding be less than or equal to the work to accomplish the same change by homogeneous deformation. While the work by homogeneous deformation, WH = ?T ;dri, can be calculated exactly by the equivalent methods of Taylor2 or of Bishop and Hill,4 the work by banding, WB, is less certain. The latter consists of 1) Wi, work by slip within a band, 2) Wb, work associated with formation of a boundary between bands, and 3) Wc, work to correct the difference in shape change arising from banding and homogeneous deformation. The Wi term can be evaluated explicitly for a band with an assumed set of slip systems, but a satisfactory analysis of Wb and Wc has not been obtained. Since WB = Wi + Wb + Wc WH, for banding to occur, however, a necessary condition is Wi = WH . Hence it seems reasonable to choose a band with the lowest value of Wi among competing bands consistent with Wi = WH, and then minimize Wb and Wc by arranging the physical configuration of the selected band. Wc is minimized by combining neighboring bands such that their net strain matches the macroscopic strain as closely as possible, and Wb is minimized by enforcing strain compatibility across the boundary between two neighboring bands, similar to the case of a grain boundary.5 It is realized that this procedure is not completely satisfactory, but it does seem to explain Ahlborn's observations reasonably well. The procedure is now outlined for the two corner orientations. a) [l00]. Fig. 1 shows a (100) stereographic projection. The results of the Taylor analysis for axi-symmetric flow by homogeneous deformation6 show that, while [loo] itself is unstable, the rotation of the tensile axis will nevertheless be confined to within about 15 deg from [loo]. Alternatively, less work may be expended by banding with slip on a pair of systems with primary-conjugate relationship, e.g., (ll1)[10l.I + (li1.)[110]. The latter represents minimum Wi for all possible bands.* Since there are four symmetrically

Jan 1, 1970

By M. E. V. Plummer, F. E. Beamish, J. C. Hole, J. M. Kavanagh

Prior researches have shown that the iron-copper-nickel content of platinum concentrates may be reduced by carbon to form a collecting alloy for the platinum metals in a manner exactly analogous to the formation of the lead fire assay button. The nature of the iron-copper-nickel alloys with the platinum metals has been investigated. Palladium and probably some of the other platinum metals form solid solutions with this alloy. ONE of the greatest known reserves of the platinum metals is to be found in the nickel, copper, iron sulphide deposits of Northern Ontario. The very large tonnage of copper-nickel ore processed makes the Sudbury district a significant world source of the platinum metals, the latter being recovered as byproducts in the electrolytic refining process for copper and nickel. Chalcopyrite, pentlandite, and pyrrhotite are carriers of the platinum metals;' these minerals contain from 0.03 to 2.0 ppm of the noble metals. The analysis of the above ores for the platinum metals necessitates an initial concentration of the minute quantities present in the ore. The method usually employed involves the extraction of the noble metals by molten lead with or without small proportions of silver. The lead is then separated from the precious metals by cupellation, a process which involves absorption by the cupel and volatilization of lead oxide, leaving the precious metals collected in a silver bead on the surface of the cupel. The collection by lead is probably achieved by a process of dissolution followed by some degree of segregation in the lead alloy since the cold button is seldom uniform in composition. With silver-lead alloys this process of liquation has been used to re- cover pure lead since, during the cooling period, crystals of pure lead separate and silver becomes concentrated toward the center of the solid.' Platinum and gold liquate in a manner similar to silver which may account for the successful recovery of platinum by fire assay even though it is considered insoluble in a solid lead medium. 3 In the case of iridium the liquation process may be a disadvantage in that the iridium may appear in the outer areas of the button and thus be lost mechanically during the handling processes. In any case the deficient alloying characteristics of lead for the platinum metals encouraged attempts to find an improved collecting alloy, and by analogy with aqueous extractions, preferably one in which solid solutions would be readily formed. Since, beyond a certain minimum solute to solvent ratio, the formation of a solid solution is accompanied by a lattice distortion, one would expect some relationship between the atomic diameters of any two metals and their tendency to form a solid solution. In one survey5 the hypothesis was put forward that when the atomic diameter of the solute differs by more than about 15 pct from the solvent, the "size factor" is unfavorable and the formation of a solid solution is restricted. On the other hand, when the atomic diameters are within this limit the size factor is favorable and solid solutions are readily formed, e.g. the transition metals of Group VIII having similar radii form solid solutions over wide ranges of composition.6 Even with a favorable size factor, elements having different crystal structures cannot form a continuous series of solid solutions. Cell dimensions alter as the concentration of the solute increases, causing a

Jan 1, 1962

By W. W. Gerberich

SINCE the original formulation of fracture mechanics concepts,&apos;y2 relatively little work has related the fracture mechanics description of metal behavior on a gross, structural component scale to the behavior of its microstructural constituents. The purpose of this note is to suggest the utilization of fracture mechanics to describe material behavior on a microscopic scale. A Fracture Concept for Two-Phase Structures. A critical displacement concept considering the tough unidirectional phase in a relatively brittle matrix is first examined. It is assumed that a flaw exists at position 1 as depicted in Fig. 1. As the crack moves from position 1 to 2 the plastic zone could be of the shape described with the size approximated by the Dugdale3 model: where c is the half-crack length, OO is the applied stress, and oyS is the yield strength. Hahn and Rosen-field4 have presented a simple fracture criterion for homogeneous materials based upon the displacement at the crack tip. They also have shown the equivalence of the critical displacement, v*, to fracture toughness by Kc = (2v*oysE)1/2 [2] The displacement at the crack tip is given by and the displacement at any distance in front of the crack tip may be determined knowing the plastic zone size and utilizing the development of Goodier and Field.5 Recalling Fig. 1, the value of v* for fracture in material M1 may be calculated from Eq. [2] providing the critical stress intensity factor is known. As the material is loaded, when vc > vM1 the crack moves from position 1 to position 2 where it encounters the tough second phase. If vc2 < vm2, then the crack will be arrested providing the width of the M2 phase is sufficiently large. This condition is necessary since the displacement at position 2 has increased due to the longer crack length. Thus, the displacement at the distance X (representing the dimension of the second phase) in front of the crack may be larger than the critical displacement for failure in the brittle material. If v, > vm, then failure will proceed in the brittle material. The value of v, may be calculated as indicated above. This latter consideration is the same as predicting fracture of a brittle second phase at some distance in front of a crack located in a ductile matrix. Experimental Evidence. On a macrostructural scale, tungsten wires in a ductile Be-Cu matrix are seen to fracture well ahead of the main crack front in Fig. 2. Utilizing a Kc value of 14.2 ksi-in.1/2 obtained by Schroder et al.6 for as-received tungsten, the critical displacement 2v*, for fracture is calculated from Eq. [2] to be about 6.5 X 10-5 in. The crack tip displacement, 2vc, is calculated from Eq. [3] to be 0.0028 in. indicating that fracture would occur at a considerable distance in front of the crack tip. From the ratio of v*/vc and the plastic zone estimate of Eq. [I], the distance in front of the crack tip at which a tungsten wire should fracture is calculated to be about 0.195 in. As shown in Fig. 2, a fractured wire occurs at a distance of 0.140 in. (fractured in three places), not at 0.250

Jan 1, 1968

By R. A. Burton, J. T. Hansford, D. A. T. Donohue

Substantial evidence indicates that many petroleum producing horizons contain naturally occurring, ordered fracture systems and that within a particular geologic zone, vertical fractures induced in wellbores often will be directed along a particular compass direction. Both conditions will seriously alter the fluid displacement behavior within reservoirs. In this study the effect of induced fracture orientation and length on sweep efficiency is determined for a five-spot pattern. In general, it is assumed that all wells are fractured and directed along the same compass direction. Using the electrical analog to steady state, two-dimensional fluid flow in porous media, boundary conditions are obtained from which flood fronts are tracked numerically. The numerical computations require a particle tracking routine for approximating flood front histories. It is shown that recovery is sensitive to the length and orientation of fractures for the pattern studied. with the proper design of fracture-pattern systems, recovery can be enhanced considerably. INTRODUCTION Hydraulic fracturing introduced in 1949l gave the industry a rather inexpensive means of increasing the fluid injection or production capacity of wells. It has been used with particular success to increase the production rate of wells completed in tight formations, such as in western pennsylvania2 where producers have fractured in depleted or near-depleted fields and observed economic responses. Once the natural energy declines in such a reservoir where all wells have been fractured, waterflooding is generally suggested as means of further increasing recovery. Of the dual objective sought in waterflooding — high injectivity and high breakthrough sweep efficiency — the former condition can be obtained if all wells in the flood pattern are fractured; the latter condition should depend on the nature of the fracture system. Considerable theoretical work has been published on the nature of fractures induced in boreholes.3-5 Although discussion persists concerning the possibility of forming a horizontal fracture at a given point within the wellbore, it is generally conceded that only vertical fractures will develop below a given depth, i.e., where the fracturing Pressure is less than the overburden load. Given the fact that fractures will be vertical in most cases of interest, it is also important to know whether there is order to fracture orientations within a given geological region. Kehle has suggested that in tectonically relaxed areas of uncomplicated geology, the stresses are fairly uniform and all fractures in the region should be parallel.5 Dunlap arrived at a similar conclusion in a theoretical investigation of localized stress conditions surrounding the borehole.6 He concluded that most vertical fractures are propagated in a preferred azimuthal direction. Fraser and Pettitt, in extending these theoretical suggestions to a specific field case, used an impression packer to record both a vertical fracture and the orientation of this fracture in the wellbore of a well in the Howard Glasscock field, Tex.7 Use of this information enhanced the waterflood recovery of the field. Anderson and Stahl also used impression packers on three fractured wells in the Allegheny field. N. Y.. and found that the fractures were oriented more or less along the same compass direction.8 Orientation of the fractures in this manner depends on the stress condition within the formation during fracturing. Elkins and Skov have demonstrated that a natural, oriented, vertical fracture system exists within the Spraberry field? Heck suggests

Jan 1, 1969

By B. F. Buie

For over 200 years meerschaum has been a significant item of trade between the Near East and countries to the west. Best-known for its use in making smoking pipes and cigar and cigarette holders, it is also used in making a variety of decorative and ornamental items. It is easily carved, and is given an attractive, lustrous finish by rubbing. No published specifications are known, but compact form, purity, uniform whiteness or light color, and uniform, porous texture appear to be requisites. Fig. I a shows the appearance of a piece of crude meerschaum from Turkey; Fig. lb a carved item; and Fig. lc, d, and e show the fibrous and porous texture as revealed by the scanning electron microscope. Neither a major industrial mineral nor a precious stone, meerschaum nevertheless holds a record of long-and continuing-association with art and personal affairs of man. It is also a mineral to which modem methods of exploration and production probably could be profitably applied. An interesting account of the preparation and use of meerschaum in the early part of this century is given by Sterrett (1907). Geology and Mining Mineralogy Meerschaum is recognized now to be the compact variety of sepiolite, the claylike variety of which is one of the minerals included in the chapter on clays. The word meerschaum, from the German meaning "sea foam," was in earlier times used synonymously with sepiolite, a word of Greek origin suggestive of the resemblance of the compact variety-then the only variety known-to cuttlefish bone. At one time meerschaum was used as the commercial name, and sepiolite for the scientific name. However, to think of meerschaum as the name by which sepiolite is known commercially is no longer valid, in view of the recent emergence of the earthy variety as a competitor of bentonite and other clay materials. Present tendency is to restrict the term meerschaum to the compact variety, and to use the term sepiolite as a more general name to include both the compact and earthy varieties. This is the terminology followed in this publication. Meerschaum typically is white to light gray, has a hardness of 2 to 2 ½ , conchoidal to irregular fracture, and specific gravity varying with porosity from about 2 to less than 1. The composition is somewhat variable,- but is near that determined by Schaller (1936) for sepiolite as 2MgO.3SiO2.4H2O. A more modern for mula based on X-ray determination of the crystal structure is given by Caillére and Henin (1961) as (Site) (Mg9)030(OH)6(0H2)46H20. The reason for the firm, compact nature of meerschaum, in contrast with the earthy variety of sepiolite, is not fully understood. It may be due to the presence of a very minor amount of some bonding material such as silica. Scanning electron microscope (SEM) photographs of a specimen from Turkey (Figs. lc-le) indicate that the meerschaum is composed predominantly, if not entirely, of crystalline fibers which merge into sheetlike forms in a complex, intertwined mass. Detailed X-ray and crystal structure data, as well as some data on thermal stability range, are given by Caillère and Hénin (1961) for the sepiolite family of minerals. Mode of Occurrence and Origin Most authors have attributed the origin of meerschaum to alteration of serpentine or other magnesian minerals. The occurrence in alluvium and other surficial deposits does not necessarily indicate that the alteration was supergene. In fact, hydrothermal origin appears more likely for some deposits, though not for all.

Jan 1, 1983

By M. P. E. Desvaux, P. Charsley

OLIP-line observations on copper alloys, using the electron microscope, have been made by a number of workers,13 but this work has been confined to a brass. In a CuAl alloys Koppenaal4 and Koppenaal and Fine5 have made observations with the optical microscope and by the use of interferometry. They found that the observed slip step heights inside the Liiders bands accounted for only 42 pet of the total macroscopic strain. The suggestion was put forward that optically unresolvable slip in other parts of the specimen accounted for a major part of the macroscopic strain. This is surprising since it is known from other workers that slip in a brass is inhomogeneous; i.e., large amounts of slip occur on individual {lll) closelys paced than being shared by a large number of closely spaced planes. Furthermore, a brass and a CuAl alloys with high concentration of aluminum exhibit similar deformation characteristics and slip-line patterns. Prior to investigations into the behavior of copper and a CuAl alloys under reversed stresses in tension and compression, some preliminary experiments have yielded results which the authors think resolve this discrepancy, and throw some further light on the behavior of a CuAl in tension. An experiment was carried out on a 10 at. pet CuAl single crystal, of gage length 7.5 cm, diameter 3.1 mm, and orientation shown in Fig. 3 (inset), for the purpose of resolving the above discrepancy. The specimen gage length was electropolished for 10 min in a 50:50 orthophosphoric acid (SG=1.75)-distilled water system, with 2 v across the cell and a current density of 0.5 amp per sq cm. The cathode was made of copper. After a tensile strain of 0.067 ± 0.001, intense slip was observed over a length 2 cm of the gage length whilst the rest of the specimen was relatively undeformed. In the lightly deformed region, slip bands of mean width 20 /x were spaced about 1 mm apart on average. The transition from the heavily slipped region (usually called a Liiders band) to the lightly deformed region was gradual, the slip-band density increasing as the "Liiders band" was approached. In the latter, the slip bands became so close together that, to the naked eye, the specimen appeared to be continously slipped, and the typical microtopography of this region is shown in Fig. 1. Twelve electron micrographs were taken at random from replicas of the Liiders-band region, and the widths of the slip lines were measured. The slip lines account for an over-all tensile deformation of 7.0 ± 0.7 pet, after allowing for the lengths of the un-slipped regions, which is in good agreement with the macroscopic strain. The distribution of slip-line widths was also measured and is shown in Fig. 3. Since Koppenaal could not resolve slip lines with height less than 540A (limit of resolution represented by dashed line), then it was deduced that he could have measured only about 50 pet of the deformation within the &apos;Liiders Band&apos;. It is concluded, contrary to the suggestion of Koppenaal,5 that virtually all the macroscopic strain is accommodated within the "Luders band" and that there is no need to invoke fine slip distributed uniformly over the gage length.

Jan 1, 1967

By B. H. Kear

All the possible ways of forming simple two-dislocation boundaries in multiple slip orientations are deduced. It is shown that the principal differences in work hardening behavior of crystals plastically deformed in these orientations can he accounted for in terms of the likelihood of formation of diffuse boundaries, or deformation bands, consisting of the products of dislocation reactions of the Lomer type. Also, it is pointed out that the break-up of boundaries under the applied stress is more likely to yield interstitial jogs than vacancy jogs, whereas glide dislocations cutting throuqh dislocations trapped in particularly stable boundam&apos;es can acquire both types of jogs. USING Frank&apos;s&apos; grain boundary formula, Ball and Hirsch2 determined the parameters of all the possible boundaries that can be built from two sets of glide dislocations in the fee structure. This paper deduces the geometrical possibilities for the formation of these two-dislocation boundaries in the different multiple slip orientations, and discusses the role of boundaries in work hardening and in jog formation. Formation of Two-Dislocation Boundaries in Mutiple Slip Orientations. The parameters of the possible two-dislocation boundaries for any crystal orientation can be deduced most conveniently using the boundary formulae due to Amelinckx,3 in conjunction with the stereographic projection shown in Fig. 1. Suppose that slip occurs in a-BC and ß-CA. According to Amelinckx, when the two systems of glide dislocations are parallel, the rotation axis, u, of the boundary is parallel to (a x ß) and the unit normal, u, defining the boundary plane is parallel to (a x ß) x (BC x CA). On the other hand, when the glide dislocations form a crossed grid, u is parallel to (BC x CA) and u is parallel to (a x CA) x (ß x BC). In Fig. 1, (a x ß) is the pole of the great circle passing through a and ß, so that u is parallel to DC, i.e., parallel to [110]. Furthermore, (a x ß) x (BC x CA) is the pole of the great circle passing through DC and 6, so that u is parallel to [110]. Hence, when all the glide dislocations are parallel, the boundary is pure tilt with parameters u = [110], v = [ 110]. Similarly, it may be shown that the corresponding crossed grid of dislocations is a mixed boundary with u = [111], u = [111]. Consider the case of a crystal compressed in the [001] orientation. In this orientation, according to Fig. 1, there are eight available slip systems. In what follows, the different types of two-dislocation boundaries that are possible in this orientation will be examined by taking different combinations of two slip systems out of the available eight, with a-BC always one of the systems. Case (i)—Slip Systems a-BC and d-CB. The formation of a tilt boundary in (101), which consists of a crossed grid of edge dislocations with vectors BC andCB, is illustrated in Fig. 2(a). As the figure shows, slip is required in the system a-BC in one part of the crystal and in d-CB in the other part, with both sets of dislocations entering the boundary from opposite sides. The rotation axis of the boundary lies in (101), depending on the relative densities of the two sets of edge dislocations in the boundary. Case (ii)-Slip Systems a-BC and ß-CA. The two possible boundaries are shown in Figs. 2(b) and (c); boundary (b) is tilt with u = [110], u = [110], and

Jan 1, 1962

By D. I. Bardos, Paul A. Beck

The 1100°c isothermal, sections of the V-Fe-Si, V-Co-Si, and V-Ni-Si systems were studied at silicon contents between 0 and 40 at. pct. The single-phase fields in the 30 and 50 at. pct Mn sections of the 1100°C tetrahedron of the V-&apos;Wn-Fe-Si system were also determined. The direction of extension of the elongated O, R, D, and a-Mn Phase fields suggests that the stability of these phases is determined largely by the electron concentration. The peculiar shape of the above ternary a phase fields, as well as of the a phase fields in the V-;Mn-Si and Cr-MTZ-Si systems is accounted for on the assumption that in manganese-(iron-, coball-, nickel-) rich alloys silicon atoms do not exclude d electrons , while in alloys low in the above components they do. This assumption also leads to the expected electronconcentrations for q and ß-Mn phases formed by transition metals with aluminurn. In earlier work it was shown that in ternary alloy systems of transition elements the a a and certain other phases with complex structure, such as the p and R phases,3 form elongated phase fields extending in a direction corresponding to a constant electron concentration. Recently similar behavior was observed in manganese-rich ternary ß-Mn solid solutions with another transition element and with silicon, germanium, or tin,4 confirming earlier indications3 that ß-Mn is also an electron phase. The alloying behavior of silicon in these manganese-rich alloys sug- gested that the four outside electrons of silicon participate in the bonding and that the predominantly d-like bonding electrons are not excluded from the silicon sites. Presumably, some of the normally unoccupied 3d states associated with the silicon atoms are in these alloys lowered to the Fermi level;4 thus silicon behaves as if it, too, were a transition element. The manganese-rich boundary of the a phase in the V-Mn-Si system,4 as well as in the Cr-Mn-Si sys-tem,4,5 extends approximately parallel to the ß-Mn phase boundary, corresponding to the transition ele-mentlike behavior of silicon described above. However, at lower manganese contents (i.e., in the high-vanadium or -chromium region) the a phase field in both ternary systems mentioned extends in a direction roughly perpendicular to that of its manganese-rich boundary, a phenomenon that is apparently inconsistent with the behavior of silicon in the manganese-rich alloys. A similar, although somewhat less pronounced, extension of the a phase occurs also in the high-vanadium (low-iron) region of the V-Fe-Si system at 1175C, but reportedly not in the V-Co-Si or V-Ni-Si systems at the same temperature.5 The present work was undertaken to investigate in more detail the extension of the a phase (as well as of other electron phases that may be present) in the last three systems and to elucidate this phenomenon, which has not been satisfactorily explained previously. EXPERIMENTAL PROCEDURES Most of the alloys were melted in an arc furnace, using a water-cooled copper crucible under helium atmosphere. The transition metals were of better than 99.9 pct purity and the silicon used was 99.98 pct pure. Alloys containing less than 20 pct V were induction-melted in recrystallized alumina crucibles under argon atmosphere.

Jan 1, 1967

By W. M. McCardell, W. O. Winsauer

The abnormal conductivity found in shaly reservoir rocks containing an electrolyte is shown to be a consequence of the electrical double layer in the solution adjacent to charged clay surfaces. This increased conductivity results from a higher concentration of ions in the double layer than in the solution in equilibrium with the double layer. It is shown that the magnitude of the increased conductivity of a shaly reservoir material is influenced by the concentration and type of ions in the equilibrium solution as well as by the colloidal nature of the rock. INTRODUCTION An important factor in the quantitative interpretation of the electric log is the resistivity factor of reservoir rock. The resistivity factor is defined as the resistivity of the rock when completely saturated with an electrolyte divided by the resistivity of the electrolyte itself.&apos; In the normal case, the resistivity factor for a particular rock sample is independent of the resistivity of the electrolyte and reflects the pore geometry of the rock.&apos; In 1949. Patnode and Wyllie&apos; showed that in some cases the resistivity factor is not constant, but instead varies with the resistivity of the electrolytic solution. It was shown that clean sands behave normally—i.e., that the resistivity factor does not vary with resistivity of the electrolyte — but that sands con- taining shale and clay may exhibit abnormally low resistivity factors when the solution used to saturate them is of fairly high resistivity. At low resistivities of the electrolyte, the resistivity factor for a shaly sand appeared to approach a normal behavior. It is evident that the resistivity factor of a shaly sand is dependent upon factors other than pore geometry when the solution used to saturate it is of high resistivity. Patnode and Wyllie, and later de Witte,&apos; assumed that the conductivity of a shaly sand saturated with an electrolyte could be represented as the sum of two quantities. One of these was assumed, in effect, to be the conductivity which would be expected if the sample were a clean sand. and the other was assumed to be a conductivity inherent in the sample itself. The latter was supposed to be constant for a given rock sample regardless of the solution used to saturate it. The source of this added conductivity was ascribed to "conductive solids." In actual practice: the effect of the abnormal behavior of shaly sands is of minor importance except when the resistivity of a formation such as a sand is high. Thus the effect is more important when the sand is saturated with a dilute brine than when it contains a more concentrated electrolyte. The effect is also more important when the sample contains oil or gas than when it contains only saline water. Recently it has been suggested that the porosity of a stratum may be estimated from the electric log by use of the resistivity of the invaded zone." This is the zone flushed with the filtrate from mud used in drilling the well. which is ordinarily very dilute brine. When the method is applied to shaly sands, the effect of abnormal conductivity becomes of importance. This report describes an investigation of the mechanism responsible for the abnormal behavior of the resistivity of shaly rock saturated with conducting solutions. The investigation

Jan 1, 1953

By L. J. Kashar

By means of a continuum-mechanics approach, the following equation for calculuting the pressure for axisymmetric cold forging has been derived: where P is the extrusion pressure; K and n are the strength coefficient and the strain-hardening exponent of the steel, respectively; a and b are strain factors, primarily dependent on the die design; and R is the extrusion ratio. Data from compression and backward-extrusion tests performed at a crosshead speed of 0.5 in. per min on a nonwork-hardening material pure lead) and on a work-hardening material (1018 steel) indicate that the predicted extrusion pressures obtained from the derived equation agree very closely with the actual extrusion pressures. Therefore, the equation can be used to predict backward-extrusion pressures from standard mechanical-test data. The decision to cold-forge a part is based on several considerations, most of them related to economics. However, the production feasibility is usually determined by the pressure needed to extrude the part and the availability of tooling that can repeatedly sustain this pressure for over several hundred thousand cycles. A major contribution to the cold forging of steel would result from the development of steels that could be forged at reduced pressures and from the development of techniques that permit the accurate prediction of the pressure necessary to cold-forge the part. The ability to predict extrusion pressures is necessary to properly design the tooling required for the cold-forging process. Attempts to theoretically predict the cold-forging pressure, especially for work-hardening materials, have been unsuccessful in previous investigations of the cold-forging process.1-3 Many empirical relations have, therefore, been proposed relating the extrusion pressure to the chemical composition,&apos; the extrusion ratio,2 the tensile strength,273 and hard- ness, 2 and the yield strength3 of the material being extruded. However, these empirical relations are valid only for the specific conditions used in their development, and, in some cases, the empirical relations had a scatter band greater than * 10 pct. A study of the extrusion process was undertaken with the objective of developing predictor equations for extrusion pressure by using a continuum-mechanics approach to the problem of metal flow. The derivation of such an equation is summarized in this paper, and data are presented that confirm the validity of the derived equation. DERIVATION OF THE EXTRUSION EQUATION If the extrusion of a material through a die is considered in terms of a work balance, it has been shown that it is possible to derive an equation relating the work necessary to move the material through the die to the deformation work undergone by the material. The work done, W, in moving the material is given by where F is the extrusion force, I, is the distance the material was moved, A, is the original cross-sectional area of the material, P is the extrusion pressure acting on A,, Ap is the cross-sectional area of the extrusion punch, and Pp is the punch pressure acting on Ap. The deformation work, WD, is given by where V is the volume of metal deformed, ay is the flow stress of the metal, and E is the total strain undergone in the extrusion. If there are no frictional losses, the work done, W, is equal to the deformation work, WD; therefore, Since the volume of a metal does not change during deformation,

Jan 1, 1968

This volume summarizes characteristics and the geological setting of porphyry copper deposits of the Western Hemisphere. Grouped by characteristics, porphyry copper deposits are described in six regions: Andean orogen, Appalachian orogen, Alaska, northern Cordilleran orogen, southern Cordilleran orogen, and the Caribbean. Each region has its own peculiarities of geologic setting, and those deposit characteristics that may be projected from one chapter to another will be used in reaching the conclusions from which to draw genetic models for porphyry copper deposits. The term porphyry in this volume denotes a type of ore deposit, rather than a rock classification. The classification of intrusive igneous rocks used in this volume is shown in Figs. 36a and 42 (pp. 103, 130). Some modern classifications suggest mineral-ratio definitions other than those used in this volume; however, most literature references cited are based on the classification shown in Figs. 36a and 42. The reader should be aware, therefore, that quartz monzonite in this volume contains from 35% to 65% potassuim feldspar and at least 10% quartz. A term used in this volume is defined where introduced within the context of a specific chapter. Distensional tectonic conditions are used in the sense of Cady (1972) in the Appalachian orogen, for example. Porphyry copper deposits are defined as large bodies of mineralized rock, usually including a porphyritic intrusive phase, that have copper sulfide minerals disseminated through them. The definition has no commercial connotation and is used strictly in a noneconomic sense to encompass the spectrum of copper mineralization associated with these deposits. Terms commonly accepted in the literature are not defined. Porphyry molybdenum and porphyry copper deposits commonly are distinguished by most economic geologists. The basis for the separation is summarized in one chapter of this volume. To permit the reader to more easily peruse the bibliography for any particular region, references will be found at the end of each chapter. The bibliography is not intended to be complete, but is designed to provide adequate minimum coverage for descriptions of deposits in the chapter concerned. Each entry is properly referenced in the text of that chapter to facilitate the reader&apos;s research into any particular topic. This volume is written from the point of view of the exploration geologist whose task it is to evaluate the structural, petrographic, mineralogic, and metallogenic characteristics of a porphyry copper deposit. The goal of the evaluation is to determine if, and where, concentrations of metals may exist in an igneous- hydrothermal system that includes the most complex set of geologic factors found in any of the many types of ore deposits. The successful porphyry copper geologist is simultaneously a petrographer, geochemist, structural geologist, and mineralogist. Some porphyry copper deposits have developed in volcanic arcs underlain by a Benioff seismic zone with a trench paralleling the arc. The most convincing example of a deposit known to have developed in an environment where subduction is an active process is the 3.3 m.y. (million years) old Dry Creek occurrence in the Aleutian arc (this volume). On the other hand, the younger deposits in the Cascades appear to have formed in a volcanic arc lacking both the Benioff zone and the offshore trench. Subduction is not widely accepted as an active mechanism for the period when the younger Cascade deposits formed. Subduction has also been questioned for deposits formed at a great distance from a plate boundary (e.g., Bingham). Regardless of the pros and cons regarding subduction, most deposits are associated with regional faults. Strike-slip

Jan 1, 1978