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By G. Rowan, M. W. Clegg

Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is show to be very good. Some observations on the interpretation of gas well tests are made. INTRODUCTION The flow of gases in porous media is a problem that has been the subject of much study in recent years [l - 71 , and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form This form of equation was first suggested by Forchheimer [9] and, later, Katz and Cornell [10], and Irmay [lll, developed a similar equation. Houpeurt [12] derived this form of equation using the concept of an idealised pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type [4], for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow 121 may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al. [13], and Aronofsky and Jenkins [14] , but the latter solutions, apart from the simple linearisation of equation (2) to yield a diffusion equation in p2 , are not so well-known. Amongst these approximate analytical solutions should be mentioned the work of Barenblatt [IS], who has applied the techniques of dimensional analysis to obtain similarity solution to a large class of non-linear equations; also, a number of Russian authors, including Barenblatt [16] , Kim [17] and others, who have used the method of moments for obtain-

Jan 1, 1965

By D. J. McAdam, G. W. Geil, R. W. Mebs

AS shown in previous papers by the authors 9-l7† the resistance of a metal to fracture, like its resistance to plastic deformation, is a function of all three principal stresses.‡ A technical cohesion limit is the technically determined resistance to fracture under a specific stress system. The technical cohesive strength thus comprises an infinite number of technical cohesion limits corresponding to the infinite number of possible combinations of the principal stresses. The technical cohesive strength, therefore, may be represented by a surface in a diagram with the three principal stresses as coordinates. As shown in previous papers, 9-I8 the technical cohesive strength increases with plastic deformation, with decrease in temperature, and with increase in the strain rate. The technical cohesion limit, therefore, is affected by the same factors that affect the flow stress, § namely, the stress system, plastic deformation, temperature, and the strain rate. More- over, the influence of each of these factors on the technical cohesion limit has been shown to be qualitatively similar to the influence of the same factor on the flow stress.9-18 Advance of knowledge about the conditions determining fracture, of metals has been retarded by the reluctance of some investigators to abandon preconceived ideas about how metals "should" behave. The incorrect idea is still prevalent that the conditions determining resistance to fracture are very different from those determining the flow stress. Attempts are still being made to express resistance to fracture in terms of a single parameter, such as a limiting value of the greatest principal stress, the maximum shearing stress, or the volume stress (one-third the algebraic sum of the three principal stresses). In these attempts, a sharp distinction is sometimes made between a ductile or "plastic fracture " and a "brittle fracture." In making this distinction, however, the meaning attached to the term "brittle fracture" sometimes is not made clear. The term could mean fracture after very little plastic deformation or it could be used to designate the type of fracture. An ordinary fracture of a ductile metal at room temperature starts as a cleavage, generally transverse to the direction of the greatest principal stress, but eventually changes to a shearing fracture. In some conditions, however, the metal fractures entirely by cleavage, with no evidence of plastic deformation during the fracture; the surface of such a fracture may have a

Jan 1, 1947

By O. N. Carlson, A. L. Eustice

The tensile properties of iodide vanadium were determined as a function of hydrogen concentration. It was shown that the presence of 10 ppm H is sufficient to cause embrittlement of vanadzum over a limited temperature range. The temperature of the observed ductility mininlum is approximately -l00°C, this being a function of strain rate and hydrogen concentration. The yield stress of hydrogenated vanadium is raised sharply in the brittle temperature range. THE present investigation was initiated to determine the effect of hydrogen on the tensile properties of high-purity vanadium as a function of temperature and the role of hydrogen in the brittle-ductile transition. Loomis and Carlson&apos; reported a change from ductile to brittle behavior in iodide vanadium at -110°C with a return of ductility at temperatures below -140°C. Vanadium wire containing 270 pprn of hydrogen was brittle at room temperature while wire containing 100 ppm was ductile under the same conditions. Roberts and Rogers&apos; reported a ductile-brittle-ductile fracture sequence in vanadium containing 400 to 600 ppm of hydrogen. Their data show that hydrogenated vanadium is ductile at 150"C, brittle at room temperature and ductile again at -196°C. Magnusson and Baldwin found a minimum in ductility in vanadium containing 80 ppm hydrogen from tensile tests performed at several strain rates. Information available on the vanadium-hydrogen equilibrium system4 is somewhat incomplete. The absorption of hydrogen is exothermic in accordance with the decline in solubility with rising temperature. The limit of solid solubility at temperatures below 400°C has not been determined due to the difficulties in obtaining equilibrium at these temperatures. Data on the hydrides of vanadium are rather limited. Roberts6 studied the structure of VD,., by neutron diffraction, and observed the ordering of the deuterium atoms below -65°C into a primitive cubic cell with a lattice constant about twice that of the disordered bcc vanadium solid solution. EXPERIMENTAL PROCEDURE Vanadium of 99.9 pct purity was prepared by the iodide refining process6 for use in this investigation. This vanadium contained the following analyzed impurities; <20 pprn calcium, 150 ppm carbon, 200 ppm chromium, 30 ppm copper, 10 ppm hydrogen, 200 ppm iron, <20 ppm magnesium, <20 ppm nickel, <5 ppm nitrogen, 150 ppm oxygen, <50 ppm silicon, and <20 ppm titanium. specimen Preparation—Tensile specimens were machined from swaged rods of iodide vanadium. The

Jan 1, 1962

US 4,141,854-Method of resolving water-in-oil emulsions from the organic solvent extraction of uranium from an aqueous ore leach solution The emulsion is treated at optimum temperature with a water-soluble acrylamide copolymer which contains 5-50% by weight of a lower alkyl substituted tertiary aminoethyl methacrylate or quaternary ammonium salts thereof The emulsion is broken, enabling recovery and reuse of the organic portion of the emulsion A M Pavilcius and M A Latko, assigned to Nalco Chemical Co Feb. 27, 1979 3 pp (252-301 1W) Filed: 12-14-77 (860,542). US 4,142,952-In the recovery of copper from an ore leach solution, the solution is contacted with a water-immiscible organic solvent containing 5 to 20 g/L of o-hydroxyaryloxime and 2 to 20 times the weight of the o-hydroxyaryloxime of nonylphenol The loaded solvent phase is separated from the aqueous phase and stripped with sulfuric acid Copper is recovered rapidly and in high yield from aqueous solutions containing high copper concentrations R F Dalton, as¬signed to Imperial Chemical Industries Ltd Mar 6, 1979 6 pp (204-106) Filed 1-3-77 (756,067). Priority: United King¬dom, 1-30-76 (3788/76), 6-15-76 (24722/76), and 10-21-76 (43711/76). Same- British 1,549,615, dated Aug. 1, 1979 US 4,148,631-In the recovery of nickel and cobalt from a mixed sulfate ore leach solution, both metals are extracted by means of a cationic extractant, the loaded extractant treated with an aqueous chloride or thiocyanate solution to back extract the cobalt, and the cobalt then recovered by solvent extraction or ion exchange with an anionic extractant Recovery is effected in a relatively few extraction steps. F Babjak, V A Ettel, and K. R Dymock, assigned to Interna¬tional Nickel Co , Inc, Apr. 10, 1979 6 pp (75-101 BE) Filed¬7-27-78 (928,401). Priority- Canada, 12-28-77 (293,967) US 4,148,813-An improved extractant for use in the recov¬ery of nickel and cobalt from an ore leach solution comprises a water immiscible organic solvent system containing solubilized mercaptide ions, e g , dodecanethiol. Cobalt and nickel mercaptides solvated in the organic phase are easily stripped in the presence of carbon monoxide and an aqueous alkaline solution A. S. Rappas and J. P. Pemsler, assigned to Ken¬necott Copp

Jan 1, 1980

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

In recent years there has been increased miniaturization of electromechanical devices to keep pace with current trends toward smaller electronic components. A major problem facing the designer, however, is the higher stresses encountered by the material as a result of shorter springs. Hence an improvement in the elastic limit, as approximated by the 0.01 pct offset yield strength, would be highly desirable. An increase of 25 pct in the yield strength, for example, will permit a 20 pct reduction in both the length and thickness of a cantilever-type spring while maintaining the same compliance. One technique of improving the yield strength that has received little commercial attention is crystal-lographic texture strengthening.1,2 Texture strengthening is expected to be most beneficial in materials of hcp structure, but considerable gain can also be expected in cubic materials. A wire with a (111) fiber texture, for example, is expected to be 20 pct stronger than randomly oriented material, and 50 pct stronger than wire with a (100) fiber texture.293 For sheet specimens with a {110}(112) texture, characteristic of many heavily rolled fcc alloys, the (111) transverse direction is expected to be the maximum yield strength direction, about 20 pct higher than that in the (112) rolling direction.&apos; In addition, the (111) direction is the direction of maximum modulus of elasticity for most cubic alloys. A large value of the elastic modulus could be desirable in designs where stiffer springs are required. To test the above idea, a 0.090 in. (-2.3 mm) thick commercial grade A (5 pct Sn) phosphor bronze sheet, a widely-used material for relay springs, was rolled from the spring-tempered condition (60.5 pct reduction) to various additional reductions up to a total reduction of 95 pct. Subsequently, additional material was obtained with a total thickness reduction of 97.3 pct Standard tensile specimens were prepared from the sheet material with the tensile axis parallel to and at 90 deg to the rolling direction. Tests were run on an Instron testing machine at a strain rate of about 0.050 min-l. Textures were determined by the use of the reflection pole-figure technique. Data were obtained using nickel-filtered CuKa radiation and with the aid of a Siemens pole figure goniometer. The X-ray pole figure studies show an incrzasing development of the texture toward the {110}(112) ideal

Jan 1, 1970

By Gifford E. White

Explanations of the basic procedure for making earth-conductivity studies by the Eltran method have already appeared in several placeS. 1,2,3 In its essentials, this method consists of applying step functions of voltage to one pair of earth grounds and measuring the transient potential resulting at a separate pair of ground points. As previously pointed out,&apos; the transient potential resulting from a suddenly applied steady voltage is the indicia1 transfer function of Carson1 6 which has been extensively studied in network theory. The discussion here, with one special exception, will ignore the problem of how the physical configuration of the earth affects the transient response voltage; it appears that this phase of the problem has been solved in only a few special cases having any direct bearing on the prospecting problem. Entirely distinct from the potential-theory aspect of the conductivity problem is the interesting material that can be had from studying the well-known network relations between cause and effect in linear circuits, and thus deducing criteria for the application of the several experimental methods available. To do this, only one assumption need be made about the nature of the earth. The earth is to be considered a linear conductor within the tolerance of ordinary measurements. The discussion will be restricted to collinear electrode configuration like that of Fig. I, since this is the only type of spread practical for use with driving currents that vary with time. Here one pair of grounds carries the driving current, and in line with these and external to them is a RECORDING Fair of potential probes. The problem will be to consider the relation between the different voltages appearing between the potential circuit terminals when various types of driving voltage sources are inserted in the current circuit. Suppose that the grounding points G, and G2 make good contact with the earth, and that a battery of sufficient voltage to produce one ampere of direct current is introduced into the current circuit by the closing of a switch. The potential transient response to such a voltage can be measured by taking an oscillogram at the potential Directors terminals, giving the time function that has been called A(l).4 This time function has been solved for analytically in the case of a homogeneous earth,"&apos; and the

Jan 1, 1946

By Gifford E. White

Explanations of the basic procedure for making earth-conductivity studies by the Eltran method have already appeared in several placeS. 1,2,3 In its essentials, this method consists of applying step functions of voltage to one pair of earth grounds and measuring the transient potential resulting at a separate pair of ground points. As previously pointed out,&apos; the transient potential resulting from a suddenly applied steady voltage is the indicia1 transfer function of Carson1 6 which has been extensively studied in network theory. The discussion here, with one special exception, will ignore the problem of how the physical configuration of the earth affects the transient response voltage; it appears that this phase of the problem has been solved in only a few special cases having any direct bearing on the prospecting problem. Entirely distinct from the potential-theory aspect of the conductivity problem is the interesting material that can be had from studying the well-known network relations between cause and effect in linear circuits, and thus deducing criteria for the application of the several experimental methods available. To do this, only one assumption need be made about the nature of the earth. The earth is to be considered a linear conductor within the tolerance of ordinary measurements. The discussion will be restricted to collinear electrode configuration like that of Fig. I, since this is the only type of spread practical for use with driving currents that vary with time. Here one pair of grounds carries the driving current, and in line with these and external to them is a RECORDING Fair of potential probes. The problem will be to consider the relation between the different voltages appearing between the potential circuit terminals when various types of driving voltage sources are inserted in the current circuit. Suppose that the grounding points G, and G2 make good contact with the earth, and that a battery of sufficient voltage to produce one ampere of direct current is introduced into the current circuit by the closing of a switch. The potential transient response to such a voltage can be measured by taking an oscillogram at the potential Directors terminals, giving the time function that has been called A(l).4 This time function has been solved for analytically in the case of a homogeneous earth,"&apos; and the

Jan 1, 1946

FOLLOWING the presentation at the annual meet-ing of the paper "Recent Developments in Classi-fication," by A. M. Gaudin and W. L. Remick, the discussion presented below took place: H. N. Spicer : I haven&apos;t been able to study this paper closely, but I would like to ask &apos;Mr. Remick something regarding the work done by the mechanical classifier. The screen test given here would appear to show that the classi-fier did very, very poor work. The 44 per cent efficiency calculated from this equation is much lower than any ordinary operation. Nothing is stated regarding the de-tails. of the operation, the slope of the classifier, the dilu-tion, the speed, and such other factors that influence results. I would also like to know something of the material that was worked. The Manhattan schist that I have seen them digging out of the subways is of a flaky nature, so that in any classifier, you might get the factor of fine flakes floating over. Was the same material used in the hydrotator test? The screen tests vary a whole lot. Mr. Remick: You will notice the Dorr classifier han-dled the circulating load. This classifier naturally was run in closed circuit. I should like to be pardoned for quoting from Mr. Bates&apos; paper of last year on "Classifica-tion in the Witwatersrand Mills." In this report only two efficiencies were given for the so-called straight type Dorr classifier. One was 44.6 per cent and the other 61.6. I don&apos;t know whether or not an average should be taken for the proper performance. I assume that that test was performed under better conditions, yet the efficiencies av-eraged only 53.1 per cent. I am afraid I am taking the words out of Professor Taggart&apos;s mouth, but he has told me that the Dorr classi-fier at Columbia is not the proper size to work with the Hardinge mill with which it is connected. This indicates only the inadvisability of putting commercial sized mat chines in a school laboratory. You cannot, he says, get the proper tonnage from the Hardinge mill to work the Dorr classifier and get the best results. Mr. Bates&apos; results show higher efficiency with the lower capacity. Now, on the other hand, I assume that the classifier described in Mr. Bates&apos; paper was probably run at the proper capacity.. It is a rather puzzling question.

Jan 4, 1927

"The greatest mining center in the state of Utah is the incorporated town of Bingham about twenty-five miles southwest of Salt Lake City. The principal industry of this vicinity, prior to the early fall of 1 863, was lumbering and the first saw-mill in the state was built near the mouth of Bingham Canyon. Early in the fall of that year, George B. Ogilvie discovered gold and shortly afterward the first mining district in the state was organized. Some writers place the discovery of gold in the canyon in the late fifties. If this be so, however, the matter was kept extremely quiet because no mining was engaged in until after Ogilvie's discovery.Bingham was a placer mining camp, producing about one million dollars' worth of dust and nuggets from placers up and down the canyon and in Bear Gulch until early in the seventies, or about ten years after the discovery of gold, when a large body of argentiferous lead ore was discovered and soon after heavy shipments were made from a half dozen or more properties.In 1 8 74, A. H. and George L. Bemis erected the first concentrating plant in the state for the treatment of sulphide lead ores.The history of the camp as a producer of copper begins in the summer of 1 88 7, when Enos A. Wall noticed, in observing prospecting drifts and inclines driven some years before, the discoloration caused by the coppery solution. As a large part of the adjacent ground had been abandoned, he located two claims, which he called the ""Dick Mackintosh"" and the ""Charles Reid,"" after two of his friends.Late in 1896, the Highland Boy Mine produced sulphide ore rich in copper, causing a revival of interest in the copper potentialities of the camp, and during the next seven years a number of new claims were located ."

Jan 1, 1925

By Clyde Williams

A MAN who is a first-class metallurgist, engineer, and scientist and an outstanding organizer, administrator, and executive and who, at the same time, has an innate ability to "make friends and influence people" everywhere he goes is an exceptional personality at any time. And if such an individual can retain this combination of virtues during a great war despite the fact that the Government loaded him with enough work and responsibility for three such men. he is a most exceptional personality. And if he can keep his head and maintain an unfailing sense of humor during the trying war years and, while dealing with hundreds of jittery metallurgists and metalworkers, with Army and Navy brass, and with red-tape-entangled war agencies by the dozen, he is a rare personality indeed. Such a man is Clyde Williams, director of Battelle Memorial Institute. who will be President of AIME in 1947. The Institute is fortunate in having him as its mentor during what may be a critical and important year.

Jan 1, 1947

By Edward Saibel

The object of this study is to investigate the effect of prior tensile strain on the fracture stress of a metal. This is done in a theoretical manner starting from the point of view developed by the author in his thermodynamic theory of the fracture of metals. The results are compared with experimental findings and a rational interpretation is given to work that shows the variation of fracture stress with prior tensile strain. Theory op Fracture In the thermodynamic theory of the fracture of metals developed earlier,&apos; it was shown that a critical strain energy per unit volume exists. This is characteristic of the material and may be calculated from basic thermodynamic data. When the area under the flow curve reaches this characteristic value, fracture occurs. The general criterion for fracture is expressed in the form « ± u. = JLJW/V [r] where L, is the latent heat of melting of the unit volume, AV/V is the ratio of the change in volume of the unit volume to the original unit volume on passing from the solid to the liquid state, uo is an initial energy density, and J is a conversion factor, which changes energy from heat to mechanical units. As a first approximation, it will he assumed that the stress-strain curve is the straight line that extends from the point of maximum load onward, extrapolated back to the axis of zero strain, for example, line AC of Fig. I. If the point of intersection of the straight line with the axis of zero strain is represented by v., and the slope of the straight line is p, the analytic form of the flow curve is a = (To + pd [2] and the strain energy per unit volume evaluated from Jud6 becomes (u,6 + pa2/2). When this latter term reaches the critical value JLbVIV (designated hereafter by M), it is assumed that fracture occurs. This leads to the following expression for the fracture stress: a; = V«r.2 + iMp [3] The strain at fracture may be calculated from Eqs 2 and 3. It is assumed in this paper that the initial energy density is either zero or that it may be neglected. Furthermore, the complicated states of stress and of strain existing in the necked region of the tensile specimen after "necking" has occurred will also be neglected for the present, so that average conditions will be assumed to prevail. Flow and Fracture Curves LudwigZ attributed to materials two fundamental properties: (I) a resistance to flow and (2) a resistance to fracture. He reasoned that at each instant the

Jan 1, 1948

By Edward Saibel

The object of this study is to investigate the effect of prior tensile strain on the fracture stress of a metal. This is done in a theoretical manner starting from the point of view developed by the author in his thermodynamic theory of the fracture of metals. The results are compared with experimental findings and a rational interpretation is given to work that shows the variation of fracture stress with prior tensile strain. Theory op Fracture In the thermodynamic theory of the fracture of metals developed earlier,&apos; it was shown that a critical strain energy per unit volume exists. This is characteristic of the material and may be calculated from basic thermodynamic data. When the area under the flow curve reaches this characteristic value, fracture occurs. The general criterion for fracture is expressed in the form « ± u. = JLJW/V [r] where L, is the latent heat of melting of the unit volume, AV/V is the ratio of the change in volume of the unit volume to the original unit volume on passing from the solid to the liquid state, uo is an initial energy density, and J is a conversion factor, which changes energy from heat to mechanical units. As a first approximation, it will he assumed that the stress-strain curve is the straight line that extends from the point of maximum load onward, extrapolated back to the axis of zero strain, for example, line AC of Fig. I. If the point of intersection of the straight line with the axis of zero strain is represented by v., and the slope of the straight line is p, the analytic form of the flow curve is a = (To + pd [2] and the strain energy per unit volume evaluated from Jud6 becomes (u,6 + pa2/2). When this latter term reaches the critical value JLbVIV (designated hereafter by M), it is assumed that fracture occurs. This leads to the following expression for the fracture stress: a; = V«r.2 + iMp [3] The strain at fracture may be calculated from Eqs 2 and 3. It is assumed in this paper that the initial energy density is either zero or that it may be neglected. Furthermore, the complicated states of stress and of strain existing in the necked region of the tensile specimen after "necking" has occurred will also be neglected for the present, so that average conditions will be assumed to prevail. Flow and Fracture Curves LudwigZ attributed to materials two fundamental properties: (I) a resistance to flow and (2) a resistance to fracture. He reasoned that at each instant the

Jan 1, 1948

By Clarence O. Babcock

Model pillars of limestone, marble, sandstone, and granite, with length-to-diameter (LID) ratios of 3, 2, 1, 0.5, and 0.25 (0.286 for granite), were broken in axial compression to determine to what extent an increase in end constraint increased compressive strength. Radial end constraints of 13 to 23% of the average axial stress in the pillar, produced by solid steel rings bonded with epoxy to the ends of dogbone-shaped specimens, increased compressive strength somewhat above that of cylindrical pillars without ring constraint. However, when the results were compared with those obtained by other investigators for straight specimens of several rock types taken collectively, with LID ratios greater than 0.5, the resulting strengths were not significantly different. Thus, the amount of end constraint produced by the solid steel rings was about the same as that produced by the friction from the steel end plates. In other tests, a radial prestress of 3000 or 5000 psi was applied prior to axial loading by adjustable hardened steel rings to increase the constraint above that obtained for the solid rings. The average radial constraint stress, expressed as a percentage of the average axial pillar stress at failure for the 3000 psi prestress, was 54.3% for limestone, 40.3% for marble, 44.7% for sandstone, and 23.4% for granite. The average radial constraint stress, expressed as a percentage of the average axial pillar stress at failure for the 5000 psi prestress, was 74.2% for limestone, 51.2% for marble, 61.6% for sandstone, and 29.7% for granite. These constraints increased the compressive strength significantly above the strength of straight specimens and solid-ring constrained specimens. These results suggest that large horizontal stresses in orebodies mined by the room-and-pillar method should increase the strength of the pillars and allow an increase in ore recovery by a reduction of pillar size when major structural defects are absent. One important objective of the U.S. Bureau of Mines (USBM) mining research program is the rational design of mining systems. In the design of room-and-pillar mining operations, pillar strength is a fundamental variable. It is customary to estimate this strength from uniaxial compression tests of rock samples and to correct this value for the length-to-diameter (LID) ratio of the in-situ pillar. This method of estimating pillar strength corrects for pillar shape but does not consider the effect of a large horizontal in-situ stress field that sometimes exists in underground formations. The purpose of the work covered in this report was to determine to what extent the compressive strengths of model pillars of relatively brittle rock loaded in axial compression were affected by lateral end constraint. In previous work, Obert l used solid steel rings bonded to the ends of dogbone-shaped specimens to study the creep behavior of three quasi-plastic rocks -salt, trona, and potash ore - during a test period of 1000 hr. These rings provided radial constraint during the loading cycle of 20 to 50% of the axial stress for specimens with LID ratios of 2, 0.5, and 0.25. He concluded that (1) "for a quasi-plastic material the end constraint strongly affects the specimen strength, and (2) as D/L increases (length-to-diameter decreases), the specimens lose their brittle characteristics and tend to flow rather than fracture." He also concluded that model pillars constrained by rings were better for use in predicting the strength of mine pillars than either cylindrical or prismatic specimens. This conclusion appears to be valid where mine pillars, roof, and floor are a single structural element. In the present study, 460 specimens of four relatively brittle rocks — limestone, marble, sandstone, and granite - were tested to failure. The study consisted of two parts: (1) the effect on the compressive strength of end constraint produced during the axial loading cycle by solid steel rings bonded with epoxy to the ends of the specimens, and (2) the effect on the compressive strength of increased end constraint produced in part by a prestress applied prior to axial loading and in part by lateral expansion of the specimen during the loading cycle. The first part of this study was reported in some detail earlier.2 EXPERIMENTAL PROCEDURE AND EQUIPMENT Model rock pillars of the sizes and shapes shown in Fig. 1 were broken in axial compression when the ends were constrained as shown in Fig. 2. he straight specimens were broken without ring constraint. The specimens of dogbone shape were broken with (1) solid

Jan 1, 1970

By R. W. Fountain, W. D. Forgeng, G. M. Faulring

Precipitation of the phase Co3Ti (Cu3Au type) from a Co-5 pct Ti a11oy has been investigated using single-crystal X-ray diffraction techniques. Oscillation and transmission Laue patterns of specimens aged for short-time periods at 600" C indicate the formation of titanium-rich and titanium-poor zones coherent with the {100} matrix planes. Longer aging times at 600° C establish that the equilibrium phase also forms on the {100} matrix planes as platelets. These observations are corroborated by electron metallography; electron diffraction studies show the phase Co3Ti to be ordered. A probable sequence of the precipitation reaction is discussed. A previous publication by two of the present authors reported on the phase relations and precipitation in Co-Ti alloys containing up to 30 pct Ti.1 The results of this investigation established the existence of a new face-centered cubic inter metallic phase, ranging in composition from about 17.0 to 21.7 pct Ti at temperatures below 1000° C The decomposition of the fcc supersaturated solid solution was studied employing hardness and electrical resistivity measurements. The changes in hardness upon precipitation in alloys containing 3, 6, and 9 pct* Ti were found to be associated with an initial increase in hardness followed by a plateau and then a second, more pronounced hardness increase. Investigation of this behavior by electrical resistivity measurements suggested that two different kinetic processes were involved, which, when interpreted in terms of the kinetic relation,2-4 indicated that initial precipitation was in the form of thin plates. On continued aging, the plates impinged during the growth process. The general features of these findings have been confirmed by Bibring and Manenc,5 while, in addition, they report the phase to be ordered. The present investigation was undertaken to provide more definite information on the structural relationships between the precipitate and the matrix. EXPERIMENTAL PROCEDURE Single crystals of a (20-5 pct Ti alloy were prepared from the melt employing the Bridgman technique. Poly crystalline rod, 1/2 in. in diam, prepared from vacuum-melted material, was machined to 3/8- in. diam to remove any surface contamination that may have resulted from hot-working. The crystals were grown under a purified hydrogen atmosphere in high-purity alumina crucibles heated by induction. Considerable difficulty was encountered in attempting to grow monocrystals because of the high melting point of the alloy and the high solute concentration. However, one crystal about 6 in. long was obtained which was essentially a single crystal except for one or two very small grains around the periphery. The as-grown crystal was solution heat-treated for 24 hr at 1200°Cin a purified argon atmosphere and water-quenched. One-quarter-in. slices were taken from each end of the solution heat-treated crystal for chemical analyses, and the remainder of the crystal was mounted and oriented by the back reflection Laue Method. The chemical analysis of the crystal was as follows: Pct Ti Pct 0 Pct C Pct N Pct H Pet CO 5.29 0.08 0.004 0.002 0.0003 Balance By proper tilting of the crystal, it was possible to obtain slices 1/32 in. thick of [loo] and [110] orientation. The solution heat-treated crystal slices were sealed in silica capsules for the aging treatments, with titanium sponge placed at one end of the capsule to act as a getter. All slices were water-quenched from the aging temperatures, the capsules being broken under the water to ensure a rapid quench. Thinning of the slices for transmission X-ray studies was accomplished by a combination of mechanical and electrolytic techniques, the final thickness being about 0.1 mm. Laue patterns of the solution heat-treated crystal indicated that no strain was introduced by the thinning technique. ELECTRON METALLOGRAPHY After X-ray examination, the structural changes attending the precipitation were followed by examination of direct carbon replicas of polished and etched surfaces of the single-crystal slices and extracted phases. The earliest indication of significant structural change was observed after aging at 600°C The structure of a heavily etched, solution-treated crystal is shown in Fig. l(a). Aside from the etch pit pattern, no regularity of background structure is observed. On the other hand, in the background of the specimen heated for 500 hr at 600°C, the etching pattern shows a directionality indicating the influence of minute precipitate particles, Fig. l(b). On electrolytic dissolution of this specimen in 10 pct HC1 in alcohol, a large volume of very small, flattened cubes

Jan 1, 1962

By R. M. Waterstrat

The phases occurring in the V-Mn system were studied by means of X-yay diffraction and metallo-paphic techniques, using are-melted alloy specimens annealed in the temperature range 800° to 1150°C and quenched. The bcc solid solution extends at 1250°C all the way from vanadium to 6-manganese. Below 1050°C the a-phase is formed, and the terminal a-manganese phase is stabilized up to about 900°C by vanadium in solid solution. IN the only previous general survey of the V-Mn system Cornelius, Bungardt and Schiedtl reported the existence of three intermediate phases corresponding to the approximate compositions VMn,, VMn, and V5Mn. The phase VMn8 has recently been identified as a o phase2 but the alloy VMn was found to have a bcc structure2 corresponding apparently to the vanadium solid solution rather than to the large cubic unit cell reported by Cornelius et al. 1 Subsequent work by Rostoker and Yamamoto3 has shown that the vanadium-base bcc solid solution extends to at least 15 pct Mn at 900°C. An alloy corresponding to the composition VMn, was examined by Elliott,4 who reported that the as-cast sample as well as samples annealed at 1200o and 1300°C had bcc structures, but that annealing at 1000°, 800") and 600°C produced two phases. One of these phases was apparently the bcc solid solution and the other resembled the o phase structure. Hellawell and Hume-Rothery5 established the phase relationships in manganese-rich alloys above 1000°C, and showed that the o phase in this system is replaced by the 6 Mn (bcc) solid solution at temperatures above 1050°C. These results suggest that a continuous bcc solid solution may exist above 1050°C between vanadium and 6 Mn. The present investigation was undertaken in order to develop more complete information in regard to this system. EXPERIMENTAL METHODS The alloys used in the present work were prepared by arc-melting electrolytic manganese having a minimum purity of 99.9 pct and vanadium lumps with a purity of 99.7 pct. The major impurities present in these metals were carbon, nitrogen, and oxygen and this would account for the small percentage of nonmetallic inclusions observed metal-lographically. The arc-melting was at first performed under a helium atmosphere and it was necessary to keep the melting times as short as possible in order to minimize the loss of manganese by vaporization. It was later found that the evaporation of manganese was considerably reduced when the melting was done under argon atmosphere. The final composition of each alloy was calculated by assuming that the total weight loss during melting was due to evaporation of manganese. Compositions which were calculated in this manner agreed reasonably well with the results of chemical analysis, as shown in Table I. Spectrographic analysis revealed the presence of contamination by tungsten, but in no case was the percentage of tungsten greater then 0.4 at. pct. The specimens were in each case broken in half and the fractured section was examined visually and microscopically for evidence of inhomogeneity. Each specimen was homogenized at temperatures near l100°C, as shown in Table I. After this treatment most specimens consisted of large columnar grains of the bcc vanadium solid solution. The etchant used in most of the metallographic work consisted of 20 pct nitric acid, 20 pct hydro-flouric acid, and 60 pct glycerine. It was found that this etchant would clearly delineate the phases present in these alloys although it does not produce any striking contrast between the phases. For certain manganese-rich alloys, a 1 pct aqueous solution of nitric acid was used. This etchant gave a brown color to the a-manganese phase, whereas the o phase was virtually unattacked and appeared very light as shown in Fig. 1. The etchants used by Cornelius et a1.l were found to produce spurious effects in some of these alloys. In particular, the vanadium-rich alloys etched in hot sulfuric acid often appeared to consist of two phases when both X-ray diffraction and etching with the glycerine-acid mixture indicated the presence of single phase bcc solid solution. A few percent of what appears to be an oxide or nitride phase was found at the grain boundaries and in the interior of the grains, especially in the vanadium-rich alloys. All alloys were annealed in sealed silica tubes containing 1 atm of pure argon and these tubes were then quenched in cold water. Although some manganese loss occurred during annealing, the loss seemed to be confined to the surface of the speci-

Jan 1, 1962

By Benjamin Petkof

The mineral mica, which has been known to man since ancient times, has played an impor¬tant role in the development of our modern industry. In the latter part of the 19th century sheet mica began finding use as a dielectric insulating material in the newly developing electrical industry. Later, when modern elec¬tronics began to develop, it became a vital insulating and dielectric material for use in electronic equipment. Both the electrical and electronic industries were greatly dependent on some form of natural mica. The manufacture of electric motors of varying sizes, electronic tubes, and other electronic items was dependent on an adequate supply of sheet mica. During World War II this material was so vital to national defense that special efforts were made to mine it in the United States as well as to obtain it from overseas mica-producing areas. However, advancing technology has successfully begun the progressive development of man-made mica-based and non-mica-based materials that can replace mica for many uses. In addition, developing technology has dictated changes that have made sheet mica unnecessary for some uses. As the demand for sheet mica declined, the demand for scrap and flake mica has continued to increase. In fact, today the domestic production and use of scrap and flake mica far outshadows the necessity for good¬quality sheet mica in this country. Historically the United States has always been dependent on foreign sources of material for good-quality sheet mica and imports practically its entire requirement. In the case of scrap and flake mica, the United States is the dominant world producer and consumer. End Uses Sheet mica (Chowdhury, 1941; Rajgarhia, 1951; Skow, 1962) is available in many com¬mercial forms, but these forms can be broadly classified into manufactured and unmanufac¬tured mica. Manufactured mica consists of mica that has been shaped, punched, or other¬wise processed into some form, suitable for a particular end use. Unmanufactured mica con¬sists of partially hand-trimmed or processed material that has not been prepared for any particular end use. Unmanufactured mica is broken into two commercial classes consisting of sheet mica and scrap and flake mica. These classes of mica differ greatly in their ultimate end uses and marketed forms. Sheet muscovite mica can be classified by color, degree of prep¬aration of the crude material, thickness, size, visual appearance, and electrical quality. In addition, phlogopite mica is also classified by its thermal stability. Scrap and flake mica consist of mine, trimming shop, and factory scrap that occurs as remnants from mining, processing, and manufacturing operations, and small particle size mica that is available from the beneficiation of pegmatites, clays, schists, or other mica-rich host rock. The end uses for sheet mica vary so greatly from those of scrap and flake mica that it is necessary to discuss them separately. Sheet Mica Sheet mica consists of relatively flat sheets of material which have been mined as naturally occurring books or runs of mica. These sheets are hand-trimmed to remove any imperfections and are punched or stamped into specified shapes for industrial use. Sheet mica can be further processed and is described or specified as block, film, or splittings based on thickness. Block mica is not less than 0.007 in. thick with a minimum usable cross-sectional area of 1 sq in. Film mica is split from the better quali¬ties of block mica to specified thickness groups ranging from 0.0012 to 0.004 in. Splittings are sheets of mica with a maximum thickness of 0.0012 in. and a minimum usable area of 0.75 in. Other small sized, lower quality block mica

Jan 1, 1975

By Donald A. Brobst

The minerals barite (BaSO4 barium sulfate) and witherite (BaCO3 barium carbonate) are the chief commercial sources of the element barium and its compounds whose many uses are nearly hidden among the technical complexities of modern industrial processes and products. Barite, the major ore mineral, is extremely vital to the petroleum industry which in 1973 consumed at least 80% of the world&apos;s produc¬tion of 4.4 million tons as a major ingredient of the heavy fluid, called mud, that is circulated in rotary drilling of oil and gas wells. The re¬maining 20% of the barite production was consumed chiefly in the manufacture of barium chemicals and glass and as a pigment, filler, and extender. Barite occurs throughout much of the world and is available from three major geologic types of deposits-vein and cavity fill¬ing, residual, and bedded-in sufficient quantity at competitive prices to meet current demands. The world&apos;s demand for barite is expected to increase, and geologic circumstances are favor¬able for the discovery of new deposits of com¬mercial value. Witherite is much less common and abun¬dant than barite, although it is more desirable in many ways as a raw material for the pro¬duction of barium chemicals. The United States has not produced witherite since about 1950; England is currently the chief producer of witherite. End Uses Most of the world&apos;s barite production since 1926 has been used as a weighting agent for the muds circulated in rotary drilling of oil and gas wells. The muds fundamentally are mixtures of water, clay, and barite in different proportions that vary according to local reservoir condi¬tions. Muds with a specific gravity as great as 2.5 are used. The mud is pumped down the hollow drill stem, passes through the bit at the bottom of the hole, and rises to the surface in the space between the drill stem and the wall of the hole. In the course of this circulation the drill bit is cooled, cuttings are removed, the drill stem is lubricated, the walls of the hole are sealed, and the hydrostatic head of the column of weighted fluid helps to confine high oil and gas pressures. The latter feature aids in prevention of gushers, thus reducing both environmental pollution and waste of oil and gas resources as well as conserving the natural reservoir pressure for greater production and rate of recovery of the products contained in the rocks. Barite is particularly well suited for drilling mud because it is clean, easy to handle, soft (nonabrasive), heavy, virtually inert chemi¬cally, and relatively inexpensive compared to many other available heavy materials. Barite is used in the manufacture of glass in continuous tanks. The addition of barite ho¬mogenizes the melt and gives greater brilliance and clarity to the finished glass. Ground barite, both unbleached and bleached by sulfuric acid, is a common industrial filler, extender, and weighting agent. The rubber in¬dustry is a major consumer of barite as a filler. Barite also is added to bristolboard, heavy printing paper, playing cards, rope finishes, brake linings, clutch facings, plastics, and li¬noleum, to name but a few uses. Bleached barite has long been an extender in white lead paint because of its weight. The low index of refraction of barite, however, makes its ability to cover marks poorer than some other sub¬stances, but its low capacity for absorption of oil is a good feature. Off-color or unbleached barite can be used as a filler in colored paints. In the construction industry, some lump barite is used in concrete aggregate to weight down pipelines buried in marshy areas and to shield nuclear reactors. Because barite absorbs gamma radiation well, its use reduces the amount of expensive lead shielding otherwise

Jan 1, 1975

By R. E. Ogilvie, J. I. Goldstein

The a and y solubility limits in the Fe-Ni phase diagram have been redetermined at temperatures above 500°C. Both a diffusion-couple and a quench and anneal technique were used. The solubility limits were measured with an electron-probe micro-analyzer. The nickel concentration at the phase boundary is increased below 700°C and the a solid-solubility range is much larger than had been previously measured. The solubility limits are also extrapolated to 300°C. It is suggested that the solubility of nickel in a FeNi reaches a maximum in the temperature interval 400o to 500°C. THE equilibrium diagram has been of great use in the field of meteoritics, where the phase relations between kamacite (a) and taenite (?) in metallic meteorites can be described by means of the Fe-Ni diagram. The study of metallic meteorites by electron-probe microanalysis has cast some doubt on the accuracy of the presently available Fe-Ni diagrams.1, 2 Recent thermodynamic studies of the Fe-Ni system also suggest that the diagram may be in error.3 For these reasons the high-temperature (800o to 500°C) part of the diagram was redetermined. INTRODUCTION The currently accepted Fe-Ni diagram is that of Owen and Liu.4 Above 910°C, there is a region of complete solid solubility, ? (fee). Below 910°C, the a (bee) phase is stable in pure iron. The effect of increasing amounts of nickel is to stabilize the y phase. The phases that form when Fe-Ni alloys are heated or cooled bear little relation to the equilibrium diagram. If an alloy is cooled from the y state and held at a temperature within the a + y field, no evidence has been found for the occurrence of the y - a transformation.5 If the alloy is cooled to low enough temperatures the y phase breaks down into a supersaturated bee phase called a2. In fact, in alloys over 27 pet Ni the y phase is retained at room temperature.6 The a, phase has the same composition as the original y. The temperature at which a2 forms, the M, temperature, has been determined experimentally.&apos; A state of equilibrium can be approached by cooling below M, to form a2 and then reheating the alloy into the two-phase region of the diagram. The y phase will then begin to precipitate out of the a2 phase and grow. The growth of the phase, however, is quite slow. Using the interdiffusion coefficients -Da of Goldstein et al.,8 it is estimated that it takes about 1 year to grow a 10-µ-wide region of ? at 700°C in a 5 pet Ni alloy. Owen and Liu4 used the technique just described to form the equilibrium phases. The phases present were determined by means of X-ray analysis. The accuracy of their diagram depends on the number of alloys available near the phase boundary at a given temperature. In this study two different techniques were used to determine the a/a + ? and ?/a + ? solubility limits. The inherent accuracy of both techniques was greatly improved over that used by previous investigators because the phase-boundary compositions were measured with an electron-probe microanalyzer. PROCEDURE The two methods used to determine the Fe-Ni diagram are the diffusion couple (D.C.) and the quench-and-anneal (Q.+A.) techniques. In the first method, diffusion couples whose diffusion path goes through a two-phase region of the phase diagram were used. A description of the technique used for making the diffusion couples has been described in a previous paper.&apos; After the diffusion treatment a discontinuity in the resultant concentration vs distance profile was measured. The nickel concentrations in the a and ? phases at the interface of the discontinuity are the solubility limits of the a and ? phases in the phase diagram at the diffusion temperature. If the interface com-

Jan 1, 1965

By J. C. Swartz

Measurements of the effect of precipitation stresses on the solubility of cementite (Fe3C) precipitates in a iron are reported. Solubilities were determined from measurements of the Snoek relaxation due to interstitial carbon after quenching from various equilibrium treatments. Stress-free precipitates were obtained by a spheroidizing treatment of vacuum-melted Fe 0.06 wt pet C. Subsequent equilibration treatments were designed to suppress nucleation of other precipitates. The results for stress-free cementite give a heat of solution of 14.8 i 0.2 keal per mole and an entropy change of 1.1 i 0.2 eu in the temperature range 400" to 715°C. Comparison with previous data indicates that the heat of solution increases about 6 keal per mole as temperature increases from 700" to 1000°C. Data on self-stressed cementite in quench-aged specimens of Fe 0.013 wt pet C indicate 1) an apparent heat of solution of 12.1 i 0.4 keal per mole in the range 280" to 690°C, 2) a strain energy of- 1.1 keal per mole Fe3C accompanying precipitation at 280°C, and 3&apos;) a gradual decrease in the strain energy of precipitation with increasing equilibration temperature. In com-parison with 2 and 3 the strain energy calculated for an isotropic model is 1.7 keal per mole Fe3C. The lower values obtained from the experiment indicated substantial stress velaxation by dislocation motion. WHEN a supersaturated solution of carbon in a iron is aged at temperatures in the range 200o to 700oC, the carbon clusters by interstitial diffusion and forms cementite (Fe3C) precipitate particles. Unstressed cementite has a volume per iron atom 9 pet higher than that of a iron;&apos; hence, cementite precipitate particles are usually under pressure from the iron matrix. The pressure would tend to increase the solubility of cementite in iron.&apos; This report describes anelastic measurements of the solubilities of self-stressed and stress-free cementite in a iron. Previous determinations of the cementite solubility are summarized in Table I. The method of cementite formation for each reference was studied to ascertain the state of stress of the cementite. The results judged to be for stress-free and stressed cementite are distinguished in the table. In the next section an estimate of the stress effect is obtained which is clearly too small to account for the large difference between the previous results in parts A and B of the table. THEORETICAL Let AGO be the standard free-energy change of the reaction Fe3C (eem.) = 3Fe (a) + C (in a) [1] in the absence of stresses. Since cementite precipitates appear to be rather pure10 and the carbon is so dilute in the iron,8 the cementite and iron of Eq. [ I] for the stress-free case have essentially unit activities and the activity of carbon equals its atom fraction xoC Then the stress-free equilibrium is expressed by RT In XoC = -?GO 121 To first approximation the change in the chemical potential of carbon due to the precipitation stresses equals the elastic strain energy W accompanying precipitation of a mole of cementite.2 Hence, in the presence of the precipitation stresses the equilibrium is described by RT In x sq = -?G° + W [3] where xsC is the mole fraction of dissolved carbon in the stressed case. An approximate value of W can be obtained from analysis of the inclusion problem in elasticity theory. The inclusion is a small portion of the matrix phase which has suffered a transformation while still imbedded in the matrix. In the absence of the constraint of the matrix the transformation would be equivalent to a uniform dilational strain eT. Both the matrix (a) phase and inclusion (0) phase are assumed to be homogeneous, isotropic materials. When the a and 0 phases have the same elastic moduli, which is approximately true for iron and cementite,11 the total strain energy per mole ß is12 2µVß(eT)2(3 +4 µx)-I [4]

Jan 1, 1968

By Ralph Hultgren, Bernard York, David W. Mitchell

It is a well-known fact that magnesium-alloy castings are apt to be coarse grained if the melt is not superheated several hundred degrees above the melting point before casting. (The casting temperature varies according to the shape of the mold. A typical casting temperature is perhaps 1400°F.) British practice is to heat to 900°C. (1650°°F.) for 15 min., cool rapidly to casting temperature, and cast.1 In Germany superheating is carried out at 850° to 900°C. (1560° to 1650°F.) depending on the amount of scrap used. It is stated that further refinement will be obtained by prolonging the period of superheating or by increasing the superheat temperature to 950°C. (1740°F.).2 In the United States superheating is carried out at i600° to 1700°F. (871° to 927°C.), perhaps even higher in some places. It is stated that superheating effects are found as low as 1500°F. (816°C.), but several hours are required.3 These commercial treatments lead to grain sizes in sand castings that may vary from 4 to 8 grains per sq. mm.§ in heavy sections and from 60 to l00 in 3-in sections to perhaps 380 in thin sections. It is also generally known that the refining effect of superheating is lost if the melt is held for some time at lower temperatures before casting. Aside from these very qualitative statements, there is little to be found in the literature as to the effect of temperature and time of superheat on the final grain size. Because of the uncertainty of these factors, the Office of Production Research and Development of the War Production Board placed a research contract with the University of California, supervised by the War Metallurgy Committee. This research, which was done under the "Restricted" Project NRC-550, is the basis of this paper, which has been released for publication by the O.P.R.D. The material studied was an alloy prepared from carbothermic magnesium. The temperatures required for grain refinement proved to be widely different from those used in practice, as described in the statements in the first paragraph. This difference is attributed to the fact that the magnesium in the specimens was of carbothermic origin instead of the electrolytic magnesium in common use. MATERIALS AND METHODS The magnesium alloy studied was one of the most popular sand-casting alloys, with a nominal composition of 9 per cent aluminum, 2 per cent zinc, and 0.r per cent (minimum) manganese and the balance magnesium. This is designated

Jan 1, 1945