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By J. R. Cahoon, H. W. Paxton

The possibility of using unidirectionally solidified, two-phase alloys as an approximation to fiber composite materials is investigated. The short-term me.chanical properties and failure modes of unidirectionully solidified A1 (rich)-Cu alloys containing ap -Proximately 0, 17.5, and 27.7 vol pct of 0 phase 'fibers" are determined at temperatures from 25" to 500" and compared with those obtained for conventionul SAP alloys. In a previous publication,' hereafter referred to as I, the possibility of understanding some of the room-temperature mechanical properties of unidirectionally solidified castings was explored. For Al(rich)-Cu and Al(rich)-Mg two-phase alloys over a substantial range of compositions, the yield and ultimate strengths and common ductility measures were very adequately predicted from the principles of fiber strengthening4 and the analysis of ductility outlined by Gurland and Plateau." The results obtained in I suggest the possibility of using unidirectionally solidified, two-phase alloys to simulate fiber composite materials where the inter-dendritic second phase or constituent acts as the reinforcing material. Recent attempts concerning the fabrication of fiber conlposites have concentrated on producing composites with a good bond between fiber and matrix and with very long fibers so that their maximum contribution to the strength of the composite may be realized. However, these objectives are difficult to attain in practice and present fabrication processes are either extremely laborious or costly.13 The slow, unidirectional solidification of eutectics has received considerable attention as a method for producing composite materials. 5,6 This method can fulfill both of the above objectives but it is currently laborious, expensive, and has the additional disadvantage that the volume fraction of reinforcing phase cannot be easily varied. On the other hand, unidirectionally solidified, two-phase alloys, also with a good bond between the phases, are relatively easy to make and the volume fraction of reinforcing "fibers" can be easily varied by changing the average composition of the alloy. The disadvantage of the cast alloys is that the mechanical effectiveness of the "elongated interdendritic reinforcements" (EIR)* may be reduced due to their rela- tively short lengths, the w factor in Eq. [2] of I. However, if the EIR have a high strength their contribution can be considerable. For composite materials containing discontinuous cylindrical fibers of various lengths the ultimate strength is given by1 where it is assumed that the composite fractures when the fibers fail. In Eq. [I], a, is the stress in the matrix just prior to failure of the composite, Vf is the total volume fraction of fiber reinforcing constituent, Vf(l+) is the volume fraction of fibers whose lengths exceed the critical length, I,, which is defined as the shortest length of fiber in which the stress can build up sufficiently to break the fiber. af is the fracture strength of the fiber material, w is a factor accounting for the discontinuity of those fibers whose lengths exceed I,, 1-/d is the average aspect ratio of those fibers whose lengths are shorter than I,, and t is the shear stress in the matrix at the fiber-matrix interface. The factor w is dependent on the length of the fibers and also on whether deformation of the matrix occurs plastically or elastically. However, for a given length of fiber, w is smaller when elastic deformation of the matrix is assumed.' It is of interest to consider the properties of simple unidirectionally solidified, two-phase alloys at elevated temperatures in view of the possibility of using suitable modifications for high temperature service. Knowledge of the creep behavior of these materials is still rudimentary (although under active investigation) and the present paper concerns itself with short time tensile properties of some alloys similar to those investigated in I (i.e., unidirectionally solidified Al(rich)-Cu alloys). Unidirectionally solidified alloys containing 5.6, 17, and 23 wt pct Cu were tested parallel to the direction of solidification at temperatures from 25" to 500°C. In the present investigation, the alloys were homogenized for 2 days at 535°C giving a matrix of homogeneous a phase (5.2 wt pct Cu) and an interdendritic constituent (EIR) which was completely Q phase (53 wt pct Cu). EXPERIMENTAL Alloys of nominal composition 5.6, 17, and 23 wt pct Cu (containing approximately 0, 17.5, and 27.7 vol pct 8 phase, respectively, after homogenization at 535°C) were prepared by melting 1200 g of A1 (99.99 pct) in a high purity graphite crucible and adding the appropriate amount of freshly cleaned copper chips (99.9 pct). The molten alloy (at 700°C) was poured into a preheated graphite mold (also at 700°C) and the ingot unidirectionally solidified by impinging water on the steel baseplate of the mold. The alloy was degassed immediately

Jan 1, 1970

By H. Sigurdson, T. V. Cherian, C. H. Moore

The phenomenon of recovery of cold-worked metals is interesting not only because of its practical importance but also because of its fundamental significance in solid state reactions. Although extensive investigations1,2 have already been made in an attempt to discover the mechanics of the recovery process, many of the observations have not yet been satisfactorily correlated to provide a completely consistent model for the process. The wide differences in the recovery rates of various properties can be cited as a typical example of one of the difficulties that are encountered. Frequently, for example, the electrical resistance will have almost completely recovered before any recovery in tensile strength can be detected. Of course, such differences in the recovery rates of different properties might be explained by assuming that each property is a unique function of the work-hardened state, and consequently each property exhibits its own unique recovery rate. The assumption that different properties are uniquely related to the work-hardened state cannot be denied. On the other hand, the properties that recover at different rates often exhibit more or less parallel changes upon work-hardening. This suggests that the microstructural changes attending recovery are not exactly the reverse of the changes attending work-hardening. Several types of imperfections must be postulated in order to account for this apparent anomaly. The different recovery rates for various properties, then, are due to the different recovery rales of the type of imperfection to which each property is most sensitive as well as the unique dependence of each property on the cold- worked state. This concept assumes that a simple model of the work-hardened state consisting only of one type of imperfection, such as Taylor's type of dislocation patterns, is inadequate to cope with the diversified phenomena attending work-hardening and recovery. Although current models for the work-hardened state are not useful for describing all aspects of the recovery process, the general trends of the recovery of each postulated type of imperfection as a function of time and temperature should be at least qualitatively deducible from the rather well developed laws of kinetics of reactions in the solid state. Consequently, recovery data might prove useful for elucidating some aspects of the complexities of the work-hardened state of metals. A preliminary attempt to study work-hardening by investigating recovery rates of cold-worked metals is outlined in the following pages of this report. Experimental Procedure Many properties recover when cold-worked metals are annealed below their recrystallization temperature. Therefore, electrical resistivity, thermal electromotive force, X ray diffraction line widths, X ray diffraction line intensities, elastic spring back, density and other physical and chemical properties have been used to study the recovery process. Major interest, however, has generally been directed toward the recovery of the mechanical properties such as hardness, yield strength, and tensile strength. But a search of the literature suggests that the effect of recovery on the true stress-true strain curve has been neglected, in spite of the current recognition of the fundamental importance of such an investigation. An investigation on the effect of recovery treatment on the true stress-true strain curves in tension, therefore, was undertaken in the present study. Commercially pure aluminum (99. + pet Al) in the form of 0.100 in. thick rolled sheet of 2S-O aluminum alloy was selected as the material for this investigation because rather extensive correlatable data are already available on the recovery of some of its properties. Tensile specimens having a 6 in. long gauge section and a uniform reduced section width of 0.500 in. were machined from the sheet in accordance with a design that has previously been reported.3 All specimens were selected with their axes aligned in the rolling direction. In order to eliminate the effects of previous work-hardening and the effects of machining, the specimens were annealed for 15 min. at 750°F before testing. During tensile testing the loads were measured by means of a proving ring (sensitive to 1/2 lb) in series with the specimen.4 Strains were determined from the extension of a rack and pinion strain gauge sensitive to a strain of + 0.0001. The stress was recorded as the true stress, namely

Jan 1, 1950

By Gerhard Bockstiegel

Kuczynski's formula has been derived for the case of nonspherical particles. TWO formulae of Kuczynski's type have been derived, one describing the increase in tensile strength, the other describing the progress of shrinkage of a powder compact. It has been strength,shown that the exponents of all three formulae each contain two magnitudes of different physical characters, viz, the geometrical factor a and the kinetic factor ß. The interrelationships between the three exponents are stated. SOME years ago Kuczynski1 experimentally showed that the radius, x, of the area of contact between very small spherical metal particles and a metallic block is related to the time of sintering, t, by the following equation x = constant tk [11 where k has the value 1/5 or 1/7. Assuming that the metal particles were perfect spheres and the metallic block was perfectly flat, he derived the foregoing equation from theoretical considerations of the process of material transport in metals, and he showed that exponent k is different for different mechanisms of transport, e.g., k = 1/2 for viscous flow (according to Frenkel2), k = 1/3 for evaporation and condensation, k = 1/5 for volume diffusion, and k = 1/7 for surface diffusion. From this Kuczynski concluded that the mechanism of transport was either volume diffusion or surface diffusion, depending on whether the value of k, as found in his experiments, was 1/5 or 1/7. Subsequently. Cabrera8 corrected Kuczynski's calculations with regard to surface diffusion, showing that the theoretical value of exponent k is 1/5 for both volume and surface diffusion. He supposed that the different experimental values of k were due to slight differences in the shape of the metal particles. An exponential relationship similar to the aforementioned was found by Okamura, Masuda, and Kikuta,4 Masuda and Kikuta, and Takasaki8 when studying the rate of shrinkage on powder compacts during sintering. The authors measured the shrinkage by means of the fraction w = Vp — V./Vp — V,,,, where V,, is the volume of the green compact, V, is the volume of the sintered compact, and V,,, is the volume of the compact in its densest state. This fraction, w, they found, is related to the time of sintering, t, by the equation w == constant tm. [21 Further, Bockstiegel, Masing, and Zapf7 observed that the tensile strength, s, of sintering iron powder compacts can also be related to the time of sintering, t, by an equation of the foregoing type, i.e., s = constant tn. [3] For exponent n the values 0.28 (S=2/7) and 0.35 ( 2/5) were obtained, and the authors pointed out that there might exist a simple interrelation between exponent n as found in their experiments and exponent k in Kuczynski's equation. The authors supposed that 2k = n, since the strength of adhesion between a metal sphere and a block (as in Kuczyn-ski's experiments) must approximately be proportional to their contact area, p. x2. Theoretical Considerations This paper is an attempt to correlate the fundamental experiments of Kuczynski's type with the results obtained with powder compacts as represented by Egs. 2 and 3. In particular, the paper is to show how the rate of sintering is influenced by the geometry of the sintering particles and by the type of material transport. As the geometry of particles conglomerating in a powder compact is very complex, some simplifying assumption has to be made, of course, in order to adapt the problem to mathematical treatment. In the following paragraph a suitable simplification is introduced, and Kuczynski's formula is derived for the case of nonsphcrical particles. Relation Between Area of Contact and Sintering Time—As the face of contact between two particles in a sintering powder compact is not necessarily a circle (as in the case of spheres sintering to a block), Kuczynski's formula is modified as follows: Let the perimeter of the face of contact be described by means of polar coordinates R, 4, as shown in Fig. la, so the area of contact, f, is determined by f= 1/2 . S112p[R(Æ) ]2 dÆ [4] Then, let the two particles be intersected by a plane perpendicular to area f. The intersection is shown in Fig. lb. According to the nomenclature in this figure, the distance, h, between the surfaces of the two particles is a function of T and Æ: h = h(r,Æ). For the particular case of spherical particles, as in Kuczynski's theory, this function becomes: h = constant r2. It shall be assumed here that in the close neighborhood of their

Jan 1, 1957

Edgar Hall, Tenterfield, New South Wales (communication to the Secretary): Mr. Klepetko* asks for information showing at what percentage antimony and arsenic, as impurities, begin to affect injuriously the quality of brass.

Jan 1, 1899

By P. Duwez, H. Martens

Dimensional changes generally occur during the sintering of metal powder compacts. These changes may have several causes and their magnitude depends upon the numerous variables involved in the process, such as the nature of the powder, size and shape of the grains, compacting pressure, rate of heating, maximum temperature, length of time at temperature, and furnace atmosphere. Among all the variables, time, temperature, and compacting pressure are probably the most important ones, and the effect of each one of the other variables can be studied separately once the effect of these is well understood. The most precise method of studying the phenomenon of dimensional changes in a compact consists of heat treating the compacts at various temperatures for different lengths of time. In this method, only very small specimens can be used, in order to achieve rapid rates of heating and cooling. The technique involved in these measurements is very simple, but is time consuming. Another experimental approach to the problem consists of measuring the change in length of a compact as it is being heated at a constant rate. Although the two variables, time and temperature, are combined into a single one (rate of heating), the results obtained by this technique may be of great interest from both practical and theoretical points of view. The purpose of this paper is to describe a systematic investigation of the change in length during sintering of compacts made of one or several metal powders. Experimental Procedure The change in lenght of compacts during sintering was measured with an automatic recording dilatometer. In this instrument the change in length and the temperature are recorded as functions of time on two separate charts and the rates of heating and cooling may be varied from 1 to 20°F per min. The temperature may be kept constant at any value up to 2200°F during any predetermined length of time and the change in length recorded as a function of time. Provision is made for atmosphere control inside the fused silica tube containing the specimen. Three different magnifications are provided, so that 1 in. on the chart corresponds to 0.002, 0.005, or 0.010 in. change in length. The mechanism following the change

Jan 1, 1950

By J. F. Myers, R. J. Tower

"THERE is nothing new under the sun." All over the world, mineral-dressing engineers are working at their problems, no two of which are alike. Each encounters equipment and process problems. Many devise simple ways and means of overcoming their difficulties. Many of these problems are quite common in the industry, yet, since no one human being seems capable of thinking of everything, these problems at some plants often are looked upon as necessary evils. The purpose of this symposium is to gather together, from competent engineers, devices and practices that have been useful to them. Most of the ideas contributed are not new, yet there is no plant operator, old timer or youngster, who will not find some idea herein that will give him a suggestion for improving his operation. Space does not permit a complete elaboration on all of the contributions offered. Each item is summarized, but this will be ample for those skilled in the art of mineral dressing. A list of contributors appears at the end of the paper, and the superior number at the end of each item identifies its source. GENERAL EQUIPMENT A signal light to show that a steel bin, containing relatively fine, moist ore, is full, can be made by suspending a copper rod in the bin to a sufficient depth to ensure ample contact with the ore. One wire of a 32-volt circuit should be attached to the rod and one to the side of the bin. Sufficient current will flow to make the signal light burn. A 110-volt circuit could be used, but 32 volts ensures safety.10 Fig I shows a circular bin for crushed ore. It is a concrete structure footed on the ground, using no supporting columns. Tailing from the sink-float was used for aggregate. Cross conveyors for discharging ore are not required, nor is a tripper for filling. Segregation is minimized by drawing from different gates. An exhaust fan on top of the bin eliminates condensation due to temperature of the ore.21 A beam with an adjustable point of suspension near the center permits rigging rolls for removal in a very few minutes. This makes unnecessary the lacing of the cable through the hub bolts on one side, around the shaft on the other, and the trouble of balancing the load.8 The ratchet handle on a Symons crusher may be replaced by a drum with a cable wound on it. When the cable is pulled by a crane or hoist it causes the drum to revolve and thus screws or unscrews the bowl. This reduces handwork and materially shortens the time required for the job.3 To spread ore feed from an apron feeder over a belt conveyor, place a heavy steel bar about midway between the top

Jan 1, 1947

By B. M. Larsen, T. E. Brower

In an earlier paper1 we discussed a simple, rapid method of taking samples of liquid steel and analyzing them for oxygen, which, though possibly not absolutely accurate (as is likewise true of all other methods), certainly yields results that are satisfactorily consistent. Accordingly, samples from hundreds of heats ill different shops were analyzed for oxygen, with results sufficient in number to be handled statistically and permit estimation of some general trends. Measurements were made in acid as well as in basic open hearths, throughout the refining period, to learn how stirring, blocking, adding ore or lime or sand, affects the oxygen content of the bath; we also followed the changes brought about by tapping, teeming, and deoxidizing. Some of these results, discussed in an earlier paper,2 bring out the dominant role of the carbon-oxygen reaction in regulating degree of oxidation both of metal and of slag, also the marked variability of concentration of dissolved oxygen [0] in excess of that which would be in equilibrium with carbon and with carbon monoxide at a partial pressure of one atmosphere. As a logical beginning on this complex problem, we take up in the present paper the variability of this excess oxygen, A[O], when other factors are as constant as they ever are in open-hearth operation; namely, toward the end of the refining period, when the bath may be regarded as in the comparatively steady state it approaches in absence of disturbing factors. This condition was chosen because by that time the significant reactions, except carbon oxidation, between slag and metal have come to substantial equilibrium; this facilitates interpretation of the complex situation and thus perinits more definite conclusions to be drawn. This excess concentration of oxygen, A[O], in the metal is needed, of course, to make the steelmaking process go at a reasonable rate; alternatively it may be regarded as a measure of the virtual pressure increment above one atmosphere, or of the degree of supersaturation, of carbon monoxide in the metal. According to our measurements, the excess concentration A[0] in liquid steel varies from about 0.009 to 0,035 per cent oxygen by weight. It is quite sensitive to change of conditions, being altered temporarily by operations such as stirring with green poles, additions of ore, lime, or sand; but as the disturbance works itself out, it resumes a level within the intermediate range characteristic of the steady state. The conditions most common in average furnace practice are covered by the following: i[O] Usual Per Cent Oxygen by Conditions Weight 1. Vigorous lime boil........... o.oog-0.01s 2. Steady state................ o.or;-0.025 3. Working of ore.............. o.023-0.035 Thus when the bath can be regarded as in a reasonably steady state—that is, when it is boiling normally, is at proper temperature with a well-shaped slag, and has been free from disturbing effects during the preceding half hour—A[0] returns from

Jan 1, 1948

By B. M. Larsen, T. E. Brower

In an earlier paper1 we discussed a simple, rapid method of taking samples of liquid steel and analyzing them for oxygen, which, though possibly not absolutely accurate (as is likewise true of all other methods), certainly yields results that are satisfactorily consistent. Accordingly, samples from hundreds of heats ill different shops were analyzed for oxygen, with results sufficient in number to be handled statistically and permit estimation of some general trends. Measurements were made in acid as well as in basic open hearths, throughout the refining period, to learn how stirring, blocking, adding ore or lime or sand, affects the oxygen content of the bath; we also followed the changes brought about by tapping, teeming, and deoxidizing. Some of these results, discussed in an earlier paper,2 bring out the dominant role of the carbon-oxygen reaction in regulating degree of oxidation both of metal and of slag, also the marked variability of concentration of dissolved oxygen [0] in excess of that which would be in equilibrium with carbon and with carbon monoxide at a partial pressure of one atmosphere. As a logical beginning on this complex problem, we take up in the present paper the variability of this excess oxygen, A[O], when other factors are as constant as they ever are in open-hearth operation; namely, toward the end of the refining period, when the bath may be regarded as in the comparatively steady state it approaches in absence of disturbing factors. This condition was chosen because by that time the significant reactions, except carbon oxidation, between slag and metal have come to substantial equilibrium; this facilitates interpretation of the complex situation and thus perinits more definite conclusions to be drawn. This excess concentration of oxygen, A[O], in the metal is needed, of course, to make the steelmaking process go at a reasonable rate; alternatively it may be regarded as a measure of the virtual pressure increment above one atmosphere, or of the degree of supersaturation, of carbon monoxide in the metal. According to our measurements, the excess concentration A[0] in liquid steel varies from about 0.009 to 0,035 per cent oxygen by weight. It is quite sensitive to change of conditions, being altered temporarily by operations such as stirring with green poles, additions of ore, lime, or sand; but as the disturbance works itself out, it resumes a level within the intermediate range characteristic of the steady state. The conditions most common in average furnace practice are covered by the following: i[O] Usual Per Cent Oxygen by Conditions Weight 1. Vigorous lime boil........... o.oog-0.01s 2. Steady state................ o.or;-0.025 3. Working of ore.............. o.023-0.035 Thus when the bath can be regarded as in a reasonably steady state—that is, when it is boiling normally, is at proper temperature with a well-shaped slag, and has been free from disturbing effects during the preceding half hour—A[0] returns from

Jan 1, 1948

By E. A. Slover

THE usual reverberatory system of smelting cop--1- per concentrate or calcine has for its component parts a furnace and one or two waste heat boilers. These parts are operated on a basis of compromise, since the furnace can send gas to the boilers at too high a temperature and the boilers by plugging, due to dust or slag, can place a definite limit on the amount of fuel the furnace can burn. Over the years the copper concentrate smelting furnace has had few advances in design. The simple rules of design such as the flame should wipe the bath and the speed of the gases should be reasonably low for dust carrying purposes seem to cover the main features. In the construction of the individual furnaces some innovations are always being introduced. Among these are charging so that the work of smelting is a complete bath process, the use of suspended brick arches in place of sprung arches, the use of basic brick, not only in the crucible, but also in roof and sidewalls, the use of various means to feed the charge, the use of magnetite or other heavy material to construct the hearth, water cooling of bridgewall and slag skimming bay, the smelting of raw charge instead of calcine, the use of preheated air, and possibly the use of oxygen-enriched air for combustion. But the general outlines of the furnaces have not changed much except as to size. Furnaces at Hurley As shown on Fig. 1, the furnace at Hurley is 126 ft long between the longitudinal buckstays and 32 ft wide at the skewback plates. The foundation is a concrete retaining wall with piers at intervals that go deeper into the earth. Purposely the wall at the burner end of the furnace is not backed-up as tightly as the other parts of the foundation so that movement due to expansion may take place here rather than into the boiler foundations. Within these foundation retaining walls of concrete, the earth has been removed to allow the placement of the crucible brick base inside of which a silica hearth is laid 4 ft 6 in. in depth. No expansion is left in the brick base and crucible where they are in contact with the hearth. The hearth itself is of quartzite crushed to 1 in. size with fines left in the product. An 8 in. layer is laid and tamped with paving tampers to about 6 in. in thickness. Then a layer of silica flour is spread and vibrated into the hearth. This operation is repeated until a depth of 4 ft 6 in. is occupied by the silica mass onion-skinned in layers of approximately 6 in. Before firing the entire hearth is covered with broken slag to a depth of 4 in. so that a seal may be formed on the hearth. The crucible is completely faced with magnesite chemically bonded brick while the outside, against the foundation, is made of silica brick. The side-walls are carried up with silica brick in which expansion joints are left at intervals. Above the crucible the sidewall is corbelled to form a shelf on which the charge may build up along the side-walls, see Fig. 2. The arch of the furnace is sprung 20 in. silica brick, with the longitudinal centerline horizontal the length of the furnace, and some 9 ft in the center above the bath. Both straight and wedge brick are used in the construction and a thin silica mortar is troweled for joints. After the arch under heat has assumed its permanent shape, a silica slurry is spread over the arch to fill any cracks that have formed, thus giving bearing surface to the brick and preventing dust from entering the body of the arch to act as a future fluxing agent. The uptake of the furnace slopes up to the boiler entrance where a brick pilaster divides the gas stream for the two boilers. Over this flared uptake is a suspended flat arch of firebrick. The pilaster and sidewalls are constructed of firebrick but the bottom of the uptake is lined with silica brick and fettled through holes in the roof with siliceous fettling. Close to the entrance of each boiler is a brick covered slot through which water-cooled dampers may be lowered in event of boiler trouble. These water-cooled dampers are hung permanently in position ready to be lowered when needed. Flexible hoses to follow the dampers as they are lowered are connected at all times and individual chain blocks are used to lower the dampers. A pump supplying water is started before the dampers enter the heat. Charging of the furnace along the sidewalls for some 80 ft from the bridgewall is accomplished by electric vibrating conveyors fed by belt from charge storage bins above the furnace. These conveyors

Jan 1, 1954

By J. J. Scott

This investigation utilizes three dimensional photo-elastic techniques to determine the stress distributions in the pillars and the roof of a room and pillar mine model. Castolite plastic was used for the construction of the model in which a stress pattern was developed by the stress freezing process. Analysis of the stress pattern was accomplished by observation of points in slices from the model with a polariscope and solving the data thus obtained by the shear-difference method. Slices through the centerline, edge of pillar and centerline of span were investigated. The results of this work provide information on the overall stress distribution in points of stress concentration in compression, shear and tension, show relative magnitude of stress throughout the model and indicate directions of the most important stress values. A generalized roof bolt pattern is developed for room and pillar mines based on the stress distribution. A digital computer was used in the reduction of data and proved to be extremely useful for investigation of this type. Underground excavations disturb the equilibrium of the earth's crust and a core of fracture, or altered stress distributions exists around the openings. This fact is well known by mining operators and investigators in the rock mechanics field. Analysis of the stress distribution in the areas around mine workings is a most difficult problem and one which has no simple and direct solution. Some of the approaches used by investigators in attempts to study stress distribution around mine openings involve mathematical analysis, photoelastic techniques, statistical analysis, model studies on brittle materials and observation of fracture patterns. Models involving imbedded strain gauges, gelatin models using imbedded strings to show internal movement, and many other unique laboratory techniques are employed. Work is also being done in mining operations where load cells, strain gauges, photostress material, convergence plugs, dynamic plugs, etc., are used to measure strain which can in turn be used to obtain stress. Some of these devices measure strain from which stress may be derived. All approaches to the solution of stress distribution are hampered by the fact that the earth is not a homogeneous, isotropic and elastic media. Geologic faults, fractures, bedding planes, vugs, variations in material composition, variations in grain size and structure, etc., make it extremely difficult to obtain results which can be universally applied to mining operations. The purpose of this investigation will be to demonstrate the use of three-dimensional photoelastic techniques to obtain the stress distribution in the pillars and roof of a room and pillar mining operation. This method utilizes full analysis of interior points, and thus it may be that small tensile or shear stresses found in the investigation will prove to be of greater significance than the more obvious points of stress concentration found by two-dimensional techniques. A digital computer was employed to simplify and to shorten the time necessary to obtain final results. Application of the computer to problems of this type may enable future investigators to attempt more elaborate analyses than have been previously considered feasible. THEORY Three Dimensional Stress Analysis-Shear Difference Solution:' Photoelastic studies are based on the fact that an optically isotropic transparent solid becomes optically anisotropic when subjected to forced deformation; the degree of optical anisotropy being proportional to the deformation of the material. There are two fundamental laws which govern photoelasticity: 1) Light is polarized in the directions of the principal stress axes, and is transmitted only on planes of principal stress. 2) The difference in principal stresses is proportional to the difference in the indices of refraction along the planes of principal stress. One method used in three-dimensional photoelastic work is to examine a slice of the object by normal incidence and oblique incidence. In normal incidence,

Jan 1, 1964

By J. P. Nichols

Modern vibrating screening dates from about 1910 at which time the forerunner of the present day two bearing and four bearing circular motion inclined vibrating screens were first introduced. These simple machines consisted of a screen box holding some kind of a screening surface to which was attached an off-center shaft or a shaft with an off-center weight which was rotated. The rotation of these shafts caused a shivering motion to the screen box and produced the first vibrating screen. In the 1920's and early 30's, the box designs were improved and the mechanisms designs were also improved and by 1940, vibrating screens were an important part of most process plants. In the early days when the screen sizes were dictated by how much could be shoveled onto the screen box and by the force that a particular mechanism could produce, not much thought was given to the proper sizing of the particular units. As mechanism and body design improved the ability to predict vibrating screen capacity at various openings became more important. In the late 1930's, a set of empirical capacities came to be used. with few modifications, these capacities are still in use today, both by those companies that use a formula involving only the amount of fine material in a feed, and by those companies using a formula in which the total feed to a particular screen is used. In either method of calculation, the empirical values are based on these ideal conditions: (1) The material being fed to the screen contains 25% oversize. (2) The feed to the screen contains 40% half size material. (3) The material has a bulk density of 1.6 T/Cu.M. (100 lbs/cu.ft.). (4) The screening surface has an open area of 50%. (5) The material is dry, free flowing and relatively cubical. (6) The maximum screening efficiency required is between 90 and 95%. It is obvious that these conditions do not occur in natural or crushed size distributions. Therefore, modifications must be made to these empirical values to allow for the calculation of a vibrating screen for a particular set of conditions. Before we consider these various modifications, let us look at what happens to material as it is acted on by a vibrating screen so that we can better understand why the modifications are nec-

Jan 1, 1982

By B. G. Slay, J. P. Pritchard, J. T. Pierce

A short discission is given of the cryotron us a supercozductitzg- switch. The parameters of interest such as gaiz, critical gate current, critical control current, and critical surface current density ave described. The photomask-photoresist process makes possible the study of much narrower dimensioned cryotrons than previously possible using mask stencils. Data is given for the above parameters as a function of width, thickness, temperuture, and crossing ratio. Photographs of the various circuits used are shown. The techniques involved in making connection to the circuits and the precautions taken to avoid side effects in the measurements are discussed. In particular data is given for critical currents of sipercotzducting. lines down to 2X 104 in. A vise in critical surface current density is obserced jor the strallev lines in both lead and tin. A discussion of the ihact of these measurements in the design of future cryotron circuitry is given. In addition to the improvement in device density achieved by simple scale reduction. additonal gains in density may result through improved device form factor. THE cryotron is a superconducting current switch, invented by D. A. Buck.' Fig. 1 shows a typical crossed-film cryotron. Usually the gate is made of tin and the control is made of lead. The critical gate current, is the current that drives the gate resistive with zero current flowing in the control. The critical control current, I is defined as the current in the control necessary to switch the gate resistive with a small monitoring current in the gate. The gain of the device, G, is defined as Since for uniform thin films G should be proportional to the gate width divided by the control width, it is convenient to define the critical surface current density, Jcg, to be the critical gate current divided by the gate wldth. The data which follows will show that, for a given control width, I, is relatively constant. Thus, by measuring Jcg the change in gain as a function of gate width may be measured without measuring I,.

Jan 1, 1967

By P. G. Carpenter, R. G. Nisle, F. W. Bubb

It is the purpose of this paper to describe an electrical computer which has been constructed to solve the equations for vapor-liquid equilibrium in multi-component systems. The instrument consists of seven component-computing units each with proper indicating means and power supplies. Each unit is a resistance network with a voltage matching servomechanism, and each provides an output voltage proportional to the mol-fractions for vapor and liquid phases. These voltages are summed and matched with a reference voltage to provide the solutions. Any reasonable number of such units may be put together to make a computer. The theory and operation of the computer is discussed. A number of applications and examples of computer results are given. The computer yields the over-all vapor or liquid fraction to a probable error of 0.002. An interpolation method is described which reduces the probable error to 0.0002. INTRODUCTION The process known as Flash Vaporization may be described as follows: A mixture of known composition of relatively volatile components is allowed to come to thermodynamic equilibrium at some given temperature and pressure by any path whatsoever. In general, a vapor and a liquid phase will be present at equilbrium. The problem is to determine the fractions of the mixture in the vapor and liquid phases, and to determine the mol fractions of the various components in each phase. The relations that exist between these various quantities at equilibrium are well known and will be given later. These equations are difficult to solve, yielding only to trial-and-error methods. The virtues of the analog computer are its speed and the automatic character of its calculations. The device is operated by turning a crank which varies the value of v, the total vapor fraction. This actuates a number of servomechanisms which perform automatically all computations. This computer facilitates the solution of such problems as (to mention a few] : Analysis of separator operation, studies of changes in composition of reservoir fluids with pressure decline, and analysis of natural gasoline plant operation. Examples of some of these problems are given in detail later. STATEMENT OF THE PROBLEM The essential equations are xm = 1+(km-l)v . . (1) Kmzm ym =------------------------. . (2) 1 + (Km-l)v ; n n S S xm= --------------------=1 1 + (Km-l)v m = 1 m=1 ......(3) n n S = S Km Zm =1 S ym 1 + (Km-1)v m=1 m = l ......(4) where ym = Vm/V = Mol fraction of m-th component in vapor phase. xm = Lm/L = Mol fraction of m-th component in liquid phase. Zm = Fm/F = Mol fraction of m-th component in mixture. KM = ym/xm = Equilibrium constant for m-th component at the given temperature and pressure. v = V/F = Mol fraction of vapor in the mixture. F = Total mols of a mixture of n components. V - Total mols of vapor in the mixture. L = Total mols of liquid in the mixture. Fm = Total mols of m-th component. Lm = Mols of m-th component in liquid phase. Vm = Mols of m-th component in vapor phase. Assuming the total mols of the mixture F and its composition (all the Fm) to be known — either from a quantitative analysis or from the amounts put together to make the mixture — the zm = Fm/F may be regarded as known quantities. From the given temperature and pressure of the mixture the K., are known (principally from experimental data). The primary problem is then: having given all the zm and Km to calculate v and all the fractions xm and ym. Having calculated these ratios, it is a simple matter to calculate V. L. Vm, Lm from their defining equations. SOLUTION OF THE PROBLEM Basic Computer Unit The computer consists of n units, each of which provides voltages xEo and YE, proportional to x and y as in

Jan 1, 1950

By J. S. Kirkaldy, G. R. Purdy

THE formation of ferrite in supersaturated aus-tenite has been the subject of considerable speculation and investigation. Aaronson has recently reviewed the data pertinent to this reaction.' Since these data in all cases refer to ternary or high-order alloys it is not possible to put them to the test of simple binary diffusion formalism. It has not, therefore, been possible to make a certain statement as to the controlling mechanisms in the process. An assessment of the difficulties inherent in the conventional statistical metallographic approach suggested that a study of the problem by means of a macroscopic two-phase diffusion couple might contribute useful information. Accordingly, such a couple was synthesized, and the rate of motion of a ferrite-austenite phase boundary (the growth of an austenite layer at the expense of a ferrite layer) was determined. Wagner originally produced a diffusion solution applicable to the motion of a planar phase interface in a binary diffusion couple, assuming local equilibrium throughout the diffusion zone. This solution, which is stated free of typographical error* in Ref. where a is the position of the interface in A space (A = x/fi), C; and CL1 are the equilibrium inter-facial concentrations in phases I and 11, C: and C*1 are the initial bulk concentrations in phases I and 11, and & and are diffusion coefficients (assumed constant). If a diffusion couple consisting of homogeneous layers of ferrite and austenite in equilibrium is raised to a higher temperature, the austenite layer will grow at the expense of the ferrite. Provided that the thickness of the ferrite layer is much less than the diffusion length of carbon in ferrite, we can set , so that Wagner's solution reduces to

Jan 1, 1963

By M. J. Marcinkowski, A. S. Sastri

A detailed compressive stress-strain analysis and transmission electron microscopy investigation has been made of the deformation behavior occurring in a 50 at. pct Ni-Ti (hypoeutectoid) alloy and a 54.5 at. pct Ni-Ti (hypereutectoid) alloy. In the case of the hypoeutectoid alloy, three stages of work hardening are observed. Stage I occurs at a very low stress and is associated with plastic deformation via martensite formation. Stage 11 is characterized by very rapid work hardening and is due to difficulties in causing further deformation in the fine martensite aggregate produced in Stage I. Stage III which occurs at very high stress levels is characterized by smaller work hardening rates and is due to the plastic deformation arising from alternate reconversions of the original martensites to martensites of varying orientation. Rapid quenching of the hypereutectoid alloy leads to very high yield strengths and is related to a fine precipitate dispersion that such treatment brings about. The present investigation represents the final phase of a three-part study directed toward an understanding of the solid-state transformations in near equi-atomic Ni-Ti alloys as well as the deformation mechanisms associated with these alloys. In the first part,"2 to be henceforth referred to as I, it was found that alternate simple shears on {112} planes and in (111) directions convert the parent B2 structure in the equiatomic NiTi alloy into two distinct close-packed monoclinic martensites. All of the marten-sites were of this type, whether they were formed by cooling or by plastic deformation, whether induced to form in bulk samples or in thin foils, or whether examined in the electron microscope at room temperature or below. On the other hand, in the second part of this investigation,3 to be reffered to as 11, it was shown that upon slow cooling to about 640°C. alloys in the neighborhood of NiTi which possess the B2 structure transform eutectoidally into their equilibrium phases Ti2Ni and TiNi3. However, preceding the formation of these equilibrium phases a series of metastable intermediate phases are formed. This paper will set as its goal the elucidation of the remarkable deformation behavior exhibited by NiTi. In particular, Buehler and Wiley4 have found equiatomic NiTi to be surprisingly soft, while Buehler et al.5 have shown this alloy to possess a memory effect: i.e., upon bending at room temperature it will revert to its original shape when heated to above about 50°C. In I it was shown that NiTi was soft in the sense that the yield stress was low; nevertheless, the alloy work-hardened at an extremely rapid rate to very high stress levels. On the other hand, the hypereutectoid alloys with somewhat higher nickel, say 54.5 at. pct (60 wt pct) have enormously increased yield strengths compared to those of the equiatomic alloys. In order to determine the atomistic processes giving rise to the above behavior, it was decided to examine samples that were wafered from bulk specimens deformed in compression to various strains using the techniques of transmission electron microscopy. EXPERIMENTAL TECHNIQUE All of the alloys used in the present investigation contained either 50 at. pct Ni (55.06 wt pct) or 54.5 at. pct Ni (60 wt pct) and were arc-melted in the form of a finger using the same techniques described in I and II. The finger was capsulated in a stainless-steel jacket and swaged at 850°C into rods. Compression specimens 0.300 in, long and 0.200 in. in diam were machined from these rods. In order to completely re-crystallize the samples and remove residual stresses, all of them were capsulated in evacuated quartz, annealed for 1/2 at 1050°C. and then furnace-cooled. Compression tests were carried out in an Instron tensile testing machine covering a range of temperatures from —196° to 200°C using procedures described previously.6'7 In all cases crosshead speed was 0.02 in. per min. Wafers 0.015 in. thick were spark-cut from the cylindrical samples at 45 deg to the compression axes after they had been deformed to the desired strain. These specimens were then spark-planed to about 0.005 in. and then electrochemically thinned for examination by transmission electron microscopy as described in I.

Jan 1, 1969

By G. E. Perry, J. F. Bruskotter, D. G. Russell, J. H. Goodrich

The depletion performance of gas wells has been investigated by mathematical simulation techniques. The gas well model which was studied consisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity on pressure was considered in studies of well performance at both constant mass flow rate and constant flowing pressure conditions. To carry out the investigation, the nonlinear, second-order, partial differential equation which describes Darcy flow of a nonideal gas through porous media was solved numerically. Some of the previous investigations of gas well performance have been of limited general use, because assumptions were introduced to simplify either the gas properties or the basic differential equation. Other studies have been rigorous in these respects but have presented a very limited set of calculated results. The present study was attempted to present a rigorous theoretical model and sufficient numerical results to permit meaningful conclusions to be drawn. It was found that all terms must be retained in the partial differential equation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balance errors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thickness product of the formation, the more pronounced are these deviations. For example, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gas in place) at a constant rate of 993 Mcf/D, the rigorous solution predicts a bottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. If higher-order terms are neglected in the differential equation, this decline in pressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equation as a basis, simple, easy-to-use approximations for predicting gas well performance for Darcy flow conditions have been developed. These simple approximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree of accuracy and enable the prediction of long-term gas well performance to be made quickly and accurately without the use of a digital computer. Both transient and stable flow period approximations were developed. INTRODUCTION In recent years income from the sale of natural gas and associated products has represented an ever-incre as ing fraction of the industry's total revenue from operations. To meet the surge in demand for natural gas, the industry has depended heavily upon established reserves and has actively pursued development of new reserves. The search has progressively led to reservoirs which yesterday were too tight and/or deep to yield the desired return on invested capital. More than ever before, evaluation accuracy is now required to forecast the criteria upon which engineering recommendations and management decisions are based. Considerable effort has been expended by both research and operations personnel on the development and application of methods for analyzing and predicting the performance of gas wells. Fundamentally, the problem is the familiar one of extracting data during the drilling, testing and early production life of a well and applying these data within an accurate simulation model to predict long-term behavior. During the past 30 or more years a voluminous literature dealing specifically with gas field problems has been generated. A recent book' lists a comprehensive bibliography of published material through 1959. Over 1,200 references are cited. Since then 39 additional articles on natural gas technology have been published in Transactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that one or more idealizations (e.g., steady-state flow, ideal gas of constant viscosity, small and constant compressibility and constant-viscosity fluid) be applied. Although existing theory may apply directly or be adapted by various artifices to describe specific gas well and reservoir behavior, no widely applicable method is available, and existing methods appear to be subject to appreciable error unless better limits of applicability are defined. The objectives of this paper are (1) to present numerical solutions to the partial differential equation describing gas flow under conditions of general interest in gas well performance prediction work, (2) to present solutions which possess a high order of accuracy for both transient and stabilized flow periods of a well producing at constant rate or constant pressure, and (3) to develop and present simplified relationships which can be used as high-order approximations to the exact numerical results for fast and accurate predictions of gas well performance at the operating level. Combined, these objectives are designed gen-

Jan 1, 1967

By Nelson P. Hulst

To those who have had the happy privilege of friendship with George W. Goetz, the announcement of his death has brought great sadness. He was born in Milwaukee, Wisconsin, February 17, 1855, and died January 15, 1897. In his boyhood days, when I first came to know him, his frank, trustful manner; his eyes brimming with truthfulness; his eagerness, never obtrusive, to gain knowledge from all whom he met; and his equal readiness to give without ostentation of his store, constituted a personality which at once commanded confidence and won friendship. I am told that as a scholar of five years he was conspicuous for brightness, a show-pupil, who was called on to recite when visitors were present at school. Yet this in no way spoiled him. His modesty was too strong a trait in his character to be overcome by any attention which might, be expected to arouse vanity. In his simple-heartedness he was pleased then, as he always was in his maturer years, to give of his knowledge for the gratification of his listeners, with never a thought of himself. So strong was this characteristic that in a brief autobiography, in the form of a letter to his wife and children, found among his papers, he excuses himself to them for recounting what he had accomplished in his life-work. As a preface to this autobiography (which, it seems, was prepared on the eve of a sudden journey to California, taken February, 1895, for his health) he says: " I am writing this rather hastily, and I

Jan 1, 1898

By Robert S. Baker

It has been demonstrated in the laboratory by A. J. Phillips1 that a transformation or conversion from beta directly to alpha may take place in a brass of 61 to 62.5 per cent copper content. The completion of the transformiation is dependent on a rapid rate of cooling from the all-beta field through the alpha + beta range to the alpha field. Phillips states that in a slowly cooled alloy containing 62 per cent copper and 38 per cent zinc the copper content of the beta is progressively decreased from 62 to 56 per cent by precipitation of alpha. Rapid cooling tends to prevent the separation of alpha with a copper content of more than 62 per cent by reducing to a minimum the time required for passing through the alpha + beta range. Upon crossing beyond the (alpha + beta) (alpha) boundary to the all-alpha region below, the material is transformed from beta to alpha. It, is essential that there be no change in composition. Phillips obtained his results by quenching a 62:38 copper-zinc alloy from 850" C. in iced brine at -8" C. No reference to the occurrence of this transformation in a manufacturing process has been found in the literature. An investigation of the microstructures of a number of hot forgings made from leaded brass rods yielded one forging in which this striking conversion from beta to alpha had occurred. The purpose of this paper is to describe the transformation and certain conditions under which it may occur during the hot pressing of brass. The conversion was noted in a shape forged from a leaded brass rod, the composition of which was: Cu, 60.26 per cent; Zn, 37.86; Pb, 1.88. In this study the lead content was disregarded and the alloy was considered to be equivalent to an alloy of 61.40 per cent copper and 35.60 per cent zinc (9812 parts = 100 parts). The possibility that the lead might obstruct or accelerate the precipitation of alpha was not studied. The lead appears as black globules in the photomicrographs and has a negligible solubility in the alloy.

Jan 1, 1932

Adams, John H., Pres. & Mgr., Alabama Lime & Stone Corpn., 1302-4-8 First Ave., Birmingham, Ala. '14 Adams, L. W., Otis Steel Co., Riverside Plant Cleveland, Ohio. '15 Adams, Leland D., Min. Engr., Mgr., Signal Mines Co., Goldbanks Quicksilver Co., 485 California St., San Francisco, Cal. '14 Adams, R. L., Min. Engr., Old Ben Coal Corpn., Mine 12 Christopher, III. `19 Adams, Robert M., Robert M. Adams Co 1201 Fidelity Bldg., Duluth, Minn. '20

Jan 1, 1925

By E. W. Davis

IF the tonnage of merchantable iron ore remaining in the Lake Superior district is divided by the average of the annual shipments for the past 20 years, it will be found that this ore supply will be exhausted in approximately 35 years. This computed exhaustion period would be an indication of the future activities of the iron-mining industry if it were not for the fact that merchantable ore is being manufactured from low-grade ore, of which there is an almost inexhaustible supply in the Lake Superior district. It is true that at present only the simplest of these low-grade ores are being concentrated to any considerable extent, but progress is being made with the treatment of the more complex ores, and now, in addition to 20 washing plants on the Mesabi Range, three plants are equipped with jigs for the treatment of ore that cannot be concentrated simply by washing. The latest addition to the ore-treating plants of the Mesabi Range is a magnetic roasting and concentration plant at Cooley, Minn., in which ore that cannot be concentrated either by washing or by jigging is roasted to the magnetic state and concentrated on magnetic separators. This plant is beginning its third season of operation, and while it is too soon to make definite predictions, there are strong indica-tions that this new process may make commercially possible the manu-facture of high-grade, merchantable iron ore from large quantities of low-grade ore now considered worthless. After the iron oxide contained in an ore has been converted to mag-netite, almost any desired grade of concentrate can be produced, using magnetic-concentration equipment of the types now in general use for the concentration of the natural magnetites of New York, New Jersey and Pennsylvania. The conversion of hematite (Fe203) to magnetite (Fe304) is easily accomplished by heating the ore to a dull red tempera-ture in a reducing atmosphere. The reaction is slightly endothermic, and while it requires 200 B.t.u. to heat to 900° F. one pound of hematite ore containing 45 per cent Fe, it requires only 100 B.t.u. to convert the oxide into magnetite. In the laboratory, using small quantities of ore, this conversion is very simple, but large furnaces suitable for commercial

Jan 1, 1936