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[†Aaronson, Alfred E., Oil Producer, Pres., Tuloma Oil Cc Tulsa, Okla. '18 ¦Abad, Leopoldo F., College of Min., Univ. of California Berkeley, Cal. '23 ¦Abadilla, Quirico A., Geol. Dept., Cia. Mexicans de Petroleo "EI Aguila," S. A., Edifico "El Aguila," Esq., Calles Aurora y Comercio, Tampico, Tamps., Mexico. '20 ¦Abbey, Robert Graham, Student, Case School of Applied Science Cleveland, 0. '21 Abbott, Clarence E., Gen'l Supt., Iron Mines Div., Tenn. Coal, Iron & R. R. Co., 1405 Minnesota Ave., Bessemer, Ala. '04] [ ]

Jan 1, 1925

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

The mechanical properties of unidirectionally solidified A1(rich)-Mg and A1(rich)-Cu castings containing up to 15 wt pct solute have been determined with re -spect to the volume fraction of interdendritic eutectic. Pioperties were determined in the directions pumllel and Perpendicular to that of solidification; the volume fraction of eutectic was varied between the "as-cast" and equilibrizcm amounts by approperiate heat treatment following solidification. The principles of fiber strengthened composites and dispersion strengthened materials are adapted to explain the mechanical properties of these castings. It is generally accepted that castings often have inferior mechanical properties when con~pared to wrought products. However, there is little quantitative data available concerning the factors which make apparently sound castings weak and/or brittle. The relative ease and inexpensiveness of the casting process have always been attractive and, therefore, an understanding of the factors which contribute to the mechanical properties of castings would seem desirable. Such an understanding may lead to an improvement in the mechanical properties to an extent where castings would become competitive in applications where presently only wrought products are considered to have the requisite properties. Such an understanding could also improve the reliability of present cast products. Much of the recent research on castings has centered about determining the extent of segregation in cast alloys. Macrosegregation, particularly inverse segregation, has been studied in some detail 1-8 and a considerable understanding of microsegregation has been obtained.9'10 The effect of solidification rate on dendrite spacing and on the amount of interdendritic eutectic in binary alloys has been established, particularly for Al(rich)-Cu alloys.""0 However, the extension of these ideas to relate the amount of interdendritic eutectic, concentration gradients, micro-segregation, dendrite spacings, and so forth, to the rnechanical properties has been limited. Dean and spear" have related the mechanical properties of an Al-Si-Mg alloy, A356-T62, to the dendrite spacing and have shown that the mechanical properties improve with decreasing dendrite spacing. Passmore et al.12 have shown that annealing at high temperature improves the mechanical properties of Al(rich)-Cu al- loys and Archer and Kempf 13 have shown that an Al-1 pct Mg-1.75 pct Si alloy behaves in a similar manner. Ahearn and Quigley 14 have shown that high temperature homogenization also enhances the mechanical properties of an SAE 4330 steel. However, in the above investigations, no underlying reasons were suggested for the improvement in mechanical properties. The purpose of the present investigation is to relate the mechanical properties of castings to some of the solichfication variables and to derive some equations by which calculations of the mechanical properties may be attempted. In particular, the effect of the amount of interdendritic eutectic and the effect of stress direction with respect to that of solidification on the mechanical properties will be considered. The Al(rich)-Mg and Al(rich)-Cu binary alloy systems were chosen for study. The A1-Mg system was chosen because its constitutional relationships are such that large volunles of eutectic (up to 24 vol pct) may be obtained in the as-cast condition and then be completely dissolved by subsequent heat treatment at about 440°C. This allows a comprehensive study relating the mechanical properties of castings to the amount of interdendritic eutectic. Also the Al(rich)-Mg eutectic is almost a single phase 15 which should make the experimental results more amenable to theoretical interpretation and calculation. The A1-Cu system was chosen for study because of the large amount of related information available concerning segregation, dendrite spacing, and so forth. Unidirectionally solidified castings were used throughout the investigation so that the effect of solidification direction with respect to the direction of applied stress could be determined. THEORETICAL It is well known that upon solidification of binary alloy castings, the nonequilibrium amount of eutectic which forms is given by 10 where fe o is the weight fraction of eutectic, Cs is the solid solubility of solute at the eutectic temperature, k is the equilibrium partition coefficient, and C, is the average composition of the alloy. In the development of Eq. [I], it is assumed that the effects of inverse segregation and diffusion in the solid are negligible, and that no porosity is present. If the casting is homogenized at a high temperature for a long period of time, some (or all) of the eutectic is dissolved and the amount of eutectic for this "equilibrium" condition may be calculated directly from the constitutional diagram. By appropriate intermediate annealing, the

Jan 1, 1970

By Craig R. Barreft, Oleg D. Sherby

The steady-state creep characteristics of pure polycrystalline copper were studied in the temperature range 400" to 950°C and in the stress range 400 to 7000 psi. Tests were conducted in dry deoxidized hydrogen and all specimens exhibited high ductility before fracture. Two activation energies for creep were established as a function of temperature. Above about T/T, = 0.65, the activation energy for creep was 48,000 cal per mole whereas between 0.5 and 0.65 T, it was 28,000 cal per mole. The observed temperature dependence of the activation energy for creep follows the same trend as exhibited by the self-diffusion coefficient of copper in copper single crystals and silver in silver single crystals. It is therefore believed that the rate-cmtrolling mechanism in creep of copper in the stress and temperature range studied is diffusion-dependent and is probably associated with a dislocation-climb process. The low activation-energy region is attributed to enhanced volume difFusion from the presence of dislocations which act as short-circuit paths for diffusion. THERE is extensive experimental evidence1,2 that the activation energy for creep, Q,, for pure poly-crystalline metals tested at temperatures above one half the absolute melting temperature (0.5 Tm) is a constant and equal to the activation energy for volume self-diffusion, Qsd This equality is generally interpreted as meaning that creep in this temperature range is controlled by a dislocation-climb process. The existence of high-temperature creep activation energies not equal to the respective self-diffusion values has been suggested both theoretically3"5 and experimentally.6-8 Two examples of apparent nonequality between Q, and Qsd have been reported for the cases of silver7 and copper,' where activation energies for creep much lower than those for self-diffusion persist to rela- tively high temperatures (up to 0.6 T,). These observations suggest that dislocation climb may not be the only important process in the high-temperature deformation of these metals. That dislocation climb does indeed occur relatively slowly in these two metals due to their low stacking-fault energy has been suggested by many investigators.9-10 Although the creep behavior of copper has been studied extensively at low temperatures, the high-temperature activation energy for creep is not well-defined. The data of Feltham and Meakin8 indicated that Q, is temperature-dependent above one half the melting temperature, equaling a value of -30,000 cal per mole at temperatures up to 550°C and increasing to a value of -49,000 cal per mole at 700°C. No data has been reported above 700°C. The value of 49,000 cal per mole is very near the value of Qsd for copper reported by Kuper et al." as 47,100 cal per mole. In view of the lack of high-temperature creep data and the apparent temperature dependence of Q, for copper the present investigation was undertaken to determine the value of Q, over the temperature range of 400" to 950°C. It was hoped that such a study would clearly document the temperature dependence of Q, and yield significant information as to the nature of the rate-controlling creep mechanisms. MATERIALS AND PROCEDURES The material used in this investigation was high-purity OFHC copper. After rolling and recrystal-lization treatments spectrographic and chemical analyses showed only 0.0008 pct Ag, 0.0002 pctCa, 0.0002 pct H2, and 0.002 pct O2 as trace impurities indicating a purity of greater then 99.995 pct. Specimens were machined from cold-rolled sheet and the gage sections polished with 2/0 emery paper prior to annealing treatments. Annealing was done in both vacuum and dry deoxidized hydrogen atmospheres. No variation in creep strength was found as a result of the different annealing atmospheres. The final annealing temperature was either 700°, 800°, or 1000°C depending on the temperature range to be studied. These treatments resulted in average grain diameters of 0.03, 0.4, and 1.0 mm, respectively. The precise mechanical-thermal history of these

Jan 1, 1964

By A. Rosen, P. Wynblatt, J. E. Dorn

The temperature, strain rate, and structure dependence of the flow stress in a poly crystalline Fe-2 pct Mn alloy was investigated between 77" and 370°K. It was possible to identify the low-temperature data from 77° to 160°K with Dorn and Rajnak's theory of the Peierls mechanism of plastic deformation. Above 160°K one or more thermally activated mechanisms must he operative; however, these were not identified in this investigation. The mechanistic basis for the rapid decrease in the flow stress of bcc metals with an increase in temperature over the low-temperature range is yet being debated. Various dislocation mechanisms have been suggested in the past but the agreement between the various proposed theories and the experimental results have not been definitive. In the present paper, the authors will demonstrate that the plastic behavior of polycrystalline iron containing 2 wt pct Mn plus interstitials agrees excellently with predictions based on the Peierls mechanism from 77" to 160°K whereas from 160" to about 370°K other as yet unidentified thermally activated mechanisms take over. Undoubtedly, the overlap of these mechanisms with the Peierls mechanism contributed to the difficulties of rationalizing the low-temperature behavior of iron and its alloys. I) EXPERIMENTAL TECHNIQUES AND RESULTS Although extensive data are now available on the effect of temperature and strain rate on the flow stress of various bcc metals and alloys, it was, nevertheless, deemed necessary for the objectives of the present study to obtain highly accurate data of the type most pertinent for checking the theories on a series of well-documented work-hardened states. Iron containing 2 wt pct Mn was used in this investigation in order to obtain a lower ductile to brittle transition temperature than that for iron.' The additional elements present were 0.004 pct C, 0.05 pct 0, 0.004 pct S, 0.003 pct P, 0.006 pct N, and 0.001 pct Si. The as-received 3/8 by 3/4 in. bars were cold-rolled to 0.100-in. thickness, recrystallized under argon for 30 min at 1073"~, further cold-rolled to 0.063-in. thickness, and finally recrystallized under argon for 30 min at 1000°K. This treatment gave a stable reproducible equiaxed grain structure having an average grain diameter of about 90 p. Prior to the final recrystallization treatment, the sheet was machined into tensile specimens 1/4 in. wide having a 1.625-in.-long gage section. All specimens were tested in controlled-temperature baths on an Instron Testing Machine. For convenience in the theoretical analyses the data will be given in terms of the shear stress for flow, 7, the shear strain rate, f, and the shear strain, y. A series of three standard strain-hardened states were obtained by prestraining specimens at 300°K and at a shear strain rate of 7.68 x lo-' per sec to three stress levels of 6.89 X l08, 10.3 X lo8, and 14.5 x 10' dynes per sq cm, respectively. Immediately following this prestrain the temperature bath was changed and each specimen was pulled in tension at either f = 7.68 X lo-' or f = 3.06 X 10"3 per sec. In terms of the accuracy that was achieved, the values obtained did not deviate more than *0.1 X 10' dynes per sq cm and * 1°K from the reported values of stress and temperature and not more than *5 pct in the reported values of the strain rate. The tensile stresses were converted to shear stresses using a factor of 1/2. The shear stress for the initiation of flow at the test temperature was determined by taking a y = 6.16 x 10'3 offset. from the modulus line at which point good accuracy could be achieved in determining y and the associated flow stress 7, with only a negligible increase in the pre-

Jan 1, 1965

By E. I. Larsen, E. F. Swazy, F. R. Hensel

High strength, high-conductivity copper-base alloys have found considerable use in the resistance welding and electrical industry in the form of castings, forgings, or wrought products. There are a number of parts utilized by these industries which would lend themselves to manufacture by powder metallurgical methods provided the required physical and electrical properties are obtainable with such methods. The present paper describes the results of a study of certain copper-base powder metallurgical products susceptible to precipitation hardening. Copper Powders The general types of commercially available copper powders are flake, spherical and electrolytic. Micrographs of these three types are shown in Figs. I, 2 and 3. The difference in particle shape is pronounced and obvious. The type of powder used is determined, or at least indicated, by the final properties desired in the finished article. The type of powder employed during the present investigation was electrolytic powder shown in Fig. 3, and was chosen because of its particular adaptability to the work described in this Paper. The screen and chemical analyses of this powder are shown in Table I. In the preparation of compacts of high electrical conductivity, the purity of the copper powder is of importance in addition to other factors, such as density and the state of internal stresses. These variables were studied briefly by pressing a number of compacts to various pressed densities, sintering them for one hour in hydrogen at 975OC and repressing. The size of the finished compacts was 1/4, by % by 8 in. The time interval from the application to the termination of pressure was approximately 20 sec. Some of the compacts were annealed before testing. The results are listed in Figs. 4 to 8, inclusive. In Fig. 4 the curves of pressed density vs. compacting pressure, and sintered density versus compacting pressure show the typical direct relationship of pressure and density. Compacting pressures exceeding about 30 tons per sq. in. result fiequently in expansion during sintering for the type of powder used. Fig. 5 indicates that variations in the initial pressed density within the range of about 5 to 6 grams per c, c., affect only slightly the pressure required to obtain a

Jan 1, 1946

By E. I. Larsen, E. F. Swazy, F. R. Hensel

High strength, high-conductivity copper-base alloys have found considerable use in the resistance welding and electrical industry in the form of castings, forgings, or wrought products. There are a number of parts utilized by these industries which would lend themselves to manufacture by powder metallurgical methods provided the required physical and electrical properties are obtainable with such methods. The present paper describes the results of a study of certain copper-base powder metallurgical products susceptible to precipitation hardening. Copper Powders The general types of commercially available copper powders are flake, spherical and electrolytic. Micrographs of these three types are shown in Figs. I, 2 and 3. The difference in particle shape is pronounced and obvious. The type of powder used is determined, or at least indicated, by the final properties desired in the finished article. The type of powder employed during the present investigation was electrolytic powder shown in Fig. 3, and was chosen because of its particular adaptability to the work described in this Paper. The screen and chemical analyses of this powder are shown in Table I. In the preparation of compacts of high electrical conductivity, the purity of the copper powder is of importance in addition to other factors, such as density and the state of internal stresses. These variables were studied briefly by pressing a number of compacts to various pressed densities, sintering them for one hour in hydrogen at 975OC and repressing. The size of the finished compacts was 1/4, by % by 8 in. The time interval from the application to the termination of pressure was approximately 20 sec. Some of the compacts were annealed before testing. The results are listed in Figs. 4 to 8, inclusive. In Fig. 4 the curves of pressed density vs. compacting pressure, and sintered density versus compacting pressure show the typical direct relationship of pressure and density. Compacting pressures exceeding about 30 tons per sq. in. result fiequently in expansion during sintering for the type of powder used. Fig. 5 indicates that variations in the initial pressed density within the range of about 5 to 6 grams per c, c., affect only slightly the pressure required to obtain a

Jan 1, 1946

By Eugene Grace

IN THE careers of the men to whom I have referred we find typified the development of the chief prob-lems of engineering. The first is to shape and direct the forces of nature and thus to bring the world's resources to add to the comfort and welfare of man-kind. That, in a word, is the problem of production. Engineers have made a supreme contribution to the solution of that problem. But I feel that we have two somewhat newer branches of engineering which must command more and more of our attention. Those are what might be termed commercial and human engineering. Of what value is all our efficiency in pro-duction if we do not distribute efficiently, economically and effectively? And of what value is any of it unless we can add to the happiness and deeper satisfaction of those engaged in industry, as well as those who enjoy its -products? I predict that the outstanding advances in business over the next ten years will be in improved merchan-dising and distributing methods. Herein lies a wide field of opportunity for the engineer. We have briefly reviewed certain qualities of engi-neers who have become successful business executives. Is it possible for us to say that the material success of all these men was due to any one characteristic com-mon to each one of them? Indeed, I venture to assert that there is one quality which, in the last analysis, is determining as to whether any roan shall realize material success in this world of ours. That quality-so notable in the character of each one of the men I have named-is sound judgment. Moments arise in every life when it is necessary to say "yes" or to say "no" to a particular proposition or to a proposed line of action. It is the man who says "yes" at the proper time and "no" at the proper time who, in the final analysis, realizes business success. The ability to do this wisely is the mark of sound judg-ment, which is necessary in a business executive. I have known many business men seemingly slow in their mental processes, possessed apparently, of little imagination and of none of the flair which gives fasci-nation to so many characters, and yet who, when crises come-be they big or be they little-are able so to steer their business courses that they move in the right direction instead of into shallow waters or upon the rocks of trouble.

Jan 4, 1928

By K. E. Gray, A. Podio

ABSTRACT Berea and Bandera sandstone samples were impacted with both 3/4-in. and 1/2-in. long wedges, each having a 60° included angle and a 0.05-in. flat, at various confining pressures, with borehole and pore pressures held fixed at atmospheric pressure. Samples were saturated with air, water, glycerine-water, solirol, mineral oil and soltrol-mineral oil mixtures to obtain a wide range of pore fluid viscosity. Penetration depth was held constant at 0.1 in. Dry and soltrol-mineral oil-saturated Berea samples were impacted at depths of penetration from 0.01 to 0.04 in. under 1,000 psi confining pressure to study crater initiation. Results indicate that viscosity of the pore fluid is influential primarily during the early stages of crater formation. Differences in bit force, crater volume and blow energy for tests parallel and perpendicular to bedding were significant, but decreased as the stress state was elevated. Crater volume, blow energy and bit force were nonlinearly related with depth of penetration. Crater volume was nonlinear with energy of blow. Fixed-penetration tests on saturated Berea yielded greater crater volume than did similar tests on dry samples. Differences in the nature of deformation for low values of bit penetration were noted between saturated and unsaturated samples. INTRODUCTION Rock failure during bit-tooth impact and scouring action constitutes a vital part of the drilling process and a difficult problem for researchers. Much study has been devoted to various aspects of the problem, and much has been learned about mechanics of rock failure. However, analytical treatment of drilling at depth remains difficult, partly because there are so many factors involved and because valid simulation of downhole conditions is extremely difficult. Forming individual craters by a bit tooth or chisel impacting, or indenting, a rock mass has been studied by many investigators.1-18 Similarity between single-tooth chisel impact and the corresponding action of a rotary bit has been discussed by Appl and Gatley, Garner, Podio, and Gatlin l8 compared the similarity in single-blow impact tests with microbit drilling data reported by Cunningham and Eenink.l9 Maurerll has used single-tooth impact data to develop a "perfect cleaning" theory of rotary drilling. Individual roller cutter-tooth impact data have been reported by Young. 20 Single-tooth tests in all of the cited literature were carried out on dry rocks. Inasmuch as any subsurface rock of oilfield interest is saturated with some fluid, it seemed desirable to study crater formation in permeable rocks saturated with a viscous pore fluid as a step, however short, toward more realistic simulation of subsurface conditions. This paper presents results of single-blow chisel impact studies on Berea and Bandera sandstones, both dry and saturated with pore fluids of various viscosities at confining pressures to 10,000 psi. EXPERIMENTAL APPARATUS AND PROCEDURE EXPERIMENTAL APPARATUS The same basic apparatus for single-blow chisel impact at elevated stress states, described in earlier papers was used in this study. l6. l8 Fig. 1 shows the complete experimental system; Fig. 2 shows a cross section of the pressure cell, with a sample ready to be impacted. EXPERIMENTAL PROCEDURE Two different rocks, Berea and Bandera sandstones, were used in this study. Both rocks have been used extensively in research, and rock descriptions can be found in a paper by Gnirk and Cheatham.15 Permeability to air of Berea is about 300 md normal to bedding and 540 md parallel to bedding. Bandera had vertical and horizontal air permeabilities of 18 and 57 md, respectively.

Jan 1, 1966

By W. A. Boyer

Mine hoisting ropes can be loaded to capacity only when the strength of each component is exactly known. Characteristic curves provide this information. When load and rate of acceleration are specified for an individual rope, the characteristic curve assumes a predetermined shape. The factor of safety is the value derived by dividing the breaking strength of the rope by the total stress on the rope where it goes over the sheave wheel. Total stress is made up of the weight of skip and cage, weight of ore, weight of rope between sheave and rope clevise or attachment, friction load, and acceleration force. Bending stresses are neglected in this discussion, as sheaves and drum diameters are assumed to be large enough to reduce these stresses to a negligible value.

Mar 1, 1956

By Sydney H. Ball

A QUARTER of a century ago, a pessimistic Belgian financier in conversation with the founder of the Belgian Congo, that great ruler, Leopold II, emphasized the danger to the colony should the synthesis of rubber be discovered. The king replied, "I do not worry. The Congo has had its ivory period; it now has its rubber period. Tomorrow it will have that of its mineral wealth; eventually that of agricultural products." That "tomorrow" arrived some twenty years ago. Through her mines the Belgian Congo has survived the present depression, and her mines for the next decade will safeguard her. The Congo, in turn. is the surest foundation industrially and financially of Belgium itself. In few, if any, political units is mining as dominant as in the Belgian Congo. In 1930, 1931 and 1932 mineral products represented respectively 67.9 per cent. 70.5 per cent and 59.3 per cent, of the total exports. In 1933 for each white person in the colony, there was produced about $1,675 worth of gold, diamonds, copper, tin ore and minor mineral products and in 1930 the per capita production, notwithstanding the larger population, was almost $2,000.

Jan 1, 1934

By Larry Dale

An approach for predicting the development of mineral resources on public lands has been developed as an aid to resource agencies. It consists of new techniques for evaluating the economic potential of the resource, the uncertainty about mine cost estimates, and the uncertainty about the occurrance of mineral deposits. New mineral sup- plies from inferred and hypothetical resources can be predicted by using these techniques. A case study illustrates their application in predicting development of copper resources in western Montana.

Jan 1, 1982

By F. V. Lenel, G. S. Ansell, M. J. Salkind

An experiment is described in which the growth of interparticle necks in an array of loose spherical silver powder at temperatures near 300°C was determined by measuring changes in the electrical resistance of the array. The activation energy for neck growth of contacts was derived by abruptly changing temperature and noting the change in the rate of neck growth. Since the experiments were run under an external load, the changes in activation energy with stress could he determined. The activation energy was found to decrease rapidly with increasing stress. It is concluded that the material transport in the experiments is one of plastic flow by dislocation motion. The variation of activation energy with stress is typical for cross slip of dislocations, an important material transport mechanism in the temperature range investigated. THE process in which powder compacts or aggregates of loose powder are held at an elevated temperature under an external load is called hot pressing or sintering under pressure by powder metallurgists. In this investigation the early stages of this process as applied to loose spherical silver- powder aggregates were studied. The powder particles were approximately 100µ in diameter and the temperature was near 300°C, i.e., below one half of the melting point of silver in degrees Kelvin, where volume diffusion is not expected to contribute to sintering. In the process, the contact or neck areas between powder particles grow. Since this involves plastic deformation of the particles under a constant external load (even though not under constant stress) it would be termed creep by mechanical metallurgists. On the other hand, the growth in neck area observed in compacts or loose-powder aggregates held at elevated temperature without the application of an external load is termed sintering by powder metallurgists. During sintering the major driving force is the stress due to surface tension. However, even when no load is placed on the compact or powder aggregate, an external stress, i.e., gravity, plays an important role in sintering in addition to those stresses arising from surface tension, as was shown in two previous investigations.'" It is therefore postulated that no sharp dividing line can be drawn between the phenomena of "creep" and "sintering". Different material transport mechanisms may be involved in either of these phenomena, but they will depend upon the temperature and the level of stress, but not necessarily upon the nature of the driving force: surface tension or external load. At the low temperatures of this investigation, an external stress much higher than the stress due to surface tension is necessary to obtain measurable rates of neck growth. In order to avoid misunderstanding this phenomenon will be called "creep". The rate of growth in contact area in the loose silver-powder aggregates was determined by meas-

Jan 1, 1965

By B. J. Reid, J. N. Greenwood

It has been shown1 that cavities are formed in the grain-boundaries of copper and 70:30 brass (as well as in magnesium) by the application of tensile stresses at elevated temperatures. For a given rate of strain, cavities are formed in brass at a lower temperature than in copper, and they are larger; it was thought that this earlier onset of cavitation in the alloy might be caused by the distortion produced in the metal lattice by the alloying element. If the cavitation is caused by the vacancy-migration mechanism, ' the distortion of the lattice would reduce the energy required for vacancy formation, and thus provide vacancies more readily to assist in the cavitation process. It was decided to study a range of alloys to find out whether increasing amounts of an alloying element would cause any progressive increase in, or modification of, the cavitation in copper. Nickel was chosen for this purpose, since it is soluble in copper throughout the whole range of alloys. A further advantage was its low vapor pressure, which enabled the preparation of the alloys in vacuum and the consequent reduction of their hydrogen content. It has been suggested that cavities may be nucleated by the migration of hydrogen atoms to the less regular atomic spacing at the boundary, and their combination to form molecules. The latter being too large to diffuse back into the lattice, form stable cavities into which vacancies could condense. PREPARATION OF ALLOYS All alloys, ranging from pure OFHC copper to 43.7 at. pct of nickel (carbonyl), were prepared in a vacuum furnace employing high-frequency induction heating. When a charge was melted, vigorous gas evolution occurred initially, after which the pressure was reduced to 10-4 mm Hg, using an oil-diffusion pump. After remaining molten for a further 1/2 to 1 hr to aid degassing, the melt was allowed to solidify in the crucible. In this way contamination by gases evolved from the surface of a separate mold was avoided. The list of alloys prepared is shown in Table I. The percentage of hydrogen present in the OFHC copper was reduced from 0.0054 at. pct to 0.0012 at. pct, as measured by a vacuum-fusion method. The alloys were cold-rolled to 0.03-in.-thick strip, and were homogenized in vacuum for 1 hr at 900°C after every 30 pct reduction. At a thickness of 0.05 in., the strip was held at 450°C for 24 hr under high vacuum (10-5 mm Hg) in an attempt to reduce the hydrogen content still further. Tensile specimens were prepared with a gage length of 1 in., and were finally annealed for 2 hr at 800°C to give an average grain diameter of 0.1 mm. TENSILE DEFORMATION The specimens were deformed in a tensile straining machine operated by a synchronous motor at a constant rate, equivalent to 1.7 pct per hr on a 1-in. gage length. The specimen and grips were contained in a vacuum jacket. A pressure of 10-2 mm Hg was maintained, which was sufficient to prevent surface tarnishing of a specimen held at 650°C for 24 hr. Tests were made between 20. and 650°C and the temperature was controlled to within ±3° over the gage length. The load was measured by the deflection of a cantilever spring. a) Mechanical Properties-The ductility curves shown in Fig. 1 fall into two groups. Figs. 1(a) and (b) for copper and the 5 pct nickel alloy, respectively, show a continuous fall in ductility with a steep fall between 200° and 400°C. Figs. l(c) to (f) show the same sudden loss of ductility between 200° and 400°C. With higher temperatures, however, there is a recovery in ductility values to a maxi-

Jan 1, 1959

[Aamot, Clav Crone, (Member '29) Met., Det Norske Aktieselskab for Elektrokemisk, Industri, Inc., Oslo, Norway. Aamot, 0, Crone, (Member '29) c/o Elektrokemisk, Radhusgaten 23, Oslo, Norway. Aase, Glenn D., (Junior Member '40) Jr. Met., American Smelt. & Refin. Co., Selby, Calif. Abadie, Henry G., (Junior Member '43) Div. Petr. Engr., Union Pacific R.R. Co., 422 W. 6th St., Los Angeles 14, Calif. Abbott, Clarence E., (Member '04) Civil Engr., V.P., Tennessee Coal, Iron & R.R. Co., 1542 Brown Marx Bldg., Birmingham, Ala. Abbott, Fred E., Jr., (Member '44) Petr. Engr., c/o Arabian American Oil Co., A.P.O. 816, c/o Postmaster, New York, N. Y. Abel, Raymond L., (Member '28) Chem. Engr., 0. 0., Pittsburgh Chem. Warfare Procurement Dist., American Bank Bldg., Pittsburgh, Pa.]

Jan 1, 1946

By A. S. Adams

A GLANCE at the list of papers1 that have been published since 1920 on the general subject of flotation suggests the variety of ideas that exist regarding the underlying cause of the phenomenon. Among these ideas, we find several coherent theories, but none that adequately and completely explain the phenomenon. Ralston2 and Bains3 suggested an electrical theory which has to do with the attachment of mineral particles to a bubble by the attraction of unlike electrical charges. This theory has its root in the fact that a bubble of air in pure water is electrified in such a way that the surface is negatively charged while the body of the water is positively charged. This result, which was first discussed by Helmholtz, also obtains when the water contains anything except a high concentration of hydrogen ions, or ions which are trivalent or tetravalent. The theory also holds that the mineral particles have positive charges on their surfaces, and so there is attachment between bubble surface and mineral particles by the old law of electrostatics, which states that unlike charges attract.

Jan 1, 1928

By John W. Vanderwilt

The unpredictable behavior of ground movement and subsidence has complicated the problems that attend the extraction of large quantities of ore. Special studies, particularly relating to coal mining, have yielded such a voluminous literature and so many involved controversial theories that a partial review would be difficult. Limited space makes any kind of a review impractical. The features to be considered cover only a relatively small part of the broad problems of ground movement and subsidence, but it is believed that this small part is critical. The practical aspects are important, since they bear directly on safety of mine workings, on recovery of ore and on dilution of ore in block caving and related systems for extracting large quantities of rock. The ground movement to be described occurs outside the vertical boundaries of a caved block in the area that is commonly referred to as being in the "zone of draw." "Draw" is a term that originated in the subsidence problems related to coal mining, and it is defined by a line drawn from the margin of the area caved underground to the most distant fracture at surface on the same side of the caved area as shown in Fig. I.' A line thus drawn is called the cave line, and its angle with respect to the horizontal is the cave angle or angle of draw. It is understood that the line is taken normal to the limit of mining, and in a vertical plane. The prevailing theories as to draw and angle of draw assume that appreciable movement occurred along the cave line, which has been described as a fracture resulting from the shearing action brought about by the weight of the overlying load. Fig. 3 shows diagrammatically the mechanics of ground movement adjacent to an area of subsidence according to the prevailing theory of draw (A, from Royce2) and, for comparison, ground movement observed in the Climax mine (B). The text in Peele's Handbook2 referring to Fig. 2 does not state the meaning of the "original position of top of workable ore" in the rectangular space above "ore in place," and the arrows are not explained. However, this presentation is most concerned with the zones outside the rectangle. According to the prevailing theory, as shown at the extreme left under A, Fig. 2, the vertical tension cracks at surface change at a shallow depth to shear fractures forming the cave line, and it is assumed that appreciable movement takes place along the cave line toward and into the subsiding caved block. The mechanics of ground movement observed in the Climax mine, as shown under B, Fig. 2, does not accord with the prevailing theory, particularly as regards the cave angle and draw. The vertical tension cracks seen at surface die out at depths of 150 to 225 ft. and shear fractures do not develop. Movement is confined at surface to a mantle of rock 50 to roo ft.

Jan 1, 1949

By Arthur H. Wilson

INTRODUCTION The stratified deposits of the coal measures are strongly laminated and exhibit a high degree of anisotropy. The stronger rocks in the sequence possess joints and shear planes, the coal itself has a closely spaced cleat pattern, and the softer rocks are capable of flowage. To calculate the general distribution of stress in such a medium by analytical means based on the theories of elasticity is difficult, and has not yet been satisfactorily achieved. Nevertheless, some estimate is required to aid the design of supporting pillars and permit the correct siting of main roadways. This is important when laying out districts for longwall extraction, particularly if the results of previous experience are not available in the area to be exploited. Although elastic stress analyses, including finite element analysis, may not be very appropriate, the basic equilibrium conditions will apply. These, combined with logical deductions based on observed fact, can be used to give appropriate solutions which experience has shown to be capable of giving acceptable results in the design of pillars associated with longwall workings. Constancy of cover load is one of the fundamental equilibrium conditions. When mining below ground, the cover is not removed, therefore the average vertical load after mining must equal the initial cover load. If mining produces a local decrease in load in any particular area, it must be balanced by an equivalent increase in load nearby. Bending moments in the strata above are capable of compensating for the turning moments which this redistribution of load may produce, and the existence of a "rear abutment", much discussed between 1950 and 1960, is not an essential equilibrium requirement. If the distribution of vertical stress is plotted three-dimensionally, then the load on any small element of area 6S will be o.6S, where o is the average stress. This also represents the volume of the "stress envelope" which lies above 6s. By making the individual areas very small and summing together, it is possible to show that the total load on any particular area can be found by calculating the volume of the stress distribution envelope which lies above it. A similar consideration applies to the stress distribution in a two-dimensional situation. If the stress distribution curve is drawn, then the area below any portion will represent the load per unit depth of section. For example, Figure 1 represents the possible stress distribution across a caved waste and associated ribside. If AW is the load deficiency [ ] These loads must balance, therefore area AW = AS, and if one can be deduced, the other will then be known. Attempts have been made to measure stress distributions in the ribside and in the waste. Stress meters in soft rocks such as the coal measures have not proved very effective. Those based on the measurement of strain have experienced difficulty in strata capable of flowage, high modulus stress meters suffer from cross sensitivity, and overcoming to obtain absolute stress is almost impossible. Load measuring instruments left in the waste have also proved largely ineffective, mainly as a result of the difficulties of protecting the leads in a caving environment. Certain logical deductions, however, can be made about the conditions in the waste. CONDITIONS IN THE WASTE Over the area of the waste the surface trough which develops is remarkably consistent, despite the geological variations which occur from coalfield to coalfield. In Britain, an accuracy of 210% is claimed for subsidence prediction based on width of extraction and depth of cover (National Coal Board, 1975). The subsidence in the USA is more variable (Adamek and Jeran, 1981), particularly with respect to the point of inflexion, but the same general pattern occurs. At the shallower depths the somewhat harder roof strata involved in the caving in the USA may suffer less compaction, giving reduced values of subsidence. Subsidence at intermediate horizons below the surface

Jan 1, 1982

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

Note by the Secretary.-—In the preceding communication of Mr. Rickard, in the present discussion, as printed in Trans., xxiii., the loss of quicksilver at Pestarena, reported on p. 569, as 230 and 234 grammes per metric ton, is stated as equivalent to about 74 pounds per short ton avoirdupois—an obvious error, which escaped correction in my reading of the proofs, and was not discovered until after Vol. XXIII. had left the press. The true equivalent is 0.46 pound or about 7 1/2 ounces (instead of pounds) per short ton.— R. w. R. Philip Argall, Denver, Colo. (communication to the Secretary) : Mr. Rickard's last contribution to this discussion* calls for some reply from me, if only by way of defending myself against the charge (p. 569) that my criticisms of his paper were "unnecessarily hypercritical and occasionally unfair." At the same time I am fully aware that our Transactions are not the place for mere personal controversy, and that the sole object of discussion is to define differences of opinion, and defend opposing views as a means of eliciting the truth. Mr. Rickard disclaims the statement, which he says I attributed to him, that in the slow-crushing Gilpin county mills the pyrites remain longer in the mortar than the other portions of the ore. My understanding of his statement was based on the following passages in his paper: " Particles of ore, which have heen pulverized to a fineness which would permit of their exit through the screen, are enabled to settle towards the bottom of the mortar. It would he expected that the heavy metallic minerals occurring in the ore would, because of their greater specific gravity, be most affected by this feature of the treatment. In practice this is found to be so. The fine slimes contain a large proportion of metallic sulphides, generally valuable on account of their close association with the precious metals, while the coarsest particles to be found in the tailings usually consist of quartz and other minerals forming the less heavy gangue (Trans., xxiii., 139).

Jan 1, 1895