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By C. Laird, C. E. Feltner

An investigation into the effect of a material's slip character on its high strain fatigue properties has been carried out using copper and Cu-7.5 wt pct A1 as representative wavy and planar slip mode materials, respectively. In copper, the constant term and exponent in the Coffin-Manson equation, ?EpNf1/2 = const, are unaffected by the temperature of testing or the history of the metal. On the other hand, in Cu-7.5 wl pcl Al, while the exponent is invariant, the constant is increased with respect to copper and increased further with decrease in temperature. The life in Cu-7.5 wt pct A1 is double that of copper at room temperature and about four times at 78°K. Fractoflaphic studies indicate that these diffevences in life are associated with the early stages of cracking. In copper, severe surface rumpling provides crack nuclei at pain boundaries independent of' testing temperature or the history of the metal. In Cu-7.5 wt pct Al, the planar slip mode of deformation prevents grain boundary folding; crack nucleation is therefore mainly transgranular and the increase in life with respect to copper is associated with a prolonged linking-up stage of such transgranulay cracks. At the lower temperature the increased difficulty of cross slip inhibits multiplication of trans-granular cracks and retards the linking-up process, giving a further enhaancement in life. It is expected that such behavior will be found general in materials of wavy and planar slip mode, respectively. STAGE II crack propagation in high strain fatigue takes place by a repetitive process of crack tip blunting in the tension part of a fatigue cycle followed by resharpening of the crack in the compression part.1-3 This mechanism has come to be called the "plastic relaxation process".3 At very high strains (lives to failure less than 103 cycles), most of the life of a specimen is spent in crack propagation by the plastic relaxation process.4,5 Since the differences in the cyclic strain hardening behavior of metals and alloys are comparatively small in this strain range,6,7 the amount of blunting at a crack tip depends primarily on the applied strain amplitude. The rate of crack propagation in this life range is therefore nearly constant with respect to material and temperature of testing. In the longer life portion of the high strain fatigue range (l03 to 103 cycles to failure), a considerable fraction of the lives is spent in crack initiation and Stage I growth. Grain boundaries have frequently4,5,8 been found to be the sites for this growth which is also associated with a surface folding process.4'5 Such folding behavior may also be general in any material having a grain structure and capable of plastic deformation. It has therefore been suggested475 that the universality of the Coff in-Manson law,9'10 constant,* where ?Ep is the plastic strain range and Nf the number of cycles to failure, is reflected in the approximate invariance of both the crack initiation and propagation behavior. It happens that, in most investigations of the phenomena associated with failure,4,5,8 materials with a wavy slip mode have been used as vehicles for the studies, or else "normally" planar slip mode materials have been tested under conditions giving rise to wavy glide deformation, e.g., stainless steels cycled at high temperature.'' The purpose of the present investigation was to determine whether or not different cracking phenomena would occur when the slip mode of a material is planar and if the associated life to failure would be different than that of a wavy slip

Jan 1, 1968

By Oscar Marzke

STUDIES on the precipitation of a face-centered from a body-centered structure-a common occurrence in alloy systems-are essential to the development of a theory for the formation of segregate structures. The separation of the alpha phase from the beta of the copper-zinc system is an example of this type of precipitation. EARLIER STUDIES ON THE SUBJECT R. F. Mehl and 0. T. Marzke1 in 1931 presented a paper giving the results of some investigations carried out by them on the segregate structures produced when the alpha and gamma phases of the copper-zinc system and the alpha phase of the copper-aluminum system precipi-tate from the beta phases of these systems. They showed that the alpha phase precipitates as needles close to the [111] directions of the beta phase. In the discussion of that paper some doubt was expressed about the nature of the segregate. More investigations were undertaken to determine the character of the precipitate in the copper-zinc system and also the orientation relationship between the matrix and precipitate. The present paper gives the results of these investigations. Since the publication of the earlier paper, several other papers on this subject have been published in this country and abroad. Haneman and Schroder2 reported that the alpha phase precipitates as needles along the [111] directions of the beta phase and that these needles align themselves to form plates on the {111} planes of the matrix. Mathewson and Smith3 pointed out that the {111} plane does not contain the [111] direction and that it would be quite impossible, therefore, for needles in the [111] direction to form plates on the {111} plane. They suggested

Jan 1, 1933

By Charles Catlett

Much has been done of late years to facilitate preliminary stratigraphical investigations, and for examination at considerable depths and in a certain character of material the diamonddrill, in its general forms, certainly stands pre-eminent among the tools for such work. But there are large classes of deposits —indeed, I may say the larger proportion in which ordinary. prospecting is done—which lie near the surface and are interbedded with soft and fine material. The method usually employed for prospecting these is by means of small shafts. These are sunk with considerable slowness and at considerable expense, depending largely upon the character of the material encountered, and are greatly interfered with by water. In this region the smallest are 3 by 4 feet, but they are usually considerably larger. Having had occasion during the past year to do a large amount of prospecting work, I have found the use of a hand-auger and drill of immense value in this respect, and in my practice it has largely superseded, and always preceded, the other forms of investigation. I believe that the information desired mas

Jan 1, 1898

By Paul H. Johnson

Chemical mining may be defined as the use of chemicals in extracting metal values from in situ broken or unbroken ores within a mine. The present means for the generation and regeneration of sulfuric acid or sulfuric-ferric sulfate solutions are inadequate for most applications. This report describes a pressure oxidation process for the generation and regeneration of these solutions from pyrites and spent iron sulfate leach liquors. While recent mining developments such as solution injection, caving, and conventional and nuclear blasting, have provided new and better means for the per-colation of leach solutions through rock masses, little has been done to reduce cost and improve the quality of the leach solutions that are required. A leach solution for chemical mining should meet certain requirements. It should be 1) inexpensive on either a small or large tonnage basis, 2) capable of selectively leaching the desired ore minerals contained in a particular ore, 3) of the proper strength or quality to do the job of leaching in an underground environment and 4) amendable to simple and inexpensive metal recovery steps. It is also important that the capital investment be low for the solution generation and; or regeneration plant.

Jan 8, 1965

By J. J. Gilman

IT is well established that dislocations exist in crystals and account for crystal plasticity.' However, the origins of the dislocations are not clear. Among the means by which dislocations might originate are: a) through crystal growth accidents, b) by the collapse of condensed sheets of vacancies, or c) by stress-induced nucleation. Theoretical calculations' have indicated that the last means should require very high stresses in order to operate. The purpose of this paper is to show that the stresses around the tips of cracks are large enough to nucleate large numbers of dislocation loops. Specifically, it will be shown that (100) cleavage cracks in LiF crystals nucleate dislocations in regions of the crystals where dislocations did not exist previously. It is believed that the use of LiF for this investigation does not restrict the significance of the 1 results. In fact, it is believed that this complements and extends previous papers by the same author which dealt with metal crystals.10,14 The dislocations were detected by means of the etching techniques that were described in a previous paper by Gilman and Johnston.3 In that paper it

Jan 1, 1958

By R. R. Goddard

By use of the frequency response method with a radioactive tracer, it was possible to determine fluid dispersion and distribution in a natural consolidated and an unconsolidated medium. Measurements were made in a linear flow system at oleic saturations of 69 per cent in the consolidated medium, and 100 per cent in both media. Dispersion and distribution were obtained by measuring the amplitude attenuation and the phase velocity of sinusoidal waves with a dual monitor apparatus. The gamma ray emissions permitted in situ measurements at any distance along the porous samples. One result of importance was that the effective diffusivity increased as the wave length increased. As a consequence, a dispersion coefficient appropriate for the injection of large slugs might exceed the value measured by use of small slugs. Since flow models based solely on fluid velocity and an effective diffusivity coefficient imply that the diffusivity should be independent of frequency, such representations were not adequate for the data of this study. A comparison was made with a capacitance model of porous media with deadend PVs, but even this model was not completely adequate. By using attenuation and phase velocity data, fluid dispersion can be predicted without postulating a differential equation satisfied by the tracer concentration, thereby eliminating the need of a complicated model to represent dispersion. INTRODUCTION The flow of similar miscible fluids through a porous medium can be fairly adequately described by two parameters: the average fluid velocity and the effective diffusivity.1-3 It has been pointed out recently, however, that significant discrepancies exist between this representation and the experimental data.4-7 An improved agreement can be obtained by introducing additional parameters based on the concept of dead-end pores. The purpose of the present investigation was to find out whether the frequency response method could be used to measure the relevant parameters. The method was used in the following form. A stream of fluid was flowed at a constant rate through a sample of porous material and the concentration of a radioactive tracer in the fluid was varied sinusoidally at a fixed frequency. The effects of flow through a porous medium are a decrease in the amplitude of the concentration wave and an increase in the velocity of the peaks of the waves above the average velocity. Attenuation and phase veIocity of the waves were measured as a function of frequency and fluid velocity. The simple two-parameter model implies that the diffusivity should be independent of frequency. Data reported in this paper show that the diffusivity decreases as the frequency increases. Hence, as shown also by many others, the two-parameter model is not completely adequate. Coats and Smith 5 used two additional parameters in their model: the volume of the dead-end pores and the rate of mass transfer between dead-end pores and the flowing stream. Their capacitance model of a porous medium containing some stagnant fluid, to which transfer occurs by molecular diffusion, did not explain the dispersion results of either the present study or of theirs. Instead, the capacitance effect can be better described as the result of extreme velocity variations within the pores of the medium, with transfer between the velocity zones by convection. EXPERIMENTAL PREPARATION OF POROUS MEDIA Data reported here were obtained with a natural Berea sandstone, and with two packings of 20/25 mesh sand. Pertinent information about these media is listed in Table 1. The sandstone core was first sealed with a non-

Jan 1, 1967

By Benjamin Smith Lyman

THE importance of topography to geology is so commonly underrated as to deserve to be pointed out again and again. The relation of topography to the different branches of geology may be seen best by a glance at them all. Geology is well understood to consist of the observation of facts about rocks as materials of the earth (geognosy ), and the explanation of those facts (geogeny). The facts to observe are: I. GEOMETRICAL, as (1) structure, including the dip and strike at different points, the size, shape, and position of basins and saddles; (2) vertical section, that is, the thickness of rock groups and of their parts ; (3) horizontal or geographical position. II. PHYSICAL, such as texture, whether sedimentary or crystalline ; and, if crystalline, whether granitic, porphyritic, amygdaloidal, globular, or concretionary; whether compact or granular; coarse or fine; pervious or impervious; hard or soft; firm or tender; with cleavage or without; massive or thin; the microscopic structure; also whether magnetic or not; soluble or insoluble; fusible or infusible; and the constituent minerals. III. CHEMICAL, that is, the composition of the rocks and of their minerals and their affinities. IV. PALÆONTOLOGICAL, as what kind of fossils are in the rocks,

Jan 1, 1873

Gentlemen of the American Institute of Mining Engineers.—As you well know an application is about to be made to Congress, by the American Society of Civil Engineers, for the appointment of a cornmission composed of persons skilled in the production and use of iron, steel, and other structural materials, whose duty it shall be to test the strength, elasticity, and other quatities of such materials ; not simply the substances used as such, but the members of large structures composed of such materials, of the forms and sizes in which they are actually used. As I understand, the papers that will be read here to-night will have for their object to show the necessity for such tests, and therefore the necessity for the commission asked for. As the representative of the Society of Civil Engineers, I have to thank you, gentlemen of the Mining Engineers, for the great zeal with which yon have taken up this subject, and seconded the efforts of the Civil Engineers; or, perhaps I ought rather to say, initiated the efforts to get a suitable commission appointed to obtain most vitally important information which it is admitted on all hands we do not now possess. In drawing up the memorial to Congress, in connection with some of the ablest and best informed of our Society, and in all the discossions on the subject, I have been struck with the emphasis with which the confession is made, that so little is known of the strength of the larger-sized members constantly used in building structures of the magnitude which the present requirements of the country now demand. I presume the remarks made to-night will bring this out very prominently. This is no disgrace, for with the means here-

Jan 1, 1882

From the beginning to the end, the attendance and enthusiasm of the 119th meeting, which was held in New York, Feb. 17 to 20 surpassed all expectations. Besides the ten technical sessions, one of which was in conjunction with the American Institute of Electrical Engineering and one a session of the National Research Council, there were two memorial meetings, one for Dr. Raymond and one for the members who died in service; two joint sessions with the Canadian Mining Institute; and a meeting devoted to pictures of copper mining, milling, and smelting. Of the 732 persons registered, 119 registered in the Institute of Metals Division. Monday's sessions were devoted to the problems of industrial organization, the Institute of Metals Division, and to petroleum and gas. Among the special features of these sessions were the topical discussions on housing and. Americanization. Americanization, too, was the topic for discussion by the Woman's Auxiliary Wednesday morning. On Tuesday, nearly 100-members of the Canadian Mining Institute were present to discuss the possibility of bringing about uniform mining laws for the United States, Canada, and Mexico, to obviate the maintaining separate legal departments and managerial forces for the several countries; and to avoid the confusion which, it is said, has led to a duplication of effort and has sometimes created a barrier to international cooperation in mining. Among the Canadian delegation were D. B.

Jan 3, 1919

By H. I. Kaplan, C. Laird

Pulsating contpresslon experiments have been carried out on coppev single crystals in order to test the adequacy of mechanisms which have been suggested for stage I cvack grouth when tension-compression loading is the mode of- applying stress. Although dejorrrzation continues slowly for many millions 01 cycles under Pulsating compression stresses both within slip bands formed in the first cycle and by the creation of new bands, the morphology of these bands is not typical of fatigue slip bands in general and neither initiation of cracks nor propagation of artificially induced cracks was observed. It is therefore concluded that 1) initiation and growth of cvacks in fatigue is a consequence of repeatedly reviersed, microplastic deformation rather than intermittent, unidirectional deforma-tion, 2) gvowth of- cracks in polycrystalline specimens FAILURE of a plain specimen subjected to cyclic tension-compression stresses is known to take place by two stages of cracking.1,2 The first stage is characterized by propagation along slip planes roughly at 45 deg to the stress axis, in the outermost layers of the specimen, and at a rate of the order of angstroms per cycle. The average macro orientation of a stage I crack is normally at right angles to the stress axis,3 however, except in a few cases, e.g., single crystals in suitable orientation, when both the micro and macro directions of propagation are at 45 deg to the axis. After a stage I crack has penetrated to such a depth that the stress on the remaining section of metal is significantly increased, stage II crack propagation succeeds stage I, at right angles to the stress axis both micro and macroscopically. Direct evidence of the processes occurring during a subjected to pulsating compression stresses is caused by the setting-up of local tensile stresses due to interactions between grains, and 3) both unslipping mechanisms and operation of the "plastic blunting process " within a single slip band are adequate descriptions 01- stage I growth, being fundamentally similar. The slip mode of a material, however, is considered to control whether unslipping or the plastic blunting process takes place. Thus materials of planar slip mode fauor unslipping while those hacing a wavy mode, and capable of cross slip, can fail in stage I by the plastic blunting process. Similarly, and perhaps more importantly, reversed torsion and tension-compression modes of applying stress may be expected to cause the unslipping mechanism and the plastic blunting process, respectively. single stress cycle4,5 shows that stage II crack propagation takes place by a repetitive plastic rounding and closing of the crack tip. This mechanism has come to be called the "plastic blunting process".6 On the other hand, the extreme smallness of the phenomena occurring in stage I growth prevents elucidation of its mechanism by direct observation. Many suggestions have been proposed for this mechanism,'"-" most of them involving some kind of random or systematic unslipping process. It is possible, however, that the mechanism of stage I growth is essentially the same as that of stage 11, but occurring on a much smaller scale.6 In this situation, it has been observed that cracks propagate along slip bands comprising dislocation cell structures and bounded on either side by regions of different dislocation density and distribution." Since there is evidence that such bands are softer than their matrix, * it may be expected that the plastic blunting process occurs within a single slip band during stage I growth, rather than on two gross bands as in stage 11, when the acting stress is greater.= The blunting of the crack tip allowed by coordinated

Jan 1, 1968

By B. Ball, D. W. Fuerstenau, P. C. Kapur

A two-phase distributed-parameter model of the flotation process has been extended to allow consideration of the important process parameter, concentrate grade. A simple expression is presented for the grade of concentrate in terms of the zeroth and first moments of the concentrate distribution. An example is given for a binary ore containing two pure minerals each having nondistributed rate constants. For extend-ing the model to the distributed rate constant case, a cubic polynomial zoas utilized to simulate the feed distribution. One particular example is considered and grade-recovery curves are generated to show the dependence of such curves on the initial feed distribution. Operating flotation plant engineers have traditionally evaluated plant performance in terms of the recovery of valuable mineral and the grade of the concentrate. In both operation and research, grade-recovery relationships have been used as a guide for selecting flotation conditions. Weissl illustrated the use of grade-recovery curves in plant operation and considered the grade-recovery relationship to be a metallurgical one. The extensive experimental work of Chi" using standard batch flotation tests on iron ores shows that, even with extensive statistical correlation of data, little insight can be gained into the basic fundamentals of these relations. Such relations must depend on the kinetic behavior of the various mineral species in the flotation circuit. In his flotation text book, Gaudin3 considered the relationship of recovery and of product grade to flotation kinetic indices, but he did not extend his calculations to yield grade-recovery relations. Although Gaudin used a simplistic model for his analysis, he did recognize that variations in flotation rates must result from variations in locking, surface heterogeneity, particle size and shape, among other things. In a recent paper,' we presented a model of the flotation process that could be readily analyzed with an analog computer. This model combines the concept of a distributed set of rate constants"" with that of the two-phase flotation model,8" resulting in a model more powerful and flexible than previous ones. The purpose of the present paper is to show how this model can be used to generate grade-recovery curves and to determine the dependence of such curves on the various kinetic parameters. In this paper, the model will be limited to the semi-batch case, but extension to the continuous case is a straightforward step.

Jan 1, 1971

By G. S. Hume

Three provinces in Canada—New Brunswick, Ontario and Alberta— produce oil and gas in commercial quantities. In addition a small amount of oil is being produced and refined in the Northwest Territories at Norman on the Mackenzie River. The production at Norman is derived from two wells drilled by Northwest (Imperial Oil) Co. in 1920 and 1923. The refined products of the oil are used locally in connection with mineral developments on Great Bear Lake. The production of petroleum by provinces and the consumption of natural gas are shown in Table 3. In addition a small amount of natural gas is produced in the southwestern part of Manitoba from shallow wells for local use. Tables 1 and 2 give detailed information. The greatest drilling activity in 1933 in Canada centered around the southern end of the Turner Valley field, Alberta. In addition to several wells previously commenced in this area, eleven new wells were begun. There were three completions to the Paleozoic producing zone in 1933 in the southern part of Turner Valley and one well was abandoned as a result of being off the favorable structure. Of two wells completed in

Jan 1, 1934

Contents A-Metal Mining B-Minerals Beneficiation F-Coal

Jan 11, 1951

By Frank C. Schrader

Page Introduction.............................. 196 Geology of the District......................... 196 Ore Deposits of the District....................... 198 Gcncral Description........................ 198 The Cerbat Mountains Group................... 199 General Description...................... 199 Tennessee Mine....................... 203 Midnight Mine........................ 203 Mineral Park........................ 204- Golconda Mine........................ 204 Other Ore-bearing Districts.................. 205 Lost Basin District ...................... 205 The Black Mountains Group.................... 206 Tom Reed-Gold Road District...................... 208 General Dcscription........................ 208 Development........................... 209 Topograplly............................ 210 Geology.............................. 210 Ore Deposits........................... 213 General Dwcription...................... 213 Zones.......................:....215 Structure of Ore Shoots.................... 217 Gold Road Mine ......................... 218 General Description...................... 218 Geology........................... 218 Ore Deposits......................... 219 Tom Reed Minc......................... 222 General Description..................... 222 • Ore Deposits.......................... 222 Development......................... 223 Character of Ore....................... 224 Other Mines........................... 224 Fields Similar to the Ton1 Reed-Gold Road District......... 227

Jan 1, 1917

By T. A. Read, M. S. Wechsler, D. S. Lieberman

IN the formation of martensite in steel, it has been observed that the habit plane does not change continuously as the alloy content is varied. Instead, it appears that discrete habits correspond to certain ranges of composition. Greninger and Troiano' found that in low-, medium-, and high-carbon steels, the habits are approximately (1l1), (225), and (259), respectively.* The work of Mehl and Van Winkle2 indicated that the change from the (225) to the (259) habit is fundamentally a consequence of the lower transformation temperature rather than the higher carbon content. Also, Otte and Read3 observed that the habit plane orientation for a chrome-carbon steel scattered within a cone of semivertex angle of 5 deg, which was outside of the experimental error in the determination of the habit plane. These observations suggest the importance of investigating what factors in the crystallography of the formation of martensite account for the several types of habit and the inherent scatter in the precise orientation of the habit plane. A theoretical treatment of the austenite-martensite transformation has been given,4 which considers the total transformation distortion to be composed

Jan 1, 1961

By John Alden

A CONSIDERABLE PROPORTION of the tonnage of aluminum used today has at some stage during its manufacture, been rolled. I. For one, therefore, was particularly pleased to hear that this Society was to hold a symposium on rolling of nonferrous metals. Metallurgists can well afford to direct their close attention to the metallurgy involved in this important operation. To one who has seen today's high production rolling mills for aluminum it is difficult to realize that the first aluminum rolling mill For sheet was installed a scant 55 yr ago, in 1892. This mill was a three-stand train of 2-high mills, driven by a steam engine and was operated for many years successfully rolling aluminum sheet. Mills for the rolling of aluminum rod were installed in 1899 to meet the demand For manufacture of electrical conductor wires and cables. Bars and rods in straight lengths were also made. While these mills were the first built for rolling aluminum products of these types some rod had previously been rolled on brass and copper mills. Not until many years later, in 1929, however, Were facilities provided for the rolling of structural shapes, such as I-beams and channels. Growth of the aluminum sheet business and the necessity for economical manufacture soon brought the realization of the economies resulting From-the rolling of sheet in long lengths and coiling it. A five-stand continuous mill driven by a steam engine, was in operation late in 1907. This took aluminum slabs coating from

Jan 1, 1948

By Granville S. Borden, Frank H. Madison

The fruits of industry are divided between capital, labor, and governments. Capital takes its redemption and remuneration through profits or dividends; labor takes its share through wages; governments take their share through taxes. Each must have a just share, and the question of what is a just share and the question of who shall make the allocation are vital current political and economic issues. Certain political philosophies con- tend that government should take all the fruits and that some dictator or politician should have irrevocable discretion and power to distribute the fruits. Believers in democracy and free enterprise adhere to the view that capital is entitled to redemption and fair remuneration; that labor shall have a fair wage; and that governments shall make equitable levies. But since all human beings, both individually and in groups, are inherently selfish, there are many variable views in regard to the question of what ratios shall be applied in a division of the fruits and who shall have the power to fix these ratios. Perhaps all parties should devote more energy to means of increasing the crop, and not so much time to quarreling over a division of the existing crop. Moreover, all three parties must guard against killing the goose that lays the mineral eggs. For example, if the tax burden becomes oppressive and the taxpayer refuses to carry it, then business stagnates, with consequent unemployment, reduction of profits, and curtailment of government revenue. If a producer assumes the increased tax burden, marginal operations must be closed down, and, again the consequences are increased unemployment and diminished government revenue. Quite often an increase in a rate of tax results in a reduction of government revenue. Perhaps the worst detrimental feature of selfishness and greed on the part of any one of the three distributees of the fruits of industry is the retardation of expansion of the enterprise. Growth means new jobs, more government revenue, better trade, and better standards of living. Explorations and discoveries have resulted in tremendous contributions

Jan 1, 1964

By C. H. Wayman, D. W. Fuerstenau

THE gas phase is one of the indispensible ingredients in flotation operations. Flotation depends on the collision of an air bubble and a mineral particle in a pulp and their ability to remain in contact long enough for adherence to take place. Before it is possible to understand the mechanics of air bubble-mineral particle encounter, it is necessary to learn more about the nature of bubbles themselves before collision with a mineral particle has taken place. To date, little work has been done on air bubbles in flotation systems. In 1945 Fahrenwald1 presented a study of the role of frothers on air bubbles and on aeration in flotation, and recently Wark and Sutherland2 discussed the work of Rosenberg3 in relation to flotation. The research reported in this present article was undertaken to investigate systematically the effect of bubble size and the concentration of certain reagents on the terminal velocity, shape, path, and drag coefficient of single bubbles in distilled water. Most of the work is concerned with the effect of a-terpineol on bubble motion in water, but studies were made with potassium chloride, potassium hydroxide, potassium ethyl xanthate, and potassium amyl xanthate.

Jan 6, 1958

By C. G. Goetzel

Until recently porous bronzes have found many applications for self-lubricating bearings in the automotive, electrical, household appliance and general machine industries. The bulk of an annual production of several million pounds of copper powder had gone into the manufacture of these articles, of which by now more than a billion are in service. However, the war has brought severe curtailment of these bearings because of the scarcity of the two main constituents, copper and tin. The development of substitute materials of equal or superior properties has led to a large-scale replacement by products made from iron powder. In spite of the diminished interest in powdered copper-tin alloys caused by this trend, it was believed worth while to investigate some mechanical properties of these materials as a reference base for substitutes. In addition, experiments using the hot-press method were incorporated to investigate possibilities of saving vital equipment or opening new fields of applications. It must be assumed that by this time the powder metallurgy process of making porous bronzes, a development that found its first industrial applications more than 10 years ago, is well known in engineering. The patent literature and bibliography is volu- minous, most publications referring to porous, self-lubricating bronzes, containing about 10 per cent tin and I to 5 per cent graphite, with porosities in the range of 25 to 35 per cent.l-7 The excellent antifriction properties of these bearings, caused by the uniform impregnation with oil, are dependent on the interconnection of the pores and the uniform distribution of the graphite inclusions. The sintering mechanism of porous bronze, with its structural changes during the transformation of the metal powder into the sintered bearing has been shown in colored photomicrographs by Hall.* Diffusion between copper and tin was found to begin within one minute, when tin-rich transitory phases were formed. After 25 min. a homogeneous matrix of alpha was reached for an alloy containing 9.5 per cent tin and 6 per cent graphite. Price, Williams and Garrand,9 studying certain metal powder combinations in which sintering is accompanied by the cementing action of a liquid phase, including a 90-10 bronze sintered at 925°C., have found that if the treatment is carried out within the liquidus and solidus temperature range of the system, a peculiar process of alternate solution and precipitation occurs. The particles of the major solid constituent are dissolved in the minor liquid phase, but thereafter are reprecipi-tated on certain nuclei, which develop into large grains, usually rounded.

Jan 1, 1945

By K. A. Jackson, J. D. Hunt

A general theory for the growth of lamellar and rod eutectics is presented. These modes of growth depend on the interplay between the diffusion required for phase separation and the formation of interphase boundaries. The present analysis of these factors provides a justification for earlier approximate theovies. The conditions for stability of rod and Lanlellar structures are consitleved in terms of the mechanisms by which the structure can change. The mechanisms considered include both small adjustments to the lnnzellar spacing due to the motion of lamellar faults, and catastrophic changes due to instabilities. It is concluded that stable growth occurs at or near the minimum interface undevcooling for a gizierz growth rate. The conseqrlences of the existence of a diffusion boundary layer at the interface are discussed. The experimental results for the variation of growth rate, undercooling, and Lanzellar spacing are cornpared with the theory. We believe that the theory presented in this paper provides an adequate basis for understanding the complex phenomena of lanzellar and rod eutectic growth. The growth of lamellar eutectics has been the subject of several theoretical and many experimental studies. The foundations for the theoretical work were laid by zenerl and Brandt2 in their analyses of the growth of pearlite. Zener estimated the effect cf diffusion, and took into account the surface energy of the lamellar structure. He found that the lamellar structure could grow in a range of growth rates at a given undercooling provided the lamellar spacing was appropriate for the growth rate. Since pearlite grows with only one growth rate and one lamellar spacing at a given undercooling, there is clearly an ambiguity in the theory. Zener removed this ambiguity by postulating that the growth rate was the maximum possible at the given undercooling. He predicted then that the product of the growth velocity v and the square of the lamellar spacing A should be constant, i.e., A2v = const. Brandt2 started out by assuming that the interface between the lamellae and austenite was sinusoidal. Because of this, the ambiguity encountered by Zener did not arise. Brandt was able to obtain an approximate solution to the diffusion equation, but, since he did not take into account the surface energy, his considerations are incomplete. Tiller3 applied some of these ideas to the growth of eutectics, and proposed a minimum undercooling condition to replace the maximum velocity condition used by Zener. These conditions are formally identical. Hillert4 extended the work of Zener. He found a solution to the diffusion equation assuming the interface to be plane. Taking surface energy into account, and applying Zener's maximum condition, he was able to calculate an approximate shape of the interface. Jackson et al.5 used an iterative method employing an electric analog to the diffusion problem to refine the calculation of interface shape. It was found that the interface shape calculated from a plane-interface solution to the diffusion equation was negligibly different from the exact solution. The method provided an analog only for eutectics for which the volumes of the two phases are equal, growing from a melt of exactly eu-tectic composition. There has also been considerable experimental work on eutectics, Several experimenters8-10 found that A2v is constant as predicted by Zener.1 Hunt and chilton10 demonstrated that ?T/v1/2 is also a constant for the Pb-Sn system as predicted. Lemkey et al.11have recently found A2v to be constant for a rod eutectic. In the present paper, we present the steady-state solution for the diffusion equation for a lamellar eutectic growing with a plane interface, for the general case, that is, with no restriction on the relative volumes of the two phases, and with the melt on or off eutectic composition. A similar solution is also found for a rod-type eutectic. Expressions are obtained for the average composition at the interface and the average curvature of the interface. These equations for the average composition and curvature are similar in form to those derived by Zener1 and Tiller,3 and provide a justification for some of the approximations made by these authors. The mechanisms by which the spacing in a lamellar structure can change are considered. The important mechanism for small changes in lamellar spacing involves a lamellar fault. Examination of the stability of lamellar faults leads to the conclusion that the growth occurs at or near the extremum.* The insta- bilities which can develop in a rodlike structure are also discussed, resulting in the conclusion that this structure also grows at or near the extremum. Comparison of the conditions for rod and lamellar growth permits a prediction of the surface-energy anisotropy required to produce rods or lamellae for various volume-fraction ratios. The diffusion equation predicts the existence of a diffusion boundary layer at the eutectic interface unless the eutectic has 0.5 volume fraction of each phase and is growing into a liquid of eutectic composition. This boundary layer is such as to make the composition in the liquid at the interface approximately equal to the eutectic composition. This boundary layer permits changes in composition during the zone refining of eutectics. Photographs of the eutectic interface of a growing transparent organic eutectic system have been made. Both the components of this eutectic are transparent organic compounds that freeze as metals do.12 The in-

Jan 1, 1967