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THE developments in construction and operation of the basic open-hearth furnace that have taken place in recent years have placed new emphasis on the vital influence played by regulation and control of the combustion system in both furnace production and furnace life. The several factors influencing flame development, such as regulation of fuel supply, air supply, air preheat, furnace draft, and furnace reversal, must be controlled closely if successful furnace performance is to be accomplished. Rugged instrumentation of distinctive design is required to supply dependable information concerning operating conditions, which is requisite to proper regulation of combustion. This chapter attempts to give a practical discussion of the various features of open-hearth practice and instrumentation related to the efficient heating of the furnace, control of temperature, and protection of the furnace structure from accidental overheating. The appended references will be helpful to readers wanting a more detailed treatment of individual topics. OPEN-HEARTH FUELS The most important open-hearth fuels are listed in Table 4-1 together with their compositions and other data useful for combustion calculations. A detailed discussion of open-hearth fuels is not attempted here, but certain factors peculiar to their application to this type of process are briefly indicated on the following pages. Very often an open-hearth shop is forced by economic factors to use a fuel to which its furnaces are not very well adapted, because the general fuel-allocation scheme for the works as a whole seems to demand it. Often a variable marginal supply of coke-oven gas or tar must be consumed by the open hearth, together with another fuel such as producer gas, natural gas, or oil, to fill out total requirements. Most furnaces employ more than one kind of fuel during their usefu1 life; however, the partial redesign

Jan 1, 1951

By Sir Robert Hadfield

Introduction.-I esteem it a great honor to be asked by this Institute to give them an address chiefly devoted to metallurgy. While it is with great regret that I find myself unable to be present to deliver this in person, I take this opportunity of wishing your society every success in its continued career of usefulness to the metallurgists of the great Republic. To be elected, eight years ago, along with Dr. J. E. Stead, F. R. S., as one of your Honorary Members, was a privilege which I greatly esteemed, for I consider that no society in America has done so much as ours for the advancement of metallurgy. Those who have Served our Society.-Where many have served so well, it is difficult, without appearing to make unavoidable distinctions, to select names from those of your members who have done so much for the cause we have at heart-the advance and progress of metallurgy. As typical, however, and not in any way meant as a complete list, there are among others the following names which in the past and to-day stand out prominently in this science of ferrous metallurgy. With most of those now mentioned I have personally come in contact, or by correspondence in some few cases, and have exchanged views, since I first came over to America 30 years ago. Holley; Jones; Weeks; Andrew Carnegie; Thomas Carnegie; Fritz; Sterry Hunt;. Egleston; Maunsel White and Taylor, who did so much for high-speed tool steel, and helped to revolutionize machine-shop practice; W. J. Taylor; Robert Hunt; Alfred Hunt of Pittsburg, who did so much in the early history of aluminum, and, alas! did. not live to see the wonderful progress which has been made in that particular branch of metallurgical industry; James Douglas; C. B. Dudley; Birkinbine; Howe; Metcalf; Barus; Langley; Raymond; P. H. Dudley; H. H. Campbell; W. R. Webster; E. D. Campbell; Talbot; Spilsbury; Gayley; Dinkey, under whose supervision and responsibility modern armor has been so successfully produced in this country, which the writer can testify from personal knowledge of , test results possesses very high Figure of Merit; Schwab; Kennedy; Wellman; Garrison; Wood; Moldenke; Webster; Swank; Unger; Richards; Sauveur; Strat-

Jan 5, 1914

By D. H. NETLAND

DURING the year 1907 an investigation of the Clinton formation in New York has been carried out under the direction of the State Geologist, and a full account of the results has been prepared for publication.1 The more important economic features of the report are summarized in the present paper. Previous knowledge of this, the type, section of the Clinton has been contributed mostly by Hall and Vanuxem in their reports for the Natural History Survey of New York, which were issued in their final form in 1842-43. Brief accounts of the ore-occurrences have been given by B. T. Putnam,2 J. C. Smock,3 A. H. Chester,4 and E. C. Eckel.5 Prof. C. H. Smyth, Jr.,6has discussed the origin of the Clinton ores in two papers, which, so far as the local occurrences are concerned, have removed all doubt that may have existed on that subject. Distribution of the Clinton Formation. The Clinton strata in New York State are restricted to a single belt, Which extends from the eastern central part to the Niagara river, which it crosses, and thence continues for some distance into the province of Ontario. The New York

Mar 1, 1909

By Waldemar Lindgren, Clyde P. Ross

To the miner, as well as to the geologist, the eastern part of Cuba is a most interesting region. Here we find, in contrast to the moderate relief predominating elsewhere in the island, an imposing mountain range, the Sierra Maestra, extending east and west parallel to the coast, its precipitous front facing the blue Caribbean Sea. In a geological sense this range is largely an unknown land, the only well-explored region being that in the vicinity of Santiago. The range also contains the most important mineral deposits of the island. They comprise, first, a series of iron deposits yielding a partly hematitized magnetite with low content of phosphorus; second, a remarkable copper-bearing vein at El Cobre; and third, various manganese deposits. Probably more deposits will be found, for the larger and western part of the range is as yet little explored and its slopes are covered by a thick tropical jungle. The following notes are based on a short visit by the senior author in January and February of 1914 to the mines at Daiquiri, El Cobre, and Mayari. For many courtesies and great assistance he is deeply obliged to Charles F. Rand, President of the Spanish-American Iron CO.; to George W. Pfeiffer, General Manager, and to the several members of his staff. Geological Features of the Sierra Maestra For our knowledge of the geology of the Sierra Maestra we are indebted to reconnaissance work by Fernandez de Castro, R. T. Hill, Mr. C. Hayes, T. W. Vaughan, and A. C. Spencer. The summary by the latter three geologists furnishes the best guide to the region.' The range is undoubtedly outlined by a great east-west dislocation. Its southern slope drops abruptly to the sea, while on the north side a much gentler declivity leads down to the rolling plateau of Tertiary limestone which occupies much of the adjacent part of the island. Viewed

Jan 1, 1916

By B. E. Eakin, A. L. Lee, M. H. Gonzalez

Expeximental viscosity and density data of lour natural gases are presented for temperatures from WO to 340F and pressures from 100 to 8.000 psia. A correlation is also discussed and results reported. INTRODUCTION This investigation is one of several efforts by the authors to provide viscosity data for pure hydrocarbons and mixtures. Results of some pure hydrocarbons and their mix tures have been presented." Several predictive methods and correlations have also been reported.'," This paper presents the experimental viscosity and density data of four natural gases and confirms a correlation in a previous study. APPARATUS The viscometer was described previously. 2,6 A bank of stainless steel pycnometers was included to determine density in conjunction with the viscosity measurements (Fig. I). DATA AND MATERIALS The natural gases were furnished by the Atlantic Richfield Co. (Samples 1 and 21, the Continental Oil Co. (Sample 3) and the Pan American Petroleum Corp. (Sample 4). Table 1 shows the composition of these gases obtained by mass spectrometer analysis. The pure component viscosity data used in the correlation have been published."".'"', '" Experimental and calculated viscosity data for the natural gases are presented in Tables 2 through 5. CORRELATION Starling and Ellington"' have reported several semi-empirical expressions based to a certain extent on the theory of viscosity advanced by Born and Green.' The final expression presented by Starling and Ellingto'n is: i'. (micropoise) -- /t,, exp rX(7') p ..... (I) Eq. 1 was modified by Lee et 01." to represent mixture and pure component data simultaneously. This equation has the form: F = K exp [XpY] :.........(2) where K=- (7.77 i 0.0063M)Ti 122.4 + 12.9M +T .................(3) ' ' ' X= 2.57 + ---1914.5+ 0.0095M .... (4) Y = 1.11 -r 0.04 X ........(5) Over the pressure and temperature range studied in this investigation, this equation represents the data on methane, ethane, propane, n-butane and four methane-n-butane mixtures with a standard deviation* of ? 1.89 per cent. Density data by Sage and Lacey" were used to fit the equations. Eq. 2 gives reliable values of the viscosity of light hydrocarbons without prior knowledge of experimental viscosity values, but accurate density data must be available. Eq. 2 was used to predict viscosity values for the natural gases studied in this paper. The particular set of parameters contained in Eqs. 3 through 5 gave values that reproduced experimental data within 25 per cent. Needless to say, in using Eq. 2 better density values will give better viscosity results. However, those engineers who do not have accurate density values at hand or the time, or such facilities as a library, computer, etc. readily available, may feel uneasy in using Eq. 2. Therefore, the authors sought the easiest but by no means best density prediction method, which was reported by Kaf 30 years ago. A set of density values, which were calculated based on Kay's method, and a generalized compressibility factor chart were used to fit Eq. 2. The results are:

Jan 1, 1967

By Raymond Mancha

THE purpose of the Coal Division's Committee on Ventilation is to cover one principal aspect of mine ventilation thoroughly each year, instead of attempting to touch upon several different subjects. The Committee for 1943 consists of four members besides the Chairman. Members, selected because of both knowledge of the current topic of mine ventilation, and diversity of occupation, are: Carel Robinson, consulting engineer with an operating background; T. G. Fear, chief engineer for the Hanna Coal Co., an operator of varied experience in mine ventilation; E. H. Denny, chief of the coal mine inspection division of the U. S. Bureau of Mines, obviously well qualified; and C. M. Smith, editor of Mechanization with a background of mine ventilation study as a member of the mining department of the University of Illinois, at present retained as a ventilation consultant by the Climax. Molybdenum Co. of Climax, Colo.

Jan 1, 1944

By R. J. Colony

MINING geology does not lend itself - very readily to a review embracing "improvements in methods," as perhaps do shop practices or laboratory procedures. The "methods" used in mining geology are simply the application of geology to mining; winning the ore, the handling of material, mechanical appliances, all belong strictly to mining proper, and have no place in a review of geology as applied to mining. A comprehensive review would necessarily cover a .very broad field, which could be subdivided into many -parts. Only a few of these can be discussed here. .Those that have been suggested to the chairman indude :

Jan 1, 1930

By A. M. Nicholas

WheN attempting to lift mill pulp containing a considerable percentage of wolframite, in an ordinary bucket elevator, difficulty was encountered from the tendency of the tungsten minerals to settle, on account of their high specific gravity. Lifts not exceeding 20 ft. (6 m.) could be accomplished without particular difficulty, because there was insufficient time for consolidation of the heavy minerals in the bottom of the bucket; but with higher lifts, the heavy tungsten minerals would settle so solidly that when the bucket turned over at the top of the elevator the contents could be only partially dumped. In this case it was necessary to lift the material a distance of 34 ft. (10m.); hence some means had to be adopted to prevent settling, at least to such an extent that the material could be dumped from the buckets. To reduce the carrying time to a sufficient extent would have required a belt speed of 475 ft. (144.7 m.) per minute, which was not feasible. It was decided to try, by vibrating the belt about midway of its span, to keep the material sufficiently agitated during elevation to prevent settling. Underneath the rising side of the belt was placed a 12-in. (30.48-cm.) idler pulley, 18 ft. (5.5 m.) up in the total lift of 34 ft. The idler pulley was set eccentric by % in. (19 mm.) and it was hoped that the vibration thus imparted to the belt, running at a speed of 280 ft. (85 m.) per minute, would prevent settling in the buckets. It was found that the pressure of the belt on the idler, due to the small inclination of the elevator, was not sufficient to overcome sliding on the idler, and the agitation was insufficient to accomplish the desired purpose. The idler was then connected to the drive shaft of the elevator through an intermediate pulley, gearing down to a speed of 20 r.p.m., so that a positive vibration was imparted to the belt; this imparted enough motion to the belt to prevent settling and the contents of buckets dumped satisfactorily. Protecting Elevator Belts When elevating, from the crusher, a rock which was very sharp and abrasive, considerable difficulty arose from cutting of the belt under-

Jan 1, 1918

By M. J. Mullikin, J. B. Conway

for use in describing combined first- and second-stage creep data. In the above ?o represents the instantaneous strain on loading, ?t the limit of transient creep, ?S the steady-state creep rate, t the time, and ? a constant leading to the exhaustion rate of transient creep. It was noted that this equation was similar in form to that proposed originally2 by McVetty. This type of equation was also suggested by Andrade and Aboav3 in studies of the shear strain of cadmium. Calculation of the constants ?o, ?t, ?, and ?s, in Eq. [ l] is somewhat involved due to the slight complexity of this relationship. In the paper by Garofalo a computer approach based on a least-squares analysis was recommended. Such an approach involves a trial and error solution but when a computer facility is available the difficulties in this calculation are of little consequence. It does mean however that the evaluation of this type of equation would become quite tedious if computer facilities were not available. Some recent studies have identified a fairly straightforward method for calculating the constants in the Garofalo equation. While not leading to a least-squares evaluation the approach is accurate and is recom-

Jan 1, 1967

THE developments in construction and operation of the basic open-hearth furnace that have taken place in recent years have placed new emphasis on the vital influence played by regulation and control of the combustion system in both furnace production and furnace life. The several factors influencing flame development, such as regulation of fuel supply, air supply, air preheat, furnace draft, and furnace reversal, must be controlled closely if successful furnace performance is to be accomplished. Rugged instrumentation of distinctive design is required to sup- ply dependable information concerning operating conditions, which is requisite to proper regulation of combustion. This chapter attempts to give a practical discussion of the various features of open-hearth practice and instrumentation related to the efficient heating of the furnace, control of temperature, and protection of the furnace structure from accidental overheating. The appended references will be helpful to readers wanting a more detailed treatment of individual topics. OPEN-HEARTH FUELS The most important open-hearth fuels are listed in Table 4-1 together with their compositions and other data useful for combustion calculations. A detailed discussion of open-hearth fuels is not attempted here, but certain factors peculiar to their application to this type of process are briefly indicated on the following pages. Very often an open-hearth shop is forced by economic factors to use a fuel to which its furnaces are not very well adapted, because the general fuel-allocation scheme for the works as a whole seems to demand it. Often a variable marginal supply of coke-oven gas or tar must be consumed by the open hearth, together with another fuel such as producer gas, natural gas, or oil, to fill out total requirements. Most furnaces employ more than one kind of fuel during their useful life; however, the partial redesign

Jan 1, 1964

By Marius R. Campbell

Does mine-sampling show the commercial value of a coal, and if so, how should it be done? This question is often asked, but seldom answered. During the past summer, while engaged in securing coal for the Government coal-testing plant at St. Louis, I had an excellent opportunity to obtain information on this subject, and the results seem to furnish an answer to the questions propounded above. Sampling for the Geological Survey Coal-Testing Plant. In organizing the work of the testing-plant, it was decided that coal in car-load lots only would be accepted for testing, also that this coal should be loaded under the immediate supervision of a representative of the plant, so as to be certain that the car-load sample would be representative. As an additional check on the work, two mine-samples were to be collected from each mine visited, and these samples, as well as the sam¬ple from the car when it was received at the testing-plant, were to be carefully analyzed at the chemical laboratory, which was established in connection with the plant and operated under the direction of Prof. N. W. Lord, of the Ohio State University, Columbus, Ohio. Mine-Sanmhling:-Mine-samples were collected with great care by me and my assistants, Messrs. J. Shober Burrows, John W. Groves and Frank W. De Wolf. The dominant idea in the regulations which were adopted for mine-sampling was that it should be done in such a manner that the sample would have the same composition as the commercial output of the mine. .

Sep 1, 1905

By Sherwin F. Kelly

THAT gold ores occur in Georgia is a fact apparently not widely known outside of that state, yet in the last hundred years nearly $18,000,000 worth of gold has been mined there. The discovery of gold-hearing quartz was made in 1823 on the "Forty Acre Lot" (which now belongs to the Columbia Mining Co.), in McDuffie County, and about seven years later the first stamp mill on record was erected near there. In recent years Georgia's gold production has dwindled to an insignificant figure. However, with the increase in gold price, interest in this district has been revived, so an electrical geophysical survey was undertaken to aid in discovering new quartz veins, on a part of the Forty Acre Lot, the adjoining Hamilton mine, and the nearby Woodall property.

Jan 1, 1934

By H. P. Greenwald

IN the year just passed the Coal Division's Committee on Rock-Dusting reviewed the status of this safety measure in American coal mines and prepared a paper thereon which will be presented at the February meeting of the Institute. This paper supplements one appearing in Vol. 139 of the "Transactions," page 87 (1940). Because that paper will be issued soon, only a summary is given herein.

Jan 1, 1944

By Arthur F. Taggart

THIS paper proposes two units (believed to be new) for designating, respectively, capacity and efficiency for primary and intermediate crushers. CAPACITY Operators know that the tonnage of rock that can be put through a particular crusher in a given time depends primarily upon the crusher setting (open setting for jaw and primary gyratory types; closed setting for cones and rolls), and secondarily on the lithological character of the feed, its maximum size, the amount of fines that it carries, its moisture content, and the method of feeding. The proposed capacity formula states a relationship between all of these factors in one empirical equation, as follows: TR = TR80KK'K" [I] in which TR, called "reduction tons per hour" is the new capacity unit; T = tons of feed per hour requiring crushing; R50 = "80-per cent reduction ratio"; and K, K', and K" are constants that approximate quantitatively lithological character, moisture content and method of feeding, respectively. T is the hourly weight of material in the feed that is coarser than the coarsest discharge of the crusher. (For marked departures from the normal specific-gravity range-2.5 to 2.7-T should be adjusted to corresponding volumes.) In the crushers under consideration, discharge from the crushing zone is limited by the minimum dimension of a particle. Passage of the particle through a square-mesh screen is limited by its intermediate dimension. Sheppard' has shown that the ratio of maximum: intermediate: minimum average dimensions of broken rock fragments may be taken as about I.5: I: 0.6 for nonslabby rocks such as are normally crushed, while for slabby rocks, such as thin-bedded sedimentaries, foliated schists and gneisses, and the blocky metamorphics, the ratio is of the average order I.3:I:0.3, with the possibility of an even smaller relative value for the thickness. Gaudin2 finds the corresponding ratio for -150 + 200-mesh pyrite to be I.4: I : 0.6. The hourly tonnage of crusher-plant feed, therefore, should be diminished by the amount thereof that would pass a square-mesh screen of which the aperture is S times the crusher setting, where S is a shape factor with the value I.7 for rocks that break exceptionally cubic; 2 for ores and rocks that exhibit no appreciable tendency to slabbiness; and 2.5 to 3, or, in exceptional cases, even larger, when the tendency to slabbiness is marked. R80 is the quotient of the theoretical square-mesh aperture that would pass 8o per cent of the feed, divided by the aperture that would pass S0 per cent of the product. It is best determined from screen tests.

Jan 1, 1941

By Victor deWolfe

INTRODUCTION The Henderson Mine, located near Empire, Colorado, utilizes a continuous panel caving system to extract ore as one of the world's major producers of molybdenum. Any mine using a caving-by-gravity technique of mining must rely on closely controlled draw of the caved ore. This control is essential to insure proper caving action, to avoid damaging load concentrations of weight and to minimize the dilution of ore with waste material. Henderson is no exception. Draw control is a major factor in all production planning, from long- range plans to short-range and day-to-day ore scheduling. Draw control is reviewed constantly and administered daily in an effort to optimize production efficiency, ore recovery, and cave management. MINING METHOD The cave at Henderson is massive, moving slowly through large panels that are 244 m (800 ft.) wide by 610 m (2,000 ft.) long. Generally two cave areas are drawn at one time. The areas under active draw vary in size but can be as large as 244 m (800 ft.) by 244 m (800 ft. ) containing 400 draw points. Each draw point contains 45,360 mt (50,000 st) on the average and takes about two and one half years to exhaust. A complete panel is worked for seven to ten years. No pillar exists between panels, but rather a buffer zone of broken ore, or "static face," is left in each panel to be drawn with the adjacent, yet-to-be-caved panel in efforts of minimizing dilution of a working area from an exhausted one. (Figure 1) Production drifts are driven on 24.4 m (80 ft.) centers through the ore body. Between the production drifts are funnel-shaped draw bells on 12.2 m (40 ft.) x 24.4 m (80 ft.) centers to receive ore from the cave. Each bell is accessed by two draw points, one from the production drift on either side, thus forming a 12.2 m (40 ft.) x 12.2 m (40 ft.) draw pattern. Extraction of the ore is by rubber-tired, 3.8 m3 (5 yd3) load-haul-dump equipment. The LHDs then tram the ore a maximum of 49 m (160 ft.) to ore passes. Cave initiation and bell development are done from the undercut drifts which are parallel to and 17 m (55 ft.) directly above the production drifts. Longhole rings are drilled and blasted from the undercut drifts to define the bells and establish the undercut for caving. (Figure 2) DRAW CONTROL Since the cave line at Henderson is constantly advancing, it is necessary to be continually initiating new cave at one end while exhausting it at the opposite end. There must exist, therefore, an angle on the ore-waste contact in the broken rock from initiation to exhaustion. The basic concept of draw control is to keep this angle as smooth and even as possible, particularly at the time of exhaustion. If this is achieved, draw points are exhausted more or less in a line, avoiding pockets of remaining ore surrounded by exhausted areas. These pockets would cause spotty ore extraction at the time of exhaustion, increasing the amount of dilution occurring while introducing the potential for significant weight problems in the production area. To arrive at the desired angle on the ore- waste contact, maximum tonnage percentages are assigned to each row of draw points increasing at 10% or 15% increments (depending on cave size and velocity of draw) working away from the cave line. The available tonnage indicated by these percentages is the maximum allowable tonnage to be extracted from each draw point until the available tonnage percent- age is increased. As the cave moves, these percentages increase for each draw point regularly. However, in general the tonnage drawn from each draw point is kept at about 50% of this allowable maximum in order to maintain adequate available tonnage in the cave to sustain production for seven months if cave initiation were to cease. This available tonnage cushion is a safeguard built into the draw control program at Henderson to accommodate fluctuations in the rate of cave advance. When draw points move past the row of 100% tonnage availability, they are drawn past the desired 50% at the same increments per row until exhausted. (Figure 3) To achieve proper draw control, the number of LHD buckets to be taken from each draw point is assigned daily. The actual buckets taken, which may at times deviate from the

Jan 1, 1981

By Philip B. Bucky

WITH the exhaustion of the sections of iron ore bodies amenable to opencut mining the iron ore miners raise the question: "How can we mine the extensions of these ore bodies in depth with the same costs as obtained in opencut work?" This question brings to the fore the relationship between mineral exploration and research on mining procedures. The iron miners must either find new de? posits amenable to their known methods of mining or develop new mining methods for deep deposits. It is understood that the oil companies will spend $30,000,000 next year in the search for new oil fields. How much the metal mining companies will spend in the search for new ore bodies is unknown, but without doubt the amount will run into several millions of dollars. If the mining companies that concern themselves with metals, nonmetallics, and fuels will set aside a substantial sum for fundamental and applied research in mining methods, they can not only lower their costs but increase their reserves thereby. Any increases in mining efficiency automatically result in increased ore reserves at no cost.

Jan 1, 1947

PRESIDENTS DAVID THOMAS 1871 R W RAYMOND 1872-1874 A L HOLLEY1875 ABRAM S HEWITT 1876 T STERRY HUNT 1877 ECKLEY B COXE 1878 - 1879 WILLIAM P SHINN 1880 WILLIAM METCALF 1881 RICHARD P ROTHWELL 1882 ROBERY W HUNT 1883 JAMES C, BAYLES 1884-1885 ROBERT H RICHARDS 1886 THOMAS EGLESTON 1887 WILLIAM B POTTER 1888 RICHARD PEARCE 1889 ADAM S HEWITT 1890 JOHN BIRKINBINE 1891-1892 H M HOWE 1893 JOHN FRITZ 1894 J D WEEKD 1895

Jan 1, 1923

By Craig R. Barrett

The influence of the stress dependence of the dislocation density on the overall stress dependence of The steady-state creep rate is discussed. Experimental measurements of dislocation densities and creep rates jor an Fe-3.1 pct Si alloy tested over a wide range of stress are presented which indicate a close correlation between the two quantities. EXPRESSING the stress dependence of high-temperature steady-state creep rates has been the subject of numerous investigations over the past decade. From these investigations have emerged a few general equations which fit most of the available data reasonably well. Garofalo 1 has proposed that for a wide range of stress and temperature the creep rate, i, can be expressed by a relationship of the form: where A, ß, and n are temperature-dependent and is the applied stress. Eq. [I] gives a stress dependence of a at low stresses and exp(nßo) at high stresses, both consistent with experimental observation where n = 5. A number of other investigatorshave proposed a similar expression where: where m and w are in general functions of temperature. Theoretical justification for Eqs. 111 and [2J comes from two different approaches, theories based on dislocation glide3-5 and theories based on the balance between work-hardening and recovery.' Dislocation glide theories predict where p is the mobile dislocation density and V is the activation volume. In order for Eq. [3] to predict a on stress dependence at low stresses with n = 5, it is necessary for p to be a strong function of stress, about proportional to u3 or u4.436 Recovery models of creep start with the general expression:' where r is the recovery rate and h is the work-hardening rate, and then employ a detailed model to determine the stress dependencies of r and h. As example, weertman2 has described a model based on pile-up hardening which results in an expression similar to Eq. [2] with m = 2 and p = 2.5. A recent, seemingly more general approach suggested by McLean is to use Friedels dislocation network growth expression to calculate the stress dependence of r. This model predicts r = p 3,2 and, as h is taken to be a relatively weak function of stress, the stress dependence of i should be about proportional to p3, 2. Once again, it is required that p be a strong function of stress to yield i This recovery model is by no means complete as the stress dependence of network growth is calculated in the absence of an applied stress meaning that r should probably be a stronger function of stress than given by p3, 2 and also some recent work by Mitra and McLean8 suggests that the stress dependence of h may be as large as Because of the importance of the stress dependence of p in determining the overall stress dependence of the strain rate it seems reasonable to examine this relationship in some detail. Measurements made on dislocation densities present during high-temperature steady-state creep generally obey the following relationship a =o0 + aGVWp [5] where uo is usually called a friction stress, a is a numerical constant about equal to unity, G is the shear modulus, and b is the Burgers vector. Depending on the magnitude of uo, data obeying Eq. [5] can give rise to a range of stress dependencies of p. For example, if we assume that the expression where 6 is some constant, adequately represents the stress dependence of p over a range of o, then from Although Eq. [6] obviously breaks down when u 5uo for uo 6 can vary over a wide range of values. In particular, if u > a, > 0 then 6 will be greater than 2. As an example the data of Ishida and McLean are plotted in Fig. 1 showing excellent agreement with dynes per sq cm) and also showing good agreement with a p cc u3 dependence when plotted on a log-log basis. As oo increases 6 tends to increase and correspondingly the stress dependence of the predicted creep rate should also increase,* as-

Jan 1, 1968

[Aalde, Kaare, ('40) New Mexico School of Mines, Socorro, N. M. Abadesco, Enrique A., ('39) Univ. of the Philippines, Manila, P. I. Abdul-Ahad, A., ('39) Montana School of Mines, Residence Hall, Butte, Mont. Abreu, Ovidio M., ('38) Univ. of Nevada, Reno, Nev. Acker, Voscoe, . ('39) Agricultural & Mech. College of Texas, College Station, Tex. Acosta S., Gonzalo, ('40) Univ. of Texas, Univ. Sta., Box 1785, Austin, Tex. Adams, Albert, ('38) New Mexico School of Mines, Socorro, N. M. Adams, Charles W.,' ('39) Michigan College of Min. & Tech., Houghton, Mich. Adams, Hugh T., Jr., ('39) Univ. of Oklahoma, Norman, Okla. Adams, Jack L., ('39) Univ. of Oklahoma, Norman Okla.]

Jan 1, 1940

[Mining Methods Guy N. BJORGE, Chairman CLYDE E. WEED, Vice-Chairman HARLAN A. WALKER, Secretary Alluvial Mining CLINTON BERNARD O. B. PERRY R. B. EARLING C. M. ROMANOWITZ BENERE H. GRANT J. B. STAPLER CHARLES THURMAN Open-Cut Mining Iron G. E. DIEHL P. G. HARRISON EARL E. HUNNER Copper Louis BUCHMAN W. H. GOODRICH J. H. DAVIS WALTER S. LARSH Underground Mining Iron ROY A. BOWEN S. R. ELLIOTT T. C. DESOLLAR W. A. KNOLL GEORGE H. RUPP]

Jan 1, 1940