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By Donald Gilbert

PRIOR to July, 1919, the sampler at each mine of the Anaconda Copper Mining Co. in Butte did his work in his own way and was responsible to the mine foreman only. At that time, the sampling at all the company's Butte mines was placed in charge of a member of the geological department and stand-ardized methods of doing the work, were adopted. These standards were incorporated in a set of instruc-tions accompanied by blueprints representing typical conditions. The main features of the instructions were as follows: All samples to be cut at breast height and horizontally, regardless of dip of vein, and the horizontal width reported. A single sample to include not more than a 5-ft. width of the breast and to weigh not less than 4 lb. for this width. Where the vein is made up of two or more streaks of different hardness or mineral content, each streak is to be sampled sepa-rately and the average value of the combined width figured. If two streaks of ore are separated by a streak of waste, which is not sampled, in obtaining the average value of the breast the waste must be figured in with a zero assay. Drifts to be sampled in the breast after each round. Raises to be sampled for each floor raised. Each end to be sampled separately and the average width and value of the two ends to be used as the average of the floor. All veins cross-cut to be sampled along the side of the cross-cut, at breast height and horizontally. Where the vein strikes at an acute angle to the line of the cross-cut, the width of sample must be corrected to show the horizontal width at right angles to the line of strike of the vein. Rill stopes must be sampled across the full mining width. In square-set stopes, each set must be sampled separately along the line of the caps. Waste portions of the vein which are mined for filling must not be included in the sample.

Jan 2, 1922

Discussion of the paper of C. M. YOUNG, presented at the St. Louis meeting, October, 1917, and printed in Bulletin No. 129, September, 1917, pp. 1369 to 1384. CARL SCHOLZ, Chicago, Ill.-Mr. Young was kind enough to' allude to the development of a mine in which I am now engaged. Several months ago the Burlington Railroad decided to open a mine in the field Which they own in Franklin County containing some 15,000 acres .(6070 ha.) of coal, ranging in thickness from 8 to 12 ft. (2 to 3.6 m.). This proposition in itself is attractive to any mining engineer, but with the backing of a large company I saw an opportunity to do some novel work in the construction line, and for several months I have been investigating and working on the problem of developing what I hope will be the largest and best equipped mine in the State of Illinois. The shaft will be sunk at a place where the coal lies at a depth of 600 ft. (182 m.) and conditions both of the surface and of the coal are ideal in every way; the seam is almost level, and we had only 7 ft. (2 m.) of surface clay to go through. We are going to hoist by skips in order to reduce the rope speed. I believe that is a long step in the direction of economy, because we not only double the output of the mine by hoisting the contents of two cars atone time, but we reduce the proportion of dead weight. In our case there will be 20 tons of coal and 18,000 lb. of skip, or 55 per cent. net and 45 per cent. tare. That, of course, necessitates less than half the rope speed for the same tonnage, and we all know that speed means power and power means cost. Skip hoisting permits the use of solid-end gate cars, which is an advantage. The cost of these cars will be in the neighborhood of $250 apiece; They are well built, with roller-bearing wheels of the most up-to-date type, spring draw-bars, and refinements of-that character which are necessary to move the loads most advantageously.

Jan 1, 1918

By H. Herbert Hughes

THE trend in modern building construction is definitely toward the use of weight-reducing materials. The basic advantage of lighter structural weight is obvious; reduction of dead load with retention of equivalent strength affords the possibility of increasing the live load, or if this is not desirable or necessary it makes feasible a reduction in size of structural steel members and corresponding savings in other phases of construction. Among the weight-reducing materials and practices rapidly gaining favor are the use of light-weight patented insulating board to replace back-up tile or units, particularly in home construction; introduction of aluminum alloys to replace steel for many purposes; manufacture of porous brick, the use of which materially reduces the weight of masonry walls and partitions; and the use of self-rising vesicular concrete, diatomite and sawdust tile, porous gypsum, or gypsum tile for nonload-bearing partitions and walls. Even building accessories are being designed to save weight and space; one of the most striking examples of this is improved radiator construction. Concrete technique is keeping pace with the rest of the industry. Burned shale aggregates now available in many sections of the country will make concrete weighing only 100 lb. per cubic foot, saving roughly 35 per cent. in weight and sacrificing none of the strength of a rock-sand mix. It may be more expensive, but actual experience has shown that the saving in dead load will effect a reduction in structural steel which in many instances will more than offset the increased cost of the aggregate. The vesicular nature of most light-weight aggregates gives the concrete especially good insulating, fireproofing and soundproofing properties; yet absorption is comparatively low. Strangely enough, however, the increased use of light-weight aggregates appears to have augmented the demand for ordinary aggregates in concrete construction rather than to have decreased it. Light-weight aggregates have widened the field for concrete structures and, since the producers do not attempt to recommend the use of their material except where weight or other special properties are important factors, impetus- has been given to sales of other aggregates.

Jan 1, 1931

By C. D. Hunter, J. B. Browning

During the year 1934, Kentucky oil and gas operators have partly overcome their past depression fears and in the oil industry, with possibly more abandonments of old oil producers than the completion of new oil wells, produced 4,814,904 bbl. of oil in 1934 against 4,501,511 bbl. in 1933. In the gas industry of eastern Kentucky, 115 gas wells were completed during 1934. This production is delivered through two 20-in., one 16-in., one 12-in., one 10-in., and two 8-in. pipe lines to supply both domestic and industrial markets in Cincinnati, Ohio; Louisville, Lexington, Frankfort, Winchester, Ashland, Covington and other Kentucky towns; Washington, D.C., and other eastern cities. The largest percentage of these gas wells and production are from the Devonian black shale area of Floyd, Pike, Knott, Martin and Magoffin counties, Kentucky. In this area the largest percentage of 1889 wells, developing 421,-215 acres, has been completed in the past 10 years, of which 55.3 per cent produce from the 400 to 550 ft. of Carbonaceous Devonian black shales. The successful results obtained from these Devonian shales are due to the physical effects of the 5000 to 6000 lb. of gelatinated nitroglycerin with which the entire 400 to 550 ft. of shale is shot. A very small number of the shale wells are natural producers and do not require shooting. Other than the Devonian shale gas production, the remaining 44.5 per cent of the gas in this field is encountered throughout the entire strati-graphic section above this horizon; namely, salt sands of Pennsylvanian age and Maxon, Big Lime and Weir of Mississippian Age. A very small percentage is encountered in the Corniferous Devonian lime and the Silurian Big 6 below the black shales. In western Kentucky, in the counties of Henderson, Webster, Hopkins, McLean, Christian, Muhlenburg, Ohio, Daviess, Hancock, Brecken-ridge, Hart, Barren and Warren, many gas wells have been completed, but, because of insufficient market, activity has been somewhat desultory. The area is served by the pipe lilies of the Kentucky Natural Gas Corporation, with headquarters at Owensboro. Their market is increasing and the gas is delivered to Owensboro, Henderson, Madisonville, and many

Jan 1, 1935

By M. ROWE, H. E. Gilliland, L. BARNES

The authors of this paper are to be commended for a clear exposition of a timely subject. However, some important conclusions, in addition to those presented in the paper, can be drawn from the results of their elaborate and rather complete numerical computations. First of all, the major part of the calculations presented in the paper are for semi-infinite slabs of oil shale (the authors designate this as Model I) and a question must be posed — Are these elaborate computations needed to arrive at realistic estimates of the shale oil displaced. Consider the model of Lauwerier* that corresponds to the authors Model I if thermal conduction parallel to the fracture be neglected. If one also neglects the finite (but relatively small) heat capacity of the material in the fracture, it is easily shown from Lauwerier's solution that the cumulative oil production would be:

Jan 1, 1969

By R. A. Oriani

The partial molal volume of hydrogen is one of the parameters that describe the elastic interaction between the solute and the stress fields about inclusions, dislocations, and cracks. As such the partial molal volume is probably of importance in the elucidation of phenomena such as hydrogen embrittlement and hydrogen yield point. A knowledge of this quantity would also be helpful in thinking about the state of dissolved hydrogen in iron. However, because of the very low lattice solubility of hydrogen in iron the usual ways of determining the lattice expansion are not practicable. It is therefore of interest to apply the thermodynamics of stressed bodies to two sets of measurements of the effect of elastic stress upon the permeability of hydrogen in order to deduce a value of the partial molal volume, VH, of hydrogen dissolved in a iron. Beck ..' and previously de Kazinczy, observed that a uniaxial tensile stress increases the permeability of hydrogen in iron and in various steels. Beck et 01. employed Armco iron and A.I.S.I. 4340 steel, whereas de Kazinczy used a steel the composition of which was 0.13 C, 0.23 Si, 0.46 Mn, 0.006 P, and 0.038 S. Upon releasing the stress the permeability increment disappeared if the stress was below the elastic limit. Both investigators employed cathodic charging to introduce the hydrogen. de Kazinczy measured the permeation through a thin-walled tube by collecting the gas, whereas Beck et al. measured the permeation through sheets of various thicknesses by a very sensitive electrochemical technique. Both investigators measured the steady-state permeation at constant rate of hydrogen ion discharge, and Beck measured in addition the hydrogen diffusivity by a time-lag technique which is independent of the boundary conditions. Beck et al. and de Kazinczy found a linear relationship between log (J,/Jo) and the stress, where Ju/Jo is the ratio of the flux of hydrogen when the metal is under uniaxial tensile stress, a, to the flux under zero stress, for the same temperature and charging current. Beck et al. found in addition that the diffusivity of hydrogen is not changed by stress. Both investigators concluded that the observed change in permeability is due to an increase in hydrogen concentration, and furthermore that the increase in concentration is due directly to the thermodynamic effect of stress upon concentration. Accepting this assessment of the situation for reasons given below, one may use the equation3j4 in order to evaluate I/H, the partial molal volume of hydrogen. This equation is valid for the domain of a/E «¦ 1 (where E is the Young's modulus) and under the assumption that hydrogen expands the lattice isotrop-ically. From the data of Beck el al, one calculates V7H - 2.0 cu cm per g-atom, and from those of de Kazinczy one obtains 1.8 cu cm per g-atom. That the increase of concentration with stress is indeed of thermodynamic origin is attested to by the facts that the experimental results conform to the thermodynamic relation, Eq. [I], and that the results are the same whether a pure iron1 or each of two different steels172 is used. Neither of these facts wou1.d necessarily be expected if the effect of stress were, rather, to increase the ratio kn/k, of the kinetic factors of the following competing reactions: H(ads) — H (dissolved) Such a change of kinetics at the surface could be an alternative explanation of the effect of stress on the permeability. Although this writer does not deem this explanation to be the correct one for the reasons given above, it must be admitted that unambiguous proof that the phenomenon has a thermodynamic origin does not yet exist. Two kinds of experiments may be suggested. One is to plate a variety of metals on the input surface of the steel and repeat the stress experiment at a variety of hydrogen charging currents. The other is to employ somewhat thicker specimens in order to be able to apply uniaxial compressive stress. Eq. [I] shows that ln(c,/c,) depends on the sign of the stress, but it is difficult to see a physical basis for which k2/kl would depend on the sign of a. The present value of V^ in a iron agrees with phragmen's5 estimate, which he based on comparisons with the lattice expansion by hydrogen of titanium, zir-

Jan 1, 1967

By Robert Glass Cleland

DURING the closing month of 1929, Walter Douglas found his health impaired by the strain of many difficult years of alternating prosperity and depression, and in April 1930 resigned the presidency of Phelps Dodge. Douglas was succeeded by Louis S. Cates. The choice broke a tradition that had been held inviolate for almost a hundred years. For the first time in its long history, the direction of the company's policies and operations was entrusted to a stranger without previous Phelps Dodge background, training, experience, or tradition. But the choice was wisely made. For a time at least, the path of Phelps Dodge was to run through rough and dubious ground, and no man in the United States was better qualified to blaze that trail than Louis Cates. After graduating from the Massachusetts Institute of Technology, Cates had served a rough and financially un- profitable apprenticeship at one of the century-old mining camps of Chihuahua, Mexico. Following his return to the United States and a brief interlude as assistant to the president of the National Steel and Wire Company, he had resumed his mining career, first as timekeeper, then as

Jan 1, 1952

By Frederick Laist

About six years ago the Anaconda Copper Mining Co. decided to investigate the possibility of extracting zinc from the ores of certain mines in the Butte district. These ores are of a complex character and contain so much iron and lead that the concentrate contains only 33 to 35 per cent. zinc. Investigations showed that while a high-grade concentrate could not be obtained by ordinary methods, such as tabling and magnetic treatment, a fair grade could be made by the Horwood process. In this method, the concentrate resulting from the flotation of all of the sulfides is given a light roast and this calcine is subjected to flotation in the presence of a large amount of sulfuric acid; the resulting concentrate contains most of the zinc and a residue contains most of the iron. The fact that the lead, copper, and silver are divided approximately equally between the zinc concentrate and the iron residue and the large consumption of acid, which ranged from 50 to 100 lb. (22 to 45 kg.) per ton of concentrates, were serious objections to this plan. The zinc recovery, moreover, was low, as a considerable percentage invariably accompanied the iron. While a profit might be made on the ores by the use of this process, it was thought that other and more promising methods might be devised. After carefully studying the field and doing some laboratory work on various processes that had been suggested, it was decided that the electrolysis of sulfate solutions was the most promising. We soon found, as have other investigators, that the only way to obtain a good zinc deposit is to have the electrolyte free from all metals more electronegative than zinc, such as copper, cadmium, lead, arsenic, antimony, etc. Arsenic and antimony are particularly injurious, causing very poor current efficiency and small yield per horsepower when present in amounts so small as almost to defy detection—1 mg. or less per liter. A pure zinc is soluble only with difficulty in sulfuric acid; an impure zinc dissolves very readily. Electrolytic zinc deposited from pure solutions is, of course, extremely pure and dissolves only about one-fiftieth

Jan 1, 1921

By H. M. Roche

MAGNETITE mining and milling in the Eastern States in 1939 showed considerable improvement over 1938. For the first eight months of the year production of magnetite proceeded at a normal rate but operations were stepped up in the last four months owing to increased domestic demand. In New York, the Republic Steel Corp. operated the Witherbee-Sherman mines at Mineville throughout the year. Chateaugay Ore and Iron Co. operated their low-phosphorus mine at Lyon Mountain for the first seven months, but on Aug. 1, Republic Steel took over this mine -and have since operated it. In Pennsylvania, the Bethlehem Steel Co, operated the Cornwall mine continuously. In New Jersey, Mt. Hops and Scrub Oak were in operation all year. The Washington mine went into production on Nov. 1 and the Richard mine on Dec. 1.

Jan 1, 1940

By B. Welber, R. Webeler

A CCORDING to accepted theory, fatigue in A] metals is connected with the occurrence of local strain hardening even at applied stresses below the yield point as a consequence of stress concentrations created by the presence of structural inhomogeneities.1 It seemed possible, therefore, that

Jan 1, 1954

By James C. M. Li

James C. M. Li (Edgar C. Bain Laboratory for Fundamental Research)—Professor Weertman has suggested the interesting possibility that dislocation tangles are formed by helical formation of dislocations stopped by long-range stresses or by jogs. Such a possibility is similar to that of "mushrooming"374 in the respect that a dislocation must first be stopped and then interact with vacancies. The effect of short-range internal stresses which may exist at the time a dislocation is stopped has not been considered. It seems that the effect of these internal stresses may be just as important as, if not more than, that of the interaction with vacancies. The internal stresses produced by dislocations of

Jan 1, 1964

By F.B. Foley, S.P. Howell

Not infrequently, in the case of the failure of a metal structure, such as a bridge, tank, airplane, gun carriage, etc., a doubt arises whether the failure was due, among other causes, to the effect of an overburden or of an explosive maliciously or accidentally exploded in contact with it. As few means of discriminating between the effects of these causes have been known and these means were of a rough qualitative character, it was surprising to find in the record of an inquiry into the failure of a structure, the statement that, by observations on the Neumann bands in the structure, it was possible to determine the speed of breakage in the metal and to distinguish between a fracture caused by an explosion and one caused by an ordinary mechanical strain. Such a criterion, if well proved, was of value to the explosives experts of the Bureau of Minea, the Ordnance Department of the United States Army and the Bureau of Ordnance of the United States Navy, but search showed no record of it in the literature nor did any of the metallurgists and metallographers consulted know of any data on which such a criterion could be based having been assembled and critically studied. However, it was universally held that there was promise in the idea and that there exkted unique facilities at the Bureau of Mines Experiment Station at Pittsburgh for the preparation, under definitely known conditions, of material for study by metallographers, and that material of value might also be obtained from the proving grounds of the Army and Navy. Therefore, with the approval of the Director of the Bureau of Minea and the Chiefs of Ordnance of the War and Navy Departments, the Chairman of the Division of Engineering of the National Research Council, on April 12, 1919, appointed a Committee on the Investigation of Neumann Bands, which has since been engaged in this study and which, after some slight change in its personnel, consists now of the following: Dr. William Campbell, Advisory Metallurgist, Bureau of Ordnance, Navy Department. P. B. Foley, Metallurgist, Bureau of Mines. S. P. Howell, Explosives Engineer, Bureau of Mines. Comdr. 0. M. Hustvedt, U. S. N., Bureau of Ordnance, Navy Department. Dr. Charles E. Munroe, Chief Explosives Chemist, Bureau of Mines.

Jan 1, 1923

By S. P. Howell, F. B. Foley

Not infrequently, in the case of the failure of a metal structure, such as a bridge, tank, airplane, gun carriage, etc., a doubt arises whether the failure was due, among other causes, to the effect of an overburden or of an explosive maliciously or accidentally exploded in contact with it. As few means of discriminating between the effects of these causes have been known and these means were of a rough qualitative character, it was surprising to find in the record of an inquiry into the failure of a structure, the statement that, by observations on the Neumann bands in the structure, it was possible to determine the speed of breakage in the metal and to distinguish between a fracture caused by an explosion and one caused by an ordinary mechanical strain. Such a criterion, if well proved, was of value to the explosives experts of the Bureau of Minea, the Ordnance Department of the United States Army and the Bureau of Ordnance of the United States Navy, but search showed no record of it in the literature nor did any of the metallurgists and metallographers consulted know of any data on which such a criterion could be based having been assembled and critically studied. However, it was universally held that there was promise in the idea and that there exkted unique facilities at the Bureau of Mines Experiment Station at Pittsburgh for the preparation, under definitely known conditions, of material for study by metallographers, and that material of value might also be obtained from the proving grounds of the Army and Navy. Therefore, with the approval of the Director of the Bureau of Minea and the Chiefs of Ordnance of the War and Navy Departments, the Chairman of the Division of Engineering of the National Research Council, on April 12, 1919, appointed a Committee on the Investigation of Neumann Bands, which has since been engaged in this study and which, after some slight change in its personnel, consists now of the following: Dr. William Campbell, Advisory Metallurgist, Bureau of Ordnance, Navy Department. P. B. Foley, Metallurgist, Bureau of Mines. S. P. Howell, Explosives Engineer, Bureau of Mines. Comdr. 0. M. Hustvedt, U. S. N., Bureau of Ordnance, Navy Department. Dr. Charles E. Munroe, Chief Explosives Chemist, Bureau of Mines.

Jan 1, 1923

By F. G. Clapp

IT is to be hoped that no casual reader will erroneously refer to the latest publication' of the Division of Public Relations of the American Petroleum Institute, as being "Petroleum Facts and Fancies." The facts are so faithfully derived and the figures are so authentically sponsored by the highest sources that no person can read this valuable volume (287 pages and numerous tables) without being convinced that every- thing therein set forth is "the truth and nothing but the truth." Yet, having read the volume from the perspective of the world's petroleum industry and with a critical attitude that comes from years of study of the subjects discussed, I find myself tempted to cogitate and to envisage a few of the fancies that come to mind as a fitting sequel.

Jan 1, 1929

By J. H. Johns, G. R. Stephan

The Climax mine has a history of dealing with ground control problems caused by major stress concentrations in the orebody. These stress concentrations, called weight, can arise in a variety of ways. The general effects of depth, rock type, and mining method give rise to weight problems, but local geologic features and daily cave line management can have even greater effects. Over the years a number of techniques have been developed for identifying weight problems in advance and for cow with them. These techniques all help us to amid interrupting the pace of cave advance and minimize the loss of production.

Jan 1, 1984

By R. Maddi, I. R. Kramer

The delay time for the initiation of slip was studied in single crystals of a brass, aluminum, and ß brass. A delay time for slip was found in ß brass when the specimens were tested below room temperature; however, one was not found for a brass or aluminum. A general theory for the existence of the brittle transition temperature is proposed. A LTHOUGH a considerable amount of effort has A been devoted to the study of the deformation and fracture of single crystals, the vast majority of the work was concerned with static tests or with tests carried out at relatively slow strain rates. The necessity for the study of a possible incubation time for slip becomes apparent when the various theories which have been postulated for the elucidation of the mechanism of slip are considered. The existence of an incubation period would strongly indicate that slip occurs by a process of nucleation and growth; whereas the absence of an incubation would present rather convincing evidence that slip occurs by a cataclysmic process. In addition to shedding light on the process of plastic deformation, an understanding of the early stages of plastic deformation may be helpful in finding an explanation for the brittle behavior of the body-centered metals under certain conditions. It is well known that these metals, such as iron, molybdenum, tungsten, ß brass, etc., will become brittle as the test temperature is lowered or the strain rate is increased. In spite of the fact that this subject has received considerable attention since the turn of the century, no adequate theory exists today which explains the phenomenon. In the ductile temperature range the metal breaks with a "fibrous" fracture after considerable slip has taken place. In the brittle temperature range the metal fails essentially by cleavage on the {loo) planes: however, some plastic flow is always present even in the most brittle fractures. It is possible, as will be explained later, to ascribe this brittle behavior to the length of the incubation time for slip. Clark and Wood,' using polycrystalline metals, showed that a delay time existed for the yield point in mild steels and that the delay time depended upon the applied stress. These authors stated that the delay time was observed only with those materials for which the stress-strain curve showed a definite yield point. In their work only the mild steel specimens exhibited a delay time at the yield point, while the other materials studied-type 302 stainless steel, SAE 4130 normalized steel, SAE 4130 quenched and tempered steel, 24s-T aluminum—did not show a delay time. These authors' in an extension of their work, found that as the temperature was lowered the delay time was increased. It is, then, the purpose of this investigation to measure or to set an upper limit on the delay time for plastic flow in single crystals of a brass, aluminum, and ß brass. The delay time will also be studied as a function of temperature. The incubation time may be measured by determining the length of time the specimen will support a stress without slip occurring when the stress is greater than the static critical resolved shear stress. In order to accomplish these measurements use was made of a pendulum which was so designed that a single crystal specimen could be placed at various positions along its length. When a pendulum is struck by another pendulum of the same length, an elastic wave is transmitted down the bar with the velocity of sound in the material and is reflected from the far end of the bar. The reflected wave then travels back and unloads the stress until it reaches the impacted end of the bar and the two pendulums separate. The length of time that the specimen is subjected to the stress is equal to the time it takes for the stress wave to travel twice the distance from the specimen to the end of the bar. The stress applied to the specimen is governed by the velocity of impact of the two pendulums. The stress at which the specimen first suffers plastic: deformation was determined in these experiments by examining the specimen under the microscope for the first appearance of slip lines and by measuring the residual strain after each impact. In these experiments the critical resolved shear stress was approached from the low stress side and no attempt was made to determine it exactly. To determine it exactly, it would have been necessary to find that stress at which slip would have just started. However, since the stresses were increased in rather small increments the critical stress is believed to be approached rather closely, as will be seen from the experimental results. The critical stress will be taken as the highest stress obtained before the onset of plastic deformation. The stresses

Jan 1, 1953

By R. N. Stevens

GRAIN boundary sliding plays a part in the high-temperature deformation of polycrystalline solids, and many investigations1-11 have been carried out to determine the deformation contributed by this mechanism. The principal method employed has been to measure one of the components of the grain boundary displacement, see Fig. 1, at a large number of boundaries, and from the mean value so obtained to calculate the elongation contributed by sliding. A formula connecting these mean values and the elongation contributed is evidently required, and many have been derived. They are usually of the form where Egh is the tensile elongation contributed by sliding, is the mean value of the component, x, N is the mean number of grain boundaries intersecting a line of unit length, and K is a dimensionless parameter known as the averaging factor. Table I summarizes the equations used by various investigators. Examination of these shows that their derivations usually involve doubtful assumptions, and are often in serious error. The purpose of this note is to point out that rigorous solutions to the problem of calculating Egb from x have been available in the literature for some years.' Since this is so little known, and also the original derivations do not make some important points clear, it is proposed to rederive the basic equations. These will be extended further, and the conditions in which the extended equations may be applied will be indicated. The mean values of the components of the sliding vector (I, d, and I:, Fig. 1) will depend on the method by which boundaries are sampled in order to make measurements.3,11 Boundaries are usually sampled by marker lines parallel to the stress axis, or lines perpendicular to the stress axis, the measurement being made at the point where the marker line intercepts the boundary. We will denote the mean values determined by these various sampling methods as follows. lT, dT and vT are mean values obtained by making measurements at pointswhere a transverse line intercepts the boundary while lL, dL, and vl, are the mean values from a longitudinal line. The number of boundaries per unit length also may depend on the direction of measurement, and so we define NT and Nl to be the number of boundaries per unit length, after creep, in the transverse and longitudinal directions, respectively.

Jan 1, 1967

JAMES E. HOWARD,* Washington, D. C. (written discussion?). -Mr. Comstock, in his classification of the possible causes of transverse fissures, has not quite caught the point of view of the writer. It appears, following the trend of thought in Mr. Comstock's paper, that three groups instead of two might bee enumerated, namely: Fatigue of the steel, quality or, preferably, grade of steel, and mill practice. All steels are liable to failure by fatigue. Stresses that are capable of causing fatigue fractures are modified in their magnitude by the grade of steel acted upon. Mill practice is a term having a very wide meaning and in its relations to the development of transverse fissures has been used with such vagueness as to include many known factors and some that are unknown in the arts. According to the grade of steel employed, fatigue fractures may be accomplished by loads of greater or less magnitude, hence there is a relation between quality, or grade, of steel and the display of fatigue fractures. Mill practice of such an order as to affect the formation of transverse fissures must be shown to exert an influence on the ability of the steel to endure repeated stresses. Different grades of steel are selected for different purposes. Steel employed for fire-box purposes is of different grade from that used for cutting tools; although each grade is suitable for its purpose, and therefore of good quality. It is conceivable that a demand might be made for steel of physical properties in excess of those of any known grade. Under such a demand, impossible of' fulfillment, it would not be proper to refer to the steels as being deficient in quality; to do so would be a failure to recognize that all steels have their limitations in strength. Service conditions peculiar to rails admit of successive advance until the conditions can no longer-be met. The failure of a large number of rails from one type of failure, when all known means of averting the failure have been employed without success, is sufficient evidence that the end is close at hand. Iron rails, for a time, successfully met the requirements of railway service but weight of equipment, motive power, and rolling stock were increased, necessitating the use of steel. The early steel rails enjoyed the reputation of being of excellent quality, although: neither chemically nor structurally would they be so regarded ,lit the present time. They did good service in their day and under the conditions then prevailing were good rails. To meet the increased weight of rolling stock there has been

Jan 3, 1919

By P. R. PaeIay, A. Slibar

Using three-dimensional, stress-deformation rate equations for a Bingham plastic, an approximate solution for the laminar flow of drilling mud between the drill pipe and casing is given for the case when the velocity gradients due to axial flow are large compared to velocity gradients due to rotation. INTRODUCTION The fact that drilling mud can be treated, to a first approximation, as a Bingham plastic has been established by several investigators12,3,4,5. A Bingham plastic is a material that is rigid until a certain combination of stresses exceeds a critical value. When the stresses are sufficiently high to initiate flow, the reduced stresses have a constant ratio to the corresponding deformation rates at each point. Prediction of pressure and torque requirements to produce the desired flow of the material have been made by analytical solutions due to Bingham6, Reiner7, and Buckingham8. One part of the present means of calculation that requires clarification is the flow between the drill pipe and casing. Present methods treat the flow resulting from the rotation of the drill pipe separate from the flow produced by the axial pressure gradient. Since the non-linear behavior of a Bingham plastic implies that solutions cannot be superposed, the present analytical investigation was undertaken to obtain a solution to the problem of combined axial and tangential flow. Equations have been proposed for the three-dimensional flow of a Bingham plastic9,10,11 and it has been shown that the proposed equations lead to the usual solutions from the one-dimensional theory". Applying these equations to the flow between two concentric cylinders the problem of axial flow only13 and tangential flow only12 have been solved. In addition to the separate problems of axial and tangential flow between concentric cylinders, the authors have determined the relationship between external torque on the inside cylinder and axial pressure gradient necessary to initiate flow". The solution given in Ref. 14 points out the complexity of the present problem. The problem considered here is the case of simultaneous axial and tangential flow. The axial flow, necessary to keep the drill bit free of removed material, results from the axial pressure gradient. Tangential flow is present since the drill pipe rotates in the hole. The solution given here is valid when the shear stresses in the drilling mud due to rotation are small compared to the shear stresses resulting from the axial flow. This case for laminar flow can be encountered in oilfield drilling. STRESS-DEFORMATION RATE EQUATIONS A detailed derivation of the equations governing the behavior of a Bingham plastic is given in Ref. 10. This section briefly outlines the physical reasoning leading to this three-dimensional formulation of the stress-deforma-tion rate law. Experiments on a certain class of materials have demonstrated the following properties: (1) when a certain combination of the stresses is below a critical value no deformation of the material occurs, (2) to a first approximation this combination of stresses is independent of the hydrostatic pressure (negative average normal stress), (3) if flow occurs the ratio of the reduced stress to the corresponding deformation rate is constant at each point of the flowing material, and (4) incom-pressibility. For the one dimensional case of shear deformation, Bingham6 formulated the governing equation as dxx, = 0 for sxx < to and µdxx = s xx = to for sxx to , . where dxx is the shear deformation rate, sxx the shear stress, to the critical shear stress, and p the slope of the sxx vs dxx curve for dxx > 0. Fig. 1 shows the behavior for pure shear between two parallel plates. Taking into account the physical properties given above and assuming the critical combination of stresses to be measured by the octahedral shear stress, the fol-lowing three-dimensional equations have been proposed.

Jan 1, 1958