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By J. H. Wernick, D. Dorsi, K. E. Benson

A LTHOUGH a considerable number of experi--ti mental investigations dealing with the roasting of sulfide minerals have been reported in the past,'"" the behavior of the single roasting particle does not appear to have received the attention it perhaps deserves. This is understandable in that the natural sulfide counterpart of the slab or sheet of metal normally used in high temperature oxidation studies is difficult to obtain and prepare, and is, in most cases, virtually impossible to maintain in one piece at roasting temperatures. The employment, on the other hand, of static aggregations of small particles in masses great enough to permit evaluation of the roasting reactions by means of thermobalances or gas analyses introduces other complications, such as localized overheating, sintering, and variable gas-solid contact. In this investigation a compromise between the above extremes was attempted. Closely sized (e.g., 30 to 40 mesh) particles of natural sulfide minerals were isothermally roasted, out of contact with one another, in an air-swept system. The progress of the roasting reactions was followed by examination in polished section of the treated particles and by X-ray and chemical analysis of their residual sulfide kernels. In this way some conclusions respecting the mechanism of roasting reactions were drawn. Roasting Furnace—The vertical tube furnace used for roasting the sulfide particles had a heated zone 10 1/2 in. long in which four retractable light gage stainless steel trays were suspended. Each tray, and an accompanying baffle, was mounted on a 2 in. iength of 3/8 in. stainless steel tubing. These assemblies were axially suspended on a 30 in. length of in. stainless tubing, by means of which they could be lifted from the hot zone to a water-cooled brass chamber at the top of the furnace. Since each tray unit could slide freely on the 30 in. tube, any desired number of the trays could be retained in the cooling chamber by the manipulation of a horizontal plunger during a momentary withdrawal of the four trays from the hot zone. Although three heating coils, each equipped with variable external resistance, were employed, it was found impossible to avoid a drop of 10O to 15OC between the temperature at the top tray and that of the lower three. Consequently, only the bottom three trays were used for roasting. Temperature readings inside the furnace were made by means of a thermocouple inserted down the tray support tube at tray levels, and a separate thermocouple, inserted adjacent to the middle heating coil, was connected to a Micromax temperature control unit. Experimental Method—The sulfide minerals were obtained in a form as free as possible from gangue and contaminating sulfides, and were crushed and screened to the required particle size range. The tray assembly was kept inside the furnace during the heating-up period and, when a steady temperature had been reached, the trays were withdrawn. Each tray was sprinkled with from 200 to 500 mg of the sulfide grains, and the assembly was lowered into the furnace without delay in order to minimize the time required to achieve the operating temperature. The furnace top was then clamped into position and the thermocouple inserted down the center tube to the required level. It was found that, when this procedure was used, the trays achieved their former temperature within 2 min, after which time the flow of dry air was begun at a rate of 1 liter per min, and timing of the run was started. At the required intervals of time the trays were successively withdrawn from the hot zone and stored in the cooling chamber by means of the retention plunger. On completion of the run the treated particles were removed from the trays to be set aside for examination. The roasted particles were mounted in Lucite on a Buehler press operating at a temperature of 146°C

Jan 1, 1958

By E. F. Koch, J. L. Walter

oriented crystals of iron and iron with 3, 5, and 6.25 pct Si were rolled to reductions of 10 and 70 to 97 pct at room temperature. Similarly oriented crystals were deformed in tension. Dislocation substructures of the deformed crystals were observed by transmission electron microscopy to determine the effect of silicon on the formation of substructures. Pole figures were obtained to relate orientation changes to substructure. When rolled 10 pct, the iron crystals and the 3 pct Si-Fe crystals formed cells, 1 and 0.2 u in diameter, respecliuely. Cells were absent in the higher-silicon crystals. Extended dislocations and possible stacking faults were observed in the 6.25 pct Si-Fe crystal rolled 10 pct and annealed at 650°C. The stacking-fault energy was estimated to be 20 ergs per sq cm. Rolling to 70 pct resulted in the formation of sub-bands (0.9 µ wide) ill the iron crystals and transition bands (containing 0.2-µ-wide subbands) in the 3 pct Si crystals. No subbands formed in the 5 pct Si-Fe crystal until it was ankzealed. SliP occurred on (112) planes ill tension. The slip traces on the 3 pct Si crystal were wary while those on the 5 pct Si crystal wvere straight. The strain-hardening coefficient for the 5 pct Si crystal was nearly zero. Cells did not form, at least at elongations up to 10 pet. The results suggest that cross slip of iron is restricted by additions of silicon beyond about 3 pct possibly by formation of immobile extended dislocations. IN a previous paper' the authors described the substructures developed in (100)[001]-oriented crystals of 3 pct Si-Fe which were rolled to reductions of 10 to 90 pct at room temperature. At low reductions (10 to 20 pct) cells, approximately 0.2 to 0.3 ja in diameter, were formed. The cell walls consisted mainly of edge dislocations. With increasing reduction (up to 50 pct) the cells were seen to elongate in the rolling direction. In certain regions of the crystal there were significant reorientations which were characterized as rotations about an axis normal to the (100) or rolling plane. These regions were called "transition bands". The regions in which there were no reorientations were called ('deformation bands". At reductions of 60 to 70 pct the elongated cells in the transition bands became sub-bands separated by low-angle tilt boundaries with angles of disorientation of about 2 deg. The elongated cell structure in the deformation band was replaced by a general distribution of dislocations. It was noted that the width of the subbands in the transition bands remained 0.2 to 0.3 µ; i .e., the width of the subbands was the same as the initial cell diameter for reductions up to at least 70 pct. From this, and from considerations of the mechanism of formation of the transition bands,' it was concluded that the subbands evolved directly from the initial cells. In order to check this conclusion, it was decided to examine the relationship between initial cell diameter and width of subbands produced by large rolling reductions. Cell size is known to be dependent upon the temperature of deformation.2,3 However, preliminary experiments with 3 pct Si-Fe crystals indicated that the change in cell size with increasing temperature of deform,ation was not sufficient for the present purpose. On the other hand, cell diameters generally reported for iron deformed at room temperature2'3 range from 1 to 2 p, a factor of 3 to 10 larger than the cells in 3 pct Si-Fe rolled to 10 pct reduction,' indicating the possibility of a marked dependence of substructure (at least in terms of cell size) on the amount of silicon in iron. Thus, the investigation was enlarged to include the study of the effects of varying silicon content on substructure in lightly rolled as well as in heavily rolled crystals of iron and iron with 3, 5, and 6.25 pct Si. The crystals used in this study all had the same orientation, (100)[001], with respect to rolling plane and rolling direction. These were rolled to reductions of from 10 to 97 pct and the substructures determined by electron transmission microscopy in both the rolled state and after annealing. In addition, stress-strain curves were obtained from (100)[001]-oriented crystals of iron and 3 and 5 pct Si-Fe to determine the effect of silicon on tensile properties. The dislocation substructure of the tensile specimens was also determined for Samples pulled to 2 and 10 pct elongation at room temperature for comparison with the substructures produced by rolling. 1) EXPERIMENTAL PROCEDURE Crystals with 3, 5, and 6.25 pct Si were prepared by annealing 0.012-in.-thick sheets of high-purity Si-Fe in purified argon at 1200°C to effect growth

Jan 1, 1965

By C. E. Gregor

Current modern trends in mining show that hoisting shafts are being expected to fulfill an important ventilation function. However, where rigid guides and supporting structures are mandatory, ventilating power costs will be high, unless the transverse structures (shaft sets) are streamlined. In the complex configurations of hoisting shaft furniture patterns, either for original design purposes, or for the adjustment of an existing shaft, a useful degree of aerodynamic optimization, by reduction of overall resistance, can only be effectively evaluated by model studies in a special purpose wind tunnel, as described herein. The author has shown that, in one particular case, an annual power cost saving of more than $50,000 was indicated, mainly by the selection of buntons and dividers of improved aerodynamic profile. Mining companies are now realizing the advantages that can accrue through proper attention to the aerodynamic aspects of mine shaft design. With progressive demands of civilization for an ever greater supply of coal and metals, and with greater depths of working, higher rates of extraction, advanced degrees of mechanization, and improved standards of environmental health and work comfort, shaft design is becoming an extremely important aspect of mining operations. In addition, because the cost of sinking, equipping, maintaining, and operating a mine shaft is continually increasing, there is a greater incentive to use a shaft for the maximum duty, consistent with economy. The current natural tendency is therefore to sink multi-purpose shafts, to install as much equipment as is safely and effectively possible to operate; and then, over and above all these functions, to use the shaft to its maximum possible ventilating capacity, as a major, or auxiliary, airway. Clearly, this latter additional function can only be employed at a significant cost, since the most economic operating airways are smooth-lined and devoid of internal rigid furniture. It is true that hoisting functions can be carried out in such shafts if rope guides are used, but only under restricted conditions. Where a manway must be provided, fixed guides and supporting structures are mandatory, and ventilation costs become accentuated. It is generally recognized that the prime element of cost in ventilating a mine can be represented by the power required to drive the fan unit. It is also known that the largest component of total mine resistance is that of the downcast shaft, where this shaft is equipped with rigid guides for hoisting purposes. The pressure loss varies directly as the resistance of the shaft, in accordance with a modification of the Atkinson equation p = RQ2/3600. Furthermore, the air horsepower drawn is given by the equation AHP = (p x 0/33000. Therefore, the power required to drive the fan unit varies as the resistance of the shaft and the cube of the air quantity. Clearly, if Q is a specified minimum, then the only way to minimize the pressure loss (and the power costs) is to reduce the shaft resistance R. (See Table I for a list of symbols.) The resistance to airflow of a shaft equipped with rigid guides and supporting structural sets consists of two components which, for the sake of analytical simplicity, can be regarded as additive. 1) Frictional resistance, represented by the viscous frictional forces within the boundary layer, as air flows along the surfaces of the walls and the periphery of the vertical elements (guides, pipes, cables, ropes, etc.) of the furniture. The friction loss can be readily calculated by the Atkinson equation, after selection of a suitable value for the friction factor K from the McElroy compilation.' KxLxO xQ2 5.2 xA3 Friction loss can be minimized by lining the shaft walls (particularly if of circular or elliptical cross-section) with a smooth continuous lining of monolithic concrete.

Jan 1, 1968

By J. Chipman, H. Towers, M. Paris

A simple radioactive tracer technique is used to measure the diffusion coefficient of calcium ion in molten slags. In a slag of 40 pct Ca0-40 pct Si0,-20 pct Al203, Dc " at 1450°C is 1.3x10-6 cm' sec-'. THE application of the principles of thermodynamics to steel and iron making problems has proved so fruitful that the kinetic approach has tended to be neglected. It seems probable that in some reactions the rate-determining step is the dif-fusivity of the reactants or of the products. But knowledge of the diffusion coefficients of the constituents of liquid slag and metal is singularly lacking. The present work was undertaken as a first step toward supplying such data for slags. Furthermore, any additional information on the physical properties of liquid slags might be expected to help in elucidating their structure. It is essentially a preliminary investigation, the course of which was determined more by the necessity of establishing a method than by the immediate intrinsic interest of the results. For example, the selection of calcium ion to be studied was dictated by the suitability of the isotope Ca45 in that it is a simple emitter with a long half-life. Of the other ions commonly encountered in slags, the isotopes of iron and manganese have relatively complex radiations as well as the normal disadvantage of requiring control of the oxygen potential of the atmosphere; Mg27 and Al29 have half-lives measured only in minutes; Si3' has a simple decay process but its half-life of 2.8 hr is too short for preliminary studies; the only useful oxygen isotope is the stable O18; and there remain only sulphur and phosphorus both of which have suitable isotopes but were rejected as being of less fundamental interest than calcium. Similarly a lime-alumina- silica slag was used in preference to calcium silicate primarily because of its low melting point and its capacity to form a glass on fairly rapid cooling. Literature Review Very few studies of diffusion in liquid silicate systems have been reported. In order to determine the origin of diopside inclusions in felspathic rocks, Bowen1 investigated the diffusion between diopside and various mixtures of albite and anorthite. Platinum crucibles were used with diopside, the heavier of the two liquids, forming the lower half of the cell and diffusion taking place against gravity. Change in concentration along the diffusion path was found by measuring the refractive index of the quenched glass. Nearly thirty years later McCallum and Barrett2 used essentially the same method to determine the diffusion coefficient of lime in lime-alumina-silica slags. In this case the interest was to find the rate-determining step in the process of slag attack on refractory materials. In an investigation of the kinetics of the sulphur reaction, Derge, Philbrook, and Goldman8 determined the diffusion coefficient of sulphur in a typical blast furnace slag by the simple procedure of melting a slag containing 2 pct S over an identical slag sulphur-free. They make no claim to a high degree of accuracy but suggest that D, is of the order of 10-6 cm2 sec-l. Other high temperature liquid diffusion studies have been concerned with metals. Holbrook, Furnas, and Joseph4 determined the diffusion coefficients of silicon, phosphorus, sulphur, manganese, and carbon in liquid iron by immersing a small carbon crucible containing pure iron-carbon alloy in a large vessel containing iron with a high concentration of the particular element. Their results were confirmed by Paschke and Hauttmann5 using a similar method. Diffusion coefficients in silicates in the glassy state have been studied by Johnson, Bristow, and Blau6 Both Na24 and Ca45 were used as tracers but only the

Jan 1, 1954

By J. T. Lapsley, I. I. Cornet, A. E. Flanigan, R. Hultgren, J. E. Dorn

WITH the greatly expanding use of magnesium during the war, it appeared necessary to the War Metallurgy Committee that procedures of heat treating common magnesium casting alloys be investigated systematically. Accordingly, the National Defense Research Committee of the Office of Scientific Research and Development placed a research contract with the University of California, supervised by the War Metallurgy Committee. Research on the solution heat treatment and aging of magnesium alloy AZ92, (formerly ASTM No. 17; also known as Dowmetal C or AM260) which was done under "Restricted" Project NRC-21, in 1942-1943, and reported, in detail in a final report to the OSRD on September 3, 1943, is the basis of this paper, which has been released for publication by the OSRD. American experience with magnesium alloys prior to World War II was limited, although some of these alloys had been in commercial use since 1909. Requirements of the aircraft industry for light alloys made it imperative to understand and utilize the advantageous strength-weight properties of magnesium castings. Magnesium casting alloys are commonly solution heat treated to increase their ultimate tensile strength and ductility; this treatment may be followed by an age hardening at elevated temperatures, which raises the tensile yield strength but diminishes the ductility. In the present investigation, AZ92 was studied to determine the effects on properties of various solution heat treatment and aging schedules. The principles of heat treatment of magnesium alloys are the same as for other non-ferrous alloys. The alloy studied, AZ92, has a nominal composition of 9 pct aluminum, 2 pct zinc, and minor constituents. Fig I shows, by the projection of isothermal sections on the concentration plane, the solubility surface1 of the ternary magnesium-rich solid solutions as determined by X ray analysis. From this figure it may be seen that above approximately 375°C (707°F), AZ92 alloy is a single phase alloy at equilibrium; below this temperature the equilibrium condition is a. two phase alloy. The beta constituent which precipitates from the solid solution exerts a hardening effect. Because the zinc concentration is only 2 pct, and because of its solubility relations, AZ92 resembles a binary alloy of magnesium with aluminum. The solubility curve1 of Fig 2 shows how rapidly the solubility of the beta phase decreases with decreasing temperatures. Unlike many aluminum alloys, magnesium alloys do not age harden at room temperatures; precipitation hardening of AZ92 alloy is performed at about 177°C (350°F). At this temperature about 3 pct aluminum

Jan 1, 1947

By Paul Merica

THOSE of you who, like myself, have had the privilege of hearing previous Howe Memorial Lectures will note, and I hope without too much disaffection, that for the first time in this series of lectures iron has been chosen as the subject. I feel sure that the predominant choice by previous lecturers of subjects relating to steel has been principally in deference to the well-known interest this subject held for Professor Howe, and that their choice has not reflected any lack of respect for the material, iron. Nevertheless, in the face of this record, I feel some diffidence in introducing this "Cinderella" of materials into the circle of distinguished subjects hitherto treated by Howe lecturers, which is relieved only by the fact that I hope to be able to present some evidence that this Cinderella has at last undergone some of those magical trans-formations which render her acceptable even in the society of her dis-tinguished sister, steel. Fortunately I can cite the old master himself in support of my choice of subject and recall to you that Professor Howe by no means overlooked or neglected cast iron in the long course of his metallurgical meditations. Indeed his attention was early arrested by a metallurgical aspect of cast iron which he believed and we still recognize as of the most funda-mental importance-namely, the genesis of graphite in gray iron and the means for the control of its quantity and distribution. He made some comments over 20 years ago regarding the nature of J. E. Johnson's oxygenated iron which indicate that even then his thoughts were taking directions which today we are finding it useful to explore in connection with the theory of high-strength iron. Had we had in the subsequent years the continuing benefit of Professor Howe's illuminating consider-ation of this important subject, our progress in the improvement of cast iron would undoubtedly have been even more rapid.

Jan 1, 1937

By G. K. Dumbauld, B. E. Morgan

Kesults of laboratory investigations of the effects of drilling muds on oil well cements are presented which show that relatively large quantities of untreated muds do not seriously interfere with the setting of cement slurries, but that relalively small quantities of treated muds seriously retard the setting of cement slurries. Laboratory results also indicate that the harmful effects of contamination with treated muds can he counteracted by the addition of activated charcoal to cements. Also described is the successful use of cement containing activated charcoal for the placement of plugs in oPel hole after previous attempts with ordinary cement had been unsuccessful. INTRODUCTION The contamination of cement slurry by dilution with drilling mud has long been considered a cause of failure in oil well cementing. The cement slurry must displace the drilling mud from the annulus between the casing and the walls of the borehole. and it is probable that some mixing of the slurry and the mud occurs even under the most nearly ideal displacement conditions. Hole enlargement, failure to center the casing in the hole, and formation of gel structure in the drilling mud increase the probability of contamination. In some cementing operations, such as the placement of a cement plug in open hole, considerable mixing of the mud and slurry is likely. Many cement failures which can be attributed logically to no cause other than contamination of the cement slurry by the mud attest the need of a better understanding of this problem. Considerable attention was given to the problem of mud contamination of cements about 20 years ago.The effects of field mud upon cement slurries prepared with different amounts of mix water were investigated thoroughly, and the data obtained were invaluable in determining the causes of the high percentage of failure in oil-well cementing at that time and in bringing about improved cementing results. Since then, many aspects of the problem have changed, due primarily to advancements in cement and drilling mud technology. Today, several types of portland cement are used in well cementing and numerous chemical additives are used in drilling muds. An excellent report on the effects of drilling mud additives on oil-well cements was issued during 1951 by the American Petroleum Institute. Data in the report revealed that many mud additives, notably organic materials in relatively small amounts, produce a marked effect on the properties of cements. Prior to this time, little information has been available on the effects of chemicals commonly used in the treatment of drilling muds upon the properties of cements. Another aspect of the problem of mud contamination of cements, which has received no attention heretofore, is the possibility of producing a cement having properties unaffected by a reasonable amount of mud contamination. In view of the need for additional information on the contamination of present-day cements by currently-used drilling Muds, the investigation described herein was initiated Several years ago with a two-fold purpose: first, to determine the capacity of cement slurries to tolerate contamination by both untreated and treated muds without loss of ability to set and develop strength within a reasonable time; and, second, to investigate the possibility of enhancing the ability of cement slurries to withstand mud contamination by incorporating additives in the cement. The data for this study were obtained by mixing drilling mud with cement slurry and testing the resulting slurry-mud mixture for rate of set and development of strength. Also, several materials were tested for their possible improvement of the property of cement slurry to withstand mud contamination; these materials were tested in both contaminated and uncontaminated cement slurries.

Jan 1, 1952

By J. H. O’Dette

BLISTER formation on wrought aluminum products has been a matter of concern to aluminum fabricators for many years. The fact that blisters make their appearance during the final stages of fabrication means that much time and effort have been expended before it is evident that the material must be scrapped. This and the loss of production are ample reasons for embarking on a research program to find out more about blistering and possible methods of control. Many excellent papers on this subject have appeared in the technical literature in the last few years. In one of the more recent papers, Kostronl gives a fairly complete review of the problem of gas in aluminum and blistering in general. From the work of the various investigators, a general mechanism for the formation of blisters has evolved and may be summarized briefly as follows: Hydrogen gas is usually present in the cast ingot, in the atomic or ionic state, in excess of the solid solubility. At room temperature the gas atoms are relatively immobile, but at elevated temperatures they become mobile and diffuse to free surfaces where they associate to form molecules. If these free surfaces are discontinuities within the ingot then the associated gas molecules collect and build up considerable pressure until equilibrium is reached with the dissolved gas around the discontinuity. Since the solubility of the gas is proportional to the square root of the partial pressure it is evident that large pressures may be built up at the discontinuities. When the metal is rolled to sheet the pressure of the gas in these, discontinuities is sufficient to deform the surface of the sheet and form a blister, particularly when the strength of the material is reduced during the annealing. Although the mechanism of the formation of blisters was fairly well known, the actual impor- tance of the individual roles played by the gas and the discontinuities was not so well established that positive methods for control of blistering were at hand. It was the object of the investigation to learn more about the nature of the discontinuities giving rise to blistering and to develop methods of control. The investigation was carried out in three stages as follows: a) A study of the more commonly used methods of removing hydrogen from aluminum, such as fluxing and holding, and their effects on blistering. b) Location of the discontinuities giving rise to blistering. c) A study, by indirect methods, of the movement of gas in the metal and its effect on blistering, and the development of methods of blister control during fabrication. Removing Gas and Reducing Blistering by Fluxing or Holding-—The work of removing gas and reducing blistering by fluxing or holding was carried out on metal of Alcan 2s (1100) composition with an artificially high gas content. The high gas content was obtained by introducing water into the melt prior to casting; the water reacted with the aluminum forming A12O3 and hydrogen. The procedure was to raise the gas content by introducing water into an aluminum melt and using half the melt to cast one ingot immediately. The remaining metal was treated again with water to make up for the reduction in gas content during holding, while the first ingot was being cast, and then given a fluxing or holding treatment and cast into an ingot. Samples for gas determination were cast from the molten metal before and after the gassing operation; before, after, and during fluxing, and while casting. Samples were also cut from sections of the ingots. Gas determinations were made on these samples using the well known vacuum fusion technique. All ingots were hot rolled at 500°C to 0.250-in. slab which, in turn, was cold rolled to 0.040 in. sheet. The sheet was coiled and annealed for 2 hr at 500 °C and then cut into 5-in. squares which were inspected for

Jan 1, 1958

By J. B. Wagstaff, R. A. Buchanan, J. F. Elliott

High speed photography through blast-furnace tuyeres showed coke particles moving rapidly. Model studies showed a raceway was formed and gave quantitative results which were correlated with actual blast furnaces. Another study showed the similarity between hanging and the flooding of a packed column. This was explored by models. THE combustion zone before the tuyere in an iron blast furnace is a vital region because here are generated: 1—most of the gases on which the furnace depends to carry out its basic operation of reducing iron ore to the metallic state, and 2—the major fraction of the heat required in the nearby regions of the furnace for the various reduction reactions, the fusion of the slag, and the melting of the iron. Since the greater part of the coke is consumed in this region, the descent of the burden must be greatly affected by the characteristics of the tuyere zone. This region then would seem to be a profitable field for study. Fortunately, a view into this important zone is available to the operator through the tuyere peep sight. Here he sees relatively dark pieces of coke "dancing" in the blast. What he sees is of considerable help in interpreting the behavior of the furnace at a given time but the very rapidly moving particles and the intense radiation obscures what is happening very deep in the zone. This investigation was initiated in the hope that a better understanding of the combustion region could be obtained by using a high speed camera with a maximum speed of 3000 frames per sec. It seemed the best practical method of "slowing down" this characteristically violent action within the highly luminous field. Model studies and tuyere probing also have been used to aid in explaining the observed phenomena. Above the combustion zone, but below the fusion zone, there is probably a region in which the coke is comparatively stationary. Here are zones in which the gases must flow up through the granular bed counter to descending liquid slag and metal. There is no easy way to observe this zone in a blast furnace, but model studies have been of some help in explaining the nature of the zone and the laws governing the flow of the fluids involved. The whole problem is difficult and involved and any approach to a complete solution may require long investigation. This preliminary report has been written, therefore, because it is believed that appreciable progress has already been made that would be of interest to others. Tuyere Studies, Chemistry and Kinetics It is well known from the early work of Kinney and coworkers1,2 that combustion of carbon before the tuyeres appears to occur in two zones: Zone A: C + O, = CO2; AH77°F. = — 14,108 Btu per lb of carbon [I] Zone B: CO2 + C = 2CO; H77°F = + 6,183 Btu per lb of carbon [2] Zone A (Fig. 1) is close to the tip of the tuyere and zone B is somewhat farther back; there being a transition region in which both reactions occur. It is interesting to estimate the rate at which coke is burned before a tuyere with a wind rate of 90,000 cfm in a modern furnace having 18 tuyeres. Approximately 0.55 lb of carbon is consumed by eq 1 per tuyere per sec. A like amount disappears by eq 2 for a total consumption of 1.11 Ib per sec per tuyere. Assuming the coke is 85 pct C and has a bulk density of 30 lb per cu ft, this figure can be converted to a total of 1.30 lb of coke with a bulk volume of 0.043 cu ft disappearing per sec per tuyere. At the temperatures prevailing in the combustion zone (according to Kozlovich,³ he maximum is about 3400°F), the rate at which carbon is con-

Jan 1, 1953

F. AT. FARMER*, New York (written discussion?)- The paper presents many phases of the welding art concerning which there are very divergent views. In many cases, the wide differences of opinion are based on the results of mechanical tests, but an examination of the mechanical test data discloses a wide variation in character of the tests made and in the details of procedure, so that it is frequently not only difficult to analyze and check the basis of the conclusions but impossible to correlate various groups of test results. It would seem, therefore, that the technique of testing welds is one of the phases of the welding art that should be studied and standardized in order that the results of mechanical tests made by different people may be strictly comparable and have the same significance to all. The vital difference between testing a specimen of steel that includes a welded joint and testing an ordinary specimen is the non-homogeneity of the weld specimen. The weld specimen has at its center a section composed of material that usually has physical, chemical, and metallurgical characteristics distinctly different from the adjoining metal. Furthermore, the section of added metal is more or less irregular and the ratio of added metal to original metal in the section is quite variable. Consequently the details of procedure and of recording data should be more minutely prescribed than in the testing of ordinary specimens. A conspicuous example f a mechanical test that requires standardization is the cold bending test, a standard test for mild steel. With the usual method, the specimen is bent around. a pin of prescribed diameter and, as all specifications usually require bending to 180° without fracture, the manner of applying the load is immaterial because the specimen is ultimately completely wrapped around the pin. But a specimen containing a welded joint at the center will usually not withstand bending to 180° because of the much lower ductility of the deposited metal in the weld. It is therefore obvious that the farther apart the points of support are the greater will be the angle attained before cracking occurs, simply because most of the bending will take place in the original metal. It is therefore highly desirable that there be prescribed a standard test that fixes exactly the distance between the supports, the curvature of the surface of supports, and the relation between this curvature, that of the loading surface, and the thickness of the specimen.

Jan 5, 1919

By J. S. Hegwer, P. M. Dunlap

An improved acid for the treatrrzent of sulfate-con-raining limestones and dolomites is described. The acid is designed to reduce he reprecipitation of dissolved calcium sulfate and the possibility of plugging permeable flow channels. In addition, this improved acid has a much lower reaction rate than that of regular acid; the advantages of a "retarded" acid are obtainable. Field testing of the acid has shown it suitable for use in sulfate-containing formations. Substantial improvements in productivity generally resulted. INTRODUCTION Acid treatments of limestones, dolomites and other formations bearing carbonate deposits are frequently unsuccessful when the calcareous formation contains sulfate, either as anhydrite (CaSO,) or gypsum (CaSO4. 2H2O). Preliminary dissolution in acid followed by redeposition of calcium sulfate appears to be a major factor contributing to poor well performance after acidizing. The precipitate is usually the gypsum form of calcium sulfate, but in higher temperature formations it may be anhydrite. The freshly precipitated crystals are nearly always very small and needle-like. They may occupy a gross volume many times that of the original anhydrite crystals and will obviously constitute an impediment to flow through newly enlarged flow channels. It is believed that the redeposition problem is most severe when anhydrite lines the fracture systems and large pores which supply the effective permeability of a formation. Microscopic inclusions of calcium sulfate also present large sulfate surface areas for dissolution in acid. In either case, great amounts of calcium sulfate may dissolve before the acid can be spent on formation carbonates. For regular spent acid (originally 15 per cent hydrochloric acid) the precipitate could be as much as 270 Ib gypsum/1000 gal acid. Two techniques have been applied by the industry for reducing sulfate plugging during acidizing. The method'.' commonly employed in the field is the attempted removal of a quantity of regular treating acid before it has reacted completely with the formation. This is practiced because the solubility of calcium sulfate is greater in a solution that is still acidic than in one which has been largely spent on the formation rock. The chance of precipitative plugging is therefore reduced if the withdrawal is successful. However, it is often impossible to get the acid out of the formation before precipitation occurs. A second possible method, which at first glance appears practical, involves addition to the acid of sequestering agents which form strong soluble complexes with calcium ions. These chemicals do increase the "solubility" of calcium sulfate in fresh acid, but to a lesser extent in spent acid. The sequestering agents have, therefore, proved unsatisfactory because the amount of sulfate eventually deposited from the spent acid may be greater than that from regular acid. Another logical approach to the problem of calcium sulfate reprecipitation is the prevention of the initial dissolution of calcium sulfate by the common ion effect. This may be accomplished by adding a soluble calcium salt to the fresh acid. The use of calcium salts in treating acids is not entirely new. An earlier suggested use of a soluble calcium salt in hydrochloric acid apparently failed to recognize the full extent to which the solubility of calcium sulfate could be suppressed. The present study extends this earlier work and adds certain improvements toward the development of a practical anti-anhydrite acid. LABORATORY DEVELOPMENT Calcium Sulfate Solubility Table 1 shows the results of a laboratory study performed to establish the effect of calcium chloride concentration on gypsum solubility. Because of the strong tendency of calcium sulfate to form supersaturated solutions, accurate solubilities are difficult to determine. These solubility data probably are reliable to within ± 15 per cent. The solubility of calcium sulfate in 15 weight per cent hydrochloric acid increases with increasing temperature. This trend is also followed in hydrochloric acid which cantains calcium chloride. This is contrary to the solubility behavior of calcium sulfate in water, wherein the solubility decreases with increasing temperature.

By A. Styka, G. Fischer, S. Tour

Described herein are the results obtained during research work involving coating titanium alloys with molybdenum by vapor-deposition methods. Results show that the method can be used successfully to deposit hard adherent wear-resistant coating of methodmetallic molybdenum on titanium or titanium alloys without changing the microstructure of the titanium base. PRODUCTION and use of titanium and its alloys have increased tremendously in the past few years. The physical, mechanical, and chemical properties of this engineering metal have caused considerable enthusiasm among metallurgists and engineers. However, as with all materials, there are some drawbacks. For example, titanium is susceptible to seizing and galling on wearing surfaces. In order to produce a good wear-resistant surface, many investigations have been conducted evaluating oxidizing, carburizing, nitriding, carbonitriding, sili-conizing, and chromizing of titanium. All of these processes require high temperatures for rather extensive periods of time. It has been possible to produce hard surfaces on titanium and its alloys by a number of these processes at the expense of a deterioration of the physical properties of the base material. A practical solution to the problem of providing titanium and titanium alloy parts with a satisfactory wear-resistant nongalling surface must be one that does not involve excessive temperatures for long periods of time. Sam Tour & Co. Inc. has completed a research and development contract for the United States Army Ordnance Corps on vapor deposition of molybdenum on titanium and titanium alloys. On the basis of results obtained from the research program, titanium alloys can be coated successfully with molybdenum to provide a hard wear-resistant surface without harm to their base mechanical properties. The remainder of this article is a description of the techniques used to apply the coating and the results obtained from wear tests on molybdenum-coated titanium. Theory Basically, the technique used was the application of molybdenum by a vapor-deposition method, thermal decomposition of molybdenum hexacarbonyl [Mo(CO)] with hydrogen as the carrier gas. The selection of this method was based chiefly on the following considerations: 1—low plating temperature which would minimize excessive grain growth, 2— low decomposition temperature of the carbonyl, 3— possibilities of controlling the hardness of the plate by adjusting the carbon content using the plating temperature and pressure as the primary variables, 4—use of high vacuum, thereby avoiding unnecessary oxidation and other complex reactions with the atmosphere. Free energy data1 show the strong tendency for titanium to combine with O2 N2 or carbon from normal temperatures to temperatures above its melting point. To maintain the titanium in a film free condition, the use of as high a vacuum as possible is indicated. The literature' indicates that the reaction product of hydrogen with titanium is unstable in vacuum at around 400°C. 5—Although it is indicated from the thermodynamic standpoint that there is little possibility of removing carbon from either titanium or molybdenum, the work of Lander and Germer -ndicates that the use of a suitable H,/CO ratio is somewhat effective in minimizing carbon deposition. 6—Availability of molybdenum carbonyl. In the simplest form, the conditions of equilibrium3 in chemical reactions involving decomposition of carbonyl are as follows: Mo (CO) ? Mo + 6CO 2CO * C + CO,. The plating rate is proportional to the rate of evolution of CO from the decomposed carbonyl, i.e., it is proportional to the pressure of the gaseous decomposition products. Carbon released from CO gas is the significant constituent for the variability of the physical properties of the product. High carbon deposition is favored by increasing pressure. Limitations are imposed in the selection of plating temperature and pressure. Excessive temperature re-

Jan 1, 1956

By Robert H. Richards

The extent to which sizing by sieves should be carried, as a preliminary to the separation, by jigging, of minerals of different specific gravities, has been a matter of controversy for many years. The subject has been investigated by several authorities, yet the ground does not seem to have been completely covered, nor are the questions involved entirely settled. For my present purpose I shall refer to but three investigators—Rittinger, Munroe, and Hoppe. In seeking additional light, I have gone over part of the old ground which has been considered satisfactorily settled; and since these preliminary tests have thrown light on some points, they have been included in this paper. In the investigations here described, I have confined myself, for several reasons, wholly to small sizes—grains of 0.1 inch in diameter and less. Rittinger's work was mainly done upon larger sizes, and there is much need among millmen of information concerning the smaller sizes. Moreover, these sizes brought the investigation within the means at my disposal. The laws that have been claimed as the laws of jigging by the several authorities are: 1. The law of equal-settling particles. 2. The lam of interstitial currents. 3. The law of acceleration. 4. The law of suction. The first of these has been considered by investigators, generally, to be the most important of all, and the larger part of the work of jigging is thought to be governed by it. But that it does not cover the whole of jigging is clear to all; and to account for the increased efficiency which we may call the extra jigging-catch, the other three laws have been advanced. The investigation described in this paper was undertaken to determine, as far as possible, to what extent each of the four laws con-

Jan 1, 1895

By J. H. Scaff, H. C. Theurer, E. E. Schumacher

The microwave region of the radio spectrum was effectively utilized in radar designs during the recent war and it has become of increasing interest in the field of communications. Work in this field has led to an important use for silicon—that of the point contact rectifiers†1 in the frequency converter of microwave (radar or radio) receivers—and has stimulated considerable interest in the electrical properties and preparation of silicon and its alloys. Silicon is an electronic semiconductor. Its conductivity at room temperature results principally from the presence of certain impurities. While for metals an increase in impurity content increases the resistivity, for semiconductors such as silicon the opposite occurs and, in general, the addition of impurities lowers the resistivity. Silicon materials may be classified into one of two groups depending upon the manner in which the impurities contribute to electrical properties. These have been termed for convenience p-type or n-type. P-type silicon develops a very large positive thermal emf against metals, has a Hall coefficient of positive sign and a low resistance direction in point contact rectification with the silicon positive with respect to the point. N-type silicon, on the other hand, develops a negative thermal emf against metals, has a Hall coefficient of negative sign and a low resistance direction in rectification with the silicon negative with respect to the point. Impurities which produce n-type silicon are called donors inasmuch as these elements contribute to electrical conductivity by donating electrons to an unfilled energy band in the silicon. On the other hand, elements which produce p-type silicon are known as acceptors as these impurities contribute to the electrical conductivity by accepting electrons from a filled energy band permitting what is known as conductivity by "holes" in which the sign of the carriers appears to be positive. A general treatment of the mechanism of conduction in semiconductors from the viewpoint of modern band theory has been given recently by Pearson,2 by Becker, Green and Pearson,3 and by Torrey and Whitmer.4 In this investigation boron and aluminum have been found to be acceptors, and phosphorus, arsenic, and antimony to be donors in silicon. Data on the effect of boron and phosphorus on the electrical properties, when present singly and in combination, have been acquired. These data are discussed in the present paper. Raw Materials Used and Methods for Adding Seeond Constituents Silicon from two sources was used in this work and these will be referred to as A and B respectively. Silicon A is a material of high purity supplied by the Electro Metallurgical Co. It is prepared by chemical purification of "commercial" silicon obtained from the arc furnace reduction of SiO2. It contains 99.8 pct silicon, minimum, with small amounts of calcium, iron, aluminum, boron, and phosphorus as the principal impurities. This material was extensively employed in these studies as well as in the commercial preparation of rectifier materials. Silicon B is a material of high purity from the du-Pont Co. It is prepared by a pyrolytic reduction of Sicl4 and is free of analytically detectable amounts of boron and phosphorus. Its use permitted study of the effect of boron and phosphorus individually on the properties. This material contains, however, spec-troscopic traees of a number of metals, some of which affect electrical and rectification properties. Typical analyses for the two grades of silicon are given in Table 1. To make controlled additions of boron to the charge it was necessary to employ a low boron content master alloy since the quantity of boron to be added was usually only a few thousandths of one percent. The alloy containing nominally one percent boron was prepared by melting chemically pure boron with silicon A using the melting techniques for 320 g silicon

Jan 1, 1950

By Roy Lindgren

SINCE the year 1643, when the first blast furnace in America for treating iron ore was built at Saugus, Mass., out of mica schist quarried in the neighboring district, the procurement of a suitable refractory for furnace lining has been a problem of concern to the operators of furnaces. The stacks built of mica schist continued to smelt iron ore until about 1836, when, according to F. H. Norton, the first firebrick were produced1, at Queens Run, Pa. Other writers speak of brick having been molded and burned in Massachusetts about the year 1834. In 1841, Andrew Russell began to produce medium refractory plastic clay brick near East Liverpool, Ohio, that were used for lining blast furnaces1. The well-known Kentucky clay-producing district was not opened up until the year 1871, but since then it has produced a large percentage of the linings for iron blast furnaces. While some strides have been made by the refractories industry during the 100 years that have passed since the first firebrick were produced, it has been only during the last two decades that any real progress has been made towards bettering the product, even though the method of production had improved. Perhaps the fault lies with the user of the brick rather than with the producer, for not sooner demanding a supe-rior product. During the past 15 years the tonnage produced per lining has increased from 500,000 gross tons to 1,000,000 gross tons, and now some furnaces are producing 1,600,000 gross tons and better on a single lining. It is true that enlarged capacity of furnaces and improved practice have accounted for some of this increase in tonnage, nevertheless better quality in firebrick must be given credit for its share. However, we are not yet ready to say that we have reached a maximum life of furnace lining. We believe that a better product can be produced and that the refractories industries of America will, through their extensive research depart-

Jan 1, 1937

By F. F. Peng, A. D. Walters, M. R. Geer, J. W. Leonard

INTRODUCTION Washability characteristics derived from float-and-sink analysis in Chapter 4 demonstrate that coal is intrinsically heterogeneous, and this heterogeneity is also evident in the proximate, ultimate, and size analyses. A range of particles from high to low specific gravity is usually seen in the run-of-mine coal. One objective of coal preparation is to recover the high quality float material (the particles of lower specific gravity) such that the recovered product meets certain quality specifications, as well as to reject or recycle low quality particles of higher specific gravity. The maximum recovery of cleaned coal at the required quality is of major concern to plant operators. However, the quantity and quality of products of coal cleaning, determined in the operation of actual commercial cleaning plants and by theoretical calculation based on run-of-mine washability studies, are known to be different with each coal. Therefore, during the last half century, coal preparation engineers have repeatedly sought methods to predict the technical and economical efficiency of separation of cleaning equipment and systems. Many formulas have been proposed by international investigators to evaluate the efficiency of various coal cleaning operations, primarily based on the yield and/or ash of the various products of coal cleaning. Performance criteria in use today are capable of defining all of the important aspects of a given concentrating operation; however each criterion has certain restrictions or limitations. It is important, therefore, to understand how such formulas can be used and the problems involved in their construction. Technical Measure of Plant Performance Conventional means for evaluating a preparation plant's performance are generally approached through the use of equipment performance mea-

Jan 1, 1979

Abdul-Ahad. A., Student, Montana School of Mines, Residence Hall Butte, Mont. '39 Abramovits, Charles, Student, Case School of Applied Science Cleveland, Ohio. '37 Abreu, Ovidio M., Student, Univ. of Nevada Reno, Nev. '38 Acker, Voscoe, Student, Agricultural & Mech. College of Texas College Station, Tex. '39 Adams, Albert, Student, New Mexico School of Mines Socorro. N. M. '38 Adams, Charles W., Student, Michigan College of Min. & Tech Houghton, Mich. '39 Adams, Hugh T., Jr., Student, Univ, of Oklahoma Norman, Okla. '39 Adams, Jack L., Student, Univ. of Oklahoma Norman, Okla. '39 Adams, Jack M., Student, Univ of Alaska College, Alaska. '39 Adams, Lewis J., Student, Agricultural & Mech. College of Texas, Box 2514, College Station, Tex. '39 Adams, Robert E., Research Engr., Battelle Memorial Inst Columbus, Ohio. '38 Adamson, George M., Jr.. Student, Univ. of Utah Salt Lake City, Utah. '39 Adkisson, J. F., Jr., Student, Agricultural & Mech. College of Texas, Box 1003, College Station. Tex. '38

Jan 1, 1939

By B. F. Oliver, F. Garofalo

Gas-metal heterogeneous reactions and zone-lrelting were sinultarneously employed to produce several high-purity irons with low interstitial contents in a levitating- zone melter. Successive zone-tneltitzg pusses were made in carious sequences of atmospheves which included prepuvified tank hy-drogeta, water vapor hydrogen, palladiuril-purified hydrogen, and vacuunm of 2 x 10-6 Torr. Different irons ranging in purity from 99.89 to 99.996 pct with residual curbon contents of 17, 8 to 10, and 3 to 5 ppm have been Drepared. No measuvable gradient in the residual carbon content was observed along the entire zone-melted length (6-10 in.) in I-ilz.-diameter bars. The absence of a carbon-concentration gradient in the solid indicates an apparent distvihution coefficient of 1, an unusual condition. Internal friction, solid-state extraction, and hot-hardness results indicate that the level of mobile carbon in a iron depends on the gas-metal heterogeneous reactions employed. Purification under an oxidizing atmosphere resulted in the immobilization of nearly all of the carbon present at leuels of 10 ppm or less. Continuation of purification in a reducing atmosphere veturued the carbon to a state of mobility which was aguin reversed by further purification in all oxidizing atmosphere. The immobilization of curbon at "vesidual levels " is believed to be associated with a strong interaction between carbon and oxygen atoms. frons with low carbon and nitrogen contetzts which did not exhibit a hot-hardness peak were produced after zone ynelting in vacuum. CARBON, nitrogen, and oxygen have strong and well-known effects on many properties of iron. These effects persist even at concentrations of 5 to 20 ppm. The intent of the present investigation was to establish procedures for the preparation of high-purity iron with concentrations of these elements in the range of 5 to 20 ppm and lower. The results reported here deal with the procedures employed to prepare high-purity iron, and with observations on the behavior of certain elements at "residual levels": particularly carbon. The details of the (levitating) zone melter in which the final purification steps are performed and the necessary control of the pertinent solidification variables have been described previously.1,2 MATERIALS AND PROCEDURES Commercial electrolytic iron was induction vacuum-melted and cast into 30-lb ingots. Melt additions and ingot analyses for carbon, oxygen, and nitrogen are noted in Table I. All ingots were melted in stabilized zirconia crucibles conditioned with one iron wash heat. Middle sections of the ingots were forged to 1-1/4-in. rounds, machined to 1-in.-diameter bars, then cut to 36-in. lengths. The zone-melting operations were performed on six iron bars (A to F) at a freezing velocity of 2 in. per hr with the freezing interface rotating2 at 200, 300, or 400 rpm. Liquid zones were passed through the bars in various sequences of atmospheres, Table 11, including prepurified tank H2, palladium-purified Hz, wet H2, and system vacuum of 2 x 1018 Torr. Wet-Hz atmospheres were obtained by bubbling palladium-purified Hz through water exhibiting a resistance of 3 megohms. This water was heated with a platinum-immersion heater and was degassed prior to use. Zone melting in a wet-HZ atmosphere resulted in oxidation of the elements which are oxi-dizable with respect to iron. Fine oxide particles were observed on the surface of the liquid zone, and were encased in the bar surface with the passage of the molten zone. Between each zone pass, the surface of the bar was removed by filing and deep etching; this was continued until the oxide formation ceased. The filings were magnetically separated and the residues analyzed by optical spectroscopy. These were especially high in silicon and manganese. Samples were removed from the iron bars, with few exceptions, following each zone-melting operation. A 0.08-in.-thick disc was cut with an Al2O3 cut-off wheel at a point 1/2 in. above the beginning of freezing. Material from each disc was used for hot-hardness measurements, resistivity-ratio measurements, and carbon, nitrogen, and oxygen analyses. Analyses for most other elements were

Jan 1, 1965

By N. L. Carwile, G. W. Geil

A metallographic study was made of deformation twinning (Neumann lamellae) in ingot iron slowly deformed in tension at —196O and —150°C. The results showed that twinning is initiated mainly during the initial stages of plastic deformation. However, the breadth of the twins generally increases with increase in strain up to fracture of the specimen. HE results of an investigation of the effect of low I temperatures on the flow, fracture, strain hardening, and strain aging characteristics, and the true stress-strain relationship for specimens of ingot iron deformed in tension were reported recently.1,2 In that study specimens of ingot iron, in different initial conditions, were slowly deformed in tension at various temperatures between —196" and +100°C. A phenomenon observed, but only briefly reported, was the formation of deformation twins (Neumann lamellae) in the specimens deformed at the lower temperatures. Preliminary metallographic examination of these specimens indicated that there was apparently some correlation between the deformation twinning and the strain of the specimen and that this factor merited further investigation. Some recent investigations have indicated a direct association of Neumann lamellae and the fracture of the metal. Bruckner".' * postulated that the twinning immediately precedes the fracture and the latter is initiated by the stopping of the propagation of twins, either at subgrain boundaries or at other structural features. Tipper and Sullivan5 postulated that Neumann lamellae are initiated by the shock or a shock wave set up at fracture in the still highly stressed unbroken metal, and that a high rate of deformation is a necessary condition for their formation. An extensive metallographic examination, therefore, was made of many of the specimens used in the study of ingot iron at this Bureau and of additional specimens deformed to selected strains under various conditions. The present paper summarizes the effects of deformation under these conditions upon the breadth and scope of the deformation twins. Other features of twinning will be discussed in another paper. Material and Testing Procedure All of the specimens were prepared from one lot of ingot iron, as hot-rolled, of chemical composition other than iron as follows: C, 0.02 pct; Mn, 0.02; P, 0.005; S, 0.018; Si, 0.002; Cu, 0.10; 0, 0.058; and N, 0.002. Cylindrical tensile specimens with a 2 in. gage length were used. The reduced section was slightly tapered from each end; the diameter (0.438 in.) at the midsection of the gage length was about 0.003 in. less than at the ends. The specimens were finished to the final dimensions by grinding and polishing in the axial direction. The ends of the specimens were machined with 3/4 in. x 10 threads and the shoulder fillets were machined to a radius of 0.75 in. The specimens were extended slowly in tension (deformation rate less than 0.5 pct reduction in area per minute) while immersed in an appropriate cryogenic liquid maintained at the desired temperature. The minimum diameter of the specimen was measured during the test by means of a specially designed reduction of area gage accurate to 0.0001 in." A detailed description of the testing equipment and the method of maintaining the desired temperature is given in a previous paper.' Each specimen, after deformation to a specified strain at a selected temperature, was sectioned longitudinally and examined metallographically. The preparation of specimens for metallographic examination was carried out in the usual manner by mechanical polishing and etching. Results and Discussion Deformation twins in specimens of ingot iron extended slowly in tension at —196" and —150°C are shown by the representative micrographs of Figs. 1

Jan 1, 1954

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969