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By F. G. Jones, R. D. Pehlke, H. E. Gardner

The solubility of nitrogen in liquid Fe-18 pct Cr-8 pct Ni-0. 7 to 2.3 pct A1 alloys has been measured up to the solubility limit for the formation of aluminum nitride in the temperature range 1600° to 1700°C uszng the Sieverts' method. The solubility of nitrogen in 18-8 stainless steel increases with increasing aluminum content. Based on a nitride composition, AlN, the standard free energy of formation of aluminum nitride from the elements dissolved in liquid 18-8 stainless-steel alloys has been determined to be: ?G° = -42,500 + 20. IT in the range from 1600° to 1700° C. EVANS and pehlke1 have measured the equilibrium conditions for the formation of aluminum nitride, AlN, in liquid Fe-A1 alloys. The present study extends that work to the more complex solvent, liquid 18 pct Cr-8 pct Ni (18-8) stainless steel. Recent work by Small and pehlke2 has dealt with the effect of fourth-element additions on the solubility of nitrogen in 18-8 base alloys. They found the effect of aluminum additions, up to 0.74 pct, on the solubility of nitrogen to be small. The present study covered the range from 0.74 to 2.28 pct aluminum, and by extending the composition range may be used to better define the effect of aluminum on the nitrogen solubility in these alloys. EXPERIMENTAL PROCEDURE The Sieverts' method was used to measure the equilibrium solubility of nitrogen gas in liquid 18-8 stainless steel alloys containing 0.74, 1.49, 1.93, and 2.28 pct Al. The solubility was measured as a function of the nitrogen gas pressure at temperatures of 1600°, 1650°, and 1700°C. The apparatus used is the same as described by Small and Pehlke.2 The 100-g melts were made from Ferrovac-E high-purity iron, Crucible Steel Co.; 99.95 pct Cr, Union Carbide Corp.; 99.9 pct Ni, International Nickel Co.; and 99.99+ pct Al, Aluminum Co. of America. The aluminum was charged at the bottom of the crucible, surrounded by nickel and iron. The chromium was packed into the interstices to minimize vapor transport of the aluminum during initial melting. The hot volume of the system, measured for each melt with argon, ranged from 45 to 55 standard cu cm with a temperature coefficient of —8 x 10-3 cu cm per °C. The melt temperature was measured with a Leeds and Northrup disappearing-filament type optical pyrometer sighted vertically downward on the center of the melt surface. The temperature calibration of the system by Small and pehlke2 was assumed. Two problems are involved in determining the solubility product of a solid, metal nitride phase in liquid iron alloys. These are: 1) establishing the point of departure from Henrian behavior at the solubility limit of the metal nitride phase; and 2) determining the composition of the solid nitride which is precipitated. Determination of the solubility product of AlN was made by admitting small amounts of nitrogen into the reaction bulb until the deviation from Sieverts' law was clearly evident in the form of a pressure halt. To obtain the solubility product at several temperatures during one run the following procedure was used: 1) add increments of nitrogen to determine the Sieverts' law line at the lowest desired temperature; 2) continue to add nitrogen to precipitate a small amount of the nitride phase; 3) increase the melt temperature 50°C to dissolve the precipitated nitride; 4) repeat step 2 until either a nitride formed or the system reached ambient pressure; if a nitride formed at 1650°C, the sequence was repeated at 1700°C. The composition of the precipitated phase was checked by an X-ray diffraction pattern obtained from powder scraped from the surface of the solidified 1.93 pct A1 melt. RESULTS AND DISCUSSlON Solubility Measurements. Fig. 1 is a typical nitrogen-absorption curve obtained from measurements on a 1.93 pct A1 alloy. Since the initial absorption of nitrogen follows Sieverts' law the nitrogen solubility is plotted as a function of the square root of the pressure of nitrogen gas in the reaction bulb. The results of the solubility measurements for all alloys studied are summarized in Table I. The slope of the Sieverts' law line for each alloy was determined. Since this is also the solubility of nitrogen at 1 atm pressure of nitrogen gas, the latter designation is used for the data. It should be noted. however, that in most cases the value lies above the solubility limit for AlN. Fig. 2 shows the effect of aluminum on the solubility of nitrogen at this reference pressure and as a function of melt temperature. The solid portions of the lines represent attainable solutions; the dashed regions lie above the limit for precipitation of AlN.

Jan 1, 1969

By J. H. Swisher

The solubility of graphite in CaO-S2O2-Al,O3 slags was measured by equilibrating slag samples with graphite crucibles and CO gas. Carbon contents as high as 2 ut pct were obtained in CaO-saturated, CaO-A1,O3 slags, and 1.3 wt pct in slags of the composition CaO.Si0,. Although the observed conditions for Sic formation were in agreement with those predicted from thermodynamic data, CaC, was found to form at a lower temperature than predicted frotn thermodynamic data. From measurements of the equilibrium carbon content as a function of CO Partial pressure, it was found that carbide ions dissolve in CaO-A12O3 melts with a valence of minus two. The carbon content increased with CaO concentration in Ca0-Al,O3 melts and increased with SiO, content along the CaO'AlO3-CaOSi0 join in the ternary system. When solid CaC2 was added to CaO-A12O3 and CaO-SiO2-A12O3 slags, it was found that one of the oxides in the slag was reduced by the carbide (Al2O3 in the forrner and SiOz in the latter). In electric furnace steelmaking, a double-slag practice is frequently used to meet alloy specifications. Initially a flush slag, which is oxidizing in nature, is used to remove phosphorus and carbon from the steel bath. Later in the refining period, the flush slag is replaced by a highly reducing carbidic slag. When calcium carbide is formed in or added to a finishing slag, the slag is effective as a desulfurizing agent and also permits alloying elements such as chromium, vanadium, and tungsten to be added to the slag in the form of oxides. The oxides are readily reduced by calcium carbide, thereby minimizing the use of expensive ferroalloys. More work has been done on the thermodynamics of silicon carbide in slags than on calcium carbide. Baird and alor' and Kay and alor' determined the free energy of formation of Sic by measuring the partial pressure of CO in equilibrium with solid silica, silicon carbide, and graphite. Using a similar technique, they determined SiOz activities in CaO-SiOz and Ca0-Si0,-A1203 slags. Rein and chipman3 also determined the free energy of formation of Sic using slag-metal equilibrium measurements. A literature survey has uncovered only one experimental study of the behavior of CaC, in slag systems. Shanahan and cooke4 report the results of some preliminary experiments on the solubility and stability of CaC, in a CaO-A1,03 and a Ca0-Si0-A1,03 slag at a temperature of about 1500". The carbon solubility as CaC, in a slag containing 50 pct CaO and 50 pct A1203 was reported to be 0.6 pct. They also review earlier work on the binary CaO-CaC, system. A eutectic exists in this system, but various investigators disagree on the eutectic temperature and composition. eal has given an explanation for carbide furnace erruptions in terms of the thermodynamic properties of CaC,; his analysis is not based on experimental data, but on compiled data for the free energies of formation of CaC, and CO.' , These data for steel-making temperatures are all extrapolated from the results of low-temperature measurements. In the experiments described in this paper, slag samples were equilibrated with graphite crucibles and with mixtures of CO and argon or with CO gas at 1 atm total pressure for measurement of the carbon solubility. Most of the work was done on Ca0-A1203 binary slags, although in some experiments CaO-SiO, and Ca0-Si0,-A1,03 slags were used. EXPERIMENTAL Slag samples of the desired composition for the solubility measurements were obtained by blending pre-fused master slags. The master slags were prepared by fusing mixtures of reagent-grade CaC03 with either A1,03 or Si0, in a graphite crucible. The master slags were crushed, then decarburized in air in a muffle furnace at 1200O C. A schematic diagram of the apparatus is shown in Fig. 1. The source of carbon for the solubility meas-

Jan 1, 1969

By R. E. Smallman, I. Milne

The deformation behavior of single crystals of Nb-Mo alloys has been investigated with particular reference to the influence of composition, orientation, and temperature. Strong solid-solution hardening was observed reaching a maximum at the equiatomic cotrlposition and can be attributed to the difference in atomic size between niobium and molybdenutrz. Changes in the form of stress-strain curve, as shown by a high work-hardening rate and restricted elongation to fracture, were observed at a composition of Nb-85 pct Mo and are attributed to the presence of MozC DreciDitate. Conjugate slip was only extensive in dilute alloy samples; at the 50/50 composition deformation rnainly occurred by primary slip, and the onset of conjugate slip gave rise to failure by cleavage on (100). The variation of yield stress of Nb-50 pet Mo with orientation was consistent with slip on (011)(111) slip systems. The temperature deperndence of the yield stress between -196" and 250°C was similar to that of pure bcc metals, but at a much higher stress level; no evidence for twinning %as found. IN recent years the deformation behavior of various pure metals in groups VA and VIA has received considerable attention, but surprisingly little work has been carried out on binary alloys made by mixing metals from the two groups. Such an investigation would be of interest since single crystals of metals of group VA have been shown to deform characteristically with a multistage deformation curve1"3 while a parabolic type of deformation curve has been reported for most of the group VIA metals.4'5 It has been suggested by Law ley and Gaigher~ that the difficulty encountered in obtaining multistage deformation curves for molybdenum in group VIA was possibly because of the presence of a microprecipitate of MozC which they observed even at carbon contents as low as 11 ppm. Recently a multistage deformation curve has been reported for molybdenum ," although the stages are not so definitive as those for group VA metals. The binary alloys of the particular refractory metals which have been investigated in single-crystal form include Ta-w,' Ta- Mo,' and Nb- Na." While a large amount of hardening was observed for alloys of the Ta-W and Ta-Mo systems, associated with room-temperature brittleness for alloys approaching the equiatomic composition, Ta-Nb remained ductile over the complete composition range with little or no solution hardening. Other systems have been investigated by hardness measurements on polycrystalline material and a discussion of the hardening of these alloys has been presented by ~udman." The purpose of the present investigation was to examine the deformation behavior of Nb-Mo alloys in detail, with particular reference to alloy composition and single-crystal orientation. In this way it was hoped to shed some light upon the restricted ductility of these alloy specimens. 1) EXPERIMENTAL PROCEDURE The starting materials were obtained in the form of beam-melted niobium rod and sintered molybdenum rod of suitable dimensions. Since niobium and molybdenum form a complete solid-solution series at all temperatures, alloy single crystals were produced by melting the two constituents together in an electron bombardment furnace (EBM). To produce specimens free from segregation a molten zone was passed over the length of each rod six times in alternate directions at a speed of 10 in. per hr. Typical specimens were analyzed for interstitial impurities by gas analysis and for metallic impurities by spectrographic analysis. The results of this analysis are shown in Table I. Many of the tensile specimens were also analyzed (after testing) by scanning the gage length in an electron beam microanalyzer, from which it was found possible to predict the approximate composition of a specimen from the original proportions of each element in the EBM. The tensile specimens were made with a gage length of 0.5 in. and diameter of 0.075 in., using a Servomet Spark machine. By careful machining on the finest range for the final i hr of this technique, surface cracks could be reduced to the level where they were easily removed by electropolishing in a solution of nitric and hydrofluoric acids. The specimens were strained at a rate of 10 4 sec-' using friction grips designed to prevent accidental straining and maintain a good alignment before straining. The orientations of the individual specimens tested are shown in Fig. 1 and the corresponding compositions listed in Table I1 together with collated experimental data. 2)RESULTS a) General Deformation Behavior. The effect of composition on the room-temperature deformation curves of similarly oriented specimens is shown in Fig. 2. The yield stresses of the pure constituents, while not the lowest reported to date, were at least comparable with existing data. Although the solution hardening was large for alloys at either end of the phase diagram, and comparable with the Ta-W solution-hardening data of Ferris et a1.,8 the low work-hardening rate characteristic of niobium was sustained until a composition of Nb-85 pct MO had been reached. Associated with the peak yield stress ob-

Jan 1, 1969

By L. R. Weisberg, E. A. Miller

Single-crystalline films of silicon of good quality were vacuum-deposited on sapphire. The improved crystallinity was achieved by the strict exclusion of oxygen from the evaporation system, including the use of a "oxygen-free" silicon source. To minimize possible contamination of the source, the silicon was sublimed from the solid at about 1390° C. using a simple electron bombardment system to heat the silicon. This resulted in deposition rates of about 5 to 7 µ per hr and film thicknesses of 4 to 20 µ. The vacuum during deposition was ordinarily about 5x 10-8 Torr, DESPITE the success achieved in the chemical vapor deposition of silicon on sapphire using Silane,1-4 vacuum deposition has not provided comparable properties. For example, Chu et a1.5 vacuum-deposited silicon on single-crystalline substrates of A12O3, Sic, ThO2, and other compounds, and, although some epi- but the use of ultrahigh vacuum (about 1 to 3 x10-9 Torr) during deposition did not significantly improve the results in the oxygen-free system. The crystalline quality of films deposited on (0001) sapphire was found to be considerably superior to (1102) sapphire surfaces. Using (0001) sapphire, single-crystalline films were deposited at temperatures as low as 780° C and as high as 1075°C, with the best crystalline quality obtained at about 1000°C. At this temperature, hole mobilities over 250 sq cm per v-sec were achieved. taxy was indicated, single-crystalline films were not produced. More recently, Salama, Tucker, and young6 evaporated silicon on single-crystalline sapphire, but only poor crystallinity was observed, and low carrier mobilities were measured. In the present experiments, good-quality single-crystalline films of silicon on sapphire have been achieved by specifically excluding oxygen from the evaporation. This included not only the use of a "clean" vacuum system but, of special importance, the use of an oxygen-free silicon source. This has also been shown to provide a dramatic improvement in silicon homoepi-taxy.7 As a result, silicon-on-sapphire films with hole mobilities over 250 sq cm per v-set were achieved, and single-crystal films were grown as low as 780°C and as

Jan 1, 1969

By Richard J. Fruehan

ThE thermodynamic activities of nickel and chromium in liquid Ni-Cr alloys have not been previously reported. There have been several investigations on the solid alloys.1-3 In the present investigation the activity of chromium in liquid Ni-Cr alloys at 1600° C was determined by the use of the following galvanic cell, The use of galvanic cells employing solid oxide electrolytes for determining the activity of metals in solid alloys was first demonstrated by Rapp and Maak4 on Cu-Ni alloys between 700° and 1000°C. Recently Schwerdtfeger5 tested the performance of the ZrO2(CaO) electrolyte at 1600°C and found it satisfactory for oxygen pressures as low as 10"12 atm. He also demonstrated the use of solid oxide electrolytes for determining the activities in liquid metal systems in measuring the activity of manganese in Fe-Mn alloys at 1500°C. Extensive investigations have been carried out in this laboratory, exploring the oxygen partial pressure lower limit at which ZrO2(CaO) electrolyte can be used satisfactorily in oxygen galvanic cells at 1600°C. In a paper to be published at a later date,9 it is demonstrated conclusively that ZrO2(CaO) exhibits insignificant electronic conductivity at oxygen pressures down to about 3 x 10"13 atm which is lower than the oxygen partial pressure in equilibrium with Cr-Cr2O3 at 1600°C. Therefore, the activity of chromium can be related to the measured reversible electromotive force of the cell in the present investigation since no electronic short circulating will occur. Fig. 1 is a schematic diagram of the cell used. The Cr-Cr2O3 electrode was made of equal weights of chromium and Cr2O3 powders which were mixed and packed into a recrystallized alumina crucible. A Pt-wire lead was embedded into the Cr-Cr2O3 compact to insure good contact. A ZrO2(CaO) crucible, supplied by the Zirconium Corp. of America, contained the Ni-Cr melt equilibrated with solid Cr2O3. The ZrO2(CaO) crucible was placed on the Cr-Cr2O3 electrode and additional Cr-Cr2O3 mixture was packed around it. Contact with the Ni-Cr alloy was made with a Cr2O3 tube, which is a weak electronic conductor. A platinum wire lead was attached to the Cr2O3 tube. The galvanic cell was lowered slowly into the hot zone of the furnace tube in order to avoid too large a thermal shock which could break the ZrO2 (CaO) crucible. The furnace was con- tinuously flushed with purified argon during the experiment. The temperature was measured with a Pt-Pt/10 pet Rh thermocouple and maintained at 1600° ± 5°C. The electromotive force was measured with a recording potentiometer. The furnace was turned off when measurements were being made in order to avoid induction effects and the reversibility of the cell was demonstrated in the usual manner. The electromotive force was measured several times over a period of approximately 1 hr. During that period the electromotive force remained constant within ± 3 pet and did not continuously drift in any one direction. After the experiment the alloys were analyzed for chromium in the usual manner. The measured electromotive forces of the cell at 1600°C, (2912°F), are listed in Table I. The activity of chromium, with solid pure chromium as the reference state, (a), was calculated using Eq. [l], , n F E I, n lna RT- U] where E is the measured electromotive force, F is the Faraday constant, and n is equal to 3, the number of equivalents per mole, (nF/RT = 18.59 volts'1 at 1600°C). The resulting activities are listed in Table I. The activity of chromium relative to pure liquid chromium was also calculated. The free energy of fusion of chromium at 1600° C was calculated using

Jan 1, 1969

By Charles E. Lundin

The character of the Er-D system was established by determining pressure-temperature-composition relationships. A Sieuerts&apos; apparatus was employed to make measurements in the temperature range, 473" to 1223"K, the composition range of erbium to ErD3, and the pressure range of 10~s to 760 Torr. The system is characterized by three homogeneous phase regions: the nzetal-rich, the dideuteride, and the trideuteride phases. These phases and their solubility boundaries were deduced from the family of isotherms of the system zchich relate the pressure-temperature-composition variables. The equilibrium plateau decomposition relationships in the two-phase regions were determined from can&apos;t Hoff plots to be: The differential heats of reaction in these two regions are AH = - 53.0 * 0.2 and -20.0 *0.1 kcal per mole of D2, respecticely. The differential entropies of reaction are AS = - 36.3 * 0.2 and - 31.0 * 0.2 cal per mole D2. deg, respectively. Relative partial molal and intepal thermodynamic quantities were calculated from the pure metal to the dideuteride phase. The study of the Er-D system was undertaken as a logical complement to an earlier study of the Er-H system.&apos; The primary interest was to compare the characteristics of the two systems and relate the difference to the isotopic effect. Studies of rare earth-deuterium systems by other investigators have been very limited in number and scope. Furthermore, there is even less information available wherein an investigator has systematically compared a binary rare earth-hydrogen system with the corresponding rare earth-deuterium system. The available information consists primarily of dissociation pressure measurements in the plateau pressure region of a few rare earths. Warf and Korst&apos; determined dissociation pressure relationships for the La- and Ce-D systems in the plateau region and several isotherms for each system in the dideuteride region. They compared these data with those of the corresponding hydrided systems. The study of these systems as a whole was very cursory and did not give sufficient data for a thorough comparison of the effect of the hydrogen vs the deuterium in the respective rare earths. The heat capacities and related thermodynamic functions of the intermediate phases, YH, and YD2, were determined by Flotow, Osborne, and Otto,~ and the investigation was again repeated for YH3 and YD3 by Flotow, Osborne, Otto, and Abraham.4 This investigation studied only these specific phases. Jones, Southall, and Goodhead5 surveyed the hydrides and deu-terides of a series of rare earths for thermal stability including erbium. They experimentally determined isotherms of selected hydrides and plateau dissociation pressures for deuterides. These data allowed comparison of the enthalpy and entropies of formation of the dihydrides and dideuterides. To date, no one rare earth has been selected to thoroughly establish the complete pressure-temperature-composition (PTC) relationships of binary solute additions of hydrogen and deuterium, respectively. The objective in this investigation was to provide the first comparison of a complete family of isotherms of a rare earth-deuterium system with those of a rare earth-hydrogen system. This would allow one to determine what differences exist, if any, in the various phase boundaries and the thermodynamic relationships in various regions of the systems. I) EXPERIMENTAL PROCEDURE A Sieverts&apos; apparatus was employed to conduct the experimental measurements. Briefly, it consisted of a source of pure deuterium, a precision gas-measuring buret, a heated reaction chamber, a mercury manometer, and two McLeod gages (a CVC, GMl00A and a CVC, GM110). Pure deuterium was obtained by passing deuterium through a heated Pd-Ag thimble. A 100-ml precision gas buret graduated to 0.1-ml divisions was used to measure and admit deuterium to the reaction chamber. The reaction unit consisted of a quartz tube surrounded by a nichrome-wound furnace. The furnace temperature was controlled by a recorder-controller to . An independent measurement of the sample temperature in the quartz tube was made by means of a chromel-alumel thermocouple situated outside, but adjacent to, the quartz tube near the specimen. Pressure in the manometer range was measured to k0.5 Torr and in the McLeod range (10~4 to 10 Torr) to *3 pct. The deuterium compositions in erbium were calculated in terms of deuterium-to-erbium atomic ratio. These compositions were estimated to be *0.01 D/Er ratio. The erbium metal was obtained from the Lunex Co. in the form of sponge. The metal was nuclear grade with a purity of 99.9+ pct. The oxygen content was reported to be 340 ppm and the nitrogen not detectable. Metallographically the structure was almost free of second phase (<i vol pct). A quantity of sponge was arc-melted for use as charge material. The solid material was compared with the sponge in the PTC relationships. They were found to be identical. Therefore, sponge material was used henceforth, so that equilibrium could be attained more rapidly. The specimen size was about 0.2 gr for each loading of the reaction chamber. The procedure employed to obtain the PTC data was to develop experimentally a family of isothermal curves of composition vs pressure. First, a specimen

Jan 1, 1969

By V. J. Southey

"This paper reviews the history of Wabana Mines from 1892 to 1966, inclusive, in order to clarify the essential factors involved in the achievement of maximum mining efficiency and in the search for an acceptable product to satisfy changing market requirements. It outlines the progressive steps taken to mechanize both surface and underground operations, and forecasts anticipated performance, assuming certain major plans could have been implemented. Results of extensive research in the treatment of the complex ore are discussed. Selected processing alternatives are compared as to feasibility in a summary incorporating estimated capital and operating costs."

Jan 1, 1969

A saturated, metal-free solution of alum can be used as a fiocculant to speed up the sampling procedure during a geochemical survey of stream silts.

Jan 1, 1969

By J. R. Bell, W. J. Childs, J. H. Bucher, G. A. Wilber

A technique for determining recrystallization times as short as 0.10 sec was developed utilizing the "Gleeble", a commercially available testing system designed for the study of short-time, high-temperaLure themal and mechanical processes. The procedure consisted of heating a small tensile specimen to a given temperature of hot deformation, loading to a given reduction in area, unloading, delaying various intervals at temperature, and then reloading- to failure. The magnitude of the ultimate load obtained upon reloading decreased with delay lime as recrys-lallization proceeded. The technique was applied to austenite recrystallization in AISI 1010 and AISI 1010 uith 0.02 pct Cb steels. For each steel the reduction in area given the specimen on the first pull was mainlairred at 30 ± 5 pct and recrystallization times deterntined at various temperatures. The results indicaled a significantly slower rate of recrystallization for the columbium-modified composition, suggested the presence of- a recovery stage in the softening process , and indicated a greatly increased softening rate at a temperatuve where significant allotropic transformation to a partially ferritic Structure could occur. In recent years increasing attention has been paid to the fact that the process of recrystallization of austenite deformed at elevated temperatures is far from instantaneous at many practical hot-working temperatures.1-3 This realization has given rise to such terms as hot cold-working1 or warm-working,2 These terms generally describe processes where the recrystallization rate at the temperature of deformation is slow enough to have an appreciable effect on mechanical properties despite a relatively high deformation ternperature. The mechanical properties of interest can be either the properties at the deformation temperature as in hot-workability studies4 or the room-temperature properties after cooling as in the many recent studies of various thermomechanical processes172 where heat treatment and deformation are intentionally combined to give a unique set of room-temperature properties. Because of this interest in processes where the austenite recrystallization kinetics can be an important variable, the development of quantitative methods of following the course of short-time, high-temperature recrystallization has received increasing attention.l,3,5 The experimental methods to date have, in general, relied upon rapidly deforming the austenite, holding at temperature for various brief intervals, quenching as G.A.WILBER and W. J. CHILDS, Members AIME,are Research-Fellow and Professor, respectively, Rensselaer Polytechnic Institute, Troy, N. Y. J. R. BELL and J. H. BUCHER, Member AIME, are Research Engineer and Research Supervisor, respectively, Graham Research Laboratory, Jones & Laughlin Steel Co., Pittsburgh, Pa. Manuscript submitted March 13, 1968. IMD. rapidly as possible, and then using room-temperature measurements to follow the recrystallization process. Although such methods can be successfully applied to certain alloy steels, the existence of the allotropic transformation during cooling of plain-carbon or low-alloy steels tends to obscure the results. Thus, such room-temperature measurements as hardness and X-ray line widths do not correlate well with the extent of austenite recrystallization before quenching,5 and results based on room-temperature microstruc-tural observations are dependent upon the success in correlating the observed structure with the prior aus-tenitic grain structure.1,3,5 The purpose of the present work was to develop a quantitative method for the determination of short-time, high-temperature recrystallization rates, based on measurements made at the temperature of deformation. EXPERIMENTAL TECHNIQUE The basic technique consisted of heating a small tensile specimen to a given temperature of hot deformation, loading to a given reduction in area, unloading, delaying various intervals at temperature, and then reloading to failure. The data were obtained in the form of traces of load and elongation as a function of time. Due to the high deformation temperature, the strain hardening introduced during initial loading was progressively annealed out with holding time after unloading and the loads obtained upon reloading decreased as this softening proceeded. Although the value of the second load at any Consistent point On the load-elongation curve could have been used as a measure of the degree of softening, the most convenient to use was the ultimate load. The softening indicated by the decrease in the second ultimate load with time is essentially a process of annealing of cold-worked material at a high deformation temperature. Although some recovery grain growth may contribute to such a softening process, it is generally considered that the major softening which must take place to achieve complete removal of substantial Strain hardening will occur by the formation of new, stress-free grains. As the results of this work indicate that essentially complete removal of strain hardening did in fact occur. the primary softening process will be attributed to recrystallization, and specific reference made where it appears that other mechanisms may be contributing to the total observed softening. It would, of course, be of interest to attempt to correlate the results of this work with the actual austenite fraction recrystallized as determined by other techniques. This was not attempted in the present work because it would have required running a large number of additional specimens and, as discussed previously, there is limited assurance that the results would accurately reflect the prior austenite fraction recrys-

Jan 1, 1969

By Joseph Cervik

Gas occurs in coalbeds in an adsorbed and a free gas state, Adsorbed gas is stored in the micropore structure and its transport is governed by Fick&apos;s law. The free gas occurs in the. fracture system and flows according to Darcy&apos;s law. These two modes of mass transport are interdependent. Production decline curves of coal-gas wells are of the constant percentage decline type and, thus, show no indications of flow characteristics peculiar to coal-gas reservoirs. The effectiveness of surface boreholes as a degasification scheme depends upon both good fracture permeability and a high fracture density. Conventional methods of reservoir engineering analysis are not applicable to coalbeds.

Jan 1, 1969

By George D. Haley

This report will be given in two sections. The first sec¬tion outlines techniques and equipment to form almond shaped fluorspar briquettes by means of briquet presses, and the second section outlines techniques of the balling disc. PART I - BRIQUET PRESSES Fluorspar has been briquetted for a number of years and the so called "peach pit" briquet is known to many steelmen. Present production is estimated at over 100,000 tons annually. Slide 1 shows an assortment of various sizes and shapes of briquettes. It is possible to form fluorspar into almost any configuration of briquet. For safety on the melting floor, pillow type briquets are preferred. Ease of mechanical handling and durability of the product are facil¬itated by an almond shape. The dimensions of the almond can vary from 1-in. to 1-1/2-in. in length, from 13/16-in. to 1-in. in width and from 1/2-in. to 1-in. in thickness. The type of equipment to pro¬duce almond shaped fluorspar briquettes is shown in Slide 2. Here we have a Komarek-Greaves and Company 300 ton briquettor equipped with almond rolls. This machine is capable of producing fluorspar briquettes at a rats of 30 tons per hour with power consumption of 35 hp per ton par hour.

Jan 1, 1969

By Manuel Gomez

The Bureau of Mines used data from 31 core samples to develop prediction equations for evaluating chemical and carbonization properties of six seam units in a lignite deposit approximately 2 miles wide and 8 miles long in the Wilcox Formation of central Texas. Statistical response surfaces, based on core analyses, were computed for 14 parameters indicative of lignite quality. These computed surfaces, and their mathematical equations, can be used to predict values of the selected properties of the lignite seams at any desired surface coordinate position between core hole locations. The wide range of application shown by this study indicates that the methods of statistical regression analysis may be useful to evaluate large deposits of lignite or higher rank coal.

Jan 1, 1969

By N. Plint, E. T. Pinkney

Copper segregation developments within the Anglo American Group are described with particular reference to the work of the TORCO Project Team. Some radical differences have been adopted in the mechan-ical approach as compared with methods used by previous workers. Most important among these are the following: (1) The heating unit is a fluidized-bed roaster. (2) A moving bed segregation chamber is used in which a packed bed of heated ore, to which reagents have been added, moves slowly downwards under gravity and is discharged at a controlled rate by means of a suitable valve mechanism. (3) The quantities of reagents used (sodium chloride and some form of carbon) are only a small fraction of those recommended by other investigators. (4) Retention times of only 2 min have been satisfactory for the complete segregation of many types of ore. Project TORCO is the code name given by Anglo American Corp. of South Africa, Ltd., to the investigation undertaken in Zambia to develop a plant capable of treating large tonnages of refractory copper-bearing ores by the segregation process. The process has now been under investigation for six years (1960-66) and during that period work has progressed from bench-scale laboratory tests through small-scale pilot-plant work to a 500-tpd commercial pilot unit. Test work has been carried out mainly on the ores of the Zambian Copperbelt and results have been encouraging. Recoveries on the order of 90% have been obtained on all Copperbelt ores tested with high concentrate grades. PRELIMINARY INVESTIGATION Laboratory scale segregation test work on Nchanga banded sandstone ore and oxidized ore from Kansan-shi was originally conducted by Professor Maurice Rey. SociCtC Miniere et Mktallurgique de Pefiarroya, in 1957. Both ores responded favorably to the process. In November, 1960, the consulting engineers of Anglo American Corp. of South Africa, Ltd., initiated preliminary investigations on the application of the segregation process to Copperbelt ores. In early laboratory work, samples were heated in a closed, externally heated tube furnace for one hour at temperatures ranging from 800 to 830°C. The free moisture content of the ore feed was 4% and reagent additions were 0.5% salt and 1.0% coal. Both salt and coal were pre-crushed to -48 mesh Tyler.* All samples except an ore from the Bancroft mine responded well to the process and recoveries of over 90% were obtained. The presence of dolomite was responsible for the relatively poor recoveries from the Bancroft ore, as tests on one of the other ores with additions of calcite or dolomite confirmed. Recoveries dropped from 94 to 45% Grades of all the rougher flotation concentrates produced were low at 10-15% copper. The laboratory investigation was then followed up on a pilot-plant scale. An attempt was made to carry out the segregation process in a coal-fired 5-ft-diam fluidized-bed roaster. The feed consisted of a banded sandstone from Nchanga to which 0.5% sodium chloride had been added. Reducing conditions were maintained in the roaster by the addition of coal in excess of that required for heating the feed. The excess coal and added salt constituted the segregation reagents and the temperature of the bed was held at approximately 750°C. Recoveries of copper and grades of concentrates were low. The reasons for lack of success were: (1) The reaction is a gaseous one and a fluidized-bed roaster is therefore unsuitable as a segregation unit. (2) Coal in excess of that required for heating was introduced into the fluidized bed and under these conditions some of the copper would be reduced in situ. The term "reduced in situ" is used here to describe any copper mineral reduced to the metallic state in its original site within the ore particles. If this copper is to be recovered by subsequent froth flotation it must first be liberated from the gangue by grinding or some other method which, in practice, is usually not feasible on ores of this type.

Jan 1, 1969

By K. I. Savage, S. C. Sun

This paper describes a process developed to recover coal, clays and pyrite from coal wastes. The process consists of fine grinding followed by coal and pyrite flotation which leaves the clays in the flotation pulp. A bituminous coal refuse containing 10% sulfur and 30% carbonaceous material was treated by this method to yield a coal product containing 4% sulfur, 10% ash; a pyrite product containing 45% sulfur (84% FeS2), 1% carbonaceous material; and a clay product containing 2% sulfur (3.5% FeS2). The coal yield was about 89%. The pyrite yield was about 77%. The process steps may be entirely flotation, or gravity separation (hydrocycloning) may be used to increase the pyrite : coal ratio in the flotation feed. Cost estimates for the process show a profit of $2.28 per ton of low pyrite grade refuse, but these do not include labor, maintenance, overhead and plant depreciation. The development of this process consisted of three parts: (1) exploratory tests, (2) op-timazation tests and (3) confirmatory tests. The objectionable qualities that sulfur imparts to coal have been commented upon from early times, and they have become more objectionable as the uses of coal have grown. In whatever form coal takes — raw, carbonized or gasified —the sulfur content remains objectionable, and therefore its compounds are removed as completely as possible. It has long been known that sulfur occurs in coal in different forms. In 1861, sulfur was said to exist in the state of sulfuric acid in combination with a base; in combination with iron as iron pyrites; as bisulfides of iron; and in combination with the organic elements of coal.&apos; Pyritic sulfur is a term loosely used to cover the sulfur associated with iron in its various forms. The mineralogically recognized forms are pyrite (FeS2), pyrrhotite (Fe 1-x S) and marcasite (FeS2). The particle sizes of pyrites vary widely. Isolated grains of marcasite smaller than 15 microns have been found disseminated through coal.2 Hair-like "veins" of pyrite filling cracks in vitrain have been found. At the other extreme, lumps or nodules of pyrites large enough for removal by hand picking have been encountered. Organic sulfur, unlike pyritic sulfur, does not exist as discrete particles, but is instead intimately associated with the coal structure and thus it is impossible to remove it or reduce its concentration by physical or mechanical means.2 In the preparation of coal for its various markets, the pyrite minerals (pyrites) are separated from the raw coal feed. This separation process concentrates the pyrites in the tailings or other waste products. It would be desirable to recover these pyrites for three reasons: (1) Pyrites are potential sources of sulfur and iron. In 1967, for the fifth consecutive year, Free World consumption of sulfur exceeded production.3 Propelled by the shortage, the domestic price of sulfur has risen from $24 to $38 per long ton (bright). (2) The refuse, when placed in piles, becomes ignited. The pyrites (FeS2) bum, giving off SO,. Thus, the pyrites are a cause of air pollution. (3) Also, the pyrites undergo chemical reaction when exposed to air. The refuse is leached by waters which result in stream pollution due to the water-soluble iron and acidic reaction products. Coal refuse also contains coal minerals and clay minerals. Therefore, any process for recovering the pyrites must successfully separate them from the coal and clay minerals. In the study discussed here, ten different bituminous coal refuse samples were successfully upgraded in pyrite content. These samples represented a wide variety of coal waste materials from Pennsylvania and other states. The variabilities of the sulfur and coal contents are shown in Table I. The extremes are Sample J, a high sulfur-low coal, and Sample B, a low sulfur-high coal. Definitions of some of the symbols or terms used in this report are given below: Mesh size—Tyler standard mesh screen sieves with an opening based on the square root of two. Fe —Indicates iron, as determined by a stannous reduction-dichromatic oxidation method. S—Indicates sulfur, as determined by the ASTM "Eschka" method for sulfur in coal.

Jan 1, 1969

By Robert M. Lewis

Chemically, mica is a complex silicate of sodium, potassium and aluminum. There are no important uses of mica where the chemical analysis is important, except that in some uses of ground mica, the content of iron oxide present as an impurity must be kept to a very low limit. Muscovite mica is frequently found containing black and red "stain" as a homogeneous part of the books or sheets. In most cases this stain or impurity is magnetite or hematite. Some mica contains impurities deposited by infiltration. This is commonly a red stain, less often brown or white. The best mica is free from all such impurities, and the greater their content, the less value does the mica have.(1) It is because of these undesirable impurities that a large segment of the fine ground mica industry relies on weathered pegmatites and alaskite ores as a source of raw material. The mica concentrates obtained from these ores are relatively clean and require moderate beneficiation to meet color and density specifications. One need only to observe the stained and decrepitated condition of the mica recovered from mica schist to appreciate the challenge that processing this material presents. Despite these adversities there are several advantages to be gained by mining and processing mica schist ores. The mica content of these ores are considerably higher than the pegmatites and alaskite ores now being mined, often containing in excess of forty percent mica. This-higher grade mica feed should promote a lower mining and milling cost with its resulting competative advantage. With more rigid government

Jan 1, 1969

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By Arcy, D&apos Banister

The productive potential of the Nation&apos;s principal active and inactive silver mining districts has been evaluated, using 1964 economic conditions and assumed silver prices ranging up to $3 per ounce. On this basis, the United States has an estimated 5 billion ounces of unmined silver, excluding minor byproduct silver in gold deposits. Approximately 3.5 billion ounces are contained in deposits requiring higher silver prices to be economically minable, and about 1.3 billion ounces are in currently operating mines. An analysis of silver consumption trends since 1954 indicates that the free world industrial market will climb to nearly 800 million ounces annually by 1985. U.S. industrial silver consumption has been projected to increase at an annual rate of 4 percent from 1965 to 1985. Average annual increase for the remainder of the free world has been 8.1 percent since 1953; this is expected to level off with an estimated average increase of 5 percent to 1975 and 4 percent from 1976 to 1985. Foreign silver production has, in the past, exceeded consumption, but in 1960 the supply deficit was over 100 million ounces. U.S. production, also traditionally exceeding demand, was suddenly overtaken at the start of World War II. By 1964 the annual deficit, excluding coinage, was over 84 million ounces. World coinage requirements of silver are fast declining and expected to total only 25 million ounces annually by 1985. In fact, coins are already becoming major short-term source of silver to fill the large deficit between industrial demand and current production. The larger, long-term deficit (to 1985, the limit of this study) must be balanced by silver from the hoards and new production from silver deposits. Eventually all of the deficit must be met by new production or silver prices will rise until consumption is greatly curtailed. To balance free world supply and demand, it is estimated that the free world must produce an additional 85 million ounces by 1975 and 375 million ounces by 1985. The estimated proportion expected from U.S. deposits is 17 million ounces by 1975 and 74 million ounces by 1985.

Jan 1, 1969

By Claude H. P. Lupis, John F. Elliott

The classic Siez~erts&apos; technique has been employed to determine the solubility of oxygen in liquid pure silver and the effect on the oxygen solubility of solute metal additions to liquid silver. The results indicate that oxygen deviates slightly from Sieverts&apos; law in pure silver as = 3.9. Gold, platinum, md palladium decrease the solubility of oxygen in silver. First-order free energy, enthalpy, md entropy interaction coefficients are determined from the data. An important aspect in the establishment of the formalisms to be applied to represent the thermody-namic behavior of components of solutions is the accuracy of the experimentally determined thermody-namic properties. Wagner developed the first-order free energy interaction coefficient.&apos; Recent papers2&apos;3 extend the treatment formally to other thermodynamic properties and define the second- and higher-order interaction coefficients. A current communication4 considers in some depth the requirements and limitations imposed because of experimental error on the use of several formalisms now under active consideration in the field. This communication reports the results of an experimental study of the behavior of oxygen in liquid silver alloys that was carried out concurrently with the development of Refs. 2 and 3 with the hope of providing sufficiently precise information so that enthalpy and entropy interaction coefficients could be determined. THE EXPERIMENTS The Sieverts technique was employed using an improved design of the reaction bulb over that developed originally by Humbert5 and subsequently improved by pehlke6 and Weinstein.7 The Vycor reaction bulb as shown in Fig. 1 was air-cooled and contained a port for the thermocouple angling off to one side and a vertical port for connections to the gas supply and

Jan 1, 1969

By C. T. Liu, J. Gurland

The deformation behavior in tension of spheroidized carbon steels was studied at room temperature as a function of carbon content, 0.065 to 1.46 wt Pct, and carbide particle size, 0.88 to 2.77 p. It was found that the Hall-Petch strength-grain size relation is directly applicable to the yield and flow stresses of the two lower-carbon steels , 0.065 and 0.30 pct C. The strength data for the medium- and high-carbon steels, 0.55 to 1.46 pct C, also satisfied the Hall-Petch relation, provided that these data are based upon the particle spacing. Beyond 4 pct strain, the flow stress data of all the steels studied could be represented by the same Hall-Petch relation with dinerent spacings for grain boundary and particle strengthening. The behavior of the higher-carbon steels was consistent with the postulated formation of a dislocation cell network during processing and initial deformation (up to 4 pct strain). The cell size was assumed to be equal to the planar particle spacing. The true stress at the ultimate tensile strength was also found to be a function of the particle spacing. At a given temperature and strain rate, the yield and flow stresses of carbon steels depend on the type and dimensions of the microstructure. Starting with the work of Gensamer et al. in 1942,&apos; experimental studies on pearlitic and spheroidized carbon steels revealed that the strength of steels is a function of two main parameters: the ferrite grain size2&apos;3 and the carbide particle spacing;1&apos;4&apos;5 on this basis, two different strengthening mechanisms have been developed to apply to steels of low and high carbon contents, respectively. In polycrystalline iron and mild steels the grain boundaries are regarded as the major structural barriers to slip. The relation between strength and grain size is generally represented by the Hall-Petch equation which is based on a linear proportionality between strength and the inverse square root of the average grain size.2&apos;3y677 However, Gensamer et al.&apos; and Roberts et related the yield strength of medium -and high-carbon steels to the carbide particle spacing alone, and they found a linear relation between the logarithm of the mean free path in the ferrite and the yield strength in both spheroidized and pearlitic steels. By means of the electron microscope, Turkalo and LOW&apos; extended the study to finer structures; they concluded that the logarithmic relation is not valid for the entire range of microstructures unless grain boundaries are also included in the measurement of the mean free path. For the specific case of spheroidized steels, Ansell and aenel&apos; found that the yield strength data,4&apos;5 when plotted as a function of mean free path, fit the Hall-Petch equation; however, T&apos;ysong found that the same data fit the 0rowanl0 relation if a planar inter-particle spacing is used. Recently Kossowsky and ~rown" studied the strength of prestrained spheroidized steels, 0.48 and 0.95 pct C, and concluded that the strength due to the carbide dispersions varies linearly with the reciprocal of the square root of the mean free path between carbide particles and dislocation networks. Such networks were first observed by Turkalo." The conclusion common to all these studies is that the available slip distance in the ferrite is the most important variable in determining strendh. Previous work on carbon steels is restricted to limited composition and strain ranges. The mechanism which governs the flow properties is not clearly understood, and, in particular, little is known about the composition dependence of the transition between grain boundary strengthening and particle hardening. The purpose of the present work is to investigate the strengthening mechanism in spheroidized steels over a wide range of carbon content, 0.065 to 1.46 wt pct, and plastic strain, yielding to necking. The spheroidized structure was chosen because of its relative simplicity and the relative ease of control and measurement of the structural parameters. The experimental work is limited to tensile testing at room temperature at constant extension rate. The effects of the carbide particles on the fracture behavior of spheroidized steels are discussed elsewhere.13 EXPERIMENTAL PROCEDURE Eight different grades of vacuum-cast carbon steels were supplied in the form of forged and rolled plate by the Applied Research Laboratory of the U.S. Steel Corp. The compositions furnished with these steels are given in Table I; the carbon content ranges from 0.065 to 1.46 wt pct, or from 1.0 to 22.3 vol pct of carbide. The steel plates were cut transversely into rods a little larger than the test specimens, 1 in. gage length, i in. diam. The rods were austenitized in air (enriched with CO by a consumable carbon-rich muffle) at 50° C above theA, orA., temperature for 2 hr and then quenched in oil with vigorous stirring. The as-quenched rods were tempered in two stages in order to obtain the desired distributions and sizes of carbide particles. The rods were first tempered at 460° C for 10 hr and then at 700" C for periods ranging from 4 hr to 3 days, in vacuum. After final machining, all specimens were vacuum-annealed again at 650°C for 1 hr in order to relieve residual stresses. The tension tests were carried out in two steps. The initial part of the load-strain curve, up to about 2 pct strain, was determined on a Riehle testing machine with an extensometer of small strain range, 4 pct strain, in order to obtain the yield and initial flow piopertiesi As soon as the first part of the test was finished, the specimen was placed in an Instron testing machine equipped with a strain gage extensometer with a maximum strain range of 50 pct. The load-strain curve to fracture was

Jan 1, 1969

By F. J. Schuh

The drilling industry long has been plagued by failures in the bottom few joints of surface and intermediate casing strings. This paper presents an analysis of the various possible causes of failure and concludes that failures are caused by short-lived, high-energy torque impulses delivered from the drill string through the bit while drilling out the cementing plugs, cement and floating equipment. The magnitude of these torque impulses is shown to be a function of the rotational momentum of the drill string, and a method is derived to calculate the magnitude of these impulses. The available methods of strengthening the bottom joints are reviewed. It is concluded that, while present methods are ineffective, a combination of improved procedures for strengthening and minor restrictions on drillout practices will prevent failures. Introduction In most cases, failure in the bottom few joints of casing strings is not discovered until electric logs record that the bottom one, two or three joints have parted from the casing string and slipped down the hole. However, in some cases the parted section of casing uncovers a high-pressure or lost circulation zone, or shifts laterally restricting the passage of drilling equipment. In these instances extensive remedial work is required to realign the parted pieces and seal the exposed formations. Several methods used to strengthen the bottom joints of casing strings include locking set screws in the couplings, putting wedges in special collars, welding straps across the couplings, welding the couplings and, most recently, using epoxy resin-based, thread-locking compounds. Since none of these techniques has eliminated the problem, this study was initiated to find the cause of failures and to evaluate the available methods of prevention. Mechanics of Casing Failures An analysis of the various possible causes of failure indicates that the casing is unscrewed rather than broken and that therefore failure must occur before the shoe is drilled. Since there is no general agreement as to the causes of casing failure, some possible mechanisms were ATLANTIC RICHFIELD CO. DALLAS, TEX. considered in this analysis. Failure of the bottom joints of casing can occur by only one of three types of stress: tension, torsion or bending. The possible mechanisms of failure were evaluated by determining the forces required to cause casing failure by each of the stresses; and, where applicable, the possibility of failure by fatigue was considered. For casing to part under tension requires a downward load of more than the tensile strength of the casing. The lightest API weight H-40 grade casing requires a bit load on the bottom of the casing of 27,000 to 34,000 Ib per inch of bit diameter (Table 1). Since maximum drill collar weights seldom exceed 10,000 Ib per inch of bit diameter, it is apparent that casing strings cannot be parted by the downward load of the drill string. The second mechanism considered was failure by bending. This mechanism requires that the lowermost casing joints be free to be deflected laterally until the bending stress exceeds the strength of the pipe. To fail, the casing (at a height L above the shoe) requires a force and deflection&apos; at the shoe of To deflect the casing shoe with the drill string obviously requires a dog-leg at the casing shoe. This dog-leg must have a rate of change equal to or greater than the change in curvature of the deflected casing, which is given by

Jan 1, 1969