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By Jean Howard

RECENT attempts to produce secondary recrystalli-zation in high-purity iron have given conflicting results. Coulomb and Lacombe1'2 did not find it but Dunn and Walter3,4 did. The latter workers have stated that (100) [001] and/or (110) [001] orientations develop depending on the oxygen content of the annealing atmosphere. This Technical Note records results which are in agreement with Dunn and Walter in so far as it shows that secondary recrystallization can be produced in high-purity iron, but does not confirm that both types of orientation are obtainable. Similar observations have been made on chromium-iron and molybdenum-iron, although when this technique is used on 3 1/4 pct Si-Fe, both types are obtained as in the work of Dunn and alter.' Pure iron strip was cold-rolled from sintered compacts prepared from Carbonyl Iron Powder-Grade MCP of the International Nickel Co. (Mond) Ltd. The powder contains about 0.5 pct 0, 0.01 pct C, 0.004 pct N, (0.002 pct S, $0.005 pct Mg and Si, and 0.4 pct Ni—that is, it is substantially free from metallic impurities other than nickel, which is thought to be unimportant in the present work. The iron powder was (a) pressed at 25 tons per sq in. into blocks measuring 3 by 1 by 0.3 in., (b) deoxidized in hydrogen (dewpoint -60°C) by heating first at 350°C and then at 600° C until the dewpoint returned to -60°C at each temperature and (c) sintered in hydrogen (dewpoint -40°C) at 1350°C for 24 hr. (when dewpoint is referred to in this Note, it is the value as measured on the exit side of the furnace). The sintered compacts were cold-rolled to 1/8 in., annealed in hydrogen (dewpoint -60°C) at 1050°C for 12 hr and cold-rolled to 0.004, 0.002, and 0.001 in. with inter-anneals at 900°C for 5 hr and a final reduction of 50 pct. Final annealing of strip between alumina or silica plates at 875" to 900°C in hydrogen with dewpoints of -20°, -55" and -80°C produced secondary grains with the (100) in the rolling plane; the extent of secondary recrystallization was greatest when the dewpoint was -55°C. Annealing in a vacuum of 2 x 10"5 mm Hg at the same temperature produced no secondary recrystallization at all. With strip thicker than 0.002 in. very few secondary crystals developed whatever the conditions of annealing. Using a processing schedule somewhat similar to that described above, secondary recrystallization was produced in two bcc alloys of iron, viz. 80 pct Fe + 20 pct Cr and 96 pct Fe + 4 pct Mo. The former was reduced to final thicknesses of 0.001 to 0.004 in. and the latter to final thicknesses of 0.001 to 0.016 in. With the chromium-iron, a final anneal at 1250°C (found to be the most effective temperature for developing secondary crystals in the 0.004-in material) with a dewpoint of -25°C produced a greater degree of secondary recrystallization than with dewpoints of -50°C or -20°C. Secondary crystals developed in strips of all thicknesses from 0.001 to 0.004 in. Final annealing in vacuum produced no secondary crystals at all. For the molybdenum-iron a temperature of 1200°C was most effective. It was found that a dewpoint of -50°C during the final anneal gave better results than a dewpoint of -25 "C on the 0.008 in. material. Final annealing in vacuum gave slightly worse results than annealing in hydrogen with a dew-point of -50°C. Secondary crystals were developed in strips of all thicknesses up to 0.008 in. The experiments show that the extent of secondary recrystallization is a maximum for certain critical values of oxygen content of furnace atmosphere and annealing temperature, and that these values are different for different alloys. The thinner the material, the less critical these values are. The general conclusions are that secondary recrystallization can be obtained in high-purity iron, chromium-iron, and molybdenum-iron, using a processing schedule similar to that which will cause the phenomenon to take place in high purity 3 1/4 pct Si-Fe. Unlike the silicon-iron, however, only the (100) (0011-- orientation has been produced in these alloys, irrespective of the temperature of final annealing and the oxygen content of the furnace atmosphere. The information used in this Note is published by permission of the Engineer-in-Chief of the British Post Office.

Jan 1, 1962

By J. Chipman, M. N. Dastur

The importance of dissolved oxygen as a principal reagent in the refining of liquid steel and the necessity for its removal in the finishing of many grades have stimulated numerous studies of its chemical behavior in the steel bath. From the thermodynaniic viewpoint the essential data are those which determine the free energy of oxygen in solution as a function of temperature and composition of the molten metal. A number of experimental studies have been reported in recent years from which the free energy of oxygen in iron-oxygen melts can be obtained with a fair degree of accuracy for temperatures not too far from the melting point. Certain discrepancies remain, however, which imply considerable uncertainty at higher temperatures; also several sources of error were recognized in the earlier studies. It has been the object of the experimental work reported in this paper to reexamine these sources of uncertainty and to redetermine the equilibrium condition in the reaction of hydrogen with oxygen dissolved in liquid iron. The reaction and its equilibrium constant are: H2 (g) + Q = H2O (g); K1 _ PH2O / [1] Ph2 X % O Here the underlined symbol Q designates oxygen dissolved in liquid iron. The activity of this dissolved oxygen is known to be directly proportional to its concentrationl,2 and is taken as equal to its weight percent. The closely related reaction of dissolved oxygen with carbon monoxide has also been investigated:3,4,5 co (g) +O = CO?(g); K _ Pco2___ [2] K2= pco X % O [2] The two reactions are related through the wat,er-gas equilibriuni: H2 (g) + CO2 (g) = CO (g) + H2O (g); K2 = PCO X PH2O [3] PH2 X PCO2 and with the aid of the accurately known equilibrium constant of this reaction, it has been shown5 that the experimental data on reactions [1] and 121 are in fairly good, though not exact, agreement. Experimental Method Great care was taken to avoid the principal sources of error of previous studies, namely, gaseous thermal diffusion and temperature measurement. The apparatus was designed to provide controlled preheating of the inlet gases and to permit the addition of an inert gas (argon) in controlled amounts, two measures found to be essential for elimination of thermal diffusion. A known mixture of water vapor and hydrogen was obtained by saturating purified hydrogen with water vapor at controlled temperature. This mixture, with the addition of purified argon, was passed over the surface of a small melt (approximately 70 g) of electrolytic iron in a closed induction furnace. After sufficient time at constant temperature for attainment of equilibrium the melt was cooled and analyzed for oxygen. GAS SYSTEM A schematic diagram of the apparatus is shown in Fig 1. Commercial hydrogen is led through the safety trap T and the flowmeter F. The catalytic chamber C, held at 450°C, was used to convert any oxygen into water-vapor. A by-pass B with stopcocks was provided so that the hydrogen could be introduced directly from the tank to the furnace when desired. From the catalytic chamber the gas passed through a water bath W, kept at the desired temperature by an auxiliary heating unit, so that the gas was burdened with approximately the proper amount of water vapor before it was introdvced into the saturator S. All connections beyond the catalytic chamber were of all-glass construction. Those connections beyond the water bath were heated to above 80°C to prevent the condensation of water vapor. After the saturator, purified argon was led into the steam-hydrogen line at J, and finally the ternary mixture was introduced into the furnace. THE SATURATOR The saturator unit comprised three glass chambers, as shown in Fig 1, the first two chambers packed with glass beads and partially filed with water and the third empty. Each tower had a glass tube with a stopper attached for the purpose of adjusting the amount of water in it. The unit was immersed in a large oil bath, which was automatically controlled with the help of a thermostat relay to constant temperature, ± 0.05ºC, using thermometers which had been calibrated against a standard platinum resistance thermometer. The performance of the saturator over the range of experimental conditions was checked by weighing the water absorbed from a measured volume of hydrogen; the observed ratio was always within 0.5 pct of theoretical.

Jan 1, 1950

By V. Steve Reed, Ed L. Reed

The in situ leach mining process generates a waste stream that is high in sulfates, total dissolved solids, and radium 226. During the mining phase, the volume of the waste stream is relatively low and consists primarily of the bleed stream. During the restoration phase, larger volumes of waste water are generated. These waste streams require environrnentally sound disposal. The low net evaporation rate in the Coastal Bend area precludes pond evaporation as a feasible disposal alternative. Reverse osmosis is a practical method of reducing the volume of the waste water handled, but the concentrated waste stream from the reverse osmosis unit must be disposed properly. Deep well injection into highly saline reservoirs is considered a sound method of disposing of the liquid waste generated by in situ mining in the Gulf Coast uranium district. Thirteen injection wells have been permitted to serve the disposal needs of the leach mining industry in Texas. Of these 13, 11 have actually been drilled. Seven applications are pending. The injection zones for the permitted wells range from depths of 3050 to 6200 feet. Pressure limitations imposed on these wells range from 500 psi to 1350 psi. The following criteria are used to determine the desirability of a disposal well site: 1. A minimal number of nearby, improperly plugged borings which penetrate the disposal zone; 2. Minimal crustal disturbance; 3. Sufficient salinity of the water contained in the disposal zone; 4. Protection of oil and gas producing zones; and 5. Sand of sufficient permeability and areal extent to handle the desired volume without fracturing the reservoir. 1. Improperly plugged borings: During the early part of the century, oil wells, gas wells and test holes were drilled using cable tool equipment, often with a minimum amount of surface casing. Production casing, when it was set, was often partly removed when the holes were abandoned. Thus, wells drilled prior to 1940 frequently have less than 100 feet of surface casing and either no production casing or the upper part of the production casing removed. Additionally, these holes are often plugged only with mud. The close proximity of these holes to an injection well location are a concern in that they can provide an avenue for injection-depth fluids to migrate up the bore hole and jeopardize shallower fresh water reservoirs. Usually, where there are more than 6 or 8 poorly plugged borings in a 2 1/2 mile radius of the well site, it is preferable to examine deeper zones for disposal well potential. The deeper zones are especially attractive where the borings are not in a cluster, which renders monitoring more difficult. Often, even the deeper disposal zones are penetrated by a few improperly plugged borings. When this condition arises, the potential for leakage through the borings can be addressed in the following ways. a. Demonstration that the static head in the boring is higher than the anticipated increase in bottom hole pressure generated at the boring by the disposal well. A 100 psi differential between these two pressures is recommended. The calculated increased pressure at a boring caused by injection should be refined using annual bottom hole pressure measurements in the disposal well. Figure 1 illustrates an injection pressure map which can be overlain on the oil well map to determine the anticipated increase in pressure expected at each oil, gas or abandoned hole. b. Shallow ground water monitoring. A shallow monitor well is drilled next to the boring and both pressure and quality measurements are made periodically in the shallow well. c. Disposal zone monitoring. Recently there has been a tendency for regulators to require disposal depth monitor wells instead of shallow well monitoring. We consider disposal depth monitoring to be a less effective method of monitoring because it provides only indirect evidence of potential problems. Assumptions have to be made for the unplugged borings, such as mud weight, that are not addressed by the disposal zone monitoring program. There is little improvement with this system to that discussed in "a" above. A shallow zone monitoring program, however, yields direct evidence of a developing problem with an unplugged boring. Leakage by the boring will be detected quickly by an abnormal increase in pressure in the shallow well. Quality monitoring will detect upward migration of poor quality fluids. The pressure data provide an early warning of impending leakage; the quality monitoring will detect actual fluid migration.

Jan 1, 1980

By David D. Rabb

Leaching or solution mining, a relatively simple and economical process for beneficiating metallic ores, is likely to find increasing application in the treatment of low-grade ores that are impractical to mine by any other means. This process may be carried out in two different ways: 1) dump leaching, where the ore is moved from its original location to be leached at another site; and 2) In-situ leaching, where the ore is leached in place by introducing the leach solution at the top, letting it flow down through the ore under gravity, and then recovering it plus the dissolved metals it contains. Whichever leaching method is used, it is almost always necessary to break up the ore before leaching. In this paper a study is reported which indicates that rock broken by an explosion-in particular, an underground nuclear explosion-is significantly more amenable to leaching then is rock broken by other methods. These results suggest that the leaching speed and efficiency could be increased by nuclear fracturing of the ore. Not only would the leach time be shortened, but the resulting increase in strength or richness of the solutions would decrease plant installation expense as well as reduce pumping and processing costs. A considerable fund of experience has been accumulated in the course of several hundred experimental underground nuclear explosions, so that the gross results of any given nuclear explosion can now be predicted with a fair degree of confidence.' From this knowledge it seems clear that, under the proper conditions, large ore bodies can be fractured much more economically-macroscopically speaking-by nuclear explosions than by other methods. The present study concentrates on smaller scale effects that is, the cracks in the chunks of rock broken by the explosion-and shows that here too, in the microscopic domain, there are important advantages to nuclear fracturing. The intense shock produced by the very fast acting, high-brisance nuclear explosive fractures the rock in a way that should significantly improve its leachability. Experimental Procedure This study compared rocks broken by nuclear explosives with rocks produced by conventional mining, quarrying, or core drilling. The test samples, granite chunks 6 to 8 in. on a side, plus core sections, came from the area of the Hardhat*2 nuclear explosion and were taken both before and after the explosion. For comparison, several samples of quarried granite were obtained from a local gravestone monument company. The general procedure was to soak the test samples in leaching solution and then determine the extent of penetration. A standard commercial copper leaching solution was used (10 gpl Cu, 10 gpl H2SO4, 5 gpl ferric Fe, 15 gpl total Fe, pH about 1.5), to which a water-soluble penetrant dye, Zyglo 1-c, had been added. Details of the procedure were as follows: 1) Sample leached in solution containing Zyglo penetrant dye. 2) Washed with water. 3) Air-dried. 4) Cut with granite wire saw. 5) One face polished with granite monument polish. 6) Sent directly to be photographed, or heated at 110°C for 2 hr and then sent to be photographed. 7) Photographed under ultraviolet light to show crack patterns. Results After 10 days of leaching at 70-75°F, the samples were removed from the solution, washed, dried, and cut in half with a granite wire saw to study the penetration of the leach solution. Since the Zyglo dye in the leach is visible under ultraviolet light, the degree of penetration of the leach (and hence the cracks in the samples) can be studied on photographs of the crosscut samples made under ultraviolet light. The photos in [Fig. 1] show how the leach solution penetrated various representative samples. Of the 71 rock samples examined, fractures were most frequent and prominent in samples from the rubble produced by the nuclear explosion [(Fig. 1D)]. Fracturing was less apparent in shaft-mined rock [(Fig. 1B)], still less evident in drift-mined rock [(Fig. 1C)], and practically nonexistent in cored or quarried specimens [(Fig. 1A)]. The samples in [Fig. lA-C] were from the same general area as the nuclear explosion, but they were obtained before the explosion. Results of the crack studies are summarized in [Table 1]. The Zyglo-treated leach solution penetrated the test samples at the rate of about 1/2 mm during the first hour, 1 mm by the end of 4 hr, 2 to 3 mm in 12 hr, and 4 to 6 mm in 10 days, showing a progressively slower rate with time.

Jan 1, 1972

By D. W. Lillie

It has been demonstrated that considerable bend ductility exists in bulk specimens of polycrystalline high-purity silicon. The possibility of hot-forming at 1200°C is suggested. EXCELLENT corrosion resistance in many media and low cross section for absorption of thermal neutrons (0.13 barn) would make silicon of interest to nuclear engineers were it not for extreme brittle-ness and the difficulty of fabrication by any reasonable means. The use of silicon for structural purposes also has been considered in view of its light weight and oxidation resistance. Johnson and Han-sen' have investigated the properties of silicon-base alloys and concluded that there was no way of making pure silicon or silicon-rich alloys ductile at room temperature. In view of reports of appreciable ductility in germanium single crystals above 550°C'." and some plastic deformation in single-crystal silicon above 900oC,' the present investigation was undertaken to define more precisely the limits of high-temperature ductility in pure silicon. After this investigation was begun torsion ductility in both germanium and silicon was reported by Greiner." Through the courtesy of F. H. Horn, a small bar of cast extra high-purity silicon was obtained and small bend specimens were made from it by careful machining and grinding. All of the reported tests results were obtained from samples from this bar (bar No. 1) and one other of similar source (bar No. 2). No complete analysis was obtained but, based on analysis of similar semi-conductor grade material, metallic impurities were under 0.01 pct total. Vacuum-fusion analysis for oxygen showed a value of 0.0018 2 0.0003 pct for the first bar tested and metallographic analysis showed no evidence of a second phase. Bend tests were carried out on an Instron tensile machine using a bend fixture with a 1 -in. span loaded at the center. Supporting and loading bars were 0.250 in. round and the load was applied by downward motion of the pulling crosshead of the machine. Specimen thickness and width were approximately 0.10 in. and % in. respectively. Loading rate was controlled by holding crosshead motion constant at 0.02 ipm. In some cases a smaller specimen was used on a 5/8-in. span with a 0.129-in.-diam loading bar. The entire bend fixture was surrounded by a hinged furnace and all heating was done in air atmosphere. Temperature measurement was made with thermocouples fastened directly to the bend fixture within less than 1 in. from the specimen. Autographic stress-strain curves were recorded during each test, and breaking load, total deflection, and plastic strain could be obtained from these curves. Stress was calculated from the beam formula S = 3PL/2bh2, where P is the load in pounds, L the span in inches, b the specimen width in inches, and h the specimen thickness in inches. This formula is strictly correct only in the elastic range but has been used to calculate a nominal stress for convenience in the plastic range. The stress given is the maximum stress in the specimen. Results The results of the complete series of tests are shown in Table I. The first group of tests (specimens Nos. 1-6) showed the beginning of plastic flow at a test temperature of 900°C, so two additional tests (Nos. 8 and 9) were made at 950°C on small-size specimens from bar No. 2. Specimen No. 8 was tested in the as-machined condition, and No. 9 was heat-treated in hydrogen at 1300°C for 2 hr, cooled to 1200°C and held 1 hr, cooled to 1000°C and held 1 hr, cooled to 900°C and held 1 hr, and finally cooled to a low temperature before removal from the hydrogen. It is apparent that the heat-treatment had a significant effect on yield strength and ductility. In addition, the magnitude of the yield point was conslderably reduced in the heat-treated specimen as is shown m Fig. 1 by tracings of the stress-strain curves. After obtaining a furnace capable of reaching higher temperatures specimens Nos. 10 to 13 were tested at 1100 and 1200°C. Strain rate was increased by up to a factor of 10 to see whether the ductility observed was excessively strain sensitive. Specimen NO. 10, strained at 0.02 ipm and 1100oC, was still bending at a deflection of 0.322 in. when the load rate was increased to 0.2 ipm, resulting in immediate

Jan 1, 1959

By E. F. Thomas

THE late George S. Rice was active in the inves--I- tigation of bumps, particularly in the last ten years of his career as chief mining engineer of the U. S. Bureau of Mines. Since most of his investigation was carried out in Great Britain, continental Europe, and—to a lesser extent—Canada, his thinking on prevention was influenced considerably by the experience of those countries. It is not surprising, therefore, that when he was called upon a few years before his retirement to investigate bumps in the U. S. and suggest ways to prevent them, he turned to longwall mining. A longwall method had been most successful in combating the bump hazard in mining coal under deep cover, especially in Great Britain, but the prevailing method there at the time was advancing longwall mining, which he knew was uneconomical under U. S. mining conditions. For this reason he proposed a modified retreating longwall system that he believed included the best features of the advancing method. As brought out by Rice,' if the cover is 2000 ft and 50 pct of the coal is extracted, the static load on the remaining pillars will be about 4000 psi, which exceeds the ultimate crushing strength in most instances. If the pillar coal is overloaded before a pillar line is established, then the abutment zone preceding a line of extraction is no place to split pillars or extract them by any method other than an open-end system. Rice therefore advocated open-end mining, preferably by longwall, but he was willing to compromise with long-face mining if the longwall method was not acceptable. Rice's system was put into operation in a mine in Harlan County, Kentucky,3 but subsequent experience has shown that it did not take into account two important factors—avoidance of pillar-line points and maintenance of adequate development in advance of the pillar-line abutment area. For ten years after Rice's retirement the USBM did little investigation and research on bumps, chiefly because so few were occurring that there was not much cause for alarm. But in 1951 there were three occurrences involving fatal injuries, and the Bureau began a statistical survey in that year. C. T. Holland, head of the department of mines at Virginia Polytechnic Institute, was retained as a consultant. The resulting study' of 117 case histories brought out these important conclusions: 1) Almost invariably the bump occurred in a locality affected by the abutment zones of one or more pillar lines. 2) In most cases the locality of the bump was influenced by the abutment zones of more than one pillar line. The term pillar-line point has been used for many years in the Appalachian region for such a situation. Point is used in the geographical rather than the mathematical sense. 3) In pillar-line extraction the following practices are safest in preventing bumps: a. The mine layout should provide for pillars of uniform size and shape along the extraction line. b. The mine layout should be planned so that no development need be done in the abutment zone of a pillar line. c. The layout should permit open-end extraction of pillar lines from the next goaf, so that it will not be necessary to resort to pocket mining, splitting pillars, or any practice that will involve driving in the direction of the goaf within the abutment zone. d. Pillars should be large enough to support area without undue roof and floor convergence before establishment of a pillar line. These are, of course, generalities, and while they are useful in laying out areas where bumps can be expected, they are of limited help in many mines that were committed to a system of mining before it was realized that they were subject to bumps. Under such conditions it becomes necessary to choose between the following alternatives: 1) Abandon the territory, except for pillars that offer no extraction problems. 2) Through experience select the pillars that are most heavily loaded, and, by augering, induce bumps from a safe vantage point so that impinged loads are relieved. This method was first developed at the Gary, W. Va. mines of U. S. Steel Corp. and later adapted to mining thick coal beds at Kaiser Steel's Sunnyside mine in Utah. No scientific method is available to determine where to drill within a loaded pillar. Although this method of unloading has worked very successfully at Gary—with one exception—

Jan 1, 1959

By Peter R. Morris

The effecl of preferred orienlation on X-vay dzffvaction measurements of retained austenzte was investigated for four precipitation-hardening staznless steels in sheet form. A method is preserzted for estimating the ervor in measurement associated with a given samplirig direction. The method was used to select an "optimum" sampling direclion in order to minimize errors in measurement due to preferred orientation. hleasuremenls of retained austenite content employing lhe proposed sampling direction are conzpaved to measuretnents enzploying the more commonly used normal direclion for a series of sawzples. THE first application of X-ray diffraction to the measurement of retained austenite in steels is due to Sekito, 1 who employed a photographic technique in which the (111) reflection from a thin strip of gold affixed to a cylindrical sample was employed as a standard. Averbach 2 introduced the "direct comparison" method in which the ratios of observed to calculated random intensity are assumed proportional to the austenite and/or martensite contents. Averbach's work forms the basis of most subsequent X-ray diffraction methods for the determination of retained austenite. Subsequent improvements are due to: Averbach and Cohen,3 who employed a sodium chloride crystal to monochromate cobalt radiation; Averbach et a1.,4 who introduced a bent sodium chloride monochromator; Mager,' who used a bent quartz crystal to monochromate chromium radiation ; Littmam, who first used a geiger counter diffractometer for this purpose; Beu and Beu and Koistinen, 11,12 who studied effects of absorption factor, surface preparation, sample geometry, integrated intensity vs peak height, choice of radiation, monochromator, and filter. The possibility of errors in measured values due to orientation effects was noted by Miller,13 who suggested examination of a surface other than the plane of rolling. Lopata and Kula 14 have developed an experimental technique in which the preferred orientation is measured in each sample. They illustrated the method for a sample containing 42 pct retained austenite. Application of their technique to the 1 to 15 pct range typical for the precipitation-hardening stainless steels does not appear feasible. EXPERIMENTAL PROCEDURE The nominal compositions of the precipitation-hardening stainless steels investigated are listed in Table I. Ingots were solution-treated, hot-rolled to approximately 0.2 in., and reduced to 0.050 in. by a suc- cession of cold rolling and annealing operations. After this treatment the 17-4PH sample was in the marten-sitic condition, while the 17-7PH, PH 14-8Mo, and PH 15-7Mo samples were in the austenitic condition. Samples of 17-7PH and PH 15-7Mo steels in the mar-tensitic condition were obtained by heating to 1750'F for 10 min and holding at -100°F for 8 hr. A sample of PH 14-8Mo steel in the martensitic condition was obtained by heating to 1700°F for 1 hr and holding at -100°F for 8 hr, followed by aging at 950" for 1 hr. POLE FIGURE DETERMINATIONS Samples were thinned to 0.003 to 0.005 in. by etching in a solution containing 250 ml reagent-grade phosphoric acid (85 to 87 pct H3PO4), 250 ml technical-grade hydrogen peroxide (30 to 35 pct H 2 O 2), and 50 to 100 ml reagent-grade hydrochloric acid (37 to 38 pct HCl). The specimens were placed in an "integrating" sample holder which provided a 1-in. oscillation in the plane of the sample. The diffractometer was aligned to measure the intensity diffracted by planes of the particular {hkl} type being studied. The sample was Set for a given latitude angle, a, measured from the plane of the sheet, and diffracted intensity recorded as the longitude angle, 0, measured in the plane of the sheet from the rolling direction, was increased from 0 to 360 deg. After a 360-deg scan of B, a was incremented by 5 deg, and the process repeated. Random standards obtained by spraying suspensions of powdered iron (bcc structure) and nickel (fcc structure) in lacquer were used to correct observed intensities for absorption and geometrical effects. Zirconium-filtered molybdenum radiation was used to determine the transmission regions of the (111) (0to 45 deg), (200) (0 to 60 deg), and (220) (0 to 45 deg) austenite and (110) (0 to 45 deg), (200) (0 to 50 deg), and (211) (0 to 35 deg) martensite pole figures. Vanadium-filtered chromium radiation was used to

Jan 1, 1968

By R. Maddin, C. H. Mathewson, W. R. Hibbard

Recent publicationsl.2 establishing the presence of cross-slip in strained metallic single crystals oriented wholly within the area of single slip as predicted from the generalizations of Taylor and Elam3 described these markings as they appeared during the initial stages of the deformation process. At that time, the plane having a common glide direction with the primary slipping plane was reported as the cross-slip plane although the specific direction was not confirmed. Consequently, in continuation of the research, it seemed advisable to investigate the micro-graphic appearance of cross-slip together with the Laue back-reflection X ray analysis and stress-strain data during the later stages of the deformation process. Accordingly, a single crystal of brass (72.75 pct Cu, 0.01 pct Fe, 0.01 pct Pb, 27.23 pct Zn) was polished mechanically and repolished electrolytically after the manner described in the earlier paper.' Three pairs of flat surfaces, parallel to the specimen axis, and (1) perpendicular to the plane containing the pole of the primary glide plane and the specimen axis, (2) perpendicular to the plane containing the pole of the cross-slip plane and the specimen axis, and (3) perpendicular to the plane containing the slip direction and the specimen axis, were polished mechanically and repolished electrolytically, resulting in a final minimum gauge diameter of 0.4864 in. in a gauge length of 3.36 in. The specimen was elongated in tension and load-extension readings were taken following the method described in the initial investigation.' Observed reorientations were obtained from a series of Laue back-reflection photograms at the center and ends of the gauge length and at various positions around the circumference of the specimen. These were interpreted after the manner of A. B. Greninger.4 Cross-slip (Fig 1 and 2) was found with the first appearance of the primary slip clusters and usually joined members of these clusters. In addition, a third set of entirely different markings (Fig 3) could be noted. The displacement of this third set by the primary slip lines was measured as 8300 at. diam (3.04 microns). Since the specimen was carefully observed at high magnifications before any deformation and no markings of any type could be noted, it would appear that this third set was formed during the deformation process prior to the initiation of classical primary slip. Additional extensions produced no unusual change in the appearance of either cross-slip or the third set of markings. The number of lines increased with increasing elongation and appeared, generally, in areas where earlier markings were present. The continuity of the clusters of cross-slip lines in Fig 4, 5 and 6 illustrates that they are neither noticeably displaced by nor do they displace the primary lines at this stage. In Fig 7, cross-slip appears in a long narrow localized band approximately 45 degrees from the stress axis. This somewhat resembles a twin band except for the lack of a sharp boundary. After a shear of 0.257, suffcient additional glide occurred on the cross-slip plane to displace the primary slip lines (Fig 8). Generally, where a large number of cross-slip lines could be observed in an area on one flat surface, few cross-slip lines appeared on the diametrically opposite position on the parallel flat (Fig 9). These, of course, were not matched observations on the same glide ellipses. It was extremely difficult to make such comparisons. The third set of markings (Fig 10) was extensively displaced by glide on the primary slip planes. A plot of the width of primary slip clusters versus their displacement of the third set of lines is shown in Fig 11. The slope and the linearity of the plot suggest that each primary glide plane slips to a constant maximum value of shear before further slip is transferred to another plane. A shear value of 0.28 was determined in this case. Heidenreich5 has presented a similar schematic representation of glide for aluminum. After the specimen had attained an elongation of 51.8 pct, corresponding to a shear of 0.973, cross-slip appeared very prominently in certain areas as shown in Fig 12, yet at diametrically opposite positions very little cross-slip could be noted, Fig 13. Classical conjugate slip was found at this advanced stage in the deformation, Fig 14, which corresponds to the axial location shown at 12 in Fig 15. It should be noted that cross-slip occurs within the conjugate slip clusters and on the same plane as the cross-slip associated with the closely spaced primary lines which constitute a background in less distinct focus. The third set of markings noted at all stages in the deformation of the

Jan 1, 1950

By G. P. Conard, R. C. Hall, J. F. Libsch

The 50 pct Fe-50 pct Co alloy undergoes a transformation from disorder to an ordered structure of the CsCl type reportedly in the vicinity of 732OC. During this process, the coercive force goes through a maximum, apparently as a result of strains associated with the coherent nucleation and growth reaction. This magnetic alloy also shows a marked increase in the ratio of residual to saturation induction, which is associated with annealing to a high degree of order with the continuous application of a magnetic field. The increase in ratio can be explained on the basis of a decrease in 90' domain boundaries and, perhaps, by an increase in anisotropy resulting from lattice distortion. THE 50 pct Fe-50 pct Co alloy undergoes a disorder-order transformation which has been reported to occur in the vicinity of 732°C1,2 The ordered structure is the CsCl type.' This magnetic alloy also shows a marked increase in the ratio of residual to saturation induction as a result of heat treatment in a magnetic field, sometimes called a response to magnetic anneal.'-' The purpose of this investigation was to study the course of the ordering reaction, the nature of the response to .heat treatment in a magnetic field, and the relation, if any, between ordering and the response. Procedure The method of approach in this investigation was to produce an initial structure as completely disordered as possible and then gradually to order the alloy by isothermal anneals at various temperatures under different conditions of the applied magnetic field. Magnetic, magnetostriction, and X-ray analyses were of primary importance in determining the property and structural changes resulting from the isothermal anneals. Rings of the 50 pct Fe-50 pct Co alloy were prepared from the elemental powders by a powder metallurgy technique, further details of which may be found in ref. 7. The initial structure was produced by annealing the specimens for ½ hr at 1000°C, cooling to and holding for ½ hr at 900°C (in the a range above the ordering temperature), and water quenching. Isothermal anneals were performed at 600°, 675°, 720°, and 740°C. For example, rings were heated to 600°C, held for a predetermined period of time, and cooled by natural cooling at a rate slightly slower than an air cool (average of 20" to 25°C per min). The tests (magnetic, etc.) were made after each heat treatment. All high temperature treatments were performed in a purified hydrogen atmosphere. The treatments at the various temperatures were carried out under one or more conditions of an applied field including 1—no field, 2—field of 20 oersteds applied on cooling only, and 3—field of 20 oersteds applied continuously during heating, holding, and cooling. Magnetic measurements were made using the standard Rowland ring technique8 with a maximum field strength of 100 oersteds. The magnetization curve, induction at 100 oersteds (B.), residual induction (Bt), and coercive force (Hc) were determined. All magnetic analysis data were based on an average of the results from three rings. A strain gage technique9 as used for the measurement of magnetostriction. The X-ray determination of the relative amount of ordered phase present was made on the ring specimen used for magnetic measurement. This was done by the back-reflection method using a rotating specimen (because of the large grain size) with unfiltered CoKa radiation and a 7 hr exposure time. Intensity measurements of the ordered line (300) were made by comparing visually the films so obtained with standard films prepared by exposing for different lengths of time a specimen given a long time anneal (high degree of order). Results In all instances the saturation induction (induction at 100 oersteds) was found to increase slightly with annealing time. This effect was small and appears to be the increase in saturation induction to be expected on ordering.10-13 The residual induction behavior was markedly influenced by the field condition during annealing, Figs. 1, 2. For the condition of no applied field, the ratio of residual to saturation induction remained essentially constant for short annealing times but showed a significant increase at longer times. With increasing annealing temperature, less time was required to produce this increase in the ratio. In the case of the 600°C anneals, the increase did not occur until approximately 20 hr, Fig. I, while on annealing at 740°C the increase was immediate, Fig. 2. Slight decreases in the ratio may be observed at 100 hr for specimens treated at 720°C and at 1 hr for those treated at 740°C. Specimens annealed in a field of 20 oersteds showed a residual to saturation induction ratio consistently higher than that for the specimens annealed without the field. The first anneal with the field (¼ hr) caused an abrupt increase in the ratio at all temperatures; thereafter, the increase in the ratio was generally similar for specimens annealed

Jan 1, 1956

By James C. M. Li

The Petch relation between the flow stress and the gain size is derived from a consideration of gain boundary sources of dislocations without the need of dislocation Pile-ups. Three mechanisms for inierpreting the yield stress: the gain boundary strength, the unpinning of Frank-Read source near a grain boundary, and the generation of dislocations from the grain boundary are compared and the condition of their equivalence is shown. The effect of the average angle of misfit of pain boundaries is found to be sma11 and so is that of the average angle of misfit of subboundaries having impurities. The effect of impurities on the ledge density in the grain boundary is treated thermodynamically and a relatwn is proposed for the variation of Petch slope with impurity activity. The effect of temperature on the Petch slope is interpreted as due to the change of ledge structure in the grain boundary. It is indicated that the effect of annealing temperature may be more important than that of the test temperature and therefore should be studied. The effect of plastic strain on the Petch analysis is deduced from a work-hardening equation in which the generation of dislocations has first-order kinetics and the annihilation of dislocations has second-order kinetics. It is concluded that the Petch slope will decrease with plustic strain if the rate of annihilation of dislocations is sufficiently large. Critical experiments which may shed light on the mechanism for the Petch relation are suggested. THE relation between the yield or flow stress, 0, and the grain size, l, was first proposed by all' and later studied more extensively by Petch and co-workers, who also proposed a similar relation for the fracture stress and deduced from these a grain-size effect of the ductile-brittle transition temperature. The microscopic mechanism used by all' and petch2 involves a pile-up of dislocations of like sign generated from a Frank-Read source. The yielding or flow takes place when the pile-up exerts sufficient stress at the grain boundary so that the plastic deformation can propagate from one grain to another. If the average strength of the grain boundary is ai and the average length of the pileup is lp, the Petch slope, k, is given by" where p is the shear modulus, b the Burgers vector, and v the Poisson ratio. This slope will be independent of the grain size if l/lp is a constant. This is possible, since, if the Frank-Reed source is situated near the grain boundary, lp = 1, and if it is situated in the middle of the grain, Ip = 1/2. cottrell,12 also using the pile-up mechanism, proposed that the stress concentration at the grain boundary will initiate Frank-Read sources near the grain boundary and in this manner a Lüders band can propagate from one grain to another. Assuming that the average distance between the Frank-Read sources and the grain boundary is 1, and the unpinning stress of the Frank-Read sources is op, Cottrell obtained the following Petch slope: This slope will be independent of the grain size if ls is independent of the same, which is not as obvious as the condition, Ip = I for Eq. [2]. In addition to this assumption, the direct relation between the Petch slope k and the unpinning stress, up, was recently questioned by Johnsonon grounds that it is inconsistent with the following observations: the independence of k with temperature and strain rate, and the small k in columbium, which, like iron, has a sharp yield point. As pointed out by ohnson," the most important objection both to the Hall-Petch mechanism, in which the strength of the grain boundary plays the role in yielding, and to the Cottrell mechanism, in which the unpinning of Frank-Read sources plays the role in yielding, is the lack of direct observation of the pile-ups. The dislocation structure in deformed iron has been examined recently in the electron microsope.'-' Dislocations appear to be generated from grain boundaries or other interfaces; they form clusters and tangles within the grain at very early stages of deformation, even in the Lüders band, if the deformation is slow or at normal and elevated temperatures. Although it is still too early to interpret bulk properties from thin-film observations, it does seem worthwhile to look for a mechanism for the Petch relation which does not require dislocation pileup. SUBBOUNDARY SOURCES In order to show that a consideration of grain boundary sources can lead to the same Petch relation as does the consideration of the strength of the grain boundary, we shall first discuss the case of a simple tilt boundary whose elastic properties have been studied in detail.17 The strength of a partially

Jan 1, 1963

By A. Paul Bond

Two series of 17pct Cr iron-base alloys with small, controlled amounts of carbon and nitrogen were vacuum-melted in an effort to detertmine the meclz-uniswls of inter granulur corrosion in ferritic stain-less steels. An alloy containing 0.0095 pct N aid 0.002 pct C was very resistant to intergranular corrosion, even after sensitizing heat treatments at 1700" to 2100o F. However, alloys containing more than 0.022 pct Ni and more than 0.012 pct C were quite susceptible to intergranular corrosion after sensitizing heat treatments at temperatures higher than 1700°F. This corrosion was observed after the usual exposure tests and after potentiostatic polarization tests. Electronmicroscopic examination of the alloys susceptible to intergranular corvosion revealed a small grain boundary precipitate; this precipitate was absent in the alloys not susceptible to such corrosion. Thc electronmicrographs indicate that intergranu1ar corrosion of ferritic stainless steels is caused by the depletion of chromium in areas adjacent to precipi-tates of chromium carbide or chromium nitride. It also seems likely that the precipitates themselves are attacked at highly oxidizing potentials. Confirma-tion of the proposed mechanisms was obtained in tests on air-melted ferritic stainless steels containing titanium. The titanium additions greatly reduced susceptibility to intergranular corrosion at moderately oxidizing potentials but had no beneficial effect at highly oxidizing potentials. A major obstacle to the use of ferritic stainless steel has been their susceptibility to intergranular corrosion after welding or improper heat treatment. It appears that sensitization of ferritic stainless steel occurs under a wider range of conditions than for austenitic steels. In addition, a greater number of environments lead to damaging intergranular corrosion of sensitized ferritic stainless steels than to sensitized austenitic steels. The chromium depletion theory of intergranular corrosion is widely accepted for austenitic stainless steels'" although there: are some objections.3 On the other hand, several alternative mechanisms proposed for ferritic stainless steels include precipitation of easily corroded iron carbides at grain boundaries,' grain boundary precipitates that strain the metal lat-tice,5 and the formation of austenite at the grain bound-arie.6 The application of the chromium depletion theory to ferritic stainless steels has been discussed extensively by Baumel.7 The present investigation was undertaken to determine which of the proposed mechanisms can be sub- A PAUL BOND IS Research Group Leader, Climax Molybdenum Co of Michigan, Ann Arbor, Mich. stantiated with experimental data obtained on ferritic stainless steels. High-purity 17 pct Cr alloys containing small controlled additions of carbon or nitrogen were therefore prepared, and then examined electro-chemically and metallographically. EXPERIMENTAL PROCEDURES Materials. Two series of experimental alloys were prepared from electrolytic iron and low-carbon ferro-chromium using the split-heat technique. In this technique, the base composition is melted, and part of the melt is poured off to produce an ingot. To the balance of the melt, the required addition is made and the next ingot cast. This process is repeated until a series of the desired compositions is cast. By this procedure the impurity levels are essentially constant within each series. All the alloys in the carbon-containing series were melted and cast in vacuum. The base composition in the nitrogen series was melted and cast in vacuum; subsequent ingots in the series were melted with additions of high-nitrogen ferrochromium, and cast under argon at a pressure of 0.5 atmosphere. Two additional alloys were produced starting with normal purity materials. They were induction-melted while protected by an argon blanket and cast in air. Table I gives the composition of the alloys. The 2-in.-diam ingots produced were hot-forged and hot-rolled to a thickness of 0.3 in. and then cold-rolled to 0.15 in. All specimens were annealed at 1450°F for 1 hr. The indicated sensitizing heat treat-s s ments were performed on annealed material. All heat treatments were followed by a water quench. Specimen Preparation. For the 65 pct nitric acid test, 1 by 2 by 0.14-in. specimens were wet-surface ground to remove surface irregularities and polished through 3/0 dry metallographic paper. For the modified Strauss test, $ by 3 by 0.14-in. specinlens were similarly prepared. Immediately prior to testing, the Table I. Compositions of the Alloys Composition, pct Alloy Cr hio C N 270A 16.76 0.0021 0.0095 270B 16.74 0.0025 0.022 270C 16.87 0.0031 0.032 270D 16.71 0.0044 0.057 271A 16.81 0.012 0.0089 27 IB 16.76 0.018 0.0089 271C 16.69 0.027 0.0085 271D 16.81 0.061 0.0O71 4073' 18.45 1.97 0.034 0.045 4075† 18.5 2.0 0.03 0.03

Jan 1, 1970

By M. V. Nevitt

In the systems Ti-Mn-O, Ti-Fe-O, Ti-Co-O, and Ti-Ni-O the bounda.r-ies of the Ti2Ni-type phases were determined at one or more temperatures and the variation of the lattice parameter with oxygen content was determined. Densities were calculated from the lattice parameters and compared with measured density values. The: results indicate that the occurrence of the phase in these systesms can be correlated qualitatively with valency electron concentration, and that the role of oxygen is that of an electron acceptor. The lower limit of oxygen solubility appears to be determined by the valencies of Mn, Fe, Co, and Ni, while the maximum oxygen concentration coincides with the filling of the 16 (c) positions of the O 7h - Fd 3m space group. THE suggestion has been made by several investigators'" that the phases having the cubic E9,-type structure, and known as 17-carbide-type, double-carbide-type and Ti,Ni-type, are members of a family of electron compounds. This concept has been given additional support by recent work8 in which new isostructural phases involving second and third long period combinations were found, and which provided further evidence of the regularity of occurrence of the phase in terms of periodic table relationships. In this laboratory attention has been focused on the isomorphs containing titanium, zirconium, or hafnium, and the role that oxygen plays in their occurrence. In some binary systems Ti,Nitype* phases occur having the formula A,B where A is the titanium group element. Based on previous workq and the present investigation, oxygen is known to be soluble in two of these binary phases, Ti,Co and Ti2Ni. It is probable that oxygen is also soluble in the other phases of this kind. In other binary systems the Ti,Ni-type phase does not occur, but does occur in the corresponding ternary systems with oxygen .3-5 The experiments described here were performed to determine whether the occurrence and composition of certain of the Ti,Ni-type phases could be related to an electronic effect and whether oxygen's stabilizing role is exerted through an influence on the electron: atom ratio. The ternary systems Ti-Mn-O, Ti-Fe-O, n-Co-O, and Ti-Ni-O were selected for study for two reasons: First, several schemes have been proposed for first long period elements which, although not in quantitative agreement, show a generally consistent trend for the variation of valency with atomic number. Although for a transition metal the term valency is difficult to define and is generally not a constant number which can be applied to all alloys, it is usually assumed to be an index of the number of electrons per atom involved in metallic cohesion. Second, the determination of the Ti2Ni-type phase boundaries was facilitated by the fact that the phase relations in several of these ternary systems have been investigated by other workers."' EXPERIMENTAL PROCEDURE___________________ The alloys were prepared by arc melting crystal-bar titanium, reagent grade TiO, and electrolytic manganese, iron, cobalt, and nickel. Each button was remelted at least three times. The metals had a minimum purity of 99.9 pct except the nickel whose purity was 99.4 pct, the major impurity in this instance being cobalt. The preparation of the manganese alloys was attended by the customary difficulties associated with the vaporization of manganese. The technique used in this case was to add approximately 10 pct extra manganese to the original charge and to continue remelting the button until the final weight was in agreement with its intended weight. At least three alloys in each system were analyzed chemically and the results, even for the manganese alloys, were in good agreement with the intended compositions. A few additional alloys in the Ti-Mn-O system were prepared by the sintering of mixed powders in evacuated quartz tubes followed in some cases by arc melting. For annealing, the alloys were wrapped in molybdenum foil and placed in fused silica tubes containing zirconium chips. The fused silica tubes were evacuated at room temperature to a pressure of 1 x l0-6 mm of Hg and sealed. These capsules were then annealed for 72 hr at an external pressure of 5 x 10-5 mm of Hg in a vacuum furnace whose temperature could be controlled to + 1°C. The success of this procedure in avoiding significant oxygen or nitrogen pickup was indicated by the bright, ductile condition of the molybdenum foil and by the complete absence of a microscopic reaction layer on the specimens. This method did not permit rapid quenching of the specimens but in no case did metal-lographic examination indicate that a solid-state transformation had occurred on cooling. Metallo-

Jan 1, 1961

By Malcolm J. McPherson, Michael Hood

Sunnyside Mines, owned and operated by the Kaiser Steel Corporation, are situated near the city of Price, Utah. The complex comprises three adjacent mines, named simply Nos. 1, 2 and 3, all connected underground. Two seams, the upper and lower Sunnyside have been worked. These dip at about 10 percent to the north-east. The surface cover is variable due to the mountainous nature of the topography. The Sunnyside upper seam varies from 5 1/2 ft (1.7m) to 9 ft (2.7m) In thickness whilst the lower seam remains at about 6ft (1.8m). The separation between the two seams has ranged from 7 to 45 ft over the mined area (2 to 14m). Longwall mining has been practiced at Sunnyside for over 20 years due to difficulties of roof control encountered when using the roan and pillar system. Number 3 mine is bounded on the north and south sides by mines Number 1 and 2 respectively. Whilst current production is concentrated into Number 1 mine, much of the future of the complex lies in the further development of deeper reserves in Number 3 mine. Workings in this latter mine were curtailed in 1978 due to difficulties in ventilation. Present developments are ventilated partially from the neighboring Number 2 mine where no workings are in progress. The layout of Number 3 mine is illustrated on the schematic Figure 1. Trunk airways extend down dip from the surface at No. 2 Canyon and the Water Canyon for a distance of some 9,600 ft. (2930m). The area between the two sets of trunk airways has been worked extensively in both seams as have the corresponding reserves on either side in the connected adjacent mines. At the present time exhausting fans are sited at the top of a shallow shaft in No. 2 Canyon and an 8 ft (2.4m) diameter shaft sunk to a depth of 1013 ft (310m) closer to the current developments (Figure 1). The current airflow system, even with an additional 116,000 cfm (55m3/s) entering from No. 2 Mine, is adequate only for the development work now in progress but will be unable to support new longwall faces further downdip. The basic ventilation problem of this mine may be stated quite simply. In a situation where all intake and return airways pass through extensive old workings, a ventilation system design was required that would be effective, efficient and economic for the foreseeable future of the mine. ORGANIZATION OF THE PLANNING PROCEDURE The procedure followed during the study is illustrated on Figure 2. Initial ventilation surveys established the current state of the airflow system and provided the necessary data for setting up a Basic Network File in a computer store. The data in this file was a mathematical model of the ventilation system of the mine. The basic network was analysed by a ventilation network analysis program in order to correlate the measured and computed airflows and to establish the basic network as a true representation of the mine as it stood at the time of the surveys. The network model could then be extended to simulate the future development of the mine and alternative ventilation designs investigated. The remaining sections of the paper outline the work involved in each of these main phases of the planning procedure. VENTILATION SURVEYS Conduct of Surveys Two types of measurements were conducted simultaneously throughout the air-carrying routes of the mine: (i) Airflow measurements were made by anemometer traverse or smoke tube at 221 selected stations. Anemometer traverses were repeated at each station until at least three gave results to within 5 per cent. (ii) Pressure drop measurements were made across ventilation doors, regulators and, wherever possible, across stoppings. Additionally, frictional pressure drops were measured along airways where such pressure drops were significant (above 0.01 inches of water gauge or 2.5 Pa over a 100m distance). The trailing hose method was used to determine these frictional pressure drops. This involved laying out 100m of abrasive resistant plastic tubing (3 mm internal diameter) with a 4 ft. pitot-static tube facing into the airflow at either end and a low range pressure gauge connected into the line. The trailing hose method was preferred to the alternative barometer technique for this study because of (a) the relative ease of access between measuring points and (b) the greater accuracy within individual airways. The anemometers used were Davis Biram Type A/2-3" (30 to 5,000 ft/min) and Airflow Developments AM-5000 digital (50 to 5,000 ft/min). The pressure gauges employed were Dwyer magnehelic instruments. These were preferred to liquid in glass manometers because of their portability and dependability under adverse mining conditions. A checklist of the equipment used in the survey is given in Appendix 1. The instruments were calibrated before and after the surveys in the mine ventilation laboratory at the University of California, Berkeley. The survey occupied two teams, each of three men, for ten working days. The work consisted

Jan 1, 1982

By Rudolph G. Wuerker

MUCH descriptive matter has appeared on the subject of suspension roof supports, or roof bolting, as it is more commonly called. The widespread introduction of roof bolting into coal mines and metal mines is truly phenomenal. Mine operators were quick to recognize the advantages of supporting wide openings without hindrance to machine maneuverability and ventilation. Although suspension roof support has long been installed at St. Joseph Lead Co. mines in southeast Missouri,'" its application to coal mining presented new problems, such as proper anchorage and bearing for the bolts, bolt diameter, and spacing of bolts. After continuous testing and experimenting at the mines, standard roof-bolting materials were determined.'!' The study reported in this paper is not concerned with such details as bolt diameter, which may be considered already solved in practice. In the tests discussed here, small models patterned on actual bolts were found to function in the same way and as satisfactorily as their prototypes. The aim of these tests was rather to investigate the influence of roof-bolting systems on the stress distribution around mine openings and to study the fracture patterns obtained in actual testing. Little was found about this in the literature, as testing of suspension roof methods and quantitative measurements are only now coming to the fore. Several suggestions and actual measurements have been made to evaluate critically the functioning of roof bolting systems, single roof bolts, and parts thereof. Outstanding among them is Bucky's outline of structural model tests.'" Since none of the suggested testing equipment was available, however, for the experiments discussed below, a different approach was chosen. The response of a mine roof under stress has often been compared to that of a beam. The slow coming down and bending through of beam or plate-like banks of shale, sandstone, or top coal is a familiar occurrence, extensively cited in the literature." It was felt that testing of roof-bolt systems installed in a concrete beam which was loaded in bending would be a fair approximation of the behavior of a mine roof underground. Another school of thought considers the roof behavior over an underground opening in connection with the stress distribution all around a circular or rectangular opening. This is more accurate, and leads to the concept of a dome-shaped zone of material destroyed under tensile stress. This is likewise a common sight in unsupported roadways where the continuous fall of roof results in what has been called the natural outline of roof fracture. This theory could not be tested and is treated separately in Appendix B. It is important to note that according to both assumptions the immediate roof fails in tension; the use of a beam in these tests, therefore, should give information valid for either of the two theories. With the testing equipment at hand it was possible to load concrete beams 6xlx0.5 ft under two-point loading, giving an equal bending moment over the center part in which the model bolts were installed. A comparison was made of the ultimate loads needed to break plain beams and beams in which roof bolts were installed. Arrangements were made with: 1—plain beams; 2—bolts with plate washers, some with holes drilled at 90" angles and others with holes drilled at 45" angles; 3—bolts with channel irons underneath; 4—bolts in holes filled afterward with cement; and 5—bolts anchored in a stronger stratum. The foregoing arrangement is made in order of increasing strength, as assumed from the theory of reinforced concrete. Likewise, laminated beams with wooden model bolts and with combinations of the foregoing set-ups were tested. All in all, 21 experiments were made out of the much greater number of combinations possible. There were, too, some trial tests. Enough observations from this limited number were made to interpret the behavior of mine roof, supported by various types of suspension bolts, at fracture. In present-day concepts, which have been proved by mathematical derivations and stress analyses, any opening driven underground will change the distribution and magnitude of the stresses existing around it. It does not matter whether the stresses become visible, as in rocks whose strength is less than the forces acting upon them, or whether they are invisible, as in the gangways lacking evidence of rock pressure. In this latter case the rocks can withstand changes in stress-distribution. To consider the mine roof as a beam, there are, with transversal loading, tensile stresses in the lower fiber and compressive stresses in the upper layers above the neutral axis of the beam. Beams of brittle material such as rock and concrete fail exactly as shown in Fig. 1. Nearly all model beams showed the same fracture pattern as that of a tension crack. The influence of support, by roof bolting or conventional

Jan 1, 1954

By A. E. Jenkins, L. A. Baker, N. A. Warner

Rates oj decarburization of levilated Fe-C droplets conlaining 5.5 to 0 pct C have been measured at 1660°C. Gas mixtures of 1, 10, and 100 pct 0, with helium diluenl were used at velocities of 12.5 and 62.5 cm per sec. Rates were independent of carbon concentration in the mell and in good agreement with the calculated rule of oxygen diffusion through the gas boundary layer. The effects of flow rale and total pressure are as predicled and the rates are approxitnalely 2.5 times those with CO2 as oxidant. The mass-transfer correlation used incorporaled the efject of natural convection as well as forced conrection. Graphile spheres are shown to oxidize at the same rate as Fe-C droplets under the same experimental codlions. It is concluded that, for high carbon concentrations in the melt, the rate of- decarburizalion is controlled wholly by the rate of gaseous diffusion. Rate measurements with pure CO, are reported for low carbon concentrations where CO bubbles nucleate within the droplet. Under these circumstances the decarburi-zation decreased with carbon concentration and it is proposed that carbon diffusion is significant in conlrolling the decnvburization rate. In an earlier paper1 decarburization rate measurements were reported for levitated Fe-C alloys at 1660°C but with CO2 as the oxidant. The decarburization rate was found to be independent of carbon concentration in the melt but slightly affected by total pressure. The authors were unable to explain the slight pressure effect but in all other respects the results were consistent with control by diffusion in the gas boundary layer. Subsequent work has been directed at finding the reason for the slight pressure effect and whether the kinetics with oxygen as oxidant parallel those with CO2. Recently Ito and Sano2 have shown that with water vapor-argon atmospheres the decarburization rate is gaseous diffusion controlled until an oxide film appears on the surface. In this work the melts were contained in crucibles. MASS TRANSFER IN THE GAS PHASE In the earlier analysis1 only forced-convection mass transfer was considered. Subsequent recognition of the existence of some free-convection mass transfer explained the observed small effect of total pressure on the decarburization rate. Steinberger and Treybal3 and Kinard, Manning, and Manning4 have developed correlations involving the linear addition of the contribution of radial diffusion, free and forced convection. Steinberger and Treybal&apos;s correlation was chosen as the most applicable to the present work since it correlated most of the data available in the literature and handled the low Reynolds number region exceptionally well. The correlation for (Gr&apos;Sc) < 108 is where Nu&apos; is the Nusselt number for mass transfer based upon the total surface of a sphere in an infinite medium, G&apos; is the mean Grashof number for mass transfer defined by Eq. [2], Sc is the Schmidt number (µ/pDAB)f, Re is the sphere Reynolds number (dpu,pf/µf), p is the viscosity of the gas (poise), p is the density of the gas (g cm-3), Dab is the binary diffusivity for the system A-B (sq cm sec-&apos;), dp is the sphere diameter (cm), u is the approach velocity of the gas (cm sec-I), and subscript f denotes the property value is computed at the film temperature Tf defined by Tf = +1/2(To + Tr) where To is the specimen temperature and T, is the approach gas temperature (oK). Natural convection occurs when inhomogeneities exist in gas density. These may be caused by concentration gradients, temperature gradients, or both. In the present work the temperature gradient between the sphere and the bulk gas was very large and in some cases, for example the runs with pure oxygen, the concentration gradient was also appreciable. The Grashof number defined by Mathers, Madden, and piret5 was used since it took account of both temperature and concentration gradients: where Gr&apos; is the Grashof number for mass transfer (p2fgd3|-yA-yA|/µ2f), Gr is the Grashof number for heat transfer (p2f gd3p|To - T,]/µ2fTf), Pr is the Prandtl number (cpµ/k)f, g is the acceleration due to gravity (cm sec-&apos;f, a is the concentration densification coefficient (1/p)(ap/ayA)T, yA is the mole fraction of component A at the gas-metal interface, yA is the mole fraction of component A in the bulk gas stream, cp is the heat capacity of the gas per unit mass at constant pressure (cal g-I OK-&apos;), and k is the thermal conductivity of the gas (cal cm-&apos; sec-1 OK-1). Mathers et al. tested this combined Grashof number

Jan 1, 1968

By J. J. Pye, J. B. Drew

Mzasurements of the surface diffusion coefficients of metals have been made. Diffusion profiles for the Ag-Ag system were obtained by means of a radioactive point source and a precision auto-radiographic technique. The activation energy for silver self diffusion (=8.1 kcal per mole) is lower than that previously reported (-10 kcal per mole) on poly crystalline wire by Nickerson and Parker. The bresent data indicate an effect due to parasitic volume diffusion at temperatures above 500°C. RELATIVELY few measurements have been made of the surface self-diffusion coefficients of metals. Nickerson and arker&apos; measured the diffusion of silver over the surface of poly crystalline wires and estimated that the activation energy was 10.3 kcal per mole. Winegard and chalmers2 carried out measurements on both polycrystalline and single crystal surfaces but did not report a value of the activation energy. They found, however, that at temperatures between 250" and 400°C the diffusion coefficients were on the order of lo-&apos; sq cm per sec and that there was an acceleration of the migration of silver on the polycrystalline sample when a change of surface shape occurred. Winegard and Chalmers used an autoradiographic technique, hereafter designated ARG, and Nickerson and Parker used a surface scanning geiger counter in order to determine the diffusion profiles. More recently, Hackerman and simpson3 measured the surface self-diffusion coefficient of copper at a single temperature (750°C), and the value of the diffusivity (- 10-5 sq cm per sec) is in agreement with that given by jostein from his thermal grooving measurements. This paper reports the results of an investigation of the surface self-diffusion coefficients of silver over a large temperature range and describes the adaptation of autoradiographic (ARG) techniques for the determination of diffusion profiles obtained from a radioactive point source. EXPERIMENTAL PROCEDURE The experimental procedure is a modification of the method employed by Hackerman and simpson3 in their measurements on copper. A brief description of their technique is as follows: A radioactive needle which sinters to the surface during the diffusion an- neal serves as the source of diffusing atoms. After the diffusion run the needle is removed and the surface is scanned with a shielded counting arrangement. The diffusion profiles reported in this paper were obtained by a modification of the above procedure which employs a precision ARG technique. Previous investigations in this laboratory and elsewhere51B have shown that under carefully controlled developing conditions and by the use of calibration sources a linear relation exists between the concentration of the isotope and the photographic density for values below unity. The use of ARG under these conditions has advantages over the counter scanning method in that cumbersome shielding and requirements for great mechanical precision of the scanner are eliminated. Also the ARG gives a complete picture of the surface which is advantageous in studies of anisotropic diffusion. A recording microdensitometer having a 0.1 p wide slit was employed. At low temperatures the disturbing effects of subsurface radiations are negligible. The diffusion anneals are carried out in the cell shown in Fig. 1. The needle is formed by grinding down a 1.0 mm rod of high-purity silver until a tip of 0.2 mm radius or smaller is formed. This tip is plated withA"&apos; which becomes the source of the diffusing atoms that are detected by ARG. The needle carrier and the crystal holder, Fig. 1 are constructed of quartz and ports are provided in the holder pedestal which allow free vapor circulation ((2.0 oz) and the carrier apron fits snugly over the crystal holder cap, insuring that the needle does not move and scratch the surface. Temperatures are provided by a stabilized tubular furnace which can be quickly positioned around the cell, thus bringing the crystal up to temperature in a time that is short compared to the diffusing times. The diffusion anneals range from 2 hr for the high-temperature samples to about 25 hr for those at the lowest temperature. The possibility of vapor transport of the radioactive metal as a contributing factor in the diffusion profile was investigated in two ways. One method was to suspend the needle directly over a dummy sample, raise the temperature, for periods of time equal to the diffusion times, and then take an auto-radiograph of the surface. Negligible radioactivity appeared. In the second method a thin slot in the crystal face on one side of the source provided a "cong path" for surface diffusion. If evaporation was the primary source of surface atoms the region of radioactivity around the source would be symmetrical. This was not the case. The profile dipped abruptly at the edge of the slot but on the other side of the source the usual diffusion profile appeared.

Jan 1, 1963

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By Y. A. Chang

Phase relationships in the system Cr-Si have been established based on the melting point, X-ray, metallo-graphic, and DTA studies. The three intermediate phases, Cr3Si, Cr5Si,, and CrSi,, melt congruently at 177V ± I@,Cr3Si, 1680"i 20°, and 1490" *20°C, respectively, while the fourth intermediate phase CrSi, melts peritectically at 1413" i 5°C to Cr5Si3 and a melt containing 51 at. pct Si. The temperatures and compositions of the four eutectic isotherms occurring in this system are given below: DTA and metallographic evidences indicate that Cr5Si, undergoes a phase transformation at 1505" i20°C. The high-temperature form of this phase could not be retained by the quenching techniques used in this study. TECHNOLOGICAL interest in the developing of composite systems, consisting of Sic on the one hand as a fiber-reinforced material and metallic substances such as chromium, nickel, or Cr-Ni alloys as a binding agent on the other hand, stimulated the present investigation of phase relationships in the binary system Cr-Si. Earlier works concerning this system have been evaluated and summarized by ansen and Anderko.&apos; Their phase diagram was based mainly on the works of Kieffer, Benesovsky, and schroth2 and Kurnakov.~ According to these authors, the three intermediate phases Cr3Si, CrSi, and CrSi, all melt congruently at approximately 1730°, 1600°, and 1550°C. However, they did not agree on the compositional stability of the fourth intermediate phase between Cr3Si and CrSi. Later Parthe, Nowotny, and schmid4 determined the structure of this phase to be tetragonal T-1 type using the single-crystal method, and concluded that this phase had a formula of Cr5Si3. Since the compilation of Hansen and Anderko,&apos; a new phase diagram for the system Cr-Si has been proposed by Elliott5 based on the works of Goldschmidt and rand,&apos; Guseva and ~vechkin,~ and Trusova, Kuzev, and Ormont8 and the earlier works quoted by Hansen and Anderko.&apos; According to this proposed phase diagram, all four intermediate phases have large ranges of homogeneity and all melt congruently. More recently, Svechnikov, Kocherzhinskii, and yupkog studied the system Cr-Si by the DTA-method. According to their findings, the three intermediate phases, Cr3Si, Cr5Si3, and CrSi,, melt congruently at 1700°, 1720°, and 1475"C, respectively, while the fourth intermediate phase, CrSi, melts peritectically at 1475°C to Cr5Si3 and a melt containing 50 at. pct Si. The temperatures and compositions of the four eutectic isotherms were found to be: In view of the discrepancies existing in the literature concerning the system Cr-Si, it was decided to rein-vestigate the phase relationships in this system. EXPERIMENTAL a) Starting Materials. Chromium disilicide and chromium or silicon powders were used in the present study to prepare the melting point and DTA samples. CrSi, was obtained by directly reacting cold-pressed elemental powders in an atmosphere of Hz at a temperature of about 1250°C. Chromium powder, purchased from Stark Chemical Co., had the following impurities in ppm: Fe, 200; Mg, 1000; and 0, 250; while silicon powder, purchased from the Welded Carbide Co., had the following impurities in ppm: Ca, 700; and Fe, 3500. b) Melting-Point Determination and Differential Thermal Analysis. Cylindrical melting-point samples of approximately 13 mm in diam and 30 mm in length with a rectangular groove in the center were prepared by hot-pressing of well-mixed powder mixtures in graphite dies. Before the melting-point determination, the hot-pressed samples were ground on a sand paper to remove any minute surface contamination of graphite. A small hole of 1 mm in diam, drilled on the center portion of the samples, served as a blackbody cavity for the temperature measurements. DTA samples approximately 13 mm in diam and 15 mm in length were prepared in a manner similar to the melting-point samples. Melting points were determined using the Pirani technique under a helium atmosphere of 40 psi. The design, performance, and operation of this apparatus have been described in detail by Rudy and ~ro~ulski.&apos;~ The temperature measurements were carried out with a calibrated disappearing-filament-type micro-pyrometer. The measured temperature was corrected for losses from the quartz window of the melting-point furnace and for deviations from blackbody conditions of the observation hole. The procedure for temperature correction has also been previously described." The DTA method of Heetderks, Rudy and Eckertl&apos; was also used to check any phase transformations of selected alloys in the system Cr-Si. It was not possible to make remated runs on the same sample once melt-

Jan 1, 1969

By R. R. Judd, H. W. Paxton

The rate of dissolution of cementite was studied in three low-carbon materials: a zone-refined Fe-C alloy, an Fe-0.5pct Mn-C alloy, and a commercial low-carbon steel. The materials were spheroidized, ad then held isothermally at temperatures above the Al. The isothermal anneal was interrupted periodically by a water quench and the specimens were analyzed by quantitative metallography for the amount of aus-tenite formed during the anneal. The results of this study were compared with an analytical model for the process, which assumes that carbon diffusion in aus-tenite is the rate-controlling step for the cementite dissolution process. The correlation between the model and the experimental data is excellent for the zone-refined Fe-C alloys; however, the Fe-0.5 pct Mn-C alloys and the commercial steel deviate from the calculated model. This deviation is thought to be a result of manganese segregation between the carbide and the matrix. The rate of nucleation of austenite at carbide interfaces was reduced by the manganese addition and enhanced by the presence of ferrite-ferrite grain boundaries. PREVIOUS investigations of the nucleation and growth of austenite from ferrite-carbide aggregates are not entirely satisfying for at least one of several reasons. The most prevalent of these is a lack of quantitative data. Engineering studies have been run on many steels with little control over important parameters such as composition and initial aggregate structure. The data obtained are valid only for material with identical chemistry and thermal history. A more informative approach to the problem of aus-tenitization would be to determine the mechanism that controls the rate of solution of carbide in austenite and how it is modified by alloying elements. This information could then be used to calculate an austeniti-zation rate for any material, provided its composition and structure are known. The object of the present work is to establish the rate-controlling step for cementite dissolution in Fe-C austenite and to investigate the modification of this rate by small manganese additions. The composition and structure of the material used were carefully controlled and all measurements were designed to allow a quantitative analysis of the kinetic process that controls the austenitization rate. A MODEL FOR DISSOLUTION OF CEMENTITE Cementite dissolution has been analyzed mathematically by a model that approximates the material used in the experiments. This model postulates a regular ar-array of identical cementite spheroids with 4 C( diam, embedded in a grain boundary- free ferrite matrix. The analysis provides a detailed description of the dissolution of one carbide spheroid and a generalization of the solution by summation over all the carbides in the material. The carbides may be isolated by defining identical, space-filling cells of ferrite around them. If the cell dimensions are greater than the diameter of the austenite sphere resulting from complete dissolution of the carbide, and no interaction (through diffusion in ferrite) takes place between cells during the dissolution process, the model need concern only one cell, since the solution in each cell is identical. In the experimental material, the dimensions of the cell, the carbide, and the final austenite sphere are approximately 24, 4, and 8 p, respectively; use of the single cell is therefore justified. The experimental observations are made on the austenite nodules that form around each carbide during the dissolution process. The model concerns the growth of these austenite nodules. The attendant shrinking of the carbide can be obtained from the same analysis by an extension of the calculations. Several a priori assumptions are necessary to make the analysis of the growth problem tractable. They are: 1) carbon diffusion through the austenite nodule is the rate-controlling process; 2) local equilibrium exists at all interfaces, 3) the austenite nucleus that forms on each carbide instantaneously envelops the carbide; 4) during the austenite growth process, the diffusion flux of carbon in ferrite is insignificant; 5) a quasi-steady state exists in the austenite concentration field; that is, at any instant during the dissolution process, the austenite carbon concentration gradient closely approximates that for a steady-state solution; and 6) the effects of capillarity on the dissolution rate of the carbides can be neglected. Referring to Fig. 1, a mass balance at the y-a interface for an infinitesimal boundary movement gives: Where rb is the outer radius of the austenite shell, C1 and C are carbon concentrations at the interface in austenite and ferrite, respectively, see Fig. 2, is the diffusion coefficient of carbon in austenite for the concentration of carbon at the interface, and t is time. The fifth assumption permits the austenite carbon concentration to be approximated by the Laplace solution for the spherical case. Therefore, where C(Y) is the carbon concentration at r, and A and B are constants. Local interfacial equilibrium fixes the boundary conditions for the diffusion problem. They are:

Jan 1, 1969