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By A. R. Troiano, E. A. Steigerwald, F. W. Schaller

The kinetics of crack propagation in a hydrogenated high-strength steel at subzero temperatures indicated that cracking progressed in a discontinuous fashion. The delayed failure process thus involves a series of crack initiations rather than the continuous growth of a single crack. The incubation time required for the initiation of delayed failure was controlled by the diffusion of hydrogen. The activation energy for the process was 9120 cal per g-alom. As the test temperature was lowered the incubation time constituted a greater percentage of the total tinze to fracture, and al -50°F the incubation and fracture times were essentially coincident resulting in instantaneous, catastroplzic fracture. A unique feature of hydrogen embrittlement is the delayed failure process in which the material fails under the action of a sustained load even though it is capable of supporting a higher load for a finite period of time.')' Delayed failure of steel and titanium is characterized by an incubation time, preceding the initiation of a crack in a highly localized region, and the subsequent growth of the crack to ultimate failure.3-5 The kinetics of crack growth in hydro-genated high-strength steels have been studied through the use of resistance measurements and have an important bearing on the mechanism of delayed failure. Delayed failure is believed to be merely a facet of hydrogen embrittlement in which sufficient time is allowed during a test for hydrogen diffusion. The current theories employed to explain hydrogen em-brittlement can be grouped into two types. one6-8 explains the embrittlement on the basis of the pressure exerted by molecular hdrogen in lattice voids or defects while the other9-10 attributes the embrittlement to the influence of hydrogen in the lattice. The mechanism used to explain the nature of the crack kinetics in delayed failure is based on the stress-induced diffusion of hydrogen to the area of maximum triaxiality.3 When the hydrogen concentration in this region reaches a critical value, a crack is nucleated. This initial crack propagates instantaneously until stopped by the higher fracture stress of the adjacent material of lower hydrogen content. The continuation of cracking must then await the further diffusion of hydrogen to the new region of triaxiality near the base of the crack where another initiation will occur. From this mechanism it follows that crack propagation is nothing more or less than a series of initiations with limited fracture. The purpose of this investigation was to examine the kinetics of crack growth in an effort to determine whether or not the process was discontinuous. Studies of crack propagation were conducted at low temperatures to retard the diffusion of hydrogen which is presumed to be the rate controlling process in delayed failure. MATERIALS AND PROCEDURE Specimen Preparation—A commercial heat of air-craft quality SAE-AISI 4340 steel, designated as Heat G, was furnished by the Republic Steel Co. in the form of %-in. hot-rolled bars. The material had the following chemical analysis: Composition of 4340 Steel—G Heat C Mn Si Ni Cr Mo 0,395pct 0.82pct 0.29pct 1.76pct 0.85pct 0.25pct Notched tensile specimens with less than a 0.001 in. radius, Fig. 1, were used throughout the investigation. The specimens were heat treated to a 230,000 psi strength level according to the following sequence: a) Normalize bar stock at 1650°F for 1 hr, b) Stress relieve at 1200°F for 4 hr and furnace cool,

Jan 1, 1960

By H. C. Fiedler

Heats of high purity iron containing 3.1 pct Si and be -tween 0.0003 and 0.0295 pct N were prepared by vacuum melting ad then pouring while in a nitrogen atmosphere with the pressure between 0 and 90 psi. Strip from a heat with 0.0184 pct N underwent complete secondary recrystallization during the final anneal. Heats with less nitrogen had too few Si3N4 particles to restrain normal grain growth, and the heat with higher nitrogen had too many particles to allow complete secondary recrystallization. In the hot-rolled structure, Si3N4 precipitates only at the grain boundaries, with the consequence that annealing after hot-rolling diminishes the ability to subsequently undergo secondary recrystallization. In contrast to this behavior, ALNprecipitates uniformly in the hot-rolled structure. Under 1 atm of nitrogen, Si3N, in 3.1 pct Si-Fe dissociates between 900" and 950°C; the solubility of nitrogen increases from 0.0010 pct at 900" to 0.0030 pct at 1200°C. The solubility of nitrogen in Si-Fe has been the subject of many investigations. Corney and Turkdogan1 heated a 2.83 pct Si alloy in nitrogen and found the solubility, under 1 atrn of nitrogen, to be 0.0019 pct at 900°C. They claimed that Si3N4 did not form in the alloy above 705°C in 1 atrn of nitrogen. Fryxell et al.2 heated samples of 3.25 pct Si-Fe containing 0.0025 pct N over a range of temperatures and then analyzed for total nitrogen by vacuum fusion and for nitrogen in solution by a modified Kjeldahl technique. At 900°C, they reported the solubility of nitrogen in equilibrium with Si3N4 to be 0.0011 pct. pearce9 found the solubility of nitrogen at 900°C under 0.95 atrn of nitrogen to be 0.0017 pct in a 3.06 pct Si alloy. He reported that Si3N4 does not form above 770°C in 1 atrn of nitrogen. Although internal friction measurements have given somewhat higher values for the solubility,4-6 if the solubility of nitrogen is as low as has been reported by most investigators, and if Si3N4 is stable up to at least 945°C at 1 atrn pressure of nitrogen as reported by Seybolt,7 a small amount of nitrogen in properly processed Si-Fe should be effective in promoting secondary recrystallization. The requirement is that in the final heat treatment there be enough small, well-dispersed particles of Si3N4 to restrain normal grain growth. Fast8 has obtained secondary recrystallization by nitriding high-purity 3 pct Si-Fe after hot-rolling to a thickness of 0.118 in., followed by processing to 0.012 in., and annealing. A large amount of nitrogen, 0.076 pct. was introduced during the nitriding heat treatment, but he has since reported9 that "a few hundredths of a percent" is sufficient. Small amounts of aluminum10 or vanadium" nitride are capable of promoting secondary recrystallization. Heats containing as little as 0.010 pct A1 or 0.042 pct V and from 0.006 to 0.009 pct N underwent complete secondary recrystallization at final gage, whereas heats with lesser amounts of aluminum or vanadium did not.l2 To be reported is the behavior of nitrogen in high-purity 3.1 pct Si-Fe, and the relation of this behavior to the ability to undergo secondary recrystallization. PROCEDURE Ingots weighing 1 lb were made by vacuum melting high-purity electrolytic iron (A104, Glidden Co.) and high-purity silicon (Monsanto Co.). The latter was used in preference to ferrosilicon to insure a low aluminum content. The design of the melting furnace permitted pouring with the furnace atmosphere either below or above atmospheric pressure. Accordingly, at the completion of melting, nitrogen was admitted to the desired pressure and the heat then immediately poured. The ingots were sound, with no indication of porosity. In Table I are listed the heats investigated, the nitrogen pressure at pour, and the nitrogen and oxygen contents as determined by vacuum fusion with a platinum bath at 1850°C, a procedure which insures measurement of the total nitrogen.13 In addition, all heats contained 3.1 pct Si and not more than 0.002 pct C, 0.003 pct S or 0.005 pct Al. It was subsequently found that the quantity of nitrogen contained in the heats in Table I does not necessarily represent that obtained under equilibrium conditions. For example, the ingot poured immediately after 1 atrn of nitrogen was admitted to the chamber contained 0.0093 pct N, whereas an ingot poured 3 min after the nitrogen was admitted contained 0.021 pct N and another poured after a 6-min delay contained 0.029 pct N. While some bleeding of the hot top occurred in the latter instance, the ingot when examined in cross section appeared sound. The ingots were heated to 1325°C in hydrogen and rapidly rolled to 0.080 in. in 3 passes. The roll speed of the final pass was reduced so as to increase the quenching effect of the rolls. The hot-rolled pieces were processed both as-hot-rolled and after heating for 3 min at 900°C in hydrogen. After cold-rolling to 0.026 in., the strips were heated for 2 min at 900°C in hydrogen, then cold-rolled to the final gage of 0.012 in. The loss of nitrogen in going from the ingot to cold-rolled strip was no more than 10 pct. The final heat treatment, which was for the purpose of develop-

Jan 1, 1970

By Robert Hamilton Morris

FATE, rather than planning, put Bob Morris into coal mining. He was a farmer's son, born at Plattsburg, Ohio, just 68 years ago (Feb. 28, 1878) though he could easily pass for ten years younger. Before he was ready for high school the family moved to Columbus, seat of Ohio State University, whose course in mining engineering attracted him because lie thought it the broadest of the engineering courses. He really wanted to be a steel metallurgist but it was a coal-mining company that offered him a job when he graduated, and this circumstance directed his entire future professional life. To. be sure it wasn't such a glorious opportunity so far as pay went -$40 a month-but his employer, the Modoc Coal & Mining Co., Modoc, Ohio, was developing a new shaft mine, thus offering some good experience. In 1902, after a year's experience, he was made superintendent of the property. Then in 1903 the Continental Coal Co. at Glouster, Ohio, offered him a better job as their chief engineer, which he retained until 1905, at the same time joining the A.I.M.E.

Jan 1, 1946

By Stuart St. Clair

In view of the great interest shown in the oil possibilities of Kentucky, one is impressed with the paucity of reliable literature on the oil fields of the state. A few brief reports by the Federal and State Geological Surveys are about the only reliable data available. When the estimated production figures, for 1918, are published by the U. S. Geological Survey, they will show a revival of the oil industry in the Blue Grass State during the past half decade. There will also be an increase in the production for 1919 and 1920, at least. Although as an oil-producing state Kentucky is small, compared with some of the other oil states, the present production and the area of undrilled proved territory is large enough to classify it as one of the important oil states of the Union. This paper will be confined to the Irvine District and the immediately adjoining areas which have been prospected with varying success. The Corniferous limestone or Irvine sand is the oil-producing formation in the area discussed. In my divisional nomenclature, the Irvine District includes the Irvine field, which extends from the town of Irvine eastward toward Campton; the Big Sinking area, which joins and lies to the south of the eastern part of the Irvine field; the Beattyville area, which lies to the north and northeast of the town of that name and joins the Big Sinking area; and the Ross Creek pool, which lies to the southwest of the big production and across the Kentucky River. Except for the Ross Creek pool, the main producing area is bounded on the east by the L. & E. R. R. and on the west and south by the Irvine Branch of the L. & N. R. R. Winchester and Lexington form the gateways and Torrent on the east, Irvine on the west, and Beattyville on the south are the principle entrances to the main fields. Evelyn, on the L. & N. R. R., south of Irvine, is the point of entrance to the Ross Creek area. Geology The geology of the Irvine District is very simple. The rock formations with which the oil man should acquaint himself lie between the lower measures of the Pennsylvanian sandstones and shales and the Devonian or Corniferous limestone, or Irvine formation. Only a very brief description of these formations will be given, as they have been described fully by E. W. Shaw.'

Jan 1, 1921

By G. Hasenfus, M. Karmis, G. Goodman

Surf ace subsidence is rapidly becoming an important environmental consideration of active as well as abandoned mining operations. The damages attributed to this phenomenon have been witnessed in both rural and urban areas and include land settlement and fracturing, structural damages to surface buildings or facilities and disruption or contamination of ground water supplies. The problem of mining subsidence has gained considerable emphasis in the Appalachian coalfield. The increased mining activity over the past few years and the particular topographic conditions, lithologic and structural environment, mining methods and hydrological patterns are all factors which have contributed to specific subsidence characteristics in this region. The objective of this paper is to discuss and review the most widely accepted methods of subsidence prediction above longwall as well as partial extraction systems in Appalachia. These include an accurate and easy to apply empirical method, which has been developed entirely from field information pertaining to the Appalachian coalfield and incorporates both geometrical and geological information of the panel in question. The second method is a development of influence functions and is founded on the zone area approach. Both methods, originally derived for longwall mining, have been expanded to include room and pillar applications and have been widely used by the mining industry in the Appalachian coalfield.

Jan 1, 1984

By A. Kenneth Schellinger

DURING the comminution of a brittle material in the presence of dry air, no known phase change or chemical reaction takes place. The energy changes associated with the comminution are those of the transformation of kinetic energy into heat energy and the energy absorption represented by the actual rupture of molecular and/or ionic bonds. The random nature of the actual grinding process in a tumbling-mill often precludes the effective application of a rupture force on each individual particle of brittle mineral present. The result must be a great deal of useless vibration on an atomic scale in both the brittle mineral and the grinding medium below the elastic limit, which vibration is eventually manifested as heat energy in the mill. The actual rupture of molecular, or ionic, bonds creates new surface on the brittle minerals; each square centimeter of this new surface then must possess a number of potential bonds, each of which could reform theoretically with the release of energy. The sum total of this potential energy of bonding per unit of new surface, minus bond satiation effects of the enclosing gas or liquid, must be the surface energy of the mineral. If the comminution of the brittle mineral were carried out within the chamber of a calorimeter, the energy released as heat could be determined rather accurately. Moreover, the total kinetic energy input to the comminuting mass (mineral and medium) conceivably could be derived by a suitable torquemeter and revolution counter if the whole calorimeter were revolved. The difference between these two energy figures should then represent the net energy (gross energy input—heat enerb output) used in creating new surface, gliding or slip on atomic planes, twinning, and possibly other lattice rearrangements within the mineral. If it be postulated further that with a hard, brittle crystalline material, such as quartz, the energy used to produce gliding, twinning, and other permanent lattice movements is a very small fraction of the total net energy absorbed, then this energy absorption within the grinding calorimeter can be ascribed to the creation of new surface energy alone. Such energy is, from the thermody-namic standpoint, the true effective work of the grinding device, in this case a tumbling-medium mill. The ratio of this effective work (in calories) to the total energy input (in calories) should express the thermodynamic efficiency of the comminution taking place under the conditions used in the grinding calorimeter. This approach to the measurement of the energetics of tumbling-mill grinding was suggested by some previous work by Fahrenwald and coworkers' with a laboratory ball mill and a thermometer. They measured the efficiency of grinding based on the formula: Pct Grinding Efficiency = Energy (calories) — Thermal Energy x 100 1npZ Output (calories) Energy input (calories) Efficiencies thus measured, while grinding quartz sand, ranged from 19.7 pct to 7.4 pct. Cook in 1915,' used this approach to the problem of grinding efficiencies in stamp batteries and obtained the energy input by stamp weights times drop distances and the energy output by means of thermometers and pulp flow rates. He calculated that 80 pct of the input energy to the stamp shoes was wasted as sensible heat in the ore pulp. No other studies of comminution by this method of energy differences came to the author's attention. Reasonable agreement as to the order-of-mag-nitude of comminution efficiencies in tumbling-media mills is lacking in the literature. There is a widespread impression among technical workers that the grinding efficiency of the industrial ball mill may be on the order of 1 pct, or even a fraction

Jan 1, 1952

By Robert A. Haney, Stephen J. Gigliotti, James L. Banfield

A series of investigations were made by the Mine Safety and Health Administration to evaluate the performance of various face ventilation systems as part of a program to reduce frictional ignitions of methane and to develop face ventilation systems that could be used with the line brattice more than 10 feet from the face. Tests were conducted in a full-scale laboratory model of a face area. Systems tested included unassisted blowing and exhaust line brattice, diffuser fan and spray fan systems. Systems were evaluated at air quantities ranging from 1.4 to 7.0 m3/s (3,000 to 15,000 cfm), and brattice-to-face distances from 1.5 to 9 meters (5 to 30 feet.). Tests were designed so that systems could be evaluated for the location of the high-point methane concentration in the face area, methane dilution capacity, and face ventilation index. The methane dilution capacity is the total amount of methane a system can dilute to 1.0 volume-percent. The face ventilation index is the efficiency at which the available face air volume is being used.

Jan 1, 1982

By H. Evans, L. A. Hunt

In the pellet-producing industry it is sometimes claimed that "The pellets are made in the concentrator," or that "The key to good pellets is in the balling operation." However, one claim is generally agreed on: If you can put in, on, and through the indurating furnace a good green ball of Proper size and adequate strength to withstand the handling, load, dehydration, and thermal shock until it is properly heat-hardened, you will have the pellet product you desire-that is, a "competent" green ball. The strength requirements that enable a competent green ball to withstand the environment of the indurating furnace are usually less restrictive than those for transporting the green ball from its source of production to the furnace. Experience has shown that different types of material may have different balling characteristics which may impose limitations on the quality of the green ball that can easily be produced under normal conditions. Therefore, if a specific material will produce a green ball that meets the physical requirements for competency in the furnace, but not for handling or transportation, various practices must be instituted to overcome this deficiency. In other words, if a normal handling system is too rigorous for the green balls that can be produced under standard conditions, then "handling with care" should be tried.

Jan 5, 1967

By Earl S. Bardwell

The determination of suitable and safe annealing temperatures is one of the most important problems arising in the operation of a copper rolling mill. Certain of the larger mills have worked this problem out for themselves and in these mills the operation has become more or less standardized. In some of the mills pyrometers are used to measure the temperature of the annealing furnaces and careful watch is kept to see that overheating does not take place. In a considerable number of the mills, however, dependence is placed entirely on the judgment of the operator. The almost total lack of literature bearing on this subject seems sufficient warrant for the publication of this paper. ' The discussion of this subject naturally divides itself into two parts: (1) The effect of annealing temperature on physical properties; and (2) changes in the microstructure of refined copper due to cold rolling and annealing. I. The Effect of Annealing Temperature on Physical Properties For the purpose of investigating this phase of the subject six test bars were selected, varying in oxygen content between the limits of 0.036 and 0.070 per cent. The chemical composition of each of these test bars was as follows: Bar Number 1 2 3 4 5 6 Copper + silver...... 99.95 99.92 99.945 99.94 99.95 99.93 Oxygen.............. 0.041 0.070 0.046 0.050 0.036 0.058 As + Sb............. 0.0038 0.0038 0.0038 0.0038 0.0031 0.0031 The bars were heated in an electric muffle to about 1,650" F. and rolled into rods. The rods were annealed, pickled, and drawn to No. 12 B. & S. gauge wire. The wire which was to be used for the annealing test was cut into 38-in. lengths and each length made into a coil 6 in. in diameter. The separate coils were marked so that they might readily be identified

Jan 1, 1915

A. G. Cockbain—The paper by Burlingame, Bitsianes and Joseph is of great interest in extending the work done on high grade sinters, particularly that of Hessle, and the development and application to them of the technique of McBriar, Johnson, Andrews and Davies on ironstone sinters. In this laboratory the work of McBriar et al. has also been continued and extended to cover high grade sinters, and a sectioning technique similar to that used by McBriar et al. was attempted on sinter cakes made in the laboratory sinter unit, using magnetite concentrates (containing 64 pct Fe). In these experiments no attempt was made to flush out the products of combustion with nitrogen before cooling. It was considered that free air penetration would occur on only a limited scale with the size of sinter cake made (14 in. sq x 12 in. deep). Chemical analyses of the zones showed generally similar features of those described by Burlingame et al. and especially the FeO rich region at and just behind the flame front, i.e. zones of ignition and combustion. This seems to indicate that the nitrogen atmosphere does not materially affect the states of oxidation in the sinter cake or at least that special care is not required unless the sinter cake is small. Burlingame et al. consider that FeO present has some significant part to play in the mechanism of sintering. This view does not find favor with the author. The reduction of iron oxides in the presence of red hot coke is a well known phenomenon, whether conducted in an atmosphere of nitrogen or in a crucible in air, and in view of the presence of some carbon in the hot sinter, especially just at the ignition zone, cessation of the progress of the flame front will in no way affect the reduction of iron oxides near hot coke. Even in a nitrogen atmosphere some CO and CO, will be generated by reduction and by continual oxidation and reduction of CO as the transfer agent, the oxidation state of the iron oxides can be lowered quite rupidly so long as free carbon exists with enough heat. Knowing the composition of the gas at the flame front (obtainable by probes), it would be possible to calculate the static oxidation state of Fe2O3/Fe3O2 in equilibrium with it and hence obtain a check on the chemical analyses to see if in fact direct reduction of the Fe2O3/Fe2O1 to FeO has taken place. Have the authors attempted this? It appears to this writer that what is required is some means of reducing rapidly the heat content of the ignition zone and immediately behind, and at the same time insuring no oxidation by the air. In ironstone sinters the difficulty of oxidation state of the iron did not arise on account of the very large slag bulk. However, in high grade sinters knowledge of this, and also the mechanism whereby high oxidation states can be obtained in the final sinter, is of great interest. R. D. Burlingame (author's reply)—The question has been raised as to whether the high FeO content found in high-fuel sinters is due to actual reduction at the advancing flame front or due to unavoidable direct reduction during the quenching period. For such direct reduction to have taken place in the freshly-formed sinter, a considerable amount of solid carbon would have had to escape combustion and be available throughout the hot sinter zone during the quenching period. A simple stoichiometric calculation with the limited data available indicates that a zone of freshly-formed sinter over 2 in. wide must have averaged roughly 2 pct C to accomplish the amount of reduction found. Furthermore, the presence of this amount of carbon would indicate that the fuel in the charge had not burned over a narrow front but over a zone at least 2 in. thick. In contrast to such a condition, the data of the present investigation indicate that the combustion of fuel is confined mainly to a narrow front in which high temperatures and reducing conditions favor. the formation of excess ferrous iron.

Jan 1, 1959

H. 0. Hofman, Boston, Mass. (communication to the Secretary*) :—The experimental demonstration by Professor H. Ries, of the fact that a mixture of clay and finely-ground flux will melt more readily than one in which the flux is less fine and therefore less intimately mixed, is very striking, and will be appreciated especially by those who have to discuss, before classes of students, fusions on a small or a large scale. The statement, that I " rather disputed" the influence of size of flux-particles on the ease with which fire-clay mixtures fused, is an erroneous inference from the paper written by Mr. B. Stoughton and myself in 1898.' We did not undertake to study the influence upon fusibility of the sizes of the particles, either of clay or flux. What we did try to find out was, whether the common practice of finely grinding raw or burnt clay, or a mixture of the two, before testing with Seger cones for resistance to heat and to fluxes, xould give the same results as if the materials were tested just as they were going to be

Jan 1, 1904

By H. H. Johnson, Eric W. Johnson

A newly developed ac technique was used to measure the electrical-resistivity changes associated with both cyclic stressing and subsequent annealing of high-purity and OFHC copper. The early stage of push-pull fatigue was explored at 293° and 4.2°K, with stresses chosen for an expected fatigue life of 2 to 8 X 105 cycles. For high-purity copper, fatigue at 293°K was accompanied by an initial increase in resistivity. After about 5000 stress cycles, no further increase was observed. Annealing studies showed that the resisticity increment could be accounted for solely in terms of an increased dislocation density, to about 2 x 1010 disl pev sq cm. Fov 42°K fatigue, however, the resistivity increased continually, with no evidence of saturation, as approximately (No. of stress cycles)1/4. This is intevpreted to result from both dislocation multiplication and vacancy production; estimated vacancy concentrations are 10-4 to 10-9. The continuous resistivity increase was inhibited by interspersed annealing treatments at 293°K, which also raised the level of the stress-strain curve. These effects are attributed to annealing of vacancies into dislocation loops. In contrast, OFHC copper fatigued at 4.2°K showed saturation of electrical vesistivity after only a few hundred cycles, and it appeared that vacancies annealed out completely between 77° and 293°K. MaNY observations suggest that both dislocation multiplication and point-defect production are important aspects of fatigue deformation. An increase in dislocation density with number of stress cycles has been demonstrated or implied by several experimental techniques, including optical metallography with lithium fluoride,' electron microscopy with copper,2 thermal conductivity of Cu-Zn alloys,3 and peak-stress measurements during cycling at constant plastic strain amplitude.4,5 At low amplitudes and/or stresses saturation of fatigue hardening and dislocation density occurs early in the expected fatigue life,4-6 frequently by a few hundred cycles. The evidence for point-defect production is somewhat less extensive, but it is nonetheless persuasive. Rosenberg7 reported briefly that, for equal stresses, copper fatigued at liquid-hydrogen temperature displays an increase in electrical resistance some ten times that which accompanies unidirectional stressing. Further, the extra resistance saturates after a few hundred stress cycles, and does not anneal significantly until a temperature of about 170°K is attained.' Point-defect production during fatigue is also suggested by 1) the softening during cyclic stressing of initially strain-hardened polycrystal-line copper9, 2) the strong temperature dependence of the yield strength of fatigue-hardened mono- and polycrystalline copper,579"0 and 3) the influence of intermediate annealing upon slip-band formation in copper fatigued at 90°K.8 It is evident that characterization of the fatigued state requires a knowledge of both point-defect and dislocation densities. For this purpose electrical-resistivity measurements are useful, but they are difficult to perform because of geometric limitations. Push-pull fatigue is necessary to obtain a macroscopic ally uniform deformation over the specimen cross section; however, the specimen must then have a low slenderness ratio to avoid plastic buckling, while the standard dc resistivity technique requires a very slender specimen for

Jan 1, 1965

By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Member, graduate Columbia School of Mines, age 35, married, best of health, dependable, desires position as manager or scout for reliable interests. Experience covers responsible positions incident to the mining and milling of gold-silver, copper, lead, and zinc ores, and the examination of base and rare-metal deposits in United States and Mexico. Salary $3600. Available April 1. No. 453. Member, mining engineer, technical training, age 32, assayer, engineer and superintendent of porphyry copper development, churn drilling and shaft sinking. Examination of prospects and development of gold prospects. Considerable flotation experience. No. 454. Young Columbia graduate, conscientious worker, with experience in inorganic analysis, surveying, draughting, and wit. post-graduate training in geology, desires position wt. prospects. Minimum salary considered, $130 in U. S. and $150 in Mexico. At present employed. Draft exempt. No. 455.

Jan 5, 1918

By VERITAS

THE most concentrated industry of major character in the United States is that of the Ford Motor CO., which is to say Henry Ford. Its sole function is to supply the public with a cheap motor car which it does to the extent of two million or so per annum. In doing this, a relatively small profit per unit is multi- plied to an enormous aggregate per annum and has resulted in the creation of one of the greatest industrial fortunes of the world. The industrial and sociological consequences of .this are bound to be immense. On the physical side the production of two million automobiles means the consumption of two or three million tons of materials, chiefly metals, in the 'direct form of the finished product', and a huge additional tonnage of coal and other things that ,are consumed en route, and also the labor of many thousands of men. In the development of a business on this scale it was but natural that the Ford Motor ,Co. should seek to supply itself with the raw 'materials it needs, and they being so largely coal and metals the company is brought into close contact with the mining and metallurgical industries. It is a huge consumer of - steel. It is the fourth largest consumer of copper. It is a large consumer of lead, tin, aluminum and zinc. The mining and metallurgical industries have, therefore, good reason to learn to know Henry Ford, his personality, his thoughts and his policies.

Jan 1, 1924

By R. I. Jaffee, F. C. Holden, H. R. Ogden

Alpha solutes increase the strengths of Ti-Mn alloys through solid-solution strengthening. The substitutional a addition, aluminum, decreases, and the interstitial solutes, carbon and nitrogen, increase the rate of nucleation and growth of a from ß. The best combinations of properties of a-ß alloys are obtained when there is a sufficient quantity of a phase in the structure to dissolve the a solutes. OF the many different titanium-base alloy systems, the predominant alloy type is the a-ß alloy. The properties of the a-ß alloys are dependent on solid-solution strengthening and heat-treatment effects involving the a-ß ratio and transformation reactions. Another variable which influences the mechanical properties of a-ß alloys is the a-stabilizer content of the alloy. An a solute may be present as an intentional addition, such as aluminum, or as an impurity element, such as carbon, oxygen, or nitrogen. It is known that these a stabilizers, when added to titanium, form single-phase alloys which are not heat treatable but which obtain their strength from solid-solution strengthening. Thus, it would be expected that a additions to a-ß alloys would increase the strength of the alloys by solid-solution strengthening of the a phase. In addition, they would affect the transformation kinetics of the ß-to-a reactions and other processes based on the instability of the ß phase. The effects of heat treatment and structure on the mechanical properties of Ti-Mn alloys have been shown in a previous paper.6 This system offers a good base to demonstrate the effects of typical a solutes on the properties of a-ß alloys. The three a solutes described in this work are aluminum, representative of a substitutional a solute, nitrogen, representative of an interstitial a solute, and carbon, representative of an interstitial compound-forming element. The effects of heat treatment and microstructure on the properties of a alloys containing these three elements are described in concurrent publications. Some of these data are used for base-line points in several of the curves used for illustration herein. Experimental Procedures Iodide titanium was used as the base for all of the alloys studied in this work. The alloys were prepared as ½ lb ingots by double arc melting in an argon atmosphere. The ingots were forged to ¾ in. rounds, vacuum annealed for 6 hr at 900°C at a pressure of 10 ' to 10-5 mm of Hg to remove hydrogen, and hot swaged to 1/4 in. diam rod. After me- chanical descaling, test specimens were prepared for heat treatment. The alloys used in this study together with the fabrication temperatures are given in Table I. Heat treatments were done in argon. For the most part, the specimens were sealed in Vyeor capsules under a partial pressure of argon. Quenching was accomplished by breaking the capsule under water. Other cooling methods used included oil quench, argon cool (simulated air cool in an argon atmosphere), and furnace cool. The times for the various heat-treating temperatures are given in Table 11. The tests performed on the alloys consisted of tensile tests on ? in. diam specimens, hardness tests, and microimpact tests. Specimen sizes have been adequately described in a previous publication.' The micrographs presented in this paper were taken from specimens cut from the shoulders of broken tensile specimens. Final polishing was done with Linde B on a slow-speed wheel, and the specimens were etched with a 1½ HF — 3½ HNO, solution. Ti-N-Mn Alloys The transformation diagram and microstructures of the Ti-0.1 pct N-Mn alloys used in this investigation are given in Fig. 1. The effect of small nitrogen additions on the binary Ti-Mn diagram is to raise the ß-transus temperature with little effect on the a solubility of manganese. Also, as has been noted previously,' high manganese-content alloys containing nitrogen, when quenched from temperatures high in the ß field, contain a subgrain boundary phase which appears to be nitrogen-rich a. Marten-site is formed when alloys containing less than about

Jan 1, 1956

By Frank Haas

THE public generally has-become aware that there is something wrong with the coal industry and a clamor has arisen for an explanation if not a remedy for this disorder. It is only reasonable that this Institute be looked to for a diagnosis to show the way for some other .agency to prepare the patient for prescription or operation. The subject is extensive, widely diversified, and beyond the efforts of an individual to cover completely; one of the objects of this paper is the initiating of a symposium on the non- technical factors essential to an understanding of the bituminous coal industry. The present condition of the coal industry cannot be described in a few words but, in effect, it resolves itself into a simple statement: The average coal operator is losing money notwithstanding a firm conviction on the part of the consumer that he pays too much for his coal. Without enumerating the many and varied. factors which contribute to this condition, this paper will be devoted to the interrelation of taxation and ownership of coal and its effect on finance

Jan 1, 1930

Ira B. Joralemon, one of the world's most noted mining geologists, died last year at the age of 91. "His long professional career," says Donald H. McLaughlin, chairman of the executive committee at Homestake Mining Co., "covered an epoch in the history of mining that was unique in its opportunities and achievements," adding that many mining companies (Bunker Hill, Bralorne Mining, Copper Range, Anaconda, Newmont, Phelps Dodge, Homestake, etc.) greatly benefited from Joralemon's experience and wisdom.

Jan 12, 1976

By J. H. Brophy, S. J. Michalik

A constitution diagram for the system Mo-Ir has been determined. The maximum solubility of iridium in molybdenum is 16 at. pct at 2110ºC and decreases to less than 5 at. pct at 1500°C. The solubility of molybdenum in iridium is 22 at. pct. Three intermediate phases appear in the system: 8 MoJr, having the p-tungsten structure; a phase, a cornplex tetragonal structure; and the hcp ? phase. Metallography, melting point determinations, X-ray diffraction and fluorescence, and electron micro-probe unalyses were employed in establishing the diagram. PREVIOUS to the present investigation, the intermediate phases in the Mo-Ir system were identified, but no detailed account of the phase diagram has been reported in the literature. Raub1 investigated alloys of Mo-Ir over an extensive range of composition between the temperatures of 800º and 1600°C. The in-termetallic compound MosIr was found to exist with nearly pure molybdenum, as the solubility of iridium in molybdenum was not detectable parametrically in this temperature range. MO3Ir was found to be iso-morphic with a ß-tungsten type structure, having a parameter of 4.959Å. An intermediate hcp phase, designated as the ? phase, ranged in composition from 52 to 78.5 at. pct at 800ºC, and from 41 to 78.5 at. pct Ir at 1200°C. Parameters noted for the ? phase were as follows: at 42.7 at. pct Ir, a = 2.771i0, c = 4.4366, c/a = 1.601; at 78.5 at. pct Ir, a = 2.736A, c = 4.378A, c/a = 1.600. Molybdenum was found to be soluble in iridium up to 16.5 at. pct Mo (83.5 at. pct Irj, with the parameter of iridium increasing to 3.845A at the solubility limit. Knapton,2 who investigated alloys between 15 and 85 at. pct Ir, essentially agreed with Raub's data, but, in addition, found a a phase in as-melted alloys near 25 at. pcto Ir. The oaphase lattice parameters were a = 9.64Å, c = 4.96Å, c/a = 0.515. The a phase was replaced by the 8 -tungsten phase on annealing at 1600°C. Knapton concluded that the a was stable only at elevated temperatures, and placed the composition of the a phase at approximately 30 at. pct Ir. The intermetallic compound Mo3Ir, with a lattice parameter of 4.965A, was included among the 8-tungsten structures reported by ~eller.' Matthias and Corenzwit,4 and Bucke15 studied the superconducting nature of MosIr, and reported a superconducting transition temperature of 8.$K. The present investigation describes the phase relationships in the Mo-Ir alloy system determined by melting point measurements, X-ray diffraction and fluorescence, and metallography. EXPERIMENTAL PROCEDURES Alloys for the determination of the phase diagram were prepared from powders. Commercial 99.9 pct Mo from Fansteel Metallurgical Corp. and 99.9 pct Ir powder from J. Bishop and Co. Platinum Works were used. The powders were weighed to nominal compositions, mixed, and then pressed, without binder, into compacts weighing 4 to 6 g. These were presintered in uacuo between 1200' and 1400°C for 1 hr, to reduce the degree of spattering during subsequent arc-melting. The compacts were arc-melted in a nonconsumable tungsten electrode furnace six times on alternate sides on a water-cooled copper hearth in an atmosphere of zirconium-getter ed argon at 500 mm of mercury pressure. In almost all cases, this procedure yielded buttons of satisfactory homogeneity. The composition of all melted buttons were confirmed by X-ray fluorescent analysis using the experimentally determined ratio of the iridium La1 line intensity to that of the molybdenum Ka1 line as a function of composition. In this determination four alloys analyzed by wet chemical methods were used as standards. An uncertainty range of ±1 at. pct has been attributed to all indicated compositions. All heat treatments and solidus measurements were carried out in tantalum resistance heating elements in vacuum conditions of 10-4 to 10-5 mm of mercury. A detailed account of this procedure has been reported by Schwarzkopf and Brophy.8 In the heat treatment and solidus measurements of iridium-rich alloys (50 at. pct Ir or greater), a tungsten lining was inserted into the tantalum resistance heating element because of a eutectic reaction which occurs between iridium and tantalum at 1948ºc.7 Heat treatments and solidus measurements carried out at compositions less than 40 at. pct Ir both with and without tungsten linings within the resistance

Jan 1, 1963

By George J. Young

(Cleveland Meeting, October, 1912.) I. GENERAL. THE recurrence of mine-fires in Nevada during the past decade is not only a matter of interest, but also one of considerable concern to engineers and mine-managers. The more important fires may he enumerated as follows: Forman Shaft fire., Gold Hill, April 21, 1903 ; shaft-house, machinery, and shaft, destroyed; loss estimated at $50,000.; Cause Unknown. Union Shaft fire, Virginia City, July 14, 1904; shaft-house, machinery, and shaft in part destroyed; loss estimated it $100,000; cause of fire stated as the careless throwing of a match in the rope-house. Sutro Tunnel fire, Virginia City, Jan. 27, 1909 ; 700 ft. of tunnel-timbering destroyed, and direct damage of $10,000; cause ' probably electric wires." Belcher Shaft fire, Gold Hill, Aug. 9, 1910; shaft-house destroyed, machinery ruined, and upper part of shaft damaged; damage, $25,000; no cause given. Belmont Mine fire, Tonopah, Feb. 23, 1911; fire started in winze ; 17 men killed. Giroux Mine fire, Kimberly, Aug. 23, 1911 ; fire originated iii shaft-station from unknown cause; 7 men killed, and $34,¬521 damage caused. (NOTE 1.-On June 11, 1912, some time after the present paper was written, a fire broke out in the pump-room on the 2475 station of the Ward shaft, Virginia City. This fire was caused by the short-circuiting and exploding of the starting-switch on No. 5 pump. The oil in the switch was scattered about and set fire to the timbers and laming of the pump-room. The pump-roan in charge notified the surface, and the * Professor of Mining and Metallurgy, Mackay School of Mines.

Oct 1, 1912