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By P. W. Bridgman

Flow and fracture are admittedly complicated phenomena of which we are yet only partially masters. There is not even nni-.persal agreement as to the details of the language best adapted merely to describe the phenomena, to say nothing of any theory. Certain points of view, however, are widely held, and there are certain general expectations as to what sort of procedures will prove permissible. A complete description of any situation involving fracture would demand a complete history of all the variables in the control of the experimenter. The experimenter endeavors so to choose his independent variables that they are adequate to determine completely the situation in the sense that when an experiment is repeated on the same initial material and with the independent variables running through the same sequence, all the other measurable properties of the system will also run through the same course. It is, I think, the universal conviction that when we are dealing with phenomena of flow and fracture, the most important of the necessary variables are the external forces acting on the various parts of the body; when the force history repeats, with certain obvious restrictions such as that temperature must be constant and non-mechanical forces, such as magnetic field, must be small enough to be ineffective, then the history of all measurable properties will repeat; in particular the alteration of geometrical shape due to flow will run through the same course, and when fracture comes, the character of the fracture will be reproduced. Complete mastery of merely the descriptive aspects of flow and fracture would demand the ability to predict the entire course of flow and complete characterization of the final fracture for every possible combination of forces, varying in time in all possible ways, when applied to bodies of all possible shapes. This full situation is obviously of prohibitive complexity. The first stage in reduction to manageable simplicity is to resolve the total situation into the sum of contributions made by small elements. Our thesis is that if each of the elements is adequately characterized, the behavior of the whole system is fixed. The element is usually taken of a simple geometrical shape, suggested by the mathematics best adapted to the particular situation. The forces acting across the faces of the elements are ultimately determined by the forces acting across the free faces of the whole system. The detailed process of finding the precise forces on the faces of all the elements in terms of the external forces involves the use of a special mathematical invention, the stress, a constructional quantity consisting of six components. The stress at any point in the body is determined by both the external force system and by the physical properties of the body at all points; quite different stresses prevail at the interior of bodies of the same shape under the same external forces in the elastic and plastic ranges. The forces on the faces of any element are, however, uniquely determined by the stress system at the element. Our fundamental thesis

Jan 1, 1945

By W. J. West, W. W. Garvin, J. W. Sheldon

One of the most important problems of reservoir mechanics is the prediction of the behavior of a gas and oil producing reservoir for a variety of production programs. In the absence of a knowledge of the behavior of even idealized systems, it has been difficult, if not impossible, to determine which production program would yield maximum economic recovery. The problem was formulated mathematically many years ago, hilt a solution of the equations had never been obtained because of their extreme complexity. The solution of the problem became possible, however, with the advent of modern computing machines. This paper describes a digital method of solving the problem and discusses some of the results which have been obtained to date. The IBM Type 701 Electronic Data Processing Machines located at IBM's New York Scientific Computing Service were used successfully to perform the computations. The flow of gas and oil through a reservoir can be described mathematically by two second-order, nonlinear partial differential equations which must be solved simultaneously. All derivatives were replaced by finite differences to bring the equations into a form suitable for digital calculations. A number of finite ditference formulations were investigated and one form was found which resulted in stable, convergent solutions. This form was used to obtain .solutions for both radial and linear systems producing by solution gas drive. The results presented in this paper are: (a) saturation profile within the hypothetical reservoir vs. time, (b) pres.strre profile within the hypothetical reservoir vs. time. (c) gas-oil ratio vs. cumulative recovery, and (d) ultimate recovery. The saturation profile clearly shows the effect of critical gas saturation. The saturation near the well-bore drops quickly to the critical gas saturation and remains essentially at that value until the remainder of the reservoir also has dropped to the critical gas saturation. The pressure profile shows a smooth variation of pressure across the reservoir. The gas-oil ratio drops slightly during the early stage of production until the critical gas saturation is reached, rises rapidly from then on and eventually passes through a sharp maximum just before the economic limit of production is reached. For the radial example presented in this paper, the average oil .saturation of the reservoir at a time corresponding to the limit of economic production was 56.5 per cent and the ultimate recovery was 6.86 per cent. The difference between change in saturation and ultimate recovery is caused by .shrinkage of the oil phase. The solution time with the 701 Computer is sufficiently short to permit an economically feasible investigation of the effects of variation of the many parameters which describe an oil reservoir. In particular, the ultimate recovery for various systems can he determined as a function of rock and fluid properties, of well spacing. and of production rate. INTRODUCTION The effective planning for maximum economic depletion of oil reservoirs is one of the major problems confronting oil producers. The most important part of the planning is prediction of the response of the oil reservoir to a particular production program. The production program can be selected by imposing certain controls available to the operator. Some of these controls are: (a) well spacing, (b) production rate, (c) time

Jan 1, 1955

By Joseph B. Perry, G. M. Kirwan

MAGNESITE is found in 22 California counties, but many of the deposits are too small or too impure to be of commercial value. Several of substantial size and quality were entirely exhausted by wartime operation. At present, three properties comprise the only known workable deposits in the state. Of these, the Western mine and the Patterson mine have been known and worked for many years, and have been described in considerable detail in various publications, therefore need only brief mention here, because of their proximity to the Bald Eagle mine. The latter, recently developed, is unusual in type of ore deposit, plant design and operation, as well as products made, and very little has been written concerning it. WESTERN MINE The Western mine, 32 miles south of Livermore, Calif., was formerly operated by C. S. Maltby. It has been a consistent producer for many years.1 The ore is of amorphous variety, occurring along fracture zones in serpentine. The veins vary greatly in width, the average being perhaps 8 ft., with the maximum indicated in one early stope of 40 ft.; 2 ft. is considered the minimum for economical mining. The strike of the veins is predominantly north and south, with dip to the west varying from 40º to 75 º. Walls are well defined and as a rule firm and easily supported. Veins range in length from a few hundred feet to 1000 or more. Their maximum vertical extent is about 350 ft., but many run less. Early mining consisted of open-cut and glory-hole work on the larger outcrops. This was followed underground by a modified shrinkage system, the waste and low-grade horses being removed by hand sorting on the tramming levels and transported to surface dumps. Filled-stope mining is used now, in order to eliminate the handling of waste, which has

Jan 1, 1938

By E. H. Griswold

PETROLEUM production engineering is essentially the application of the laws of 'physics and mechanics to the production of oil. A true production engineer is one who can apply the principles of mechanics, hydraulics, thermodynamics, and other physical arts so as to facilitate' the efficient and economical recovery of oil. To this end he must have wide knowledge of practical field operations and a working knowledge of geology, with a thorough understanding of the underground state of the fluids which he seeks to control. Generally speaking, there have been two schools of production engineering, the California development and the Mid-Continent development. In California the preliminary production engineering was done by representatives of the U. S. Bureau of Mines and the State Mining Bureau, and was essentially subsurface work in regard to casing patterns, water shut-offs, and completion procedure, inasmuch as these were problems of the utmost immediate importance to the California industry. The oil companies were impressed with the value of such work and placed engineers, or more strictly speaking, engineering geologists on their field staffs. These men, realizing the need of further technical study in the mechanical phases of producing operations, added mechanical and mining engineers, and out of the blend developed what is now known as a production engineer.

Jan 1, 1932

By L. W. Blau

THE entrance of geophysics and geochemistry into petroleum engineering may be viewed with apprehension by some engineers. They may not remember the time when "practical oil men" opposed the invasion of engineers into the field of petroleum production. By their excellent contributions they established themselves. In the popular mind, engis veers are practical men whereas physicists and chemists are suspected of being theoretical. It will be best to annihilate this misconception right now at the beginning of a closer relationship between petroleum engineers. geophysicists, and geochemists.

Jan 1, 1943

By J. S. Kirkaldy, D. H. Weichert, G. R. Purdy

Two-phase diffusion couples have been used to simulate the growth of proeutectoid ferrite in ternary Fe-C-Mn austenites. It has been shown, theoretically and expermentally, that the results fall into two classes: a high-super saturation class in which the major role of manganese additions is to influence the boundary conditions for carbon diffusion; and a low-supersaturation class in which the partition of manganese is required. In the latter case, a drastic inhibition of the reaction rate is to be expected. As an aid to the kinetic analysis, a portion of the iron-rich comer of the Fe-C-Mn constitution diagvam has been determined. The conclusions drawn from this work have a direct bearing on the kinetics of the grain boundary ferrite precipitation reaction and thus yield insight into the manner in which alloying elements can influence the rate of austenite-decomposition reactions. THE role of alloying elements in the austenite-decomposition reactions has provoked considerable interest, since it is apparent that an understanding of this phenomenon will yield insight into the harden-ability problem. In the present investigation, attention is focused upon the proeutectoid-ferrite transformation in the system Fe-C-Mn, and upon the manner in which manganese additions affect the growth rate of ferrite. When hypoeutectoid austenite is supersaturated, the ferrite first formed usually exhibits two distinct types of morphology. At low super saturations, grain boundary layers grow into the austenite grains with an approximately planar interface, and usually possess at least one incoherent phase boundary. At high supersaturations, Widmanstiitten plates appear, which bear an orientation relationship' to the parent austenite. In this case, there is a chance of partial lattice matching along the sides of the plates and an attendant semicoherent interface structure. Purdy and Kirkaldy2 have used a two-phase binary Fe-C diffusion couple to demonstrate that carbon volume diffusion controls the incoherent reaction, while Rouze and rube,' using thermionic-emission microscopy, have shown that the thickening of Widmanstatten ferrite plates is appreciably slower than expected for carbon-diffusion control. This suggests that the plates are bounded by partially coherent, low-mobility interfaces. The redistribution of alloying elements during transformation has been the object of studies by Aaronson4 and owmman,5 who have shown that no alloy partition occurs during ferrite precipitation in the systems Fe-C-Cr and Fe-C-Mo, respectively. More recently, Aaronson et al.6 have shown that some manganese partition occurs at low super-saturations in the system Fe-C-Mn, but that no partition occurs at higher super saturations. Pickle-simer et al.7 observed that no manganese partition occurred during the early stages of the pearlite transformation in a manganese steel, and concluded that volume diffusion of the alloying element is not the rate-deter mining factor. The diffusion coefficients pertinent to this investigation have been measured by Wells, Batz, and Mehl8 (carbon in austenite), R. P. smith9 (carbon in ferrite), Wells and Mehl 10 (manganese in austenite), and Kirkaldy and Purdy11 (diffusion of carbon on a manganese gradient in austenite). Kurdjumov 12 has shown that the diffusivity of substitutional elements in ternary austenites up-quenched from martensite may be greatly enhanced, due, apparently, to the presence of a persistent defect structure. The recent work of Krauss 19 showing high densities of tangled dislocations in reversed Fe-Ni martensite is in agreement with this conception. THEORETICAL Diffusion in ternary or higher-order systems may be described with the aid of Onsager's extenbion of Fick's first law,14 in which the flux of each of the n components is assumed to be a linear function of all concentration gradients:

Jan 1, 1964

By DeVerle P. Harris

Risk for most mineral investments is greater than that of average business ventures, because the physical and economic characteristics of the mineral deposit are never known with certainty. Inasmuch as the merits of a potential mineral investment cannot be fully appraised without consideration of the impact to the investor of the possible unfavorable events associated with the adoption of the project, methods of risk analysis are important in project evaluation and investment selection. The conceptual framework for risk analysis and the means by which some of the recommended practices might be implemented are examined. In addition to the normal business risk due to market forces, the physical and economic characteristics of the mineral deposit are never known with certainty, for only partial or indirect information is available, such as data from drill cores or surface and underground workings. Consequently, risk for most mineral investments is greater than that of average business ventures. Inasmuch as the merits of a potential mineral investment cannot be fully appraised without consideration of the impact to the investor of the possible unfavorable events associated with adoption of the project, methods of risk analysis are important in project evaluation and investment selection. This paper examines the conceptual framework for risk analysis and means by which might be implemented some of the recommended procedures. Utility Theory A discourse on risk and its impact upon investment selection quite often leads the reader into the concept of utility theory, for utility theory is a device constructed by economists to measure the satisfaction an individuai receives from a good; in the case of investment analysis, that good is the outcome of an investment. It briefly is reviewed here to describe the reaction of the individual to risk and as a stepping stone to other techniques more suited to risk analysis at the level of the firm. Utility theory proposes that an investor possess a utility map (curve), such as indicated in Fig. 1, which indicates the value in utiles of potential monetary rewards to an individual with some specific endowment of resources. Points on this map are obtained from the following relationship:

Jan 1, 1971

By L. F. Porter, G. J. Dienes

The effect of netltron irracliation on mart ensite transformation in the iron-nickel system was studied by means of electrical resistance and magnetic induction measuremertts. Irradiation lowers the M8 temperature of the allay, causes changes in the electrical and magnetic properties of the high-temperature phase which indicate either an accelemtion of phase separation or a clustering of nickel, and enhances strain recovery on specimens partially transformed to martensite prior to irradiation. Possible mechanisms to account for the effects; are discussed. 1 HERE is a good deal of evidence to indicate that neutron irradiation is capable of affecting phase changes in metals and alloys. While the mechanism of the effect often is not well understood, such studies hold promise of improving our understanding not only of irradiation damage but also of the phase changes involved. To date systematic and detailed investigations have been made of the influence of nuclear radiation on order-disorder transformations in the copper-gold, nickel-manganese, and copper-zinc system, and on precipitation reactions in the copper-iron, nickel-beryllium, and copper-beryllium system.' These solid-state reactions are diffusion controlled and the results can be explained largely on the basis of enhanced diffusion due to the presence of irradiation produced vacancies. Reversion of low-temperature eutectoid phases to the high-temperature phase has been observed in the fissionable uranium-molybdenum and uranium-niobium systems.2 Here it is necessary and logical to postulate a displacement spike mechanism to account for the effect. The only case of irradiation induced diffusionless transformation in metals is the allo-tropic transformation of p to a tin reported by Flee-man and Dienes. 3 They found that neutron irradiation markedly decreases the incubation time for transformation, but the mechanisnl is not well understood. Another diffusionless transformation which one might expect to be influenced by neutron irradiation is the martensite transformation. This transformation is known to be sensitive to strain, structural hardening, and the presence of imperfections.6,7 Since the transformation is diffusionless, one also

Jan 1, 1960

By Albert L. Toenges

COAL mining technique progressed slowly until the advent of mechanized mining. The cutting machine was a forward step, but had only a limited effect upon improving the percentage of coal recovery. Previously, the physical fitness of the loaders and the total output of the miners fixed mine production. The miner was an independent contractor and supervision over his working place was superficial. Rising costs and the inroads of substitute fuels demanded increased output per man to lower the unit production cost. Therefore, the amount of coal loaded mechanically in underground bituminous mines has risen from 0.3 per-cent in 1923 to 7.4 in 1929, to 20.2 in 1937, and to 48.9 percent in 1943. When loading devices were introduced it became necessary to adapt them to existing systems of mining, or to alter the mining system to fit the machine. An increased amount of supervision was required as output depended upon proper operation of the machine rather than on the physical fitness of the individual.

Jan 1, 1946

By J. W. Schroeder

SEAMLESS pipe, the product produced from piercing a solid round billet of steel by the Mannesmann process, was first produced in the latter half of the 19th century, the Mannesmann machine having been patented in 1885. The products of other processes also have been termed seamless pipe; for example, the cylindrical section produced by "cupping," which consists of forming a cup from a flat plate or disk and further elongating the cup into a tube by passing it through a set of reducing dies. The purpose of this paper is to discuss some of the more important metallurgical factors and their relationship to the economical production of seamless pipe produced by the Mannesmann piercing process. The first seamless tube plant in America was established at Shelby, Ohio, in 1891, and was employed in the manufacture of bicycle tubing. For a number of years the bicycle industry was the only user of seamless tubing, and this tubing was produced by hot-rolling pierced billets imported from Europe and finishing on the cold drawbench. At the turn of the century, the automotive industry was responsible for an increase in the demand for seamless tubing. The growth of this industry was the dominant factor leading to the phenomenal growth of the petroleum industry, which in turn created a tremendous demand for seamless pipe. In addition; the old lapweld iron boiler tubes for stationary and locomotive boilers were replaced gradually by seamless tubes. Since 1929, the production of seamless steel pipe and tubes has increased over loo pct. In 1929, 1,459,9031 net tons of seamless pipe was produced, including both hot-finished and cold-drawn material, as compared with 3,087,3122 net [ ] tons in 1948. Table I gives the distribution of seamless pipe by classes for 1948. METALLURGICAL PROBLEMS From a metallurgical standpoint, the production of seamless pipe has presented many problems. Practically every type of steel, carbon and alloy, with the exception of the superalloys developed during World War II, has been pierced and rolled successfully into tubing. This includes bessemer, open hearth, by the stationary and duplex processes, and electric steels. The range of sizes produced is no less staggering to the imagination, when it is considered that the hypodermic needle, which is 0.016 in. diam with a wall thickness of 0.004 in., and pipe for gas or oil transmission lines, with a 26 in. OD, are both seamless tubes. Between these extremes, the range of diameters and wall thicknesses meets most present-day demands for seam-

Jan 1, 1951

By E. Gaujot

IN connection with the question of coal waste and economy in mining, we would call the attention of those interested to an apparatus invented by M. Dernencourt, Superintendent of the Anzin Division of the Anzin Coal Company, North of France. This apparatus is known in France and Belgium under the name of prop screw-jack (vis botte), and has been used with good results in the above-named countries for some years past. M. Ponson gives, in his " Trait6 de I'exploitation des Mines," a description of it (page 533), but as the description given is old, the work not widely known in this country, and as some valuable improvements have been made since, I thought it might be useful to give a description of it, having seen it in 'operation in 1867, while in Europe to attend the great Exposition, and on a scientific tour to the mining districts of France, Germany, Belgium, and Italy. The prop screw-jack is composed of the following pieces : I. The body or column B, Fig. 4 [Plate (I)], of oak or yellow pine, sawed square, the bark taken off, and any length, proportionate to the vein. The smallest are 10 inches diameter at the base, and 9 inches at the top, the height being from 12 to 15 inches less than the size of the vein. In the axis of this column, and at the top end, is a cylindrical opening or hole, C, 22 inches diameter, 10 inches deep, for the screw, S. II. Two wrought-iron rings, R R, to strengthen the two extremities of the column ; the rings must be put on hot. III. A cast,-iron washer, E, with hole in centre a little larger than the screw, to be put on the top of the column, and on which the nut is to rest; the top side of this washer must be faced on the lathe, also the bottom of the nut, to prevent friction. IV. The screw, S, having a total length of 12 inches and a diameter of 24 inches (for very high veins this diameter may be increased to 3 inches), and has on its top a wrought-iron plate, T,

By W. Francis

Before attempting to describe the application of recently acquired knowledge to the classification of coal it will be as well to consider the objects at which a scientific classification should aim. Here one can not do better than to follow the example of Clarence Seyler,l by quoting from Huxley's "Classification of Animals:" "By the classification of any series of objects is meant the actual or ideal arrangement together of those which are like and the separation of those which are unlike, the purpose of the arrangement being to facilitate the operation of the mind in clearly conceiving and retaining in the memory the characters of the object in question. Thus there are as many classifications of any series of natural or other bodies as they have properties or relations to one another or to other things. But the statement of the characters of the class ... is something more than an arbitrary definition ... it expresses firstly, a generalization based on and constantly verified by very with experience; and, secondly, a belief arising out of that generalization—in other worda. the definition of the class is a statement of a law of correlation or coexistence . . . from which the most important conclusions are deducible." In that same sense writes John Stuart Mill, in the chapter on classification in his "Logic:" "The ends of scientific classification are best answered when the objects are formed into groups concerning which a greater number of general propositions can be made, and these properties more important, than could be made respectiug any other groups into which the same things could be distributed. The properties, therefore, according to which objects arc classified should, if possible, be those which are causes of many other properties, or, at any rate, which are sure marks of them." Now in the case of coal, the properties which have been used from time to time for classification purposes are the ultimate analysis, volatile matter, caking power, calorific power, burning properties, etc. Seyler has shown that there is a general law of correlation or coexistence between the ultimate composition and the other properties. The ultimate composition, therefore, of the natural series of bodies known as coal is the

Jan 1, 1930

By AIME AIME

HARVEY MUDD, mining engineer and distinguished citizen, has achieved that balance between professional and civic activities for which many of us strive but few attain. His able direction of mining operations is known to many Institute members but perhaps few know that he was in 1936 recipient of the annual award given by the City of Los Angeles to that citizen who contributed the most valuable and unselfish service to the community. Mr. Mudd was born in Leadville,

Jan 1, 1944

By H. P. Stuwe

It is investigated whether a model of sphere packing permits the computation of the lattice parameters and their variation with concentration in various a phases; it does, except in phases containing silicon. Several observations indicate that a particular role is played by the "E-atoms" in the lattice. THE phase is formed by many alloys of the transition elements.'-' Its structure has been described by Bergman and Shoemaker,5,8 Dickins, Douglas, and Taylor,7 and Kasper, Decker, and elanger.' There are five kinds of crystallographically equivalent positions for the 30 atoms in the unit cell which have been designated by these authors I, 11, 111, IV, and V or, in the same sequence, A, B, C,D, and E, as shown in Fig, 1. For the purposes of the present paper two elements of the lattice will be discussed separately: The lattice planes perpendicular to the c-axis which are made up by the atoms A, B, C, and D and which determine the a-parameter; and the close-packed "vertical rows" of E-atoms which determine the c-parameter. asper,9 and Frank and kasper10 described the a phase and other complex structures as sphere packings. In these papers particular attention is paid to the coordination polyhedra. Lattice positions with an equal number of nearest neighbors are considered equivalent regardless of their crystallo-graphic description. This seems to work very well for the explanation of ordering phenomena in the a phase as far as information on this is available." If the description of the phase as a sphere packing is valid it should be possible to draw two further conclusions: 1) It should be possible to calculate the lattice parameters from the atomic radii of the components, and 2) It should be possible to predict the variation of the lattice parameters with concentration within one phase field. Both points are discussed in this paper. PROCEDURE Measurements of lattice constants were done with a symmetrical back-reflection X-ray camera. With Cr-radiation, about a dozen a1 lines could be observed with most samples. From the (550/710)- and 720-lines the a-value was computed. With this value the c-parameter was calculated from the (333)- and (413)-lines. Finally, the position of all the other lines was computed from the lattice parameters thus obtained. In this way the validity of the indexing could be checked and, at the same time, this proce- dure gave an estimate of the accuracy of the lattice parameters. A correction was made for film shrinkage. The atomic radii used in the computations are the Goldschmidt radii for coordination number 12. Actually, some of the atoms have a coordination number of 14 or 15, but the error thereby introduced is small. * For the computation of lattice constants from the atomic radii an "average atomic radius" of all components was used, i.e., complete disorder was assumed. Although this seems to be true for some systems like OS-Cr,4 it is not true in others.11,13,14 The ordering model, however, which has been suggested by Kasper on the basis of extensive research lets both kinds of atoms contribute to both the ''vertical rows" and the lattice planes perpendicular to them, so that even with ordering of this kind the assumption of complete disorder cannot introduce a very serious error in calculating lattice parameters. RESULTS Bergman and shoemaker6 gave a table of the interatomic distances in the Fe-Cr phase. If we disre-

Jan 1, 1960

By C. E. LAWAL

WITH the object of adapting high-school vocational courses to the industrial needs of the community, a few high-school officials in West -Virginia working with the School of Mines of the State university decided to try an innovation this year. The purpose of this experiment was to teach coal mining in two high schools situated in mining communities. We thought that if a course in coal mining would be included in the list of optional courses offered in the high school, it might interest some of the boys, and if the course were properly taught it would undoubtedly be of inestimable value to those boys who later decided to take up mining work as their vocation. This coal-mining course was started last September in the Berwind and Gary high schools in West Virginia. The high-school officials in their conferences with' us decided that we should work up the outline of this course and they would assign the science teachers of the schools as instructors, with ,the understanding that we would help 'these instructors with this work. We consented to all this and submitted -an outline to the school officials which they are following this year.

Jan 1, 1929

By M. Cohen, W. J. Harris

The recent application of lineal analysislt2 to the austenite-martensite reaction has made possible a quantitative study of the kinetics of this transformation during rapid cooling. Martensite range curves can thus be constructed to portray the onset of the reaction at Ma and its subsequent progress as a function of temperature down to and below the ambient. It now seems in order to investigate other aspects of the martensite transformation, using this quantitative method of approach. One of the least understood characteristics of the austenite-martensite reaction is that of stabilization which has been defined by Troiano and Greninger3 as 'la lowering of Ma, resulting from aging, without change in chemical composition of the parent solid solution." In other words, if the hardening quench is arrested at a predetermined subcritical temperature (TA) for a sufficient period of time, more austenite may be retained at a given lower Or reference temperature (Tr) than if the steel had been cooled directly and rapidly to Tr in the first place. For the purposes of the work at hand, the extent of stabilization produced by the isothermal treatment at Th is measured explicitly in terms of the excess austenite (6) that exists in the steel at T,, over and above the amount that is normally present after direct quenching to T,. T, is conveniently taken to be room temperature, but this choice is not essential and is sometimes undesirable. The holding temperature (TA) may be above or below M,, and still cause stabilization depending upon the themistry of the austenite. stabilization has been found to occur in the presence of bainite4 and of martensite6,6,7,8 as well as in the absence of either,g The phe-nomenon of stabilization is not concerned with (and may even be obscured by) ferrite formation or any other type of phase change occurring at T~ that alters the chemistry of the remaining austenite. Such a structural change would obviously influence the martensite transformation during subscquent cooling. Stabilization, however, is more subtle; it appears to manifest itself without detectable variation of the austenite composition, whether in the presence or absence of transformation products. There are relatively few direct references to stabilization in the literature. The stabilizing effect of room temperature aging and tempering on the subzero transformation of retained austenite has been clearly shown in plain carbon,6,8 low alloy6s7.8 and high alloy tool steels.10'5 ssa- with the as-hardened steel, the degree of stabilization increases with tempering time and temperature through

Jan 1, 1949

By Eugene F. Poncelet

GLASS squares compressed on edge by steel jaws in poor contact with them developed jagged "partial-contact" cracks caused by the formation of local tensile stresses. Compressed by steel jaws in perfect contact, they developed smooth "release cracks" during release of the pressure, caused by the formation of local tensile stresses during the release of the pressure. All these cracks were parallel to the pressure. A Microflash photograph of a disintegrating specimen under sufficient pressure reveals a network of fractures roughly normal to each other, also "release cracks" and a disintegration cloud. The Griffith theory is amended to account for the formation of a first crack. A new theory, based on the theory of thermal agitation and wave propagation, is proposed to account for the progress, velocity and forking of cracks. The network of fractures is shown to have been caused by reflection at a free boundary of pressure pulses emanating from a first crack. Postulating equal distribution of energy in the pulses emitted on either side by a crack in particles, the smaller fragments are shown to continue fracturing preferentially while some of the coarser fragments remain as residual pieces. As comminution of the smaller fragments proceeds, the solid is reduced to a collection of residual particles of smaller and smaller sizes, accounting for the disintegration cloud. EXPERIMENTAL PROCEDURE Apparatus A crushing device was built, consisting of a steel frame and two polished, hardened steel jaws to crush plate-glass samples. This device was placed between the plates of a hydraulic press (Fig. I). For centering the pressure, the upper jaw was guided vertically and provided with a rounded top. Later it was replaced by a steel jaw ground out of a 2 1/2-in. steel ball, the lower surface being ground to an optical flat (Fig. 2). Four rollers were used to eliminate side thrust. Screws and centering blocks served to center the specimen in the crushing device. Hard steel shims placed under the shoulder of the upper jaw limited the "follow through" of the jaw after failure of the specimen. Stress distribution was first examined with a polariscope mounted on an optical bench, using monochromatic light. It was found convenient to mount polaroid, quarter wave and monochromatic plates directly on the device itself. A Microflash unit* was used as light source for the photographs. A gold-paint pattern was fused on the plate-glass specimens and connected into the spark-

Jan 1, 1944

By H. I. Aaronson, H. A. Domian, G. M. Pound

The thernodyna,nics of I the Proeutectoid ferrite re-action ha1.e been investigated on the bases of three diifevent descviptions of the statistical thernzodynamics of interstitzal solid solutions. Especially at low ternperatures, substantial dijeretzces are found in the valltes of the extrapolated y/y + a and cr/a + y equilibriurn curls, and in the To- co7nposilion metastable eqliilibriunz curl-es thus co,npited. Although neither actiztity nor phase-diagram date are able to distingrish udeqiutely among the various descviptions, the statustics of Lacher, Fouller, and Guggenheinz provide the ?nost conplete epresentation az3ailable of the single carbon-ctrbon interaction energy (w) nzodel of an intevstitiril solid solution, and the relationships deduced frojrl then2 are accordingly pre.ferred. The findings tlzut w in austenite 'aries significu?ztly uith tenpevntrue and that phase-diagawr data arc not accurately con?palible usith eqcrctions deduced on the basis of actility infoation indicate, hou'e13er, that a wzore cornplex nlodel of the uustenite , und pvobably of the .feyrite, solirl solutions will have to forn the basis of f4tuve statistical t1.eat1nents. Some suggestions for such a ruodel arc advanced. Althoug11 w represents a vepltlsio energy in austozite, it was found to corvcsporzd in ferrite to a binding energy, in qualitatit.e accord zc,itlz the internal-friclion results of Keefer and wert. ThE transformation of austenite to proeutectoid fer-rite is becoming recognized as an exceptionally useful vehicle for quantitative studies of the kinetics of phase transformations.'" Reasons for this popularity include well-characterized microstructures which develop on a convenient scale with acceptable kinetics within a considerable temperature-composition region, the absence of great sensitivity to common impurities, and, especially. the availability of a unique wealth of the ancillary information indispensable for the quantitative interpretation of kinetic measurements, including phase diagram,3 crystallographies diffusivity,5 inter-facial energy,=17 elastiit," specific vlume, ''' and ativity'-' data. Development of considerable amounts of additional thermodynamic information from activity data is of particular importance with respect to kinetic studies, since much of this information is needed in temperature-composition regions not directly accessible to presently available techniques for the measurement of equilibrium properties. A generally useful approach to the thermodynamics of solid solutions, which is of especial value in this situation, is based upon the formulation of the free energy of such solutions as a function of temperature and composition. The free energy of solid solutions has been resolved into many components. Particularly in the case of interstitial solutions, with which we shall be concerned in the present study, however, only the positional entropy component has been intensively studied. The other components are conventionally taken into account by fitting equations for the activity of the interstitial species or the temperature-composition path of phase boundaries, derived principally from positional entropy considerations, to experimental information on these quantities through adjustment of one or more constants in the equations. A number of studies of the thermodynamics of interstitial solid solutions have been made primarily on this basis,'"25 but only Kaufman, Radcliffe, and cohenZ2 (hereafter KRC) and ener''% ave applied the results of such studies to develop relationships for the thermodynamic quantities of interest in the austenite —- proeutectoid ferrite transformation. KRC made use of a model developed by cheil'' (on the basis of a previous study by ohansson'), and subsequently rede-rived correctly by Speiser and retnak,' in which a carbon atom is considered to inhibit occupancy of a certain number of its nearest-neighboring interstitial sites. schei120 determined the number of sites in austenite thus excluded by matching calculated and experimentally measured curves for the variation of carbon activity with the mole fraction of carbon. zener17 used a different approach. He assumed that the positional entropy of carbon is ideal both in austenite and in ferrite (i.e., no excluded interstitial sites), and included all other contributions of carbon in a temperature-independent "free-energy change" accompanying the transfer of 1 mole of carbon between the two phases. This quantity was determined by "pinning" an equation derived for the boundaries of the a + y region to experimental data on the compositions of these boundaries at a single temperature. In the present investigation, three different approaches to the thermodynamics of the proeutectoid ferrite reaction are examined comparatively: I) the method of Zener; 2) the model employed by KRC and predecessors; and 3) the more detailed statistical thermodynamic treatment of the same model developed by acher and Fowler and uenheim, ' in which the problem of overlapping regions of influence of individual interstitial atoms is resolved. In order to make these comparisons, it is necessary to undertake an extension of one aspect of Zener's method; since the Lacher- Fowler -Guggenheim (LFG) treatment has not been previously used in the present context, the necessary thermodynamic "superstructure" for this treatment will be developed in parallel

Jan 1, 1967

By Louis J. Demer, Paul A. Beck

As reported in a previous publication,1 isothermal grain growth in high purity aluminum and in an aluminum alloy with 2 pct magnesium can be adequately described by means of the empirical relation: [ ] or in some cases, by the simpler relation, [ ] Here, D is the average grain size after an annealing period t. The annealing period includes the time for complete recrystallization R, and the time for grain growth [to]. DA is the grain size as recrystallized, n is a parameter depending on the temperature and on the material. The effect of 2 pct magnesium in solid solution was to decrease D, and to increase R, A and n at a given temperature. The present work was undertaken in order to investigate the above listed effects of magnesium in solid solution, as functions of the magnesium content. The work also includes the study of certain anomalous effects observed in the recrystallization and grain growth of the 2 pct magnesium alloy at 350°C. EXPERIMENTAL PROCEDURE The method of producing the ingots used in this work was described in detail1 and need not be reproduced here. The materials used were high purity aluminum, furnished by the Aluminum Co. of America, of lot analysis shown in Table I and magnesium from a high purity distilled stock of magnesium crystals. [ ] Ingots were prepared for a series of binary aluminum-magnesium alloys of increasing alloy content. The numbers used to designate these ingots and their magnesium contents by chemical analysis are given in Table 2. [ ] The analyses showed no difference in composition between the top and the bottom of the ingots. Spectrographic analysis of the ingots for elements other than magnesium showed, within the limits of accuracy of the method, no increase in impurities over the amounts given in the lot analysis for the high purity aluminum in Table I. Careful microscopic study of ingot 21 in the as-cast condition, at magnifications up t0 1500X, revealed a cer-

Jan 1, 1948

By S. N. Kesten, Richard Murphy, A. H. Land, W. F. James

Introduction—by W. F. James and A. H. Lang This paper describes the geology and present state of development of uranium and thorium deposits in Canada. It is expected that this information will be added to that now being assembled from available American and British data to provide a background for engineers and others who may be called upon in the future to examine or search for radioactive deposits. Some generaliza- tions regarding the Canadian deposits are included, but many of these are necessarily tentative. The information contained in the paper is up to date for the end of 1948. The information contained in this paper has been derived from many sources. Much of it is from the records of the Canadian government-owned Eldorado Mining and Refining (1944) Limited and from examinations of government and private properties made by officers of the Geological Survey of Canada. Some information on privately-owned properties has been quoted from other sources mentioned in the text. The information has been assembled by W. F. James of Eldorado Mining and Refining (1944) Limited and A. H. Lang of the Geological Survey of Canada, who have written the sections for which they are credited. The description of the Eldorado mine is based on reports by Richard Murphy, formerly chief geologist for Eldorado; the report by Mr. Murphy was published previously by the Canadian Institute of Mining and Metallurgy,' to whom the writers are indebted for permission to repub-lish. The section dealing with the geology of and development work in the Goldfields area, where Eldorado has important holdings, is by S. N. Kesten, field geologist for Eldorado. The geological diagram of the Goldfields area (fig. 2) was kindly supplied by A. M. Christie of the Geological Survey of Can-

Jan 1, 1951