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By J. E. Dorn, S. K. Mitra

The low -temperature tensile and creep behaviors of single crystals of copper were evaluated and analyzed in such a manner as to provide an estimate of the separate contributions of short-and long-range stress fields to strain-hardening. Furthermore, the average force-displacement diagram for thermally activated intep-section of two dislocations was estublished. This diagram plus a knowledge of the variation of dislocation spacing and the long-range back stresses with strain permits on accurate prediction of creep rates. The calculated activation energy for intersection under conditions of a constant strain rate increases linearly with the absolute tempevatus-e as required by theory. AN understanding of the detailed mechanisms for strain hardening constitutes one of the principal unsolved problems in dislocation theory. Two major models for strain hardening have been advanced in the past. The one that has received greatest attention assumes that strain hardening arises exclusively from long range interaction stresses between moving dislocations and piled-up arrays of blocked dislocations on the slip planes. This type of interaction was first announced by Taylor' who revealed that the back stress fields due to a simple uniform array of positive and negative dislocations entrapped in the deformed crystal would result in parabolic hardening. Shortly thereafter Andrade and Henderson" demonstrated that the strain hardening of fcc single crystals was not parabolic, as previously thought, and finally it was recognized that a typical stress-strain curve consisted of three successive stages of deformation, niz., the easy glide, Stage I, linear hardening, Stage 11, and the parabolic hardening, Stage 111, ranges. The objections to Taylor's somewhat na'ive model, which were presented so forcefully by cottrell; were largely removed by the more realistic details incorporated in Mott's analysis.5 But because Mott's theory for hardening via long range stress fields gave somewhat analogous results to that of Taylor's (inasmuch as it also predicted a parabolic rate of strain hardening whereas the observed rate of strain hardening in Stages I and I1 were linear), it was not widely accepted. Major consideration was therefore given to models, such as those which were advanced by Friedel and seegere that were formulated for the ad hoc purpose of yielding linear rates of strain hardening. The second major thought regarding strain hardening is based on the concept that it arises principally from short-range stress fields due to the interactions between intersecting dislocations. Cottrell and stokes7 showed, several years ago, that the constancy of the flow stress ratio at two temperatures regardless of the strain was inconsistent with the concept that strain hardening arose exclusively from long-range back stresses. The argument that strain hardening was primarily due to local interactions of intersecting dislocations was presented in considerable detail by asinski.' Extending Basinski's method of analysis of the intersection process, Mitra, Os-borne, and dorn recently demonstrated that indeed the strain hardening in aluminum single crystals arises principally from local effects coincident with intersection; however, these conclusions, too, must be modified, as will be shown later in this report. The present investigation, devoted principally to the low-temperature deformation of copper single crystals, was initiated in an attempt to ascertain whether or not the same conclusions arrived at for aluminum also apply to metals, such as copper, which have much wider stacking faults. It was soon observed that the strain hardening in copper could not be attributed exclusively to local effects between intersecting dislocations. Previously no analytical method for arriving at the possible simultaneous contributions of long-range stress fields and localized forces on intersecting dislocations was available; consequently, the separation of these two factors could not be readily accomplished. In the present report a method of estimating the separate contributions of each of these two factors to strain-hardening will be presented. The authors will show that both long-range stress fields of the type contemplated by Seeger and Friedel as well as short-range forces of the type considered by Basinski are responsible for strain hardening in fcc metals at low temperatures. This method of analysis also accounts for, in a satisfactory way, the effect of stress, temperature, and strain on the creep rate under constant stress. Furthermore, in the course of presenting their methods of analysis the authors will also reveal the rather complete agreement of their experimental data with the concepts of the theory for thermally activated intersection of dislocations. INTERSECTION MODEL As shown by seegerl0 the strain rate arising from thermally activated intersection of dislocations is given by

Jan 1, 1962

By D. W. Gillmore, C. C. Wright

DEWATERING is a major problem in the preparation and utilization of fine-sized coals now being recovered in increasing amounts from colliery effluents, refuse banks, and silt ponds. Of the various methods which have, been proposed for dewatering fine coal, gravity drainage is probably the oldest and most widely used, and yet little information on this subject has been published. Consequently a laboratory investigation of gravity drainage phenomena was undertaken not only to provide basic data for predicting the drainage behavior of fine coals in cars, bunkers, basins, and silos, but also to obtain some understanding of the moisture retention properties of fine coal. Because of practical interest in the problem, a reproducible laboratory technique, which simulated plant conditions as closely as possible, was developed for the evaluation of drainage variables. The ap- paratus selected consisted of vertically-mounted lucite columns, nominally 4 to 8 ft in length and 2, 3 or 6 in. in diam; the bottom of the column was provided with a rubber stopper through which was inserted a -in. diam drainage tube; a wad of glass wool was placed on the upper part of this outlet tube to retain the coal and a plug was temporarily located at the lower end to prevent drainage during charging of the column, see Fig. 1. The most satisfactory testing procedure is as follows: 1—The fine coal, which has been thoroughly

Jan 1, 1953

By D. W. Gillmore, C. C. Wright

DEWATERING is a major problem in the preparation and utilization of fine-sized coals now being recovered in increasing amounts from colliery effluents, refuse banks, and silt ponds. Of the various methods which have, been proposed for dewatering fine coal, gravity drainage is probably the oldest and most widely used, and yet little information on this subject has been published. Consequently a laboratory investigation of gravity drainage phenomena was undertaken not only to provide basic data for predicting the drainage behavior of fine coals in cars, bunkers, basins, and silos, but also to obtain some understanding of the moisture retention properties of fine coal. Because of practical interest in the problem, a reproducible laboratory technique, which simulated plant conditions as closely as possible, was developed for the evaluation of drainage variables. The ap- paratus selected consisted of vertically-mounted lucite columns, nominally 4 to 8 ft in length and 2, 3 or 6 in. in diam; the bottom of the column was provided with a rubber stopper through which was inserted a -in. diam drainage tube; a wad of glass wool was placed on the upper part of this outlet tube to retain the coal and a plug was temporarily located at the lower end to prevent drainage during charging of the column, see Fig. 1. The most satisfactory testing procedure is as follows: 1—The fine coal, which has been thoroughly

Jan 1, 1953

At its meeting on February 21, 1933, the Board of Directors passed the following resolution defining and expressing the policy of the Institute with respect to official participation or action in controversial matters: WHEREAS, the Board of Directors at its last meeting passed the following resolution: "The Board of Directors, having been appealed to by several Local Sections for advice concerning the attitude and policy of the Institute relating to the endorsement of candidates for public office, the following statement of

Jan 1, 1938

INTRODUCTION The after-tax rate of return that properly discounts future cash flows is usually referred to as the "discounted cash flow-rate of return" (DCF-ROR). The method is also referred to as the internal rate of return, true rate of return, and investor's rate of return in some literature. According to Stermole (1974, p. 188) industry polls indicate that the DCF- ROR method is the number one economic evaluation decision method used by more than 90% of the industrial companies that use for- mal economic evaluation procedures. Other economic evaluation methods that have been used in the past, such as payback period, accounting ROR, etc., have largely given way to DCF-ROR analysis because they fail to account properly for the time value of money. DCF-ROR is generally defined as that rate of return that makes the present worth of future generated cash flow over the life of the project (including after tax salvage value) equal to the present worth of all after-tax investments. The "present worthing" of future cash flow involves discounting future cash flow to a present value according to the mathematics of compound interest at some interest rate. The determination of the interest rate that equates the present worth of future after-tax earnings with the present worth of all after-tax investments necessary to create such earnings is properly called the discounted cash flow rate of return analysis. Although present worth calculations are usually used for determining the DCF-ROR, the same results can be obtained by comparing income and costs of any equivalent point in time, i.e., future worth, etc.

Jan 1, 1980

By W. F. Carew, F. A. Crossley

IT has been reported that the Ti-8 pct A1 alloy is ductile as water quenched from 800°C but brittle as annealed at 650 °C." The present, somewhat limited, investigation was undertaken to discover the cause of the embrittlement. In order to evaluate to some extent the continuity of the embrittling phenomenon, alloys of 6, 8, and 10 pct A1 were studied. Subsequent to the completion of most of this work, Ence and Margolin reported that a Ti,A1 phase exists and that two or more unidentified compounds may exist in the Ti-A1 system.' Materials, Equipment, and Techniques The alloys were prepared using Kroll process sponge of 124 Bhn hardness. In addition, some 8 pct A1 material was made with iodide titanium. The sponge-base alloys were prepared as melts of 4 lb or more by double arc melting. The iodide Ti-8 pct A1 alloy was prepared as 200-g buttons. The alloys were forged at temperatures of 980" to 1150°C. Results of chemical analyses are given in Table I. A Baldwin-Southwark 60,000-lb capacity tensile machine, equipped with an autographic stress-strain recorder, was used for the tensile tests. Standard tensile test specimens, 0.252 in. diam, were used. Standard Charwy V-notch impact specimens were tested using a -kiehle machine. specimens were sealed in evacuated Vycor bulbs for heat treatment. Powder samples for Debye-Sherrer anal- ysis were prepared by filing and screening through 325 mesh. The —325 mesh fraction was taken in an effort to concentrate a microstructural constituent assumed to be less ductile than the a phase. The powder samples were stress relieve2 by annealing

Jan 1, 1958

By Harold A. Linke

THE following article presents notes and data compiled and computed by the writer for use in the determination of: size and slope of mill launders, details of junction boxes and downspouts, and distribution of pulp. It also includes pulp formulas, volume of discharge through bushings, paths of discharging streams, banking of turns and curves. In the design of a concentrating mill, the draftsman usually considers launders to the extent of providing ample "head" for transmission of pulp from one department of the mill to another. The superintendent of construction aims to build his launders wide and deep, and on a slope steep enough to ensure positive flow. So launders are laid generally on too steep a slope, with the result that the repair gang works to maintain launder bottoms and sides against the erosive action of the conveyed pulp. To this end many kinds of liners have been devised: concrete, mastic, white iron, glass, rubber. True, the reduction of slope to the point where a pulp will flow with minimum wear, will minimize labor and expense; but when the desired slope is not predetermined, the millman hesitates to readjust his launder slopes by cut-and-try methods. To the end that the desired size and slope may be found readily, the writer has: (1) conducted experiments with pulps of different specific gravity, screen analysis and dilution; (2) gathered a few graphic data from standard reference works (such as Peele's Mining Engineer's Hand- book and Taggart's Handbook of Ore Dressing); (3) computed several tables; and compiled results that have proved dependable for Utah Copper ore. It is quite possible that the following tables and graphs may not be applicable to all ores, but it is hoped that they may prove helpful, even in slight degree, in alleviating a portion of the trouble and migraine of some other millman.

Jan 1, 1939

By J. D. Grace

Screening by centrifugal force is a unique subject, for all vibrating screens, with but one exception, depend on gravity alone to pass material through a sizing mesh or screen cloth. Centrifugal screening is one of the greatest advancements made in screening since the development of vibrating screens. It makes possible sizing in a range previously im-practical by mechanical methods. The centrifugal screen is specially designed for fine sizing from No. 4 separations to finer than No. 100 separations. Centrifugal force provides a positive control of factors that make fine particle separation practical and effective as opposed to gravity which is a fixed force acting only in a fixed direction, The centrifugal screen provides a control of the force of material against the screening surface, and also controls the distance of departure of the material from the surface and its rate of return. The centrifugal screen has a rotating drum that becomes a natural fan blowing air outward through the material being screened and carrying float dust and fines through the apertures with it. Screening by centrifugal force is an unique subject, for with the exception of only one vibrating screen presently on the market, all vibrating screens depend upon gravity to pass material through a sizing mesh or screen cloth. This one screen that sizes by centrifugal force and utilizes gravity only to convey material along the screen, is the Symons V-Screen. The requirements of the industrial minerals industry to meet ever-increasing stringent fine sizing specifications by a practical mechanical method accentuates the weakness of gravity, a fixed force acting in a fixed direction, as a prime force for fine sizing. It was apparent a force other than gravity was needed. This led to the development of a centrifugal screen to meet modern demands for practical fine sizing operations. Gyratory-type screens in use today were originally designed in a day when a 1/4-in. separation was normally considered fine sizing and 1/8-in. separations were extremely fine sizing. Although gyratory-type screens are sometimes used for separating below 1/8-in., they are not practical screens for this purpose. They were not designed to do this type of work. A growing demand for a practical means of making positive mechanical separations in a range of from 1/8 in. downward led to the development of the vibrating screen. These screens utilize higher speeds and lower amplitudes of vibration than

Jan 1, 1967

The key-note of good writing, as of good manners, is B natural. Sincerity is the first requisite for effective writing. When a man says what he knows or believes, he is likely to be interesting, because each human being possesses an individuality, a point of view, or a range of sympathy that makes him different from his fellows. To say or to write what you do not think, for the mere sake of talking or writing, is a verbal exercise that must be performed with extraordinary skill if it is to be attractive. Affectations are rarely attractive, rarely effective. To be natural is to be yourself, not a poseur; to give the reader the best of yourself, instead of re-warming the baked meats of yesterday. Quotations-which are second-hand thoughts-will serve occasionally when the thing you want to say has been said so well by another that it would be waste of energy to try to say it better; gut, as a rule, the utterance of the writer himself is more interesting than the quotation, because the writer brings something of himself to bear on the subject, and for the moment is more in touch with the reader than any dear departed author. Therefore, say things as best you can in your own way, neither in borrowed words nor in the phraseology that mimics another. Write as if you were speaking to a person whom you desire to persuade or convince. You will then write better than you speak, because, in the first place, you can be more deliberate, and, secondly, you can revise what you have written. Speaking and writing are similar mental acts, with a difference: the difference between eating food raw and eating it cooked. Some kinds of food gain nothing by being cooked; likewise some kinds of utterance are not bettered by being written down first; but most expressions of thought, especially

Jan 1, 1931

By M. F. Burr, F. V. Lenel, G. S. Ansell

The mechanism of materials transport was studied in a model experiment in which a silver sphere was sintered to a silver plate under an applied external stress near 800° C. For this purpose the rate of growth of the neck between the sphere and the plate which is proportional to the strain rate of the creep process involved in a neck growth was determined by measuring the change in electrical resistance of the away. This rate of neck growth will depend upon the magnitude of the applied external stress. By measuring the rate just before and just after a change in the external load and therefore the applied stress, the relationship between strain rate and stress can be derived. For material transport by slip in a pure metal it is expected that the strain rate should be proportional to the 4.5th power of the stress, while for transport by diffusional flow the strain rate should be proportional to the first power of the stress. It was found that for stresses above 5 X 10' dynes per sq cm (70 psi) the exponent in the stvain rate-stress relationship was near 4.5 while for a stress of 0.7 x 108 dynes per sq cm (10 psi) an exponent of 1.8 was determined indicating that under the conditions of the experiment the transport mechanism for creep in silver shifts from diffusional flow to slip in the region of 0.7 x 106 dynes per sq cm (10 psi). The importance of these findings for an understanding of the mechanism of material transport in conventional sintering (without an external load) is pointed out. In a paper by Early et al.,' the mechanism of material transport during sintering was treated as a creep process. It was pointed out that two possible types of creep processes could operate during sintering. In one of these material transport takes place by vacancy diffusion due to a gradient in chemical potential. The vacancy sinks in this diffusion process may be either grain boundaries, as in Herring-Nabarro microcreep, or regions beneath a surface of small radius of curvature. The diffusive transport may be by volume, grain boundary, or surface diffusion. In the other mechanism, creep takes place by slip, i.e., dislocation motion with its rate generally controlled by dislocation climb. One method of distinguishing between these two modes of materials transport is to investigate the creep rate, i.e., the rate of material transport as a function of stress. For material transport by vacancy diffusion, the creep rate is proportional to the stress.' For creep by slip, controlled by dislocation climb, the creep rate is proportional to a power of the stress. For pure metals this power is 4.5;374 for dispersion-strengthened material a fourth power relationship can be derived.5 This difference in the stress dependence of the strain rate is illustrated schematically in Fig. 1, in which the logarithm of strain rate is plotted vs the logarithm of the stress for material transport in a pure metal by vacancy flux and by dislocation climb. The stress range in which the two types of material transport overlap would be expected to be relatively small. In the experiments described by Early and coworkers compacts pressed from spherical copper powder were sintered isothermally under an applied axial external load in a dilatometer. During sintering the magnitude of the applied external load was changed and the rate of axial shrinkage of the compact before and after the load change determined. In order to find the stress dependence of the strain rate the magnitude of the stress acting on the neck area between the spherical particles before and after the load change had to be calculated. This stress is the resultant of the stresses due both to the externally applied load and to surface tension. The stress due to surface tension is a function of the geometry of the powder compacts. It can be determined, at least for simple geometrical arrays,'76 but it is difficult to obtain exact values of the stresses for actual powder compacts when only average values of particle diameters and of neck diameters between particles are available. The calculation of stress and the strain rate-stress relationship is therefore only very approximate.

Jan 1, 1968

By J. L. Huitt, B. B. McGlothlin, D. K. Lowe

Published correlations for the principal aspects of hydraulic fracturing were combined into a digital computer program to facilitate the study of interrelated variables. The computer program includes individual relationships for fracture width during pumping, fracture area generated, propping agent embedment, flow capacities of propped fractures and transport of propping agents in horizontal fractures. The effects of more than 20 treatment and formation parameters on the predicted results of hydraulic fracturing treatments were studied. The effects of these parameters were determined for (I) fracture width during injection, (2) fracture width after the overburden comes to rest on the propping agents, assumed not to be crushed, (3) generated and propped fracture area, (4) location and concentration of propping agents in the fracture when injection ceases, (5) flow capacities of the various propped sections of the fracture and (6) expected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters on well productivity are discussed. The parameters that were found to have the most pronounced effects on hydraulic fracturing treat~nents are injection rate, treatment volume, fracturing fluid coefficient, size and amount of propping agent, spearhead volume, well drainage radius and formation capacity. INTRODUCTION Many correlations have been published for predicting effects of various parameters that are considered in the design of hydraulic fracturing treatments. The Carter equation' can be used to predict generated fracture radius as a function of fracture width, fracturing fluid leakoff and other parameters. Fracture width can be determined by use of the Perkins and Kern correlation' in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et aL4 have reported methods of predicting the location of propping agents in fractures when pumping ceases. The former study is applicable to the case where the ratio of propping agent diameter to fracture width is less than 0.1. The latter is applicable when this ratio is greater than 0.1. These studies showed that the propping agent placement in horizontal-radial fractures depends principally on how the individual particles are transported in the fracture by the carrying fluid. Particle transport in fractures is determined by local fluid velocity in the fracture, fluid and particle properties, and the size of the particle relative to the fracture width. The distribution of propping agents, effective overburden pressure and formation rock strength control the propped fracture width6 by controlling the extent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated or the various regions of the fracture. The flow capacities and the radial extent of these regions can be combined with reservoir information to predict the productivity increases for fractured wells. In all these studies, the effects of certain treatment and/ or reservoir parameters on one facet of fracturing can be predicted only if other facets which the parameters affect are fixed. For instance, fracture width and radius are interrelated; that is, to calculate the value of one, the value of the other must be known. Also, some parameters influence more than one aspect of fracturing. For example, prop-pant transport is a function of both fracture width and fluid viscosity. but fracture width is itself a function of fluid viscosity. Since these calculations are complex and the parameters interrelated, it is not possible to write an equation with which the over-all effects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are most significant in hydraulic fracturing treatments have been incorporated into a digital computer program. COMPUTER PROGRAM The program, which was written for an IBM 7094 computer, can be used to predict results of most of the combinations and values for the treatment parameters that are ordinarily considered for fracturing treatments. A spearhead of fracturing fluid and a propping agent-carrying fluid with different fluid properties can be taken into account. Also, the total volumes and relative amounts of the spearhead and carrying fluids can be varied. Two different propping agents (as used in tail-in operations) and a wide range of formation properties and injection rates are considered. The computer program (Fig. 12) consists of several sets of calculations. First, the final flooded fracture radius and average fracture width at the cessation of pumping are calculated. This is done by simultaneous solution of the Perkins and Kern fracture width equation and the Carter equation for flooded fracture radius (equations used in the computer program appear in the Appendix). The next step is to determine local fluid velocity in the fracture as a function of time and radius. Since it is not possible to write this function in closed form expression, a table of velocity values is generated by the program and stored for subsequent use. The time span from the beginning of

By Tony B. Szwilski, K. Unrug

INTRODUCTION Since the introduction of longwall coal mining systems, reliable predictions of roof support requirements at the face and the roof caveability in the gob area have been major contributors to the success of the longwall face by means of safety and face productivity. That is, the successful operation of a longwall is well-served by good regular caving of the gob. In recent times, with the advent of increased coal face mechanization and capital investment, the evaluation of the feasibility of longwall mining has become essential. In the United States, where a face unit for a face length of about 150 metres may cost around $6 million, a quantitative system that would assist in selecting the best equipment for the coal would prove extremely beneficial. There have been many such varied investigations in the past few years. A vast -amount of work has been invested principally by West Germany [3, 7, 8, 91 , Poland [I, 101 , United Kingdom [4, 5, lo], France [4], and South Africa [4]. It is the object of this paper to review this previous research work and give an outline that may be used as guidelines for long- wall evaluation. Essentially, for the initial design phase for a longwall system, account must be taken of the geometry of the coal panel, its position relative to the surface (depth), direction of the coal cleat system, faults and in-situ stresses and other neighboring workings in the same coal seam and other seams both above and below. The advance of the coal panel disturbs the stress field and in doing so creates an abutment zone around the face. At this stage the condition of homogeneity of the surrounding rock mass does not apply. The magnitude of the rock strata pressure may exceed the ultimate strength of the rocks and create zones of clastic, plastic and elastic material, the limits of which are difficult to determine. The collapse of the gob and resulting expansion of the displaced waste roof rock, create a statically undefined support complicating an already unclear rock structure. For example, it is often a point of debate whether, indeed, the vertical strata pressure develops to regain the original magnitude of virgin stress. Under these post-failure circumstances an analytical approach based on simplified and idealized assumptions can only be considered a very general approximation. Theoretical concepts, however, may be adequately supplemented by empirical methods that are based on numerous underground observations and surveys [3, 4, 7, 8]. These methods employ the use of rock indices that very handily correspond to the competence of the roof rock mass. Scale model work [3, 41 , using equivalent materials representing the surrounding rock mass within the coal seam zone, have given valuable qualitative and sometimes quantitative data in addressing the behaviour of the rock mass around longwall panels. To characterize the state of art of caveability predictioqthe principal concepts will be reviewed with special emphasis placed on practicality for the planning of longwall operation. It has been the general observation of the authors that many of the literature surveys published in English often neglect reference to other international mining literature. It is with this point in mind that an overall review has been written including mining concepts identified with the principal coal mining countries. THEORETICAL CONCEPTS Arching Theory For the development of this theory, assumption has been made that an extracted height, h, in a coal seam results in an extracted panel of width, w . Also, the coal seam is horizontal and the rock strata of both the roof and floor are homogeneous. The primary (virgin) stress distribution will change in the roof as well as the floor. As a result of lack of support caused by the excavation (in the gob area) an additional load is developed due to the redistribution of the load around the sides of the panel, referred to as the abutment, R, where: [ ]

Jan 1, 1982

By E. R. Gilbert, D. E. Munson

Creep of copper under 75 to 1.50 kg per sq cm stresses at temperatures near the melting point was found to he a complex reaction controlled by three mechanisms acting in parallel. In order of appearance with decreasing temperature, the auerage activation energies, Qc , are 168, 79, and 24 kcal per mole. Stress dependence of the minimum creep rate was found to he an exponential for the two high-Qc processes and a power law for the low-Qc, process. Transition of control occurs from one mechanism to another. The relative transition temperature depends upon the applied stress, and the range oiler which the transition occurs depends upon the difference in the activation energies of the mechanisms. The creep behavior at high temperature is explained by the climb of dislocations through thermally or mechanically formed jogs, CREEP in pure fcc metals at temperatures in excess of one half the absolute melting point is normally controlled by dislocation c1imb.1,2 A climb model which seems applicable, according to an extensive analysis of data,3 was derived by Weert-man.4 This model assumes jog-saturated dislocations and predicts an activation energy, Qc, nearly equal to that for self-diffusion, USd. Although the requirement of jog saturation is restrictive, agreement between theory and experiment seems adequate. Many other theoretical treatments, including an early model by Mott,5 include detailed consideration of jog formation as an initial requirement for climb. These models predict activation energies for creep which differ from those of self-diffusion. Seeger6,7 postulates an observed activation energy related to the stacking-fault energy. Thus, Usd <Qc<5Usd + Uj where Uj is the jog-formation energy. Seeger incorporated qualitatively the influence of the relative numbers of thermal and athermal jogs. Expanding this concept, Shoeck8 explicitly states a function based on formation mode and relative numbers of vacancies: e r ci exp {-uf/k T} exp {-Um/k T} [ 1 ] where Uf and Um are energies of vacancy formation and migration, respectively. The concentration of jogs, Cj, depends upon the manner of jog production. For intersection jogs, Cj is not sensitive E. R. GILBERT, Junior Member AIME, formerly with De- to temperature; for thermal jogs, Cj is proportional to exp {—Uj /k T}. Schoeck regards each mode as a distinct mechanism; therefore, the mechanisms may act together.299 The diversity predicted by theory, surprisingly, has not been substantiated by experimental results. A significant investigation must include the extremes in stacking-fault energy. Extensive creep studies of aluminum10 and nickel,11,12 high stacking-fault energy metals, have been made. Comparable studies on a low stacking-fault energy metal, such as copper, have not. It is the purpose of this paper to report the results of an investigation of the creep of copper under conditions which favor thermal jogs. EXPERIMENTAL Cylindrical compression creep specimens (0.240 in. in diameter by 0.400 in. long) were machined from cold-drawn rods of electrolytic tough-pitch copper containing 0.0007 Mg, 0.002 Fe, 0.001 Ni, 0.0005 Ag, Cd < 0.005, and Pb < 0.005 wt pct impurities. Undetected spectrographically was a nominal 0.04 wt pct 0, which occurs as a Cu2O constituent distributed discontinuously at grain boundaries. Vacuum annealing at 900°C for 15 min produced a stable 0.03-mm average grain diameter. Testing was carried out using apparatus similar to that described by sherby,13 modified by enclosing platens and a push rod in a vacuum cylinder. Normally this arrangement resulted in pressures less than 10 Only a slight surface tarnish, less than 0.0005 in. in thickness, occurred during the test. The applied stress, corrected for atmospheric pressure, was maintained within 2 pct of the desired true stress by the addition of lead shot at fixed strain increments. Creep strain was measured with dial gages as a relative displacement of the upper and lower platens; accuracy of measurement was 0.0001 in. Two creep-test methods were used, the differential or cyclic temperature14 and the isothermal, to obtain creep data at stress levels of 150, 100, and 75 kg per sq cm over the temperature range of 620° to 1032°C. Minimum creep rates were used from both test methods; this was considered proper because comparable temperature tests or cycling to the same temperature gave the same creep rate, within experimental error. The cold vacuum test chamber, with the unstressed specimen in place, was heated to temperature by placing a preheated furnace over the chamber. Temperature equilibrium was attained within 30 min. For the cyclic tests, the stress was removed during the 5 to 10 min necessary to effect the temperature change and re-

Jan 1, 1965

By P. H. Brace, N. A. Ziegler

THE study of the relations between gases and metals is one of perennial interest to all who are connected with the production of high-grade metallurgical products. The data reported here are the outcome of work of which the object is to determine the effects of dissolved gases upon the properties of metals and to gain a more detailed knowledge of the reactions between gases and molten metals, particularly iron, under definitely controlled conditions. We have attempted to reduce our margin of error by dealing with relatively large quantities of metal, from 4 to 13 lb. (2 to 6 kg.), and keeping the ratio of refractories to metal as small as practicable. The ingots produced are large enough to provide adequate material for making determinations of magnetic and other physical properties. In choosing the bell-jar type of furnace we were influenced by the results of considerable experimentation along the same general line which indicated that, for the scale on which we were to work, it was important to have the furnace structure independent of the vacuum enclosure. The use of a bell-jar surrounding the entire furnace accomplishes this and also gives great freedom of observation during operation and ready accessibility for the replacements which are necessary after each run. Our choice of analytical method was made in the light of the results secured by H. M. Ryder, who used a method similar in principle for the analysis of very small quantities of gas extracted from strips of metal heated electrically in high vacuum. We have presented some selected preliminary experimental data as being illustrative of the quantity and nature of the gases which occur in iron of different origins, but do not urge any hypothesis at this time. THE FURNACE Our furnace may be described as "a high-frequency induction furnace of the bell-jar type." It is similar in a general way to that described by Cain and Peterson&apos; though we have introduced certain refinements of

Jan 1, 1928

By L. B. Slichter

After statement of the principles of similitude which apply to electromagnetic modeling, charts showing the inductive response of conducting spheres as dependent upon frequency, conductivity, and size are exhibited in this paper. The shape of the curve which relates intensity of response to frequency is significant in indicating the advisability of low frequencies in the exploration for conducting bodies, when consistent with the securing of a large percentage of the ideally possible response. Comparisons of theoretical response and that observed with models are shown, and relationships with the subject of applied electromagnetic prospecting are indicated. Maxwell Field Equations The Maxwell field equations summarize the physical laws that govern electrical field phenomena; they are the basis for the solution of electromagnetic problems. These concise equations, with adequately formulated boundary conditions, specify the complete electrical condition of continuous media, and the development of their solution amounts merely to a more convenient re-expression of phenomena already completely described. Thus, the immediate content of the field equations themselves is sufficient and sometimes convenient for the treating of certain questions (such as those relating to electromagnetic models) which are independent of the special factors of geometry, or the nature of an impressed field. The four Maxwell field equations are written below, in c.g.s. gaussian units: curl E = -B/c [21 div eE = 4pp [31 div B = 0 [41

Jan 1, 1932

By Charles S. Barrett

Metallurgists are making use of the stereographic projection to a steadily increasing extent. In the last five years no less than 20 papers in American metallurgical journals alone have employed the stereographic projection; recent books on physical metallurgy, plastic deformation, X-rays and their applications, and crystal structure use it. Mineralogists have used the stereographic projection for many years in the description of symmetry classes and crystal planes, for it presents an accurate, easily understood plot of any angular relations in crystals with all unessential features eliminated (such as the accidentally determined size and shape of crystal faces). In metallography and physical metallurgy the projection is much used for the analysis of markings appearing on polished grains: slip lines, twins, cracks, structures formed by precipitation, magnetic-powder patterns, etch pits, etc. Data from certain types of X-ray photograms are most conveniently analyzed by its use, particularly those for determining the orientation of single crystals or the preferred orientation of grains in an aggregate. Calculations of how to tilt or cut a crystal parallel to a certain crystallographic plane or to reflect X-rays from a certain plane are rapidly carried out. It has been adopted almost universally to the exclusion of other methods by those studying the deformation of metallic crystals, save where the accuracy required is greater than a few tenths of a degree. Any directional property in a crystal or polycrystalline material can be shown on a stereographic projection; for example, the modulus of elasticity, yield point, etc. It has been repeatedly called to our attention that there is need of an elementary explanation of the principles and methods of stereographic projection, covering all the common applications in the field of metallography and physical metallurgy. The following contribution is an attempt to fill this need. The description of each method is supplemented with references to publications in which the method has been used. For convenience to the reader, these illustrative references are chiefly in American journals, particularly the publications of the American Institute of Mining and

Jan 1, 1937

By M. H. Waxman, M. Gondouin, H. J. Hill

Streaming-potential experiments were conducted within the Muddy- and Dakota-sandstone interval of a Denver basin well. Analysis of the data shows that, for this case, streaming potentials opposite sands were higher than those opposite shales when the mud was fresh. Streaming potentials opposite shales, however, were of sufficient magniiIlde to be important in SP interpretation. They were linearly dependent upon pressure differential, and they increased with mud filtrate resistivity. The magnitude of streaming potentials opposite sands was influenced by the characteristics of the original mud cake formed at the time of drilling. Use of mud samples taken at the time of logging may not always be satisfactory for determining streaming-potential corrections. Both the streaming and electrochemical potentials were found to be affected by the previous history of the borehole system. Following a change in mud characteristics, several days were required for SP stabilization. This was, in part, due to the mud cake acting as an imperfect shale membrane. INTRODUCTION Laboratory investigations by Wyllie,1 Salisch,2 Moore," Sen Gupta and Bannerjee,0 and Hill and Anderson&apos; have shown that streaming potentials developed across mud cakes deposited on permeable filter beds are of sufficient magnitude to be critically important in SP interpretation. Streaming potentials across shales have been reported by Schenck,&apos; Gondouin and Scala; and Hill and Anderson." The magnitude of the shale streaming potentials obtained by Schenck and by Gondouin et a1 led these authors to conclude that in many cases the shale streaming potential would approximately equal the mud-cake streaming potential. Hill and Anderson, however, obtained somewhat lower magnitudes of shale streaming potential. The field experiment described in the present paper was a cooperative project carried out by the respective operations and research departments of Schlumberger Well Surveying Corp., Shell Development Co. and Shell Oil Co. The primary objective of the experiment was to determine in the borehole the streaming-potential behavior of both shales and mud cakes under conditions approaching, as nearly as possible, those normally encountered in logging practice. METHODS AND EQUIPMENT WELL A Muddy- and Dakota-sandstone vie11 in the Denver basin was chosen for the experiment. Both sandstones were water-bearing and, since reservoir pressures in these sandstones are abnormally low (gradient of approximately 0.25 psi/ft), it was expected that studies of streaming potential could be conducted from low-pressure differentials (approximately 200 psi) to about 27000 psi by bailing mud from the hole, filling up and then applying wellhead pressure. The selected well encountered the Muddy sand-

By John Wulff, J. H. Hollomon

THE opinion has been widely held that the corrosion of alpha brass occurs by the selective solution of zinc. As late as 1939, Fink1 and Evans2 suggested that in the initial stage of the corrosion the selective solution of zinc produces copper-rich areas, which subsequently act as cathodes that facilitate the deposition of copper. Previously Abrams3 had shown that most of the copper found on corroded brass was redeposited and not residual, although he did not consider the nature of the initiation of the corrosion process. Enough data exist to indicate that any metal surface is sufficiently heterogeneous to provide the anodes and cathodes necessary for the initiation of corrosion.4,5 Thus, for alpha brass we need postulate not an initial selective solution of zinc, but only the existence of local differences in electrochemical potential. The heterogeneity responsible for potential differences may arise from oxide and other films as well as from alloy concentration gradients. Even though selective corrosion may be possible in some alloy systems, previous data on alpha brass as well as the experimental work reported in this paper do not require this supposition. Bengough and May,6 in a discussion of Abrams&apos; paper, first suggested the addition of small amounts of arsenic (0.03 per cent) to alpha brass to prevent the redeposition of copper (dezincification). This suggestion was later substantiated by Nixon.7 In their studies of the inhibiting influence of arsenic, Evans and Fink were led to the selective-solution hypothesis in order to explain the initial corrosion of such alloys. They believed that an arsenic film covered anode areas and prevented the formation of copper-rich spots capable of acting as cathodes for the deposition of copper. They did not consider, however, the mechanism by which the arsenical film was formed. Bengough and May,8 in another publication, suggested that the commonly found gray or black arsenical film may act to: (I) carry oxygen to the brass surface, (2) increase the discharge potential of copper on brass, (3) precipitate cuprous chloride from colloidal suspension in chloride solutions. Masing9 assumed that the film found upon arsenical brass was metallic arsenic. His measurements of hydrogen overvoltage of bulk arsenic led him to believe that the inhibition of dezincification occurs because the overvoltage of a brass surface is lowered by the arsenic film. He reasoned that this film would permit the more rapid reduction of hydrogen at the cathode, which would prevent the redeposition of copper. In a recent paper,10 we have pointed out that the film formed during the corrosion of arsenical brass and copper in stagnant solutions is essentially arsenious oxide (As203),

Jan 1, 1942

By J. L. Taylor, P. Duwez

The phase boundaries in the ternary system Ti-Cr-Al have been established at 1800° and 1400°F for alloys containing more than 60 pct Ti. The martensite transformation temperature has been measured for the titanium-rich alloys. THE studies of binary alloys of titanium with the transition elements which have been published so far1-0 ndicate clearly that the solubility of these elements is always much greater in the high temperature body-centered cubic form of titanium (ß phase) than in the low temperature hexagonal form. In this category of alloying elements are iron, nickel, chromium, manganese, vanadium, molybdenum, tungsten, columbium, and tantalum. Although studies of the nontransition elements have been rather limited, early work on titanium binary alloys&apos;" has shown that most of them were not very soluble in the a form, with the exception of aluminum, for which the solubility in a is about 25 pct.13, 12 In addition to this large solubility in a, aluminum is also soluble in ß titanium to the extent of about 35 pct and the transformation temperature from ß to a is raised with aluminum content. This effect is also typical of aluminum, in contrast with that found for the transition elements which lower the ß to a transformation temperature. Therefore, it may be anticipated that tprnarv titanium alloys with aluminum and any one of the transition elements will constitute a class of ternary alloys having characteristic features absent in alloys involving two transition elements. Chromium was chosen as a typical transition element for the present study because ternary alloys of Ti-Al-Cr commercially produced have been found to possess very interesting physical properties (MST-3 pct A1-5 pct Cr of Mallory-Sharon).&apos;" Binary Systems The binary systems Ti-A1 and Ti-Cr have been established recently by several investigators. The data used in this investigation were taken from the complete diagram of Bumps, Kessler, and Hansen." This diagram agrees quite well with earlier investigations." For the Ti-Cr system, the phase boundaries at 1800" and 1400°F were taken from refs. 6 and 7. The binary system Cr-A1 has been studied recently by Bradley." This system is rather complex and contains not less than seven intermediate phases. The present study was limited to the titanium corner of the ternary system (less than a total of 40 pct Cr plus Al) and none of the phases present in the Cr-A1 binary alloys were found in the ternary alloys investigated. Experimental Technique Microscopic observation and X-ray diffraction measurements were used to identify phases and de-

Jan 1, 1954

By Eugene McAuliffe

The term "mechanical mining" carries an ambiguity which justifies a preliminary word of explanation. . All mining activity conducted in this day is more or less mechanical; that is to say, power expressed in the form of electricity, steam or compressed air is used in some portion of practically every mining activity of consequence. "Mechanical loading" is more nearly correct than "mechanical mining" in reference to present practice. The first substantial effort made in the direction of mechanical mining, subsequent to the application of steam for hoisting and underground pumping purposes, was that of substituting for hand labor undercutting and shearing by power-driven machines. The undercutting of coal by hand represented at one time the most arduous task confronting the miner. Occupying a kneeling position in the thicker beds, or lying on his side in the thinner coal, the task was tedious and exhausting. The first attempt to substitute crude air-driven, and later electrically driven, "punchers," as the percussion type of machine was called, met with much the same opposition on the part of the workers as was expressed by workers in the other industries when any innovation, whether labor-saving or otherwise, was introduced. We should not be too critical of this attitude of mind shown by the mine workers. The peculiarly isolated character of the work carried on in semidarkness by a class of men who to a large extent lived and held themselves aloof from the other branches of society led long ago to the development of a craft consciousness which they have found difficult to surrender. It was not until 1891 that a definite record of the results obtained by the use of undercutting machines of all types was made available, the quantity undercut in that year totaling 6,211,732 tons of bituminous coal from all American mines. The volume of bituminous coal undercut by machines in 1928 totaled 369,687,007 tons, or 73.8 per cent. of the nation&apos;s production. In the light of this experience, we can properly feel that the work of introducing the coal-loading machine as a substitute for hand shoveling is making substantial progress.

Jan 1, 1931