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By Henry F. Hebley

In preparing this paper it has been the aim of the writer to keep the problems of both producers and consumers in mind. Until now, no attempt has been made to familiarize each group with the other's practice and limitations. This paper is an effort to acquaint the readers with some of the factors pertaining to the problem and cost of mining and preparing steam coal, and also to the economics of producing steam with such coal. In recent years all lines of endeavor have turned to intensive mechanization in order to lower the unit cost of production. The average fuel consumption in steam electric generating stations has dropped in 20 years from 4.0 lb. to 1.4 lb. per kilowatt-hour; while the modern power station can generate 1 kw-hr. on a fraction under 1 lb., or 13,000 B.t.u. coal. Also, the amount produced per man has in that same period risen from 3.8 to 8.2 tons, owing to the use of modernized equipment below ground for coal cutting, drilling, shooting, loading, hauling and hoisting. Unfortunately, the rapid speed of 5 tons per minute of operation at which the coal is loaded mechanically precludes any appreciable removal of impurities at the coal face, so that the raw coal is hoisted containing a markedly higher percentage of impurities than the hand-loaded coal, which was subjected to the scrutiny of the miner during loading. Also, during the past 20 years, certain seams of coal lying close to the surface have been made economically available by the improved design of electrically operated shovels and draglines for the removal of overburden running as high as 56 ft. This strip coal frequently contains so much ash in the raw state (Table 1) that it would have no sales value. Therefore, coal preparation must be adopted to beneficiate the raw product. Some seams in the United States have a decreasing ash content with decreasing size, owing, in all probability, to the fact that the coal is friable while the impurities are hard, causing a concentration of the low-ash material in the fine sizes. Illinois No. 6 coal being rather hard, naturally the reverse is true.

Jan 1, 1938

By Henry F. Hebley

In preparing this paper it has been the aim of the writer to keep the problems of both producers and consumers in mind. Until now, no attempt has been made to familiarize each group with the other's practice and limitations. This paper is an effort to acquaint the readers with some of the factors pertaining to the problem and cost of mining and preparing steam coal, and also to the economics of producing steam with such coal. In recent years all lines of endeavor have turned to intensive mechanization in order to lower the unit cost of production. The average fuel consumption in steam electric generating stations has dropped in 20 years from 4.0 lb. to 1.4 lb. per kilowatt-hour; while the modern power station can generate 1 kw-hr. on a fraction under 1 lb., or 13,000 B.t.u. coal. Also, the amount produced per man has in that same period risen from 3.8 to 8.2 tons, owing to the use of modernized equipment below ground for coal cutting, drilling, shooting, loading, hauling and hoisting. Unfortunately, the rapid speed of 5 tons per minute of operation at which the coal is loaded mechanically precludes any appreciable removal of impurities at the coal face, so that the raw coal is hoisted containing a markedly higher percentage of impurities than the hand-loaded coal, which was subjected to the scrutiny of the miner during loading. Also, during the past 20 years, certain seams of coal lying close to the surface have been made economically available by the improved design of electrically operated shovels and draglines for the removal of overburden running as high as 56 ft. This strip coal frequently contains so much ash in the raw state (Table 1) that it would have no sales value. Therefore, coal preparation must be adopted to beneficiate the raw product. Some seams in the United States have a decreasing ash content with decreasing size, owing, in all probability, to the fact that the coal is friable while the impurities are hard, causing a concentration of the low-ash material in the fine sizes. Illinois No. 6 coal being rather hard, naturally the reverse is true.

Jan 1, 1938

By E. W. Engle

For several years the Fansteel Products Co. has been engaged in e production and development of various of the rarer metals. It is at present engaged in the commercial production of tantalum, tungsten, and molybdenum in a very high state of purity. The information contained in this paper is partly a general compilation from various sources and partly information obtained as a result of recent years of work in the laboratory of this company. Tantalum, tungsten, and molybdenum form a group peculiar to themselves among the commercially available metals. Their very high melting points (tantalum 2770' C., tungsten 3350' C., and molybdenum 2550" C.) set them apart so far as the metallurgical processes for their production are concerned. Further, when properly prepared and treated they will stand a somewhat unusual degree of cold work, that is work below the temperature at which marked crystal growth takes place. Such cold-worked metal may show a high tensile strength; tantalum to 130,000 lb. per sq. in., tungsten to 490,000 lb., and molybdenum to 260,000 lb., in the form of fine wire. In physical appearance, these metals are not unlike some steels; they may be better described by saying that polished tantalum somewhat resembles lead; polished tungsten, iron; and polished molybdenum, nickel. The polished surfaces of all three remain untarnished in ordinary air. Air containing corrosion-producing impurities will, in general, show molybdenum the least resistant to corrosion and tantalum the most resistant. Molybdenum has, however, a high degree of resistance to corrosion by hydrochloric acid, a property that should render it of commercial interest. On the other hand, it is markedly attacked by some of the weaker organic acids. The three metals oxidize rapidly when heated at or above a dull red in air. This feature limits their use in many applications where their high melting point and strength make them appear usable. Tungsten and molybdenum, at red heat, are quite inert to hydrogen and nitrogen; while tantalum has a rather remarkable affinity for all the ordinary gases, which results in its becoming embrittled in their presence. This

Jan 1, 1925

By A. L., Bailey

All who are even generally aware of the tremendous rate of increase in coal washing operations must realize the growing importance of the float-and-sink test. I believe it is conservative to estimate that, in the past decade, the dollar volume of float-and-sink testing has increased tenfold. It is a simple matter of economy, then, to examine the factors that determine the cost of adequate float-and-sink testing. When the Coal Preparation Section of the Bureau of Mines entered upon a greatly expanded program of such work in connection with the synthetic liquid fuels investigations, it seemed advisable to examine these factors experimentally. The principal consideration that differentiates float-and-sink test sampling from general purpose sampling, is that the original particle size must be preserved. Therefore, the total cost of the test will be directly affected by any standard that might be proposed to limit sample bulk reduction at any given particle size. For this reason, the relationship of sample size to variability of results was the first factor to be studied experimentally.

Jan 1, 1949

By J. J. K. Daemen, C. Fairhurst

Introduction The stress field around a supported tunnel can be considered as being composed of: i) the virgin (pre-mining) stress in the rock ii) the (elastic) change in this stress field caused by creating the opening iii) the (time-dependent ) change in the stress field produced by (i) and (ii) as a section of the rock breaks up iv) the (time-dependent) influence of the stress build-up in the support. Several authors have examined the conditions necessary to produce static equilibrium between the support, the rock, and the regional (in-situ) stress field. The analysis used by Labasse (1) is typical. Consider a circular tunnel radius R in a hydrostatic stress field (P), and a radial pressure pi exerted by the support. According to Labasse, the radius ‘b’ to which the rock will break* for a given support pressure, pi, can be calculated from: - the equilibrium equation: [ ] As a zone of broken rock develops around the opening, the stress circle for a point on the elastic-broken rock boundary moves to the right in the Mohr diagram until the radial stress in the broken zone s equal to the radial stress in the elastic zone.

Jan 1, 1971

By Paul R. La Pointe

GEOTECHNICAL OBJECTIVES OF UCG PROGRAM Underground coal gasification (UCG) is one of several in situ extraction technologies for utilizing deep, otherwise unmineable coal. This technology involves the injection of air or oxygen into the target coal seam, ignition of the coal and recovery of product gases. Geotechnical characteristics of the coal and enclosing rock strata strongly influence the success of this Process. The flame front follows the coal cleats (Hill, 1979), and cleating and bedding control the manner in which coal collapses into the cavity, thereby affecting recovery efficiency (Ramirez and others, 1982). Moreover, coal seams typically behave as fracture dominated aquifers in which cleat orientations govern subsequent contaminant dispersal. For these reasons, the Anaconda Minerals Co. undertook a detailed study of fracturing within the Wyodak-Anderson Coal in the eastern Powder River Basin (PRB) near its Rocky Hill UCG test site (Fig. 1). STRESS HISTORY AND FRACTURING IN THE POWDER RIVER BASIN Vertical jointing, or cleating, in coals may arise from shrinkage shortly after deposition under low confining pressures, or later in time, soon after burial but after the coalification process is well advanced (Ting, 1977). There is much evidence to support the formation of cleating after coalification (e.g. Hawkes and Mellor, 1970; McCulloch and others, 1974), which suggests that the stress state existing at that time strongly influences cleat formation. McCulloch and others (1974) argue that the typically better developed face cleat forms parallel to the plane containing [ol] and [o2]. Where the relation between cleats and stess has been studied (McCulloch and others, 1974; Stone and Snoeberger, 1977; Ward, 1977; Kulander and Dean, 1978), the highly systematic face cleat strongly parallels the [o1] direction. Stone and Snoeberger (1977) report face and butt cleat measurements of N70E and N29W for the Felix Coals 220 m stratigraphically above the Wyodak at the Hoe Creek UCG site (Fig. 1). Structural trends also indicate the past state of stress in the PRB. Glaze and Keller (1963) suggest that the NE-SW regional compression during the late Permian formed major N-S fold lines and basement magnetic anomalies. Mapel (1959) describes folds having N60W and N30W rends in the northern PRB, as well as a large normal fault trending northeast. Glass (1976) also describes normal faults trending northeast. Similarly, Olive (1957) mapped normal faults

Jan 1, 1984

By D. F. DeSante, A. S. Tetelman

MICROCRACKS are often introduced into commercial metals during fabrication processes such as swaging, cold rolling, deep drawing, and welding. These microcracks act as strain concentrators and may be capable of causing premature catastrophic failure of a component or weld. The present investigation was undertaken to determine whether high-temperature annealing treatments may be capable of reducing or negating the detrimental effects of such existing microcracks. Internal microcracks, ranging from 0.1 to 0.85 mm in length and averaging 0.23 mm, were introduced into polycrystalline Fe-3 pct Si tensile specimens (0.155 mm grain size) by the cathodic charging of hydrogen.1'2 The typical appearance of such microcracks and their associated strain patterns (made visible by the technique of dislocation etch pitting3) is shown in Fig. 1. The stress fields of the dislocation loops formed during plastic relaxation stabilize the microcracks so that, when the internal hydrogen pressure is removed: the microcracks stay open, rather than disappear as perfectly elastic cracks would be expected to do.' As shown in Fig. 2, such stopped microcracks cause a 36 pct decrease in the macroscopic cleavage fracture strength at -196°C.

Jan 1, 1969

By George B. Clark, Edward E. Hornsey

Pulses from large underground explosions which traverse the rock beyond the "fracture" and "plastic" zones do not behave as a spherical elastic model. Observed attenuation is greater than that predicted by the elastic wave equation, and the pulse form changes in a different manner, i.e., it usually lengthens with the first power of the distance. To more clearly define a mathematical real earth-wave model, detailed analyses of the spherical elastic and the Voigt viscoelastic models have been made, and results compared with observed wave forms from large confined chemical and nuclear explosions. TRANSIENT SPHERICAL ELASTIC WAVES Scope of Investigation Transient elastic spherical waves were investigated in detail. However, an elastic model is not, in general, an exact representation of wave propagation in rock. An understanding of transient elastic waves is desirable for gaining insight into explosive-generated wave phenomena because it can be employed for comparison of more complex and realistic models, such as the Voigt model, or others which may simulate real earth waves. The study was concentrated primarily on the peak values of the radial wave parameters : displacement, particle velocity, acceleration, stress, and strain.

Jan 1, 1972

By Yeatman, Pope

FOR many years geologists have felt that mining companies should adopt a more liberal policy in the publication of their reports. The increasing usefulness of the geologist to the mining profession in recent years demands that consideration be given to this question. Prior to 1900, the call for geologists of high reputation by mining companies was probably mainly in connection with lawsuits arising from the interpretation of rights or ownership as defined by the "Law of the Apex," and from problems such as finding the continuation of the vein or whether the vein followed was the main one or a branch. Later, outside of legal questions, the most intensive and general use of their services arose from the search for oil. Geologists to determine the position of the formations

Jan 1, 1938

By R. E. Rick-Secker, W. M. Baldwin, R. McC. Baker

The development of residual stress in strip during rolling has not been systematically studied. A few scattered papers1 -3 mention the existence of residual stresses in rolled strip or touch upon some of their consequences,4 but there is no report of experimental studies in the literature describing the effect of roll diameter, strip thickness, reduction per pass, metal or metal temper on the magnitude of residual stresses developed in strip. A knowledge of the effect of these factors is of utmost importance since the present trend in some mills to roll thicker castings brings the rolling operation directly into that set of conditions which, as will be brought out in the present paper, can develop residual stresses of a high order of magnitude. Fundamentally, residual stresses are developed when a metal is inhomogeneously unloaded from a plastic stress state. A quantitative treatment of the problem requires a reasonably complete understanding of both the plastic stress state existing in the metal during deformation and the elastic stress state that would exist in the metal if the metal deformed as a perfectly elastic body. Our knowledge of either state during rolling is so meager that we can make no more than certain limited predictions. The external stress state* operating between the roll and the metal consists of Fig i—External stress state operating on metal being rolled (after siebel and LUEG5) compressive stresses acting almost perpendicularly to the strip surface but varying in intensity both across the width of the strip and along the length of contact between the roll and the strip. An example of such a stress distribution is shown in Fig I. The nature of the internal stress state, produced by this distribution, is not known. Various investigators,5-7 however, have felt that a qualitative similarity must exist between the internal stress state so produced and that produced in a wide strip that is compressed between two flat-nosed punches. In the latter case the external stress state is represented by a uniformly distributed compressive stress acting per-pendicularly over the face of the tool. The

Jan 1, 1949

[ ] DISCUSSION F A LORIA*-The method of testing gun steel for resistance to surface cracking described in this paper was restricted to the examination of small, rod-shaped specimens The writer would like to point out the importance of other factors in producing defects in forged and bored gun tubes which would not be apparent in this investigation because of the nature of )he test Actual section size would accentuate the possibility of internal wall (bore) defects arising from unequal expansion between the internal and external wall surfaces on firing, resulting in internal tearing Checks and tears on the inside walls arise from internal tensions and nonuniformity on cooling, but the internal tearing can be reduced by using alloys of low expansion and of good thermal conductivity so as to reduce the difference between the outer and inner wall surfaces Also, the possibility of the location of inclusion segregates within a machined gun tube becomes more likely than in a small test specimen The effect of these nonmetallics on gun life and performance is evident when one realizes that the inclusions are soft yet brittle They reduce the amount of plastic deformation which can take place before cohesive failure occurs Once localized fracture has occurred at the position of a chain of these inclusions, a sharp notch (crack) is formed which produces stress conditions more favorable to cohesive failure than to plastic deformation These cracks aid erosion by providing channelways for the explosive gases, eventually leading to the tearing out or spalling of blocks of metal Oxidation of the surface may be partly responsible for the change in the surface of gun steel during firing observed by the author The appearance of burn on the surface is an indication that high temperatures were reached on firing, resulting in a slight oxidation of the surface Since the color of the oxidized film depends on both temperature and time, a higher temperature is required for a given color to form when it is caused by explosive heat, which acts for only an extremely short time at a given spot, than when it is caused by ordinary tempering The cross section of the gun steel specimen, Fig 16, illustrates that the repeated firing temperatures were high enough to cause

Jan 1, 1948

By C. Zener, J. H. Hollomon

IT Is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect o rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. EARLIER INVESTIGATIONS A clear analysis of the conditions necessary for plastic flow and for fracture was first given by Ludwik,1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis, both a flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracture is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence or now stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The. curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated' by the authors. According to this principle of equivalence, strain rate E and temperature T affect the flow stress only through a single parameter p of the form: p = EeQ/RT [I] In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. Combinations of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944

By J. W. Snavely

THE high tension belt conveyor is introducing a new and tremendously expanded era of low cost bulk material handling. High tension belt conveyors are generally those installations involving very long centers, high lifts, or drops, in which the belts are stressed up to their maximum tension values, and further, where the belt construction provides tension capacity far beyond what is possible with conventional belt constructions. With these high tension installations, the magnitude of the forces involved demands careful refinement of accepted design practice in order to achieve optimum balance of all factors. No attempt will be made to evaluate the relative merits of belt conveyor haulage with other means of transportation. For present purposes, it is assumed this has already been done in favor of belt conveyor. Neither will any attempt be made to evaluate the various conveyor belt constructions now available or to balance the advantages of various types of mechanical equipment. It is also assumed that the basic haulage information on which the conveyor design is based is accurate and complete. A sustained maximum, uniform load on the belt at all times must be achieved through proper feed control and the use of adequate surge storage to level the peaks and valleys of any varying demand for the material being handled. General Belt Capacity Considerations The belt conveyor capacity tables published by various belting and conveyor equipment manufacturers vary to a considerable degree, and the ratings given are quite conservative. Of necessity, these published ratings are based on the handling of average materials under average conditions. In applying a high tension belt, all possible capacity from the belt must be obtained in order to hold its width to a minimum and thereby limit the initial cost. Two factors are involved, loading to maximum cross section area and traveling at a maximum practical speed. Belt Loading: Proper treatment of the loading of the belt will result in maximum cross section to the load, and published capacity ratings can be exceeded, sometimes by appreciable margins. On the 10-mile conveyor haul used in the construction of Shasta Dam, California, although the rated capacity of the belt line was 1100 tons per hr, at times the system handled peak loads of 1400 tons per hr, almost 25 pct better than the rated capacity. One of the large coal companies has been able to exceed rated capacity by as much as 50 pct. Loading conditions which must be controlled are: 1. Large lumps must be scalped off and rejected or the load must be primary crushed before being placed on the belt. 2. The material weight per cubic foot must be accurate, must be known for all the materials being handled, and must be known for the complete range of conditions of the individual material being handled. Long centers and high lifts magnify small differences into serious proportions. 3. Uniform feeding to the belt is most important. Various types of feeders are available, which can be used to place a constant predetermined volume of material on the belt, or, where an appreciable range of material weight exists, through electrical control actuated by current demand, to place a predetermined uniform tonnage on the belt. One long slope belt in a coal mine in Pennsylvania is being fed at three separate stations with the controls so arranged that whenever the maximum load is going onto the belt from the first station, the other two stations automatically cut out. Whenever the load from the first station drops back, the other two stations again automatically cut in. 4. Careful design of the chutes and skirts is necessary to get the load centered on the belt with a minimum of free margin along each edge. Some free margin at the edge of the belt is necessary to prevent spillage, but if the load can be kept accurately centered, this free margin area can be reduced, and more material can be carried on the belt. What can be accomplished in this respect will vary widely, depending on the nature of the material being hauled. The chute and skirt design must also protect the belt. 5. The design of chutes and skirts should also get the load traveling in the same direction and close to belt speed, so that the load comes to rest on the belt as quickly as possible. The design of the chutes and skirts is worthy of careful study, and after a system is put into operation it should be experimented with to get the best results. Belt Speed: High belt speeds should be used in high tension work. Obviously, high belt speeds enable haulage on a narrower belt, reducing initial cost. The major portion of belt wear takes place at the loading point and around the terminal pulleys. The

Jan 1, 1952

By E. C. van Reuth

FIFTY-three alloys have been examined in the Fe-W and Co-W alloy systems in an attempt to verify the finding of o phases in these systems as reported by Goldschmidt.' The alloys were examined metallographically and by X-ray diffraction. The 10-g specimens were made by powder metallurgy techniques. Very fine, high-purity powders were compressed in a double-acting die at 120,000 psi after hydrogen reduction. All compacts were then sintered for 200 hr at 950°C in a helium atmosphere. Metallographic investigation and X-ray diffraction proved this time to be sufficient to allow complete homogenization before the subsequent high-temperature anneal. Each specimen was then sealed into an evacuated silica capsule and annealed at 1400"or 1500 C (except two) for 25 hr. (The 60 pct Fe and 55 pct Co alloys taken to 1610"and 1680°C respectively were held at these temperatures for 1hr. However, since these structures were at equilibrium before the anneal, and in view of their resultant structures, it is assumed that they reached equilib-

Jan 1, 1960

By A. Manganwidjoyo, W. A. Wiebenga

The aim of this paper is to disclose some of the correlations between rock parameters, hidden in Wuerker's "Annotated Tables of Strength and Elastic Properties of Rocks," 1956. The empirical relations concern dry rocks of varying porosity. Curves and equations interrelating the specific gravity, compressive strength, bar velocity, and Poisson's ratio are presented. In 1956 Wuerker published his "Annotated Tables of Strength and Elastic Properties of Rock", in which various physical properties of rocks determined by different authorities, are tabulated systematically. The tables are primarily intended for use by mining-, quarrying- and ore-dressing engineers. Since the list of measured parameters for each type of rock includes properties such as — grain size, specific gravity, porosity, compressive strength, static elastic cons:ants (moduli of elasticity, rigidity, specific damping capacity and longitudinal bar velocity) the tables are also of considerable interest to the practical geophysicist. Correlations between rock parameters may enable geophysicists, geologists and civil engineers to transiate measurements from one parameter to another. Even if these translations are of limited accuracy, or valid only within certain specified ranges, they often serve a useful parpose. The aim of this paper is to disclose some of the correlations between rock parameters concealed in wuerker's Tables. Throughout this paper the following symbols and units are used unless otherwise stated: Sg is Specific gravity, the ratio of the density of a specimen to the density of water at 4°C. P is Porosity, in %, the ratio of the volume of voids in a specimen to its total volume. CS is Compressive strength in 1000 p.s.i., the stress under which a specimen will fracture when undergoing a standard compression test. V is Bar Velocity in kilo-feet/sec, the velocity of longitudinal seismic waves measured in a slender bar type specimen. Vc is Bulk or Constraint Velocity in kilo-feet/ sec, the velocity of longitudinal seismic waves measured in a very large specimen.+is Reciprocai bar velocity in millisecs/ft (1 millisec = 10-3 sec). cis Poisson's ratio, the ratio of the lateral to longitudinal strain of a body under longitudinal stress. CORRELATIONS Specific Gravity (Sg) vs. Porosity (P) Figure 1 is a diagram illustrating the relatiooship between specific gravity and porosity for approuirr~ately 70 samples of dry rocks. A curve fitted by estimation to this data yields the empirical formula: Sg =-0.0268P + 2.67 * 0.2 (1) Considering unit volume of a porogs specimen then

Jan 1, 1961

By J. J. Gilman

WHEN a zinc crystal is immersed in liquid N, and then plastically bent, it is observed that it bends a certain amount and then fractures. This fracture occurs at a fairly reproducible radius of curvature, and the radius varies systematically with the crystal orientation. Because this phenomenon provides an unusually well-defined set of fracture conditions, it is possible to examine various possible fracture criteria and select the best one. Zinc crystals of various orientations were bent about axes lying in their glide planes (0001) and perpendicular to their glide directions [1210]. The crystals were 0.150 in. diam and had chemically polished surfaces. They were immersed in liquid N, while they were being loaded on an Instron testing machine. A three-point bending jig was used to load them. Table I lists the beam radius at which fracture occurred for each orientation. Each value is the average of at least six measurements. The normal stresses on the cleavage planes, at the time of fracture, were calculated as follows: First, from the fracture radius, R,, the orientation angle, x,, of the (0001) plane at the outer fiber was calculated. If x, = angle between the (0001) and the rod axis prior to bending, d = rod diameter, and X, = angle between the (0001) plane and a tangent to the bent crystal, then1 sinX, _ 2R, sin xn 2R, + d Since the glide shear strain is given by' y ' cot X, — Xo the glide strain at fracture, x,, can be calculated. Next, it is necessary to know the tangential stress in the outer fiber at fracture. This depends on the plastic flow curve, so a series of tensile tests were performed at —196°C on another set of zinc crystals. A curve of the average resolved shear stress versus glide strain was prepared. From this curve, shear stresses, r,, corresponding to the glide strains in the bend tests were taken. These values are listed in Table I. Then the normal stresses in the outer fibres, u,, were calculated from the relation U, = r, tan X, This analysis assumes that the fiber stresses in a bent beam are the same as the stresses in simple

Jan 1, 1959

By E. S. Machlin

The possibility that formation of voids under creep-rupture conditions may take place by the condensation of vacancies has been investigated theoretically. It has been concluded that nucleation of voids under creep-rupture conditions by vacancy condensation is highly improbable. However, growth of pre-existant voids by vacancy condensation is probable. A number of predictions made in this theory have been verified by the data. It has been predicted and checked that the product of rupture life and steady-state creep rate for preannealed metals and single phase alloys is an approximately invariant quantity, independent of stress, temperature, and atomic number for a given type structure. The direction of the effect of cold work on this product has been predicted and found in agreement with experiment. A number of experiments to evaluate the vacancy condensation mechanism further are described. SEVERAL papers have appeared recently which speculate on the origin of voids formed at grain boundaries under stress.' ' The object of this paper is to examine quantitatively the proposition that the voids produced in a creep test are a result of vacancy condensation. A result of this paper is a theory of creep-rupture. Void Nucleation Application of standard nucleation theory" to the problem of void nucleation leads to the following conclusions: 1—Homogeneous nucleation of voids requires a supersaturation ratio (concentration of vacancies in supersaturated to that in saturated solution) of 400 for a reasonable surface energy of 1000 erg per cm-and 1.4 for the improbably low surface energy of 10 erg per cm. 2—Heterogeneous nucleation of voids at plane interfaces between two phases requires a supersaturation ratio of 2.5 for a typical contact angle of 145 3-—Void nucleation about a solid particle may be accomplished at a supersaturation ratio of 1.17 for a typical value of work of adhesion? of 60 erg per The work of adhesion is the surface work 10 replace two solid-vauor surfaces by a solid-solid interface. enr ' between an oxide and a metal in the presence of a surface active element such as sulphur. Estimates of the supersaturation ratio at which voids are produced in diffusion experiments yield a maximum of 1.01. Inasmuch as the foregoing mechanisms of void nucleation probably will not operate at this level—too low a surface energy is required—the investigatol. is led to the conclusion that voids must already exist. That is, nucleation of voids probably does not occur. Rather, existing submicroscopic voids grow out to visible size. Already existing voids might be produced during solidification or working. Supercritical sized parlicles which contain cracks may act as heterogeneous void nuclei. Gas pockets may act as void nuclei. Experiments are desired to determine the nature of the heterogeneous void nuclei which grow out to voids in both diffusion and creep experiments. Void Growth Void growth might occur in at least two possible ways, depending upon whether the already existing void nuclei are at grain boundaries or within the grains. In the case of a spherical void far from a crystal boundary, vacancies are generated during creep as a consequence of the migration of suitable dislocation jogs' and are also annihilated at sinks. Under these conditions, a steady-state concentration of vacancies is built up in the crystal, defined by the condition that for any differential volume the rate of generation of vacancies in that volume equals the rate of annihilation of those vacancies." This equality would lead to the development of a gradient of vacancy concentration radially outward from the void surface up to a radius where the vacancy lifetime becomes equal for all directions of vacancy migration. The distance over which this vacancy concentration gradient extends equals about 2vD,T* where D, is the vacancy diffusivity and T:' the vacancy lifetime in a crystal outside the gradient in a zone of constant vacancy concentration. The vacancies generated in the region over which the gradient exists will annihilate more often at the void than elsewhere. Approximately a little over one-half the vacancies generated in the gradient zone will annihilate at the void. Hence, the growth rate of the void is given by on where R is the radius of void in centimeters, is the atomic volume, and R is the rate of generation of vacancies, number per centimeter" per second. R D and T* may be estimated in terms of other physical parameters." In particular, R = n.j e/b [3] where n is the average number of vacancy produc-

Jan 1, 1957

JAMES.E. HOWARD, ? Washington, D. C. (written. discussion ?).-It is a pleasure to participate in the discussion of a paper on the endurance of steel to repeated alternate stresses. For many purposes the prime and only function of the metal is to resist strains and stresses: stresses of long duration in one direction only; stresses that alternate between a maximum and a. minimum in' one direction; and stresses of different de-

Jan 4, 1919

By R. W. Gould, B. G. LeFevre, A. G. Guy

The resistivity anomaly known as the K state was studied in Ni-Mo alloys containing 10.5 and 14.0 at. pct Mo. Both these alloys exhibit a large K effect which depends on the mechanical and thermal treatment. On the basis of X-ray diffuse scattering studies which were correlated with resistivity measurements, it appears that the K state in dilute Ni-Mo alloys can be associated with changes in the degree of short-range order within the a phase. An interesting phenomenon that has received much attention in recent years is the K state. The K state is marked by anomalous changes in some of the physical properties of certain alloys without the occurrence of observable microscopic structural changes. One of the early pieces of work in this area was by Thomas' who studied alloys of Ni-Cr, Ni-Cu, Ni-Cu-Zn, Fe-A1, Fe-Si, and Ni-A1. Upon annealing specimens which had been previously cold-worked or quenched from an elevated temperature he found an anomalous increase in resistivity over a certain temperature range. He also found that specimens which had been appropriately annealed to develop the K state showed a decrease in resistivity upon subsequent cold working. These effects are opposite to those found in normal alloys. Although the resistivity anomaly has been rather arbitrarily taken as the "definition" of the K state, there are several other interesting effects which accompany the resistivity increase. In Ni-Cr alloys,2, 3 for example, it was found that the hardness increases with increasing resistivity. It was also found that specimens which have been treated to develop the K state can be cold-worked for as much as an 80 pct reduction of area without an increase in the hardness. In Fe-A1 and Fe-Si alloys4 the K state is accompanied by an increase in flow stress and by a lattice contraction. In Ni-A1 alloys,5 specimens which have been treated to develop the K state also show an increase in elastic modulus. In Ag-Pd alloys6 the increased resistivity observed on annealing a cold-worked specimen is accompanied by an increase in the thermoelectric power and an increase in the Hall coefficient. The explanations of the K state phenomena are varied and depend upon the particular alloy in question. Several theories have been advanced to explain the increased conductivity with cold work on the basis of changes in the electronic configuration of the alloy as a result of local lattice distortions.7"9 Most investigators, however, believe that some type of local order in the solid solution, either short-range order (SRO) or clustering, is responsible for this effect. Theories concerning the relationship between ordering and the K state have for the most part been speculative, since there is little direct X-ray evidence that can be correlated with the above property changes. Much of the previous work on the K state was done in the Ni-Cr system where the small difference in the X-ray atomic scattering factors of the components nickel and chromium makes it very difficult to use X-ray diffuse-scattering measurements to determine the role of local order. In the Ni-A1 system, however, Starke et al.10 succeeded in detecting a connection between local order and the K state. It was found that a small but measurable K effect correlated with increasing SRO in the nickel-rich a phase. The manner in which local order might increase the resistivity of K state alloys is not completely clear. Since most of the known K state alloys contain at least one transition element, significance has frequently been attached to the presence of an unfilled d shell. It has been suggested that during the formation of the K state the number of conduction electrons decreases as a result of the transfer of s electrons to the d shell where they are more tightly bound.1'11'12 Koster and Rocholl13 have proposed that SRO can cause an increase in resistivity for alloy systems in which the number and mobility of charge carriers are reduced when the percent solute is increased. According to this hypothesis, the local environment of a given solvent atom changes in the same manner with increasing percent solute as it does with an increasing degree of SRO; hence the change in physical properties should tend in the same direction. In this hypothesis, SRO is considered only in a statistical sense, and the increased resistivity of the K state is attributed to a change in the mean distribution of electrons and holes in the s and d states as a result of SRO. From the work of Chen and Nicholson on Ag-Pd alloys,6 it appears that the K state can occur in systems for which the d shell is completely filled. These investigators explained the increased resistivity by picturing the SRO as small domains of some form of long-range order (LRO). According to ~ibson,'~ the number of effective electrons can be reduced by the creation of a new Brillouin zone boundary near the Fermi surface of an alloy as a result of the changing crystallographic symmetry that accompanies the formation of a superlattice. This idea may be expressed in terms of the superzone concept.15 In the present work the role of local order in the formation of the K state in Ni-Mo alloys was investigated. The principal tools used in this study were X-ray diffuse scattering and electrical resistivity measurements; however, these data were supplemented by electron microscopic and field-ion microscopic data. The purpose of the work was to determine whether or not the K state in Ni-Mo alloys can indeed be attributed to the formation of SRO as has been proposed by previous investigators.

Jan 1, 1969