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By M. J. Hordon, M. A. Wright

The well-defined increase in fatigue life observed o many metals cyclicly strained at vacuum levels below 10-1 to 10-3 torr has been attributed to the critical retardation of oxygen or water vapor chemisorption at the crack tip during crack propagation.1-3 In the absence of strongly adsorbed surface films, crack re-welding during cyclic compression or dislocation escape from the plastic zone around the crack tip has been proposed to account for the observed decrease in the rate of crack growth. The increase in the critical pressure required for the transition in crack growth rate with temperature experimentally determined for aluminum was found to be generally in accord with the adsorption rate model.4 However, although the adsorption mechanism would also predict an increase in transition pressure and fatigue life with increase in cyclic loading rate, and such effects were noted by Snowden5 for lead and Hordon3 for aluminum, the opposite results were reported by Kramer et al.B in studies on aluminum. The present note describes some recent measurements of the fatigue properties of 1100-H14 aluminum at low pressures to determine the specific effect of cyclic strain frequency in the transition pressure range. Flat cantilever-type specimens of 1100-H14 aluminum shaped to produce a uniform strain gradient along the gage length were tested in reverse plane bending at constant deflection amplitudes in two independent multi-specimen vacuum fatigue systems. One series of tests using 2-in. gage length specimens was conducted in an ion pumped apparatus with 107 torr and 50 cps capacity, denoted as Unit I, utilizing fixed mechanical cams to impose the strain amplitude. An independent test series using shorter 1-in. gage length specimens was conducted in a cryopumped apparatus designed for extremely low pressures below 10-10 torr, denoted as Unit II, using an electromechanical vibrator at non-resonant frequencies up to 150 cps to provide the deflection. Both vacuum fatigue units and associated test procedures have been described previously.3'7

Jan 1, 1969

By A. M. Gaudin

The study that is presented here was undertaken in order to condense information concerning comminution, and covering a great variety of conditions, into one or several rules which would be of use in the development of a systematic theory as well as in many directly practical ways. As the result of this work, the following conclusions appear justified: 1. Rocks may be classified, from the point of view of comminution, into two general classes which are (a) structurally homogeneous, and (b) structurally heterogenous. Structurally homogeneous rocks are those in which fracture takes place through grains and grain boundaries alike; heterogeneous rocks are those in which fracture passes in preference through grain boundaries. 2. If a sized product composed of structurally homogeneous rock grains is crushed, a product results in which the relation between the percentage weight of grains of various sizes and these sizes themselves follows a definite law. This is not true of structurally heterogeneous rocks. 3. Ball milling with structurally homogeneous rocks, and under certain conditions, presents exceptions to this rule. 4. In ball milling with structurally homogeneous rocks, there exists a critical ratio of size of feed to size of balls, above which the machine operates essentially by surface wear, and below which it operates essentially by breaking across the body of the particle. 5. In ball milling, with structurally homogeneous rocks, and when the size of feed grains exceeds the critical size, the particles worn off are of a substantially definite size which depends upon the ball size. 6. In the case of a typical heterogeneous rock, such as Manhattan schist, particles are crushed in such a way that there is a greater proportion of grains of the size that is the average grain-size of the rock than there would be in that range of size with a structurally homogeneous rock. This has been found to be true with all the crushers tested. 7. Different methods of crushing produce grains of different shapes. 8. The importance of sizing the — 200-mesh portion of a crushed product, in crushing-efficiency investigations, has been greatly under-

Jan 1, 1926

By C. Hays, R. E. Swift, E. G. Kendall

Investigations of the Zr-Pt system, by metallography, incipient melting, and X-ray diffraction, determined the phase relationshifis from 0 to 50 at. pct Pt. Phase fields in the Pt-~ich region were outlined, and three intermetallics (ZrPt, Zr2Pt, and ZrPtd were located. A eutectic between Zr and Zr2Pt, and a eutectoid veaction between Zr and a Zr + Zr2Pt, were established. The maximum solubility of Pt in P Zr was approximately 13.5 wt pct, as opposed to less than 1 wt pct solubility in a Zr. EARLIER work on the Zr-Pt system was limited to an X-ray study on the intermetallic compound, ZrPt3, by H. J. Wallbaum,1 It was reported that ZrPt3 existed at 86.52 wt pct Pt, and had a hexagonal structure, isomorphous with TiNi3. Wallbaum's data revealed the following structural particulars: a = 5.633A, c = 9.21A, and c/a = 1.635A. Other studies allied to Zr-Pt alloys concerned only 1) Pt-rich alloys (0.05 to 5.0 pct Zr) for corrosion resistance,2 2) a Zr-base alloy with 5 pct Pt and 0.124 pct C for oxidation resistance,3 and 3) electroclad-ding of Zr with Pt for in-pile corrosion resistance of Zr to uranyl sulphate. 4 Metallographic, incipient melting, and X-ray diffraction techniques were applied to accurately resolve the phase relationships in the 0 to 50 at. pct (68.2 wt pct) Pt region, and to outline the phase fields in the Pt-rich area. Three intermediate phases: Zr2Pt, ZrPt, and ZrPt3, were also established by the same methods. PROCEDURE Melting stock for this program was of the highest purity obtainable. The Zr was iodide crystal bar with a low hafnium content of about 0.05 wt pct (Westinghouse "Grade 3"). The as-received Zr was treated to remove the surface film of corrosion product that resulted from a standard autoclave grade designation test. Next, the bars were processed to yield material suitable for arc melting and free of contaminants. Sheet platinum metal (Baker and Co. "Grade 2") was used for alloying additions. This material con-

Jan 1, 1962

By P. LaRochelle, K. Y. Lo, A. L. Tamuly Phukan

In many civil or mining engineering works, the stresses and deformations of natural or excavated slopes due to the combined effect of self-weight and initial stresses are of interest. Because of the mathematical complexities of this problem, however, no complete exact solution exists for the simplest case, that of assuming the stress-strain relation of the rock to be perfectly elastic. Efforts have therefore been directed toward numerical and experimental technique. The stresses within an elastic slope have been obtained by LaRochelle,1 using the photoelastic and finite difference method to determine the difference and sum of principal stresses. Subsequently, Finn,2 Hoyaux and Ladanyi,3 and Duncan and Dunlop4 attempted to solve the same problem by using the finite element method. The problem was also investigated by Brown and Goodman5 and Brown and King6 who emphasize the importance of the effect of loading or unloading procedure on the stress distribution within the slope. Although the geometry of the slope and the boundary conditions involved are identical or similar, the results obtained by these various authors by no means agree. It is therefore necessary to review briefly the results of elastic analysis in order to lend credence to the methods used in the solution. Although the stress-strain behavior of some rocks may be reasonably approximated by the elastic modrl, other rocks generally exhibit an elasto-plastic behavior with strain hardening or strain softening as shown in Fig. 1. Experiments show that for most rocks, the stress-strain relationship is approximately linear from the origin to the point P (neglecting the small concave region under low stresses). At P, the curve deviates

Jan 1, 1970

By J. O. Brittain, E. P. Lautenschlager, F. Felberbauer

This investigation was undertaken to evaluate the effect of a dispersed phase in a iron upon the strain hardening and the stress dependency of dislocation velocity as inferred from the strain-rate sensitivitv. Experiments were made in a-iron specimens with controlled amounts of carbon and/or A12O3. They were tested at various temperatures between 195' and 373 'K under a variety of conditions oj-concentration, strain rate, and quench aging. The resulting yield strength, flow strength, and strain hardening increased with addition of Al2O3. The parameter m, measured from changes in strain rate, was xsed to describe the stress dependency of the dislocation velocity. m was found to increase with additions of A12O3, increasing carbon in solution, and with increasing temperature. When applied to a recent model for yielding based upon dislocation multiplication and velocity characteristics, the values of m alone did not successfully predict yielding for the materials of this investigalion, but had to be adjusted with a consideration of the number of unlocked dislocations nucleated heterogeneously at discontinuities or inclusions. The change of yield strength with Al2O3 Interpar-ticle spacing appeared to obey a theory of Orowan. EVER since the concept of dislocations has been introduced to explain plastic deformation in crystalline materials, the origin of dislocations and the source of the number of dislocations required to account for plastic deformation have been persistent questions. Ruling out the possibility of homogeneous nucleation,' Gilman2 drew attention to the various cases of heterogeneous nucleation as the source of dislocations, whereas Frank and Read3 introduced the Frank-Read source. However, Gil-man found that the Frank-Read sources did not play a dominant role in the deformation of LiF crystals, but that small precipitates are often, if not always, associated with the nucleation of dislocations. In LiF crystals, however, most of the dislocations arose through the multiplication of moving dislocations in a mechanism described by Koehler4 and Orowan,5 Thus, relatively few precipitates could account for a large number of dislocations. A similar observation of dislocation nucleation at inclusions of precipitates was made by Stein and LOW' on Si-Fe crystals. Their crystals contained

Jan 1, 1964

By R. Kossowsky

USING etch-pit techniques, Johnston and Gilman' have shown that the stress dependence of dislocation velocity can be represented by the expression where r, is the dislocation velocity, a is the applied stress, and oa, is the stress to produce a unit velocity. Noble and Hul12 showed that the exponent m is strain-dependent and increases rapidly in the work-hardening region. This was explained by arguing that in the work-hardened material the applied stress required for any given velocity will be greater than in the annealed material by an amount equal to a back stress due to work hardening. schadler3 has stressed the importance of substructure as a possible source of error in dislocation velocity measurements, and took care to make velocity measurements in which dislocations moved such short distances that interactions with boundaries were avoided. schadler3 also pointed out that, if standard testing equipment is used, measurements of m from flow stress data could be seriously in error in materials with a high initial work-hardening rate. Noble and Hu112 have further argued that, due to the strain dependence of m , the extrapolation to zero strain4 to obtain the true value of m can be justified only in the preyield region. Microstrain experiments in high-purity iron5,6 have led to the conclusion that aiA (Ref. 5) (defined as the stress to first produce a permanent set of 10-6 in. per in.) and oflow are not controlled by the same deformation mechanism. It has been proposed5,6 that aA is governed by the lattice resistance to the motion of screw dislocations in a given slip plane and that oflow is controlled by the lattice resistance to a full-scale cross slip. The purpose of this note is to extend Noble and Hull's argument further and to show that measurements of m from flow stress data can be in error due to the rapid increase in stress in the microstrain region6 when stress is increased beyond aA. Double z-one-refined single crystals of molybdenum (with the (101)[ 111] slip system operating and a Schmidt factor of 0.475) were used in an experimen-

Jan 1, 1968

By C. W. MacGregor

In the testing of materials there exist various methods of recording graphically the behavior of a material subjected to tensile stress. Probably the most common method is to plot the tensile stress So, obtained by dividing the load P by the original area of cross section A0 at the start of the test, as a function of the strain e0, which is obtained by dividing the ?Lo or the change in the gauge length by the original gauge length Lo. A list of the symbols used here is given in Table 1. This method, while it has proved useful in the routine testing and comparison of various materials, does not have a very sound physical basis, as was first pointed out by P. Ludwikl, and consequently does not afford a very deep insight into the true physical behavior of the material under stress. Among the objections to this method may be mentioned: (1) that by dividing the load P at any stage of the test by the original area A. a fictitious stress is obtained, which does not actually exist; (2) that the strain e0 = ?L0 is not an exact expression for the true strain for large values of ?LO in per cent of Lo; (3) that when necking starts the strain varies considerably along the gauge length and the above expression no longer gives the true strain existing at any point on the outside of the bar; and (4) that the axial strain varies over the cross section of the necked portion and e0 does not represent an average of these strains over the cross section. Stresses taken from such a diagram would be only approximate and, if used to compare results of a test on a given material under simple tension with results obtained under combined stresses, certain errors would be thus introduced. In order to overcome some of these objections, various methods have been suggested, both as to the quantities to be measured and as to their graphical representation. In some cases the so-called "true stress," obtained by dividing the load P by the actual area of cross section A existing when the load P was applied, is plotted as a function of the strain

Jan 1, 1937

By H. Rush Spedden, A. M. Gaudin

ALTHOUGH the number of minerals that are ferromagnetic) or highly paramagnetic is strictly limited, it has been known for some time that many minerals have slight but supposedly characteristic magnetic susceptibilities. With the exception of pyrrhotite, however, sulphides have been thought nonmagnetic. A new magnetic separator has been made available recently in limited quantity to research laboratories. This device, the Frantz Isodynamic Separator, has been used for the separation of various nonsulphides from each other. Its application to the separation of sulphides, however, does not seem to have been reported. In the Richards Mineral Dressing laboratories, the success achieved through the use of this device in separating associated sulphides has been so startling as to lead us to believe that it constitutes a magnificent adjunct to heavy-liquid separation and to quantitative mineragraphy as a tool for the mineral investigator. THE SEPARATOR The separator (Fig. I) consists of: I. A powerful magnet, the strength of which can be adjusted by means of a rheostat; 2. A vibrating chute of nonmagnetic metal on which the mineral to be separated is made to flow (Fig. 2); 3. A feed bin and adjustable feeder; 4. Receptacles for the collection of products; 5. Means for changing, setting, and accurately reading the two slopes of the chute; viz., the cross slope and longitudinal slope. The separator is made operative by the special shape of its pole pieces, which ensures a strongly converging field. It is said by the makers of the machine that the pole pieces apply a constant mechanical force to a particle of given susceptibility, regardless of its position in the operating space of the separators.* Susceptible particles, therefore, behave as though of lower specific gravity than under ordinary circumstances. This effect, combined with the slopes of the chute and the action of the vibrator, causes a stratification not unlike that obtainable on a shaking table. The chute is of rectangular cross section, and shallow; it is broadened toward the discharge end and divided longitudinally by a partition into two compartments that lead to the collecting receptacles. Although the separator probably can be used to make separations at fairly coarse

Jan 1, 1943

By H. Rush Spedden, A. M. Gaudin

Although the number of minerals that are ferromagnetic‡ or highly paramagnetic is strictly limited, it has been known for some time that many minerals have slight but supposedly characteristic magnetic susceptibilities. With the exception of pyrrhotite, however, sulphides have been thought nonmagnetic. A new magnetic separator has been made available recently in limited quantity to research laboratories. This device, the Frantz Isodynamic Separator, has been used for the separation of various non-sulphides from each other. Its application to the separation of sulphides, however, does not seem to have been reported. In the Richards Mineral Dressing Laboratories, the success achieved through the use of this device in separating associated sulphides has been so startling as to lead us to believe that it constitutes a magnificent adjunct to heavy-liquid separation and to quantitative mineragraphy as a tool for the mineral investigator. The separator (Fig. I) consists of: 1. A powerful magnet, the strength of which can be adjusted by, means of a rheostat; 2. A vibrating chute of nonmagnetic metal on which the mineral to be separated is made to flow (Fig. 2); 3. A feed bin and adjustable feeder; 4. Receptacles for the collection of products; 5. Means for changing, setting, and accurately reading the two slopes of the chute; viz., the cross slope and longitudinal slope. The separator is made operative by the special shape of its pole pieces, which ensures a strongly converging field. It is said by the makers of the machine that the pole pieces apply a constant mechanical force to a particle of given susceptibility, regardless of its position in the operating space of the separators." Susceptible particles, therefore, behave as though of lower specific gravity than under ordinary circumstances. This effect, combined with the slopes of the chute and the action of the vibrator, causes a stratification not unlike thai obtainable on a shaking table. The chute is of rectangular cross section, and shallow; it is broadened toward the discharge end and divided longitudinally by a partition into two compartments that lead to the collecting receptacles. Although the separator probably can be used to make separations at fairly coarse

Jan 1, 1943

By H. Rush Spedden, A. M. Gaudin

Although the number of minerals that are ferromagnetic‡ or highly paramagnetic is strictly limited, it has been known for some time that many minerals have slight but supposedly characteristic magnetic susceptibilities. With the exception of pyrrhotite, however, sulphides have been thought nonmagnetic. A new magnetic separator has been made available recently in limited quantity to research laboratories. This device, the Frantz Isodynamic Separator, has been used for the separation of various non-sulphides from each other. Its application to the separation of sulphides, however, does not seem to have been reported. In the Richards Mineral Dressing Laboratories, the success achieved through the use of this device in separating associated sulphides has been so startling as to lead us to believe that it constitutes a magnificent adjunct to heavy-liquid separation and to quantitative mineragraphy as a tool for the mineral investigator. The separator (Fig. I) consists of: 1. A powerful magnet, the strength of which can be adjusted by, means of a rheostat; 2. A vibrating chute of nonmagnetic metal on which the mineral to be separated is made to flow (Fig. 2); 3. A feed bin and adjustable feeder; 4. Receptacles for the collection of products; 5. Means for changing, setting, and accurately reading the two slopes of the chute; viz., the cross slope and longitudinal slope. The separator is made operative by the special shape of its pole pieces, which ensures a strongly converging field. It is said by the makers of the machine that the pole pieces apply a constant mechanical force to a particle of given susceptibility, regardless of its position in the operating space of the separators." Susceptible particles, therefore, behave as though of lower specific gravity than under ordinary circumstances. This effect, combined with the slopes of the chute and the action of the vibrator, causes a stratification not unlike thai obtainable on a shaking table. The chute is of rectangular cross section, and shallow; it is broadened toward the discharge end and divided longitudinally by a partition into two compartments that lead to the collecting receptacles. Although the separator probably can be used to make separations at fairly coarse

Jan 1, 1943

By Howard Pyle

CORE analysis is a recent development in the field of petroleum technology. The earliest work on this subject was done in connection with evaluating and planning secondary oil recovery by water-flooding. Present-day analysis of sands of flush fields requires new and independent interpretations of the data provided by cored material. Particular attention is being paid to the development of rapid, routine methods for measuring physical characteristics of sandstone, such as permeability, porosity and grain size, as well as the sand's fluid content. Permeability may be defined as the fluid-passing capacity of a rock. For a sandstone to be permeable it must be possible to pass a measurable quantity of fluid through the material in a finite period of time. The common unit of permeability is the darcy, which may be defined as the rate of viscous flow, in milliliters per second, of a fluid of one centipoise viscosity through a porous medium having a cross section of one square centimeter, under a pressure gradient of one atmosphere (76.0 cm. Hg) per centimeter.1 For convenience the subunit millidarcy, or one-thou-sandth darcy, is often used. Porosity is defined as the fluid-containing capacity of a rock and is usually expressed as a percentage ratio of the total pore volume to the rock or bulk volume. Since measurement of only the effective or communicating pore volume is often made, porosities are distinguished as total or effective.2,3 Net effective porosity is defined as the net pore volume available for oil and gas. Oil and water content of sand is measured and expressed either as the percentage saturation of the total pores or of the bulk rock. The oil content may also be expressed as the percentage saturation of the net effective pores. In connection with water-flooding, methods of core analysis were developed to furnish data that could be used in determining the quantity of recoverable oil,4-6 and the probable rates at which various sands or divisions of a sand open to the wells would take water or produce oil. In flush fields, the analytical data are used to predict the productivity of a cored interval. They indicate the presence of oil, gas and water and may

Jan 1, 1939

By Martin A. Mayers

It has long been recognized that it would be highly desirable to be able to predict the temperatures at various points in a burning fuel bed and their variations with changes of the properties of the fuel and the rate of air supply. Experimenta1 investigations of fuel-bed temperature1-4 have not been lacking, but the absence of any theoretical background has made it impossible to use the results of these tests as a basis for prediction, except in a very general may. A mathematical analysis", based on a somewhat simplified theory of the distribution of lieat in a fuel bed, lias recently been completed by the author. Even though numerical values of some of the coefficients are not known, the calculations result in some conclusions of general significance. Thus, for example, it appears that when the temperatures throughout the fuel bed can be calculated, the rate at which ignition of the fuel by underfeed action can be maintained can also be calcu1ated. The uncertainty concerning the values of the coefficients referred to above is serious limitation on the use of that method. The following paper presents a discussion of these coefficients and includes estimates of their values based on the data now available. A brief description of the theory on which the analysis is based, and some results of the calculations showing their degree of agreement with experimental results, are presented by way of introduction to the discussion of the coefficients. For a more. extended discussion of the theory, see the A.S.M.E. paper5. Theory and Comparison with Experiment The theoretical analysis is similar to that used in the calculation of the stationary temperatures in a conducting solid in the classical theory of heat concluction. The fuel bed is pictured as a uniform, continuous, porous solid through the interstices of which air can be blown and ill which combustion can take place. The solid lias a finite thermal conductivity, so that heat may be transported in any direction, against the flow of air as well as in the same direction. While it is true that nothing

Jan 1, 1938

By Martin A. Mayers

It has long been recognized that it would be highly desirable to be able to predict the temperatures at various points in a burning fuel bed and their variations with changes of the properties of the fuel and the rate of air supply. Experimenta1 investigations of fuel-bed temperature1-4 have not been lacking, but the absence of any theoretical background has made it impossible to use the results of these tests as a basis for prediction, except in a very general may. A mathematical analysis", based on a somewhat simplified theory of the distribution of lieat in a fuel bed, lias recently been completed by the author. Even though numerical values of some of the coefficients are not known, the calculations result in some conclusions of general significance. Thus, for example, it appears that when the temperatures throughout the fuel bed can be calculated, the rate at which ignition of the fuel by underfeed action can be maintained can also be calcu1ated. The uncertainty concerning the values of the coefficients referred to above is serious limitation on the use of that method. The following paper presents a discussion of these coefficients and includes estimates of their values based on the data now available. A brief description of the theory on which the analysis is based, and some results of the calculations showing their degree of agreement with experimental results, are presented by way of introduction to the discussion of the coefficients. For a more. extended discussion of the theory, see the A.S.M.E. paper5. Theory and Comparison with Experiment The theoretical analysis is similar to that used in the calculation of the stationary temperatures in a conducting solid in the classical theory of heat concluction. The fuel bed is pictured as a uniform, continuous, porous solid through the interstices of which air can be blown and ill which combustion can take place. The solid lias a finite thermal conductivity, so that heat may be transported in any direction, against the flow of air as well as in the same direction. While it is true that nothing

Jan 1, 1938

By Robert Warner

The growing importance of screening makes an accurate measure of the quality of a sizing operation desirable. Screen efficiency is considered equal to the percentage of true undersize in the feed obtained as undersize from the screen. This method is unreliable, as it gives the same credit for removing minus 200-mesh material as for removing material just able to pass the aperature of the screen. A more accurate measure of screen efficiency is to consider only the work done on the "difficult" grains, that is, those grains of which the intermediate diameters closely approach the screen aperture.. The application of this method is given, together with the derivation of formulas and an example of their use. Is AN accurate measurement of the efficiency of a screen under a given set of operating conditions valuable? If so, what is the efficiency; of, a screen and how can it be measured? Sizing, especially of the finer sizes of material, has increased in importance in the development of flow sheets as a result of the perfecting of the rapid vibrating screens. More consideration should be given screens in the preparation of ball-mill feed, where they permit the admission of a dryer feed than, the classifier. Where possible, the introduction of a screen ahead of the primary ball-mill, and the diverting of ore below, say, 4 mm. to a secondary mill, might result in a greater overall economy because of the thicker feed and the better, adjustment of crushing media and mill operation to the reduction demanded. With the present trend back toward a combination of gravity methods and flotation, rather than flotation alone, the accurate, economical sizing possible with the new screens makes fine jigging a method to be considered. W. 0. Borcherdt1 and John Bland2 discuss the screening problem and also the value of close sizing in the concentration of some of the rare-metal ores. If a screen is to be used, it should be selected in competition with others; other things being equal, that screen which makes the cleanest oversize should be preferred. The quality of the screening and the tons

Jan 1, 1924

By Arthur C. Green

A group of 13 cities situated in Los Angeles and Orange counties in Southern California is engaged in constructing an aqueduct to carry water from the Colorado River at a point near Parker, Arizona, to a distribution point near Riverside, California. The aqueduct will have a total length of approximately 241 miles, and is designed to deliver 1605 cu. ft. of water per second, or a little more than one billion gallons per day. The aqueduct crosses a barren, desert waste and the project includes approximately 91 miles of 16-ft. tunnel. The large amount of tunnel driving that has been done in this country in the past few years has resulted in some remarkable developments in equipment and methods. The building of the Colorado River Aqueduct,, with its 91 miles of tunnels, has called on the best engineering knowledge in the country. New and better equipment has been designed for all phases of the work, and this equipment has been coordinated and adapted to the various conditions with a high degree of efficiency. The result has been that records for tunnel driving have been set under adverse natural conditions that exceed the estimates for progress under good conditions. All of the tunnels in the main aqueduct, except the Valverde and Bernasconi at the western end, have a finished diameter, inside the concrete lining, of 16 ft. Fig. 4 shows a section of the tunnel with the concrete lining in place. Fig. 5 illustrates the finished tunnel in three typical sections. The standard tunnel grade is 3.432 ft. per mile in the 16-ft. tunnels, but the Valverde and Bernasconi tunnels have a steeper grade and a finished diameter of 15 ft. 3 in. The rough bore of the large main aqueduct tunnels averages 12.95 solid cubic yards of material per foot of advance in timbered sections and 10.76 solid cubic yards per foot in unsupported sections. Tunnel Driving While the Conway mucker has been used on tunnel work for years, a larger and more powerful Conway was designed to meet the require-

Jan 1, 1937

By R. E. Ricksecker, W. M. Baldwin, R. McC. Baker

INTRODUCTION 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 compressive stresses acting almost perpendicularly to the strip surface but vary [ ] ing 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 perpendicularly over the face of the tool. The elastic internal stress state in this case is complex-the principal stresses showing

Jan 1, 1948

By R. G. Davies

Above 500°C, where dislocation climb is rate controlling, it is observed that the activation energy for creep is independent of the apblied stress, although it varies from 62 kcal per mol at 15 pct A1 to 73 kcals per mol at 20 pctA1 due to the change in short-range ovdw with composition. Below 500°C, when the nonconservative motion of jogs upon dislocations is thought to be rate controlling, the activation energy is stress dependent. A sudden increase in the creep rate, for which no explanation is availab2e, occurs at the highest stress at all temperatures. CREEP has been the subject of numerous research publications during the past decade with most of the attention focused upon high temperature steady state creep, i.e., above 0.5 TM, where TM is the absolute melting temperature, as it is the most amenable to theory. Many of the proposed theories involve the climb of dislocations out of their slip plane, which allows them to circumvent obstacles or to annihilate dislocations of opposite sign on other slip planes.' For pure metals it is observed that the activation energy for this creep is equal to the activation energy for self diffusion.' The position is much more complicated in alloys as there are many possible microcreep mehanisms, as well as dislocation climb, which could be rate controlling. There has been little systematic investi- gation of alloys, but Weertman (lead and indium base alloys)3 and Lawley, Coll, and Cahn (Fe-A1 alloys)4 suggest a microcreep process as the controlling factor. A Cottrell-Jaswon atmosphere mechanism is proposed for the lead and indium alloys, and a mechanism involving crystallographic order for the Fe-A1 alloys. Lawley et al. showed that the formation of a super-lattice, either of the FeAl or Fe3A1 type. decreased the rate and increased the activation energy for creep. From the measurements of lattice parameters,= resistivity,' magnetic properties,7'8 internal friction: and dilatometry10 the ordered region is thought to commence at -19 at. pct Al. However, a recent investigation by the author indicates a value

Jan 1, 1963

By L. Adler

Analysis of a mine roof can be based on fixed-end beam behavior. The author here analyzes the effects of zero restraint at deflecting beam supports. Formulae are given for determining permissible support deflections. Analysis of a mine roof in a bedded deposit usually follows the assumption that the behavior of the roof is analogous to a beam with both ends fixed. Yet it is recognized that the end restraint itself varies with the thickness of cover, so that at shallow depth the restraint is minimum, and at great depth, maximum.' Consequently, an analysis on the basis of fixed ends or full restraint represents only one extreme in the possible range of conditions. Since the actual amount of restraint is difficult to ascertain, a more rational approach is to consider the two extreme cases of end restraint. Such situations regarding uncertainty of the restraining effects of supports are not uncommon in structural analysis, and are handled in a like manner.' Since previous studies9)4 have dealt with full restraint, this paper will analyze the effects of zero restraint at deflecting beam supports. In such a case a mine roof with several intermediate supports becomes analogous to a uniformly loaded continuous beam on simple supports, as shown in Fig. 1A. Such a structure is statically indeterminate to a degree equal to the number of intermediate supports, n. Therefore, with the three equilibrium equations, n additional equations are needed. A number of methods exist to analyze this problem, but The Theorem of Three Moments is Simplest. The continuous beam is divided at each support into a sequence of simply supported single span beams, with the unknown end moments, as appears in Fig. 1B. Continuity requires that the common ends of adjacent beams have the same slope (Fig. 1C). eiB= B(i+l)~= ei(i+l)and MiB= Mti+I)A= Mi(i+i). [1I A Glossary of all terms is given in Table I. Furthermore, if we first consider that the supports do not deflect, the slope at a support is the sum of the slopes due to each of the individual loads shown in Fig. 2, yielding:

Jan 1, 1961

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

By D. A. Woodford

In a constant-load creep test, if the density of nlobile dislocations is assumed constant for strains exceeding that corvesponding to the minimum creep rate, it is shown that the creep rate may be approximated by the equation where E is the nominal strain, o0. is the initial stress, and a' the stress fov unit dislocation velocity. The constant C contains the mean density of mobile dislocations and n is a measure of the stress sensitivity of dislocation celocity. This equation is shoum to be applicable to published data on an alloy steel and on nickel. The degree of plastic instability and hence the creep ductility is dependent on the calue of n for these materials. When instability becomes gross and local macroscopic necking occurs, the assumptions are no longer valid. On the basis of this equation, and the strain-time relation derived from it, a method of predicting the creep behavior at different stresses is suggested. MOst analyses of creep data have been concerned with time-dependent transient creep or time-independ- ent secondary creep in constant-stress tests. The far more widely used constant-load test has been neglected in terms of a mechanistic approach. In general, since the strains involved are usually small, the same laws for transient creep may be applied to both types of tests. However, there is no steady-state creep in a constant-load test since the stress increases continuously. Any apparent steady state observed on a strain-time plot is either fortuitous or illusory, and is generally revealed as a continuously varying creep rate on a carefully constructed strain rate vs time plot.* Transient creep may be understood in terms of a simple differential equation representing the change in mobile dislocation density with time:' where p is the density of mobile dislocations. The first term on the right is related to first-order kinetics of dislocation multiDlication and the second to second-order kinetics of exhaustion. On the basis of this equation, several authors2-4 have found good agreement with experimental transient creep curves for a number of materials. When k1p = k2p2, a steady-state creep

Jan 1, 1968