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By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"' and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By B. C. Allen

Grain-boundary gvoocing was studied irz chronziu?n. molybdenum, tungsten, and the solid-solution alloys, Cr-35Re. Mo-33Re, and W-25Re at 0.6 to 0.9 of the absolute liquidus temperature under an inevt atmosphere , foveign nzetal zlapor, and liquid metal. The controlling mechanism of matter transport was deduced frolr groove size and shape. kinetics of growth, and cotnparisoz with theoretical relatiotzships derived by Mullins. Grooves in chowzizon formed prittzarily by volume diffusion tkrongk kelium or argon at 1 atm pressure and by e1)apovation-condensatiotz in a static vacuum. Groozles in the other nzetals and alloys forrned priniarily by sirface diffusion, the coefficients of which were calculated. Carbon was found to decrease the acti7:ation energy for surface diffusion on molybdenun. Sitrface diffusizities weve sinzilav for iWo-0.0ZC and Mo-33Re. The presence of about 1 -?nm pressure of silver or tin vapor did not affect the neckanis)n of grooz;e formation. In liquid titz or silz:er, pain bolindary gvooves formed by zolume diffusion in the liquid. BASED on theories of ullins," the mechanisms of grain-boundary grooving have been determined for low-melting metals such as copper in an inert atmospheres or in liquid lead.4 The purpose of this investigation was to study grain-boundary grooving in the refractory Group VI-A metals, chromium, molybdenum, and tungsten, and the bcc solid-solution alloys, r-35e, 0-33e,= and -25e,' at 0.6 to 0.9 of included to see whether Mullins' theories were applicable to them as well. EXPERIMENTAL WORK The materials chromium, molybdenum, tungsten, Cr-35Re, Mo-33Re, and W-25Re were in the form of 0.050-cm-thick sheet assaying 99.98 pct or better. The nominal carbon level was generally 30 ppm. The oxygen + nitrogen + hydrogen content was -50 ppm. Mo-33Re and W-25Re were prepared by powder-metallurgy methods and supplied by Chase Brass and Copper Co. The remaining materials were arc-cast. Chromium and Cr-35Re were prepared at Battelle by arc melting, extruding, swaging, and rolling. Mo-0.003C was supplied by Climax Molybdenum Co., and Mo-0.02C and tungsten by Universal Cyclops Corp. As a source of liquid metals, tin and silver granules assaying 99.98 pct were used. Spectrographic analyses indicated the presence of -100 ppm each of iron and silicon. Vacuum melting reduced the combined gas content to c5 ppm (2.60,, 0.9N2, 0.4H2 in tin and l.602, 0.7N2, and c0.04H2 in silver). Specimens were prepared for grain-boundary grooving. Coupons 0.5 by 1.5 cm with a small hole in one end, or substrates 1.5 by 1.5 cm, were cut from sheet. The specimens were annealed in containers of the same material to provide a vapor-solid equilibrium as well as to protect them from gaseous impurities. Outgassing was done at 2 x 10"5 mm for 15 to 30 min at 1150°C for chromium and Cr-35Re, 1750°C for molybdenum and Mo-33Re, and 2600°C for tungsten and W-25Re. Then recrystallization to a stable grain size of about 0.5 mm was accomplished by annealing at least 1 hr at 1600°C for chromium, 1800°C for Cr-35Re, 2350°C for molybdenum, and 2300°C for Mo-33Re in a rhenium-element resistance furnace under 1 atm of static argon or helium. The atmosphere was gettered by tantalum radiation shielding. Tungsten and

Jan 1, 1967

By J. M. W. Mackenzie

The interactions between oil drops and mineral surfaces have been examined for the cetyltrimethylammonium bromide (CTAB)-quartz and sodium dodecyl sulfate (SDS)-hematite systems. The results have been interpreted using a electrical double layer interaction model, a "sweeping-penetration" model based on steric interactions and a free energy of adhesion model. The adsorption of long-chain ions at the mineral interface was also studied and found to follow a Fuerstenau-Modi model of combined Coulombic and chain-chain interaction forces. The basis of the emulsion flotation process and the feature which makes it differ from conventional flotation is: encounter, followed by adhesion, between oil drops and mineral particles which are suspended in an aqueous environment. The manner in which the adhesion between these two phases contributes to the flotation process may be through the formation of min-eral-oil drop-mineral linkages, mineral-oil drop-air bubble linkages, or a combination of both. Possible flotation mechanisms derived from these adhesion processes are shown schematically in Fig. 2 while Fig. 1 shows an example of the first mechanism for quartz particles which have been floated using a cetyltrimethyl-ammonium bromide (CTAB)-Nujol emulsion as collector. In Fig. 2 the three phases, mineral, oil, and air, for convenience have been shown as having approximately equal size. This would not always be the case in an actual emulsion flotation operation. For the flotation of sand-sized particles of approximately 0.5 mm diam, the mineral particles would be at least ten times the size of the largest emulsion drops present in the system, while in the flotation of —10u slime particles, the mineral phase may be of the same order of size as the oil phase. The air bubbles in a flotation cell are normally about 1 to 2 mm in diam and therefore, in general, would be larger than the oil drops. Although the relative size of the three phases does not alter the basic adhesion processes between oil drops, mineral particles, and air bubbles, which depend on the physical and chemical properties of the interfaces involved rather than on the extent of these interfaces, it does alter the degree of deformation of the oil drops and air bubbles which will occur on adhesion. For mechanisms 1 and 2 to take place, the oil-water and mineral-water interfaces must be partially replaced by a mineral-oil interface while in mechanism 2 there is the additional requirement that the oil-water and air-water interfaces must be replaced by an oil-air interface. In view of the importance of the oil drop-mineral particle encounter and subsequent adhesion stages to both of the emulsion flotation mechanisms discussed, a study has been made of some physicochemical factors which control these processes for Nujol-cetytri-methylammonium bromide (CTAB)-quartz and Nujol-sodium dodecyl sulfate (SDS) -hematite systems. Experimental Electrokinetic Measurements.—The zeta potential of mineral particles was measured using a streaming potential technique similar to that described by Fuerste-nau.1 The streaming potential was measured using a multirange electrometer while the plug conductivity was measured using a 50 cycle sec1 bridge. Measurements were made on 28 x 65 mesh particles. Contact Angle Measurements.—A captive bubble technique was used to measure the contact angles for air bubbles and oil drops. The angles were measured on fracture faces of unmounted minerals which proved easier to clean than polished mounted specimens and should more closely represent a flotation system. Reagents: These have been described in a previous publication.0 Minerals: Rock crystal quartz from the New England district, N.S.W., was used for contact angle and streaming potential measurements. The quartz was hand

Jan 1, 1971

By Stirling Huntley, R. H. Johnson

Pennsylvania will be remembered, as long as oil is produced, as the cradle of the industry of petroleum in North America. It was on Oil Creek, near Titusville, Venango Co., that Col. Edwin L. Drake, superintendent for the Seneca Oil Co., brought in the first commercial oil well on Aug. 28, 1859. Great difficulty was experienced in getting the well down to the producing depth of 69 ft. (21 m.) with the spring-pole system then in vogue for punching shallow water wells, so the novel expedient of driving an iron tube through the surface clays and quicksand was finally resorted to. The well had an initial yield of 25 bbl. a day on the pump, but soon went off, though 2000 bbl. were produced by the end of the year. With the Drake well a success, a young industry sprang into being, the rapid growth of which has been second to none in the country and the value of whose product is only surpassed by that of coal. For years the only producing territory, the Pennsylvania-New York field attained its greatest production in 1891, when the bringing in of the McDonald pool, between Pittsburgh and the West Virginia line, gave a total of over 33,000,000 bbl. At present the field, combined with West Virginia and southeast Ohio, gives 25,000,000 barrels. Geology and Stratigraphy In general, the Appalachian field is a huge geosyncline, the axis of which runs roughly northeast-seuthwest, from north of the New York state line south through Brookeville, Kittanning, Pittsburgh, Washington, through the southwest corner of the state of Pennsylvania into West Virginia. Minor folding has accompanied or followed the dominant fold of the field, and it is from these structures near the Pennsylvania-West Virginia line and their influence on the accumulation of oil and gas that I. C. White, state geologist of West Virginia, obtained his evidence for anticlinal guidance of prospecting. Many horizons in the geologic column of the field serve as reservoirs, and there arc several pools that have wells producing side by side from different and widely vertically separated strata. The strata show a promising succession of porous sand and conglomerate horizons alternating with numerous gray and dark brown 01. black shales, admittedly

Jan 1, 1921

By R. H. Frazier, C. H. Lorig, F. W. Boulger

THERE are both advantages and disadvantages in using semikilled steels in place of killed steels. One advantage of semikilled steels is they provide a higher ingot-to-product yield. This is especially important to shipbuilders in the time of national emergency. By using semikilled steel for hull plates, a greater number of ships can be built from the same ingot tonnage. Consequently, if semikilled steel plates are adequate for the service, the advantage of the higher product yield is of considerable importance. The performance of hull plates is closely associated with the ductile-to-brittle transition temperature, and this, in turn, is strongly dependent on the composition of the steel. A low transition temperature is desirable because it indicates that the steel is less likely to fail at low ambient temperatures. Killed steels are known to have lower transition temperatures than semikilled steels. It is believed that the better qualities of killed steels in this respect are due mainly to the low oxygen contents of the steel. The principal deoxidizers, aluminum, silicon, and manganese, lower the oxygen content. Fundamental studies1-0 have shown that the oxygen content remaining after the addition of one of these three elements is influenced by the residual amounts of the other two present. In the current study, therefore, various amounts of silicon and aluminum were added to steels containing different manganese contents for the purpose of studying the influence of silicon and aluminum on the notched-bar properties of hot-rolled steels. Eleven types of steels were studied. The temperature at which the plates were finish-rolled was care- fully controlled at 1850°F. All plates were rolled to ¾-in. thickness, and tested in the as-rolled condition. The total number of steels prepared in the laboratory for this study was 95. The charge consisting of ingot iron and ferrosilicon equivalent to 0.10 pct Si was melted in a 200-lb induction furnace under an atmosphere of argon to insure low, uniform nitrogen contents. After the charge was melted and the desired temperature was obtained, the melt was partly deoxidized with either silicomanganese or aluminum. Aluminum was used for this purpose in only those steels with very low silicon contents, where the finished steel was to contain some aluminum. This initial deoxidizing addition was made to obtain consistent recoveries of subsequent additions of ferro-manganese, ferrosilicon, and aluminum. Carbon, in the form of graphite, was added, either just prior to tap or to the final aluminum addition. The entire heat of 200 lb was poured directly into a 6x6-in. big-end-up mold. The ingots of semikilled steel were capped with a steel plate. The killed steels, on the other hand, were poured with a hot-top containing 14 pct of the total volume of the ingot. The ingots were processed by heating to 2250°F, followed by forging to slabs 1¾ in. thick and 6 in. wide. After reheating to 2250°F, the slabs were rolled to 0.9-in. gage, using reductions of approximately 1/6 in. per pass. The 0.9-in. thick plates were immediately recharged in a furnace held at 1850°F. After 30 min in the furnace at 1850°F, the plates were rolled to ¾ in. in one pass. Following the final pass, the plates were stacked on edge on a brick floor, with a brick separating one from another, where they were allowed to cool in air. Drillings for chemical analysis were taken from the plates at locations corresponding to the top and bottom of each ingot. Carbon, manganese, silicon, phosphorus, sulfur, and nitrogen contents of each sample were determined. The analysis of each steel was carefully controlled so that the contents of

Jan 1, 1957

By R. H. Sweetser

The Committee on Evaluation of Coal for Blast-furnace Coke reports progress in the working out of the problem of evaluation. There has been no full meeting of the Committee but there have been several conferences with two or more of the members present, and the different members have expressed themselves freely on the five points that have been under consideration since the meeting of the Committee in New York on Feb. 16, 1932. The need of a method of coal evaluation, not only of coking coals but all other kinds, is obvious. Under NRA it becomes imperative that coals of the same size from the same seam be priced according to their variations in quality, especially in reference to cleanliness in respect to freedom from extraneous ash-forming materials. In looking over the correspondence that has passed between members of our Committee, it is evident that much of the confusion and misunderstanding would disappear if we could realize that practically all of the variations in value of coal from the same seam of coal are due to variations in the amounts of extraneous materials that are contained in the coal as it passes over the scales for shipment. It is not now a question with our committee as to the differentials in value, or in prices, between different kinds of coking coals or between noncoking and coking coals; our present problem is to arrive at the method for determining the scale of values of the coal from a certain coal seam according to the increase or decrease of extraneous ash and moisture from a predetermined base line adopted for that particular coal. The five points mentioned above are the same as discussed at the meeting in February, 1932, except that the temperature for determining the moisture content has been changed from 212" F. to 221" F., at the suggestion of Dr. A. C. Fieldner. The points are: 1. It is proposed that the coal industry adopt as a base line for evaluating all coals the analysis of the coal as it passes over the neighing device that determines the tonnage of coal bought and sold. 2. It is proposed that the Committee on Evaluation of Coal for Blast-furnace Coke approve the adoption of the base line for Pittsburgh seam coal presented by F. A. Jordan at the annual meeting of A.I.M.E.

Jan 1, 1934

By J. L. Huitt, S. R. Darin

The use of a partial monolayer of propping agent to obtain a high flow capacity for a hydraulically induced fracture is discussed. From the results of laboratory work it was shown that a modified form of the Kozeny-Carman relation could be used to describe the flow in the partial monolayer propped fracture. With equations presented in the paper, the density pattern of the propping agent (number of particles per unit of fracture surface) that results in the maximum flow capacity for the fracture can be determined. The maxitnum flow capacity obtained with a partial monolayer is often an order of magnitude greater than the flow capacity obtained in greater width fractures containing multilayers of the propping agent. INTRODUCTION One of the predominant factors controlling the success of a hydraulic fracturing operation is the propping of the fracture. The trend in hydraulic fracturing recently has been an increase in the ratio of propping agent-to-fluid. The primary purpose of this increased ratio is to sustain a propped fracture of greater width. It was shown in a recent study' that for some formations low concentrations of propping agent would result in "closing" or "healing" of the fracture. In some cases, in an effort to insure sufficient propping agent concentration, the fracturing operation is designed to obtain a pack of the propping agent in the fracture. The placing of a pack of propping agent in the fracture provides a fracture of maximum width; however, the width alone does not control the flow capacity of the fracture. The flow capacity is dependent on the permeability of the fracture, as well as the fracture width. Thus, increasing the permeability to obtain larger flow capacities is as important as obtaining a greater width fracture. By increasing the concentration and particle diameter of the propping agent, fractures of sufficient flow capacities are obtainable for effective well stimulation in a number of formations. However, in some of the recovery techniques, the fracture capacity obtained by commonly used practices in fracturing is inadequate. One such recovery technique is gravity drainage via a horizontal fracture placed near the base of the productive zone. For this recovery technique, the fracture capacity desired is usually one to two orders of magnitude greater than the fracture capacity normally obtained in fractures propped with the size of sand commonly used (20-40 mesh). By the use of particles of larger diameter, the permeability of a pack2 is increased; however, even a multilayer pack results in a fracture flow capacity lower than that desired for some formations. For example, a fracture of 1/4-in. width, packed with 8-12 mesh sand of about 2,000 darcies permeability, would result in a fracture flow capacity (permeability X fracture width) of only 40,000 md-ft. If the fracture flow capacity needed is an order of magnitude greater than that cited in the example, an approach different from the formation of a pack in the fracture is needed. One approach is a partial monolayer of large-diameter propping agent. In working with this type of fracture system, it was found that the flow problems were unique to the system; therefore, the study discussed in this paper was made. THEORY AND RELATED STUDIES Previous studies, although related to that described in this paper, have not pertained directly to the flow in a fracture propped with a partial monolayer of propping agent. However, studies such as flow between parallel plates,' flow in packed columns,' fracture flow capacity' and flow in simulated fractures reduce the scope of this flow problem considerably. A fracture propped with a partial monolayer of dropping agent may be considered to be between two extremes — between an open fracture and a bed of particles packed In a conduit of fracture geometry. Thus, it seems appropriate to review the extreme cases.

By E. A. Gulbransen, A. Pebler

Pressure-composition isotherms have been determinedfor the systems ZrMo2 -H2 between 0" and 900°C at hydrogen pressures between 10-4 and 760 Torr. Tkese studies plus X-ray diffraction analyses of selected compositions show that these intermetallic compounds form a complete series of hydrogen solid solutions within this temperature and pressure range. The partial molar enthalpies and entropies of solution of hydrogen in the three intermetallic compounds were calculated. The solubility of hydrogen in these Laves phases can be related to their free electron concentration. ThE reaction of hydrogen with inter metallic compounds of zirconium with Laves phase-type structure has both theoretical and practical interest. The in-termetallic compounds have structures different from any of the pure metals. In addition the electron to atom ratio of the intermetallics varies appreciably. In the nuclear materials field, these materials are of interest since intermetallic compounds may exist as precipitates in commercial zirconium alloys with transition metals. From studies on the hydrogen reaction, one can establish the stability of the intermetallic compounds relative to the hydrides of the component metals. The intermetallic compounds may also be used as getters for hydrogen and as materials for hydrogen storage. This paper will present the results of equilibrium and structural investigations of the ZrCr2-H2, the ZrV2-H2, and the ZrMo2-H2 systems for the temperature range of 0" to 900°C and the pressure range of Torr to 1 atm. A complete thermochemical analysis will be made of the measurements. Some of the results have been referred to in a survey paper' covering the types of hydrogen behavior observed in zirconium alloys. LITERATURE ZrCr2 is the only intermetallic phase in the Zr-Cr system.' It exists in two allotropic modifications. Between 900" and 1000°C the hexagonal MgZa (C14) structure transforms into the cubic MgCu2 (C15) structure. Beck4 has previously shown that the intermetallic ZrCrz takes up hydrogen into solid solution up to a composition H/ZrCr2 = 1.14 at room temperature and 1 atm hydrogen. A ZrCr2 hydride was stated to have a fcc structure. The binary Zr-V system has been investigated by williams5 although Rostoker and Yamamoto 6 had given earlier a partial phase diagram. ZrV2 was the only intermediate phase found in the system. wallbaum7 reported earlier that the compound ZrV2 hp the MgZm (CJ4) type structure with a = 5.288A and c = 8.664A. This was not comfirmed by Elliot8 nor by Matthias, Compton, and corenzwit9 who reported that ZrV2 has a cubic MgCua LC15) type structure. The latter authors gave a = 7.429A. Also, several authors do not agree on the temperature of the peri-tectic horizontal. It appears that ZrV2 may exist in several modifications. A high capacity for occluding hydrogen was reported by Beck4 who found H/ZrV2 = 1.38 at room temperature and 1 atm of hydrogen. ZrMoz is the only intermetallic phase in the Zr-Mo system.10 ZrMoa is formed by a peritectic reaction of the melt with a molybdenum-rich solid solution. ZrMo2 has the C15-type structure with a = 7.59A. MATERIALS High-purity chromium, vanadium, and molybdenum were used together with grade 1 crystal bar zirconium to prepare the alloys. Table I lists the chemical analysis and the sources for the metals. Ten-gram alloy compacts were levitated and melted in an inert argon

Jan 1, 1968

By W. A. Tiller

The unidirectional freezing of a semiinfinite liquid from one end has been treated by calculating the solute and temperature distributions in the liquid and solid phases with time, when the solid-liquid interface advances at a rate proportional to (time)lt2. The nucleation probability for new grain formation is calculated as a function of the constitutional and thermal properties of the alloy, the pouring conditions and the catalytic efficiency of the nucleating agents. The transition from columnar crystal formation to equiaxed crystal formation is assumed to occur at a critical nucleation frequency for a particular alloy and the quantitative dependence of the ratio (columnar zone length/equiaxed zone length) upon the freezing conditions has been predicted. The effects of (i) fluid flow in the liquid, (ii) heat transfer through a mold wall, and (iii) a finite ingot length, have been explicitly tveated as departures from ideality. These departures from ideality are found to have very important consequences on the ingot stmcture. In Part I&apos; of this series, a qualitative description of the general ingot structure was developed. The factors that determine i) the ratio of the equiaxed zone length to columnar zone length and ii) the grain sizes in these zones, were discussed. In the present paper, topic (i) will be treated quantitatively, and it is intended that topic (ii) will be treated quantitatively in Part 111. The complete treatment has been split in this manner for ease of development and coherency of presentation. The treatments are quite mathematical in nature and, although some of the conclusions to Part 11 depend upon the treatment presented in Part 111, it was felt that the intended audience would find the material more readable and more useful in its present form. To this same end, it seems worthwhile to reiterate some of the qualitative aspects of grain nucleation during ingot solidification before embarking on the mathematical description. QUALITATIVE ANALYSIS In the conventional method of casting, a liquid alloy with a certain degree of superheat is poured into a mold. The outer rim of liquid metal cools rapidly to the liquidus temperature of the alloy and begins to undercool. As the degree of undercooling increases, nuclei of solid begin to form in this chill layer, this nucleation being catalyzed by certain heterogeneous particles in the liquid. The grains in the chill layer which are generally of random orientation, begin to grow inwards because of heat conduction through the mold. The grains usually develop a columnar shape since the frequency of nucleation of new grains in the liquid ahead of the advancing interface is generally insufficient to seriously impede the growth of the original grains. Due to the slow diffusion rate of solute in the liquid, a solute distribution is formed in the liquid adjacent to the interface which is either an excess or a depletion if the partition coefficient, ko, of the solute is < 1 or > 1, respectively. Thus, the liquidus temperature of the liquid adjacent to the interface is a function of position. The actual temperature in the liquid is also a function of position and the temperature gradient at the interface decreases as the interface moves away from the mold wall. Since the rate of advance of the interface decreases with time, the equilibrium temperature distributions and the actual temperature distributions as a function of interface position, X, can be illustrated as in Fig. 1. Thus, a region of liquid may exist in which the actual temperature is below the liquidus temperature. This liquid is contitutionally supercooled and therefore unstable with respect to the nucleation of new grains. Now, since the supercooling in Fig. 1 increases as the interface moves further away from the mold wall, the nucleation rate of new grains will increase. When the nuclea-

Jan 1, 1962

By Robert E. Green, Edmund G. Henneke

Expressions are derived for the orientation factors associated with dislocation damping due to dislocation motion in the basal slip plane. The results of the calculation of these factors for zinc crystals aye pvesepzted and the relevance of these results to ultvasonic-attenuation measuvements is discussed. In this paper expressions are derived for the orientation factors associated with damping of sound waves due to dislocation motion in the basal slip plane of hexagonal crystals. For zinc crystals, the orientation factors for dislocation motion in one slip direction only, as well as for simultaneous motion in all three basal slip directions, have been calculated at 1-deg intervals. The results of these calculations are presented in the form of contour diagrams in a sector of a standard polar coordinate graph. The calculations have been carried out for both the traveling- and the standing-wave conditions. The relevance of these results to ultra sonic-attenuation measurements is discussed. Associated with the calculation of the orientation factors, the modes of elastic-wave calculation were also evaluated, according to the procedure previously employed by Hinton and Green.&apos; The results of these calculations are not presented here since similar results have been reported earlier by Mus-grave.2 However, it should be mentioned that, although the qualitative features of Musgrave&apos;s results are preserved, the quantitative values are somewhat altered since different values for the elastic constants of zinc were used. ORIENTATION FACTORS It is convenient to refer to three different sets of coordinate axes, Fig. 1, in the following calculations. First, there are the Miller-Bravais axes which are used in describing the Miller-Bravais indices of planes and directions in a hexagonal crystal. These axes are denoted in the conventional manner by a,, a,, a,, and c. The second set of axes used is a rectangular Cartesian coordinate system located as shown in Fig. 1. Note that the x axis coincides with the close-packed direction al [2110], the z axis coincides with the c axis [0001], and the y axis is orthogonal to these two lying in the [0110 ] direction. Finally, a form of Eulerian angles is used to locate the position of the specimen axis. The angle between the specimen axis and the c axis is denoted by 0 and the angle between the projection of the specimen axis on the basal plane and the a, direction is denoted by ø. The majority of observations on plastic deformation of metal crystals indicates that such deformation is caused by the motion of dislocations on a limited number of crystalline planes and in a close-packed direction. In crystals with hexagonal symmetry the most prominent slip plane is the basal plane (0001) and the slip directiops- are one of the close-packed directions, [2110], [ 12101, or [ 1120]. To properly set the stage for the following work, several points must be clarified. First, we want to consider the contribution to the attenuation of elastic waves by dislocations only. While the Granato-Lucke, model for dislocation damping is presently the one most quoted, it is not necessary to refer the present work to it. The only assumption that need be made is that the motion of dislocations absorbs energy from the elastic wave and therefore attenuates it. It is immaterial here how this energy absorption occurs. However, because dislocations have been observed to move most freely on the (0001) plane for hexagonal crystals undergoing plastic deformation, it will be assumed that it is the dislocation motion on this plane which attributes to the observed attenuation. The basic orientation factor, Ok, is essentially the same as that used by Green and Hinton for fee crystals,4 defined by the equation

Jan 1, 1968

By L. S. Darken, H. A. Wriedt

An investigation has been made of nitrogen absorption by the lattice defects in a low-carbon steel afte~ Plastic deformation. Specimens in which defects were distributed by various combinations of cold rolling and vacuum heat treatment were equilibrated with controlled ammonia + hydrogen mixtures at 300° to 450°C to study the relation between the solubility and the thermodynamic activity of nitrogen. The results are interpreted in terms of nitrogen being absorbed upon two different types of defect sites, called A sites and B sites. The concentrations of these sites are calculated for specimens with various histories of straining and annealing; and the thermodynamic relations descrihing the equilibrium distribution of nitrogen among the A, B, and ordinary interstitial sites in ferrite are evaluated as follows: THE generalization that the solute atoms in a solid solution interact with imperfections in the solvent lattice is now universally recognized and the subject of an extensive literature. All types of imperfections—point, line, or surface—exhibit these interactions, but the relative importance of each type depends upon its concentration, the strength of its interaction with the particular solute atom, and whether the interaction is attractive or repulsive. The strength and sign of the interaction vary with the vectorial displacement of the solute atom from the imperfection in the crystal. The concentration of lattice defects increases during plastic deformation and the effect of the imperfections upon the solute atoms is usually perceived only after cold work or irradiation. Two experimental methods have previously been used to observe the effects of interaction between nitrogen atoms and lattice imperfections in a iron. Internal friction, which was first used for this purpose by Dijkstra,1 has been applied more often than the electrical-resistivity method of Cottrell and Churchman.2 The method of the present investigation has not been used before.* Uniform specimens of steel with a metastable defect structure are produced by cold rolling and subsequent heat treatment below the recrystallization temperature. Variations in the defect structure are obtained by varying the amount of strain and the heat-treatment conditions. The specimens are then saturated with nitrogen at moderately elevated temperatures in ammonia + hydrogen mixtures having various thermodynamic activities of nitrogen below saturation with Fe4N. From the nitrogen contents of analyzed samples, the metastable equilibria of interactions between the defects and nitrogen can be established and the concentration of sites for nitrogen atoms in the lattice defects calculated. A steel was used in the present experiments instead of purified iron or iron alloys because the amount of nitrogen absorbed at defects is larger in the steel over a much wider range of experimental conditions and could therefore be measured more accurately. The effect of alloy composition is discussed in Part II of this paper; it is sufficient to say here that impurities and phase heterogeneity in ferritic alloys favor the generation and/or retention of larger defect concentrations during plastic deformation and annealing at 300° to 500°C. MATERIALS AND EXPERIMENTAL PROCEDURE The experimental specimens were prepared from stock of a low-carbon steel, which will be called "X steel" here, with the composition: C, 0.12 pct; Mn, 0.43 pct; P, 0.010 pct; S, 0.034 pct; Si, 0.007 pct; As, 0.086 pct; Cu, 0.022 pct; Ni, 0.009 pct; Cr, 0.003 pct. The stock was all from a single ingot made by the basic open-hearth process, which was hot-rolled to strip 0.080 in. thick.. This hot-rolled strip, given the code designation "XH", was the starting material for preparing a series of cold-rolled sheets. The latter are designated "XC27",

Jan 1, 1965

He was born at Montreal, Canada, in 1875. His earliest education was received in Montreal hut was continued from 1885 to 1892 at schools and academies in Brooklyn, Whitestone, and Flushing, L. I. For his technical education he returned to McGill University, where he graduated in 1897. His first professional occupation was as transitman enga.ged in the running of township lines in the Rainy River District of Ontario. In 1899, he was made assistant chemist at the Cuggenheim smelter at Aguascalientes, Mexico. From 1900 to 1903, he was chief chemist for La Compañia Minera de Peñoles, at Mapimi, Durango. We have no information as to his pursuits during the next eight years, but from 1911 until 1914, when he became a member of the Institute, he was chief engineer for the Bankhead mines in Alberta, Canada. Lieutenant-Colonel Alfred Winter Evans Lieutenant-Colonel Evans, who was in command of the Third Battalion of the New Zealand Rifle Brigade, and had been cited in Distinguished Service Orders and received the Distinguished Conduct Medal, was killed in action on Oct. 12, 1917. Alfred Winter Evans was born in Natal, South Africa, in 1881, and received his preliminary education in the Durban High School. For the next five years he attended St. George&apos;s School at Harpenden Heights, England, until 1898. Returning to South Africa, he worked . for three months of 1898 as underground sampler for the Crown Deep Gold Mining Co., at Johannesburg, and for six months of the following year he was shift-boss for the Crown Deep, Ltd. At the outbreak of the Boer War he took an active part and was engaged on military service from 1899 to 1902. At the close of the mar, he came to New York and attended the Columbia School of Mines, where he graduated with the degree of E. M. in 1906. A part of that year he spent as assayer to a mining company at Poland, Arizona. In 1907, he returned to South Africa and engaged as underground contractor in charge of mining and development at a number of the South African mines, notably the French-Rand, the ViIIage Main Reef, the City Deep, and others. In 1908, he acted as shift-boss for the Fer-rerra Gold Mining Co. at Johannesburg. In 1909, he was appointed acting general manager for the Consolidated Goldfields of New Zealand,

Jan 1, 1920

By C. A. Rowland, R. C. Nealey

Wet grinding rod mills have been used for 50 years to grind ores and to make specification sand. The application of wet grinding rod mills is well understood. Until recently, there have been very few installations of dry grinding rod mills. The selection of dry grinding rod mills follows the basic principles established for the selection of wet grinding rod mills. The basic Bond Formulae1 [ ] is used to select mills when using grindability test results as the basis for selection. W is multi- plied by the 1.3 wet to dry grinding factor established from wet and dry ball milling experience, and then by any other applicable inefficiency factors.1 Dry grinding rod mills have also been selected by scaling up bench scale continuous rod mill tests and pilot plant tests.

Jan 12, 1968

By K. Leutwyler

The authors present an interesting review of various applications of rather well known theories. Their rearrangement of the original working equations is strictly computer oriented and serves well to that effect; however, the new appearance will be confusing to the slide rule-wielding members of the profession. In reviewing discrepancies existing between calculations made by Baker Oil Tools, Inc. field engineering staff members and computer output submitted based on the authors&apos; program, the following error in concept was discovered in Eq. 4. The authors quote the length change due to helical buckling in the following form We appreciate Kurt Leutwyler&apos;s awareness of Archimedes&apos; principle, and concur that the final term in the denominator of Eq. 4 results in a small error. Examples checked revealed less than I ft error, and corrective expressions for the four possibilities of displacement follow. The portion of the denominator within extra large brackets represents the original term W,, = weight of outside fluid displaced per unit length. The authors interpreted the expression "displaced" in general oilfield terminology as a fluid displacement, such as "mud displaced with water, etc." A review of the theory forming the basis for these helical buckling calculations discloses that this displacement is meant to be interpreted in the Archimedean sense, i.e., fluid displaced by the solid body. here the tubing and the seal nipple. Lubinski* illustrated the point by summing moments due to mechanical and hydraulic forces acting on a free body immersed in fluid. This moment summation, always in the Archi,medean sense, yields effects of the real forces, including W,, and the fictitious force on the bending mechanism. I would be interested to hear the authors&apos; comments regarding this theoretical point, which nevertheless is not mute since its lack of recognition seems to result in erroneous calculations. We must not remain mute to Leutwyler&apos;s suggestion that these equations, although computer oriented, are confusing to the slide rule engineers. Such input information as density in pounds per gallon, pipe diameters in inches, pumping rate in barrels per minute and pipe length in feet is not confusing to most of us. Yet there may be some rugged individuals in field positions who carry tables of conversion constants and have committed to memory such items as coefficients of thermal expansion and Poisson&apos;s ratio; however, even this type of individual would welcome a simplified equation occasionally. M

[Abstmct of remarks by R. II. Sweetser arid suhscqueut discussion at the New York Meeting, February, 1926. The Transactions mill ultimately contain a report of work resulting from these discussions. Need for a standard of ualuration.—There should be an accepted method for evaluating the different kinds of bituminous coals based on their carbon just as that for iron ores is based on iron. Variation in the classes of coals and their desirability fol the different industrial uses is analagous to the case of iron ores. The iron people have developed a standard. In the past coals have not been intelligently distributed because the public has not been informed as to its uses. Many operators have known nothing about the final disposal of the coal shipped from their mines. Sales agents and retailers have had no means of evaluating coals except to make the price as high as the market will stand. Producers and distributors need to know how much more valuable the coals would be if prepared so as to contain less objectionable material. Mr. Swectser cnlletl on the Goal and Coke Committee of the Institnte to organize a study through producers and users to develop a method scientifically and comnereially sound E. A holbrook said that the information exists but the public is unwilling to investigate. He praised Ashley&apos;s1 nomenclature of the different kind of coal which has been accepted by the Coal Mining Institute of America and recommended to the American Enginecring Standards Commitee. G. S. Rice pointed out the wider variety and distribution of consumption of coal compared to Iron ore. C&apos;. M. Young approved Mr. Sweetser&apos;s remarks and hoped lor a research institution, probably endowed, to study utilization of coal after it comes from the ground. Mr. Sweetser cited incidents to prove his former statements. He said that a reduction of 1 per cent. ash in the coal would cut down the cost of pig iron at a blast furnace 30 c. a ton, that the coal men should tell what the iron men would have to pay to get better coal. H. J. Prryn endorsed the need of blast-furnace operators to know the kind of coal from which their- coke is made and the latler&apos;s ash content, as this affects coke consumption. A. C. Fieldncr explained that the difficulty of evaluating coal on the basis of chermical analyses for calorimetric tests is: (1) representativr

Jan 1, 1927

By Nathaniel Arbiter

In attempting to assess the contributions of Antoine Gaudin to the profession which he illuminated for almost a half-century, we will need to examine a very broad canvas. He was active in three significant areas: as a teacher; in research, both through his own endeavors and those of his students; and as a consultant to the mining industry and to the Government. Beyond these specific contributions, there was the major personal influence he had on scores of students, friends, and colleagues in the profession. If a single measure of the man&apos;s contribution is to be found, it will be the extent and direction in which he influenced the practice of his profession. To find this we should examine the state of miner- al processing when he began his activities in the 19201s, the progress which has taken place over the past half-century, and the part his activities played in this advance. However, there is a provocative and broader examination which I have chosen to make instead. This is to examine the past century in mineral processing through the lives of three men who, by common agreement, stand on the heights, both in teaching and in their contributions to industry: Robert H. Richards, Arthur F. Taggart, and the man whose memory we honor this evening, Antoine M. Gaudin. Their careers, by coincidence, cover just a century. This is also AIME&apos;s first century, and the first century of mineral industry education in the United States. In fact, mineral processing itself on any significant scale in the country encompasses only a century and a quarter. BEGINNINGS OF PRACTICE IN THE U.S. Before the 1840’s, U.S. mining, except for coal and iron ore, was on a small scale and was confined to the eastern states, with processing practically nonexistent. The 1840&apos;s saw the beginning of Michigan native copper production, including ore dressing; the 1850’s, iron ore production in Minnesota; and the 1860’s, lead production and processing in Missouri. But the most explosive event was the California gold rush after 1848, which not only brought tens-of-thousands of fortune hunters to the West, but also catalyzed broad mining activities and processing within the following decades. This was not only in California but, after the first fever of the gold rush subsided there,

Jan 1, 1976

By J. N. Ong, J. P. Ratledge, J. H. Boyce

SINCE German operators opened the Tsumeb mine in the early 1900&apos;s, continuous operation has been interrupted only by enforced shutdowns during two world wars and the depression of the 1930&apos;s. Original metallurgical practice was blast furnace smelting. This was applicable only to low zinc ore, leaving large tonnages of high zinc ore to be stockpiled on the surface. A gravity concentrator using tables, buddles, and jigs operated for several years, but differential flotation of the ore did not get beyond the experimental stage. When the property was put up for sale by the South African Custodian of Enemy Property there was an estimated 434,000 tons of ore on surface dumps. The dump material, assaying 4.48 pct Cu, 15.8 pct Pb, and 10.9 pct Zn, had become highly oxidized during a stay of many years on the surface. But these dump ores had to be used in evaluating possible metallurgy because the shaft became flooded after the 1940 shutdown and underground ore was unavailable. Many companies examined Tsumeb but quickly lost enthusiasm because of the formidable metallurgical problems presented by the dump ore. However, on the basis of extensive test work, the present company decided that differential flotation would be successful and purchased the property after competitive bidding. Geology and Mineral Association is Complex The Tsumeb mine lies near the northern boundary of South West Africa at an altitude of 4200 ft. The village of Tsumeb is 335 air miles northeast of Wal-vis Bay, territorial port of entry. The orebody is a hydrothermal replacement deposit associated with an irregular intrusion of aplite cutting folded pre-Cambrian dolomite beds. In plan the deposit is a lens of 250x600 ft maximum dimensions. In section the orebody dips 55" south from the surface to 2000 ft, below which there is a reversal in dip to 75" north. Mineralization is localized in the aplite and in the adjoining brecciated dolomite. In the upper levels the ore is largely confined to a single lens, but below the 1890 level massive sulphide ore forms north and south lenses that partially enclose a pipelike body of medium to low grade disseminated ore, part of which is of too poor a grade to mine. Drilling below the 24th, or bottom level, has disclosed that a high percentage of the mineralization from the 3000 to 3300-ft horizons is comprised of copper and lead oxides. The deep oxidation may be local, since it appears due to circulating waters in a major fault cutting the orebody. Tsumeb ranks as one of the highest grade base metal deposits in the world. It is geologically and mineralogically famous for 41 copper, lead, zinc, vanadium, and germanium ore minerals, but its complex mineral assemblage is not attractive to metallurgists. In addition, there is a gradual change in oxidation intensity from the upper levels to the lowest level now operating, which is the 24th. This is well illustrated by the copper minerals. In the upper levels malachite and azurite are predominant, in the intermediate levels chalcocite, and in the lower levels tennantite. Throughout the mine there are sufficient heavy metal soluble salts to activate zinc, and large amounts of depressants are required even for so-called clean sulphide ores. When the same sulphide ore is exposed to prolonged oxidation aboveground, as was the case with the dump ores, reagent requirements become fantastic. Plant Construction First staff members arrived at Tsumeb in March 1947, and by May essential services had been restored and mine unwatering began. In 2 1/2 months company employees built a temporary jig and sorting plant for treating existing dumps to provide a saleable product during high metal prices. Meanwhile, concentrator design and construction was contracted to a South African firm, with subcon-

Jan 1, 1956

those who are to lie in the torn fields of France. Today we read of Lieut. William Hague, whom we said good-by to hardly more than a month ago-—so clean, ao young, so strong—who, abandoning the professional career in which he had won such commendation and which held for him such promise, leaving his wife and his little boy to whom he was so dear, answered at once the call for men of his training, and is now dead "in the service of his country." There are many friends of that courtly and dignified gentleman James D. Hague who recall, both here and in Stockbridge, the parental pride in the promising lad of such a little time ago—the eager schoolboy at Milton, the rather grave youth at Harvard, his entry into new experiences in the Western mining world, and who, seeing him during his stay at Camp Upton, realized that the old Puritan stock was still sound and true—and now with him the struggle is over and the sacrifice made. Captain William Teasdale Hall Captain Hall, who was admitted to Junior Membership in the Institute in 1915, while still a student of mining at the University of Toronto, was killed in action in France on May 19, 1917. Captain Hall was born in Toronto in 1893, and received his academic training at Harbord College, from 1908 to 1911, when he entered the University of Toronto, School of Practical Science. During the three summer vacations of his university course, he was employed by the O&apos;Brien mine at Gowganda, next by the McIntyre Mining Co., at Porcupine, and finally by the Mines Branch of the Geological Survey, which was conducting magnetic surveys to the north of Port Arthur. When war was first declared, Mr. Hall endeavored to join the artillery as an officer, and for the purpose secured a provisional lieutenancy with a Hamilton battery, but he did not receive an overseas appointment, and on being graduated as a mining engineer in 1915, he was offered a position in Chile, which he accepted. He left Toronto on May 27, 1915, and was engaged in Chile as a mining engineer for nearly a year. In the latter part of April, 1916, he decided to offer himself again for service at the front. He crossed the Andes and sailed for LiverpooI, where he landed on May 13, 1916. On May 27, 1916, Captain Hall was given a commission as a lieutenant in the Royal Flying Corps, 21st Squadron. He went to the front on Sept. 1, 1916, and remained there continuously. His

Jan 1, 1920

By A. Kenneth Schellinger

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

Jan 1, 1952

By R. L. Orr, O. D. Sherby, J. E. Dorn

Creep data for pure metals at temperatures above those at which rapid recovery occurs (above about 0.45 the melting temperature) are correlatable by means of the equations and These correlations were applied successfully to data for aluminum, iron, nickel, copper, zinc, platinum, gold, and lead as well as for simple alloys. For a given metal, AH is a constant about equal to the activation energy for self-diffusion. THE early recognition that creep is stimulated by thermal activation prompted numerous investigators&apos;, &apos; to apply the same laws that are valid for the viscous behavior of liquids to analyses of creep data. To a good first approximation these laws are summarized by the equation were i is the creep rate; T, the absolute temperature; R, the gas constant in cal per degree per mol; T, the applied stress; AH, the activation energy in cal per mol; S&apos;, a constant dependent on the entropy of activation, the frequency of activation, and the contribution of each activation to the strain; and B&apos;, a constant dependent upon the size of the flow unit that is activated. Although Eq. 1 describes the flow of viscous fluids very accurately, its application to the creep of solids has been disappointing. Two reasons for the failure of Eq. 1 for creep are now known: First, the decelerating creep rates during primary creep demand that the internal structures of the metals are changing and that these changes might be reflected by changes in one or more of the three creep parameters S&apos;, AH, and B&apos;. Consequently when the conventional methods of evaluating these parameters are employed by comparing the secondary creep rates at a series of temperatures and at a series of stresses, the true effects of temperature and stress are masked because of simultaneous changes in one or more of the creep parameters. Second, as will be illustrated more fully later, three distinctly different types of investigations have shown that the stress term for high temperature creep enters the analysis as and not as t/T. This rather unexpected result points sharply to a significant fundamental difference between the mechanisms for the viscous behavior of fluids and the high temperature creep of metals. More recent extensive investigations",&apos;4 on the creep of high purity aluminum and several of its dilute a solid solutions have shown that where E is the total creep strain; temperature compensated time = for a constant temperature test; t, is the initial stress in a constant load test or the constant true stress in a constant stress test;" and t is the duration of test. • Eq. 2 is valid for either constant stress or constant load tests; but the total creep curve is difierent (i.e. the function, f, is differentl for each test. The fundamental origin of the validity of Eq. 2 is thought to arise from some equivalence of substructures in constant load creep tests at equal values of 0 or E. Both X-ray and metallographic examination revealed that practically identical lattice distortions and subgrain sizes are obtained for the same creep strain under the same load over wide ranges of test temperature.&apos; Furthermore the room temperature tensile properties following equal creep strains at different temperatures under constant loads were also identical, illustrating that identical substructures were indeed obtained.&apos; " A second type of correlation was obtained by differentiating Eq. 2 with respect to time, giving For the secondary creep rate, denoted by i,, But Eq. 2 reveals that 0, is a function of a, alone because the secondary creep rate in a given constant load test is always reached at a fixed value E,". Therefore where is the function that was introduced a number of years ago by Zener and Hollomon." Eq. 4 is not only valid for creep but will permit correlations between constant load creep and tensile data where e, is the rate of tensile straining and (TC is the engineering ultimate tensile strength.

Jan 1, 1955