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By C. B. Alcock, M. G. Hocking

The kinetics of the growth of sulfate layers on blocks of Cu20 has been studied between 688" and 800°C. At 788c the over-all weight increases followed the parabolic rate law, with k = 216 30 sq mg per cm4 min, using a 1:1 entering gas mixture of SO2:02. At 757 after an initial linear period the parabolic rate law was followed, with k = 57.8 10 sq mg per cm4 min. The gas mixture required a platinum catalyst to produce the maximum SOs pressure. The sulfation rate at 757' and 788c was high until all the CUZO had changed into a core of CuO, when it became very much lower. At 757°C marker experiments showed that the sulfates (CuO. CuS04 and CuSO4) grow outwards from the oxide surface, but CuO. CuS04 mixed with CuO was found beneath the markers. At 688 markers were found at the CuO. CuS04/CuS04 interface. Visual observations at 757 showed a liquid eutectic moving beneath the sulfate surface. causing very rapid sulfation and extruding to solidify as thick 'needles" up to 8 mm long. Marker experiments have shown conclusi.cely that CuO grows on Cu20 in air by the outward migration of copper. ThermODYNAMIC measurements on the sulfate and basic sulfate of copper, reported recently,' are followed here by measurements of the rates of formation of these sulfates on cuprous oxide, in order to provide a background for the understanding of roasting processes. peretti2 and McCabe and Morgan3 have shown that the phase Cu20 lies next to Cu2S when the sulfide is roasted under conditions where sulfates will be formed. Since this would present too complex a system for kinetic study, the present work4 has been based on the kinetics of sulfation of the oxide phase. The results of a study of the kinetics and mechanism of the sulfation of cobaltous oxide have recently been reported.4,5 Results on the sulfation of cuprous oxide have also appeared,6 but are at variance with those to be reported here. This seems to be because the previous workers6 did not obtain constant SO3 pressures from the SO2/O2 sulfating gas mixtures used, as will be discussed later. Wadsworth, Leiter, Porter, and Lewis found that the sulfates produced when SO2/O2 mixtures are passed over Cu20 at red heats are CuS04 and the basic sulfate CuO.CuSO4. When the decomposition of CuS04 was followed' by differential thermal analysis, a stage corresponding to CuO .CuS04 was reached before decomposition into the oxide occurred. APPARATUS The vertical furnace used for quantitative studies was a conventional resistance-heated and propor- tionately controlled furnace with an even zone (1 deg) which was 4 cm long. The gas mixtures of SO2 and 02 were made by mixing measured flows from capillary flowmeters and drying over phosphorous pentoxide before passing them into the Pyrex top-piece of the furnace assembly. A mullite tube of bore 2% cm was used as reaction vessel and at the bottom of this tube was a trap for SO3, which condensed as a colorless liquid. The residual gas was led into a fume cupboard for ventilation to the atmosphere. The furnace used for visual observations of needle growth and other phenomena consisted of a transparent silica reaction tube of bore 3 cm, having an optically flat silica window sealed into its wall. The reaction tube was clamped vertically, inside a mullite tube of bore 4 cm and length 42 cm which was heated by Kanthal windings. The window in the silica reaction tube was arranged opposite a hole 3 cm wide and 2 cm tall which had been cut in the wall of the mullite winding tube 19 cm from its top end. A binocular microscope was used to look through the window, illumination being provided by a focusing microscope-lamp offset sideways and downwards. The oxide block to be sulfated was suspended from the removable Pyrex top-piece to the reaction tube, by means of which it was inserted at the start of the experiment, and through which entered the S02/02 gas mixture. The variation of the temperature inside the reaction tube with horizontal and vertical displacement from the window was investigated, and, while it can be said that the temperature was constant 1 deg, its value at a given position was known only to 12 deg. In both furnaces, the oxide block to be sulfated was suspended from a small silica hook immediately downstream from a platinum thimble used as catalyst, which was held on a long silica rod from a Pyrex spring attached to the removable Pyrex top-piece of the furnace. The spring was only included in the quantitative sulfating furnace; its sensitivity was 1.4 cm per g and it was found to be free from creep in a 16-hr test when carrying the working load. The extensions were followed by a cathetometer which could be read to 0.001 cm, corresponding to i0.7 mg. Extensions of the spring were measured on adding weights between 5 and 500 mg to the working load (thimble + oxide block), and Hooke's law was closely obeyed. SAMPLES Cuprous oxide blocks were prepared by oxidizing Johnson Matthey "Specpure" copper sheet of 1 mm thickness (impurities: iron at 3 ppm, silver at 2 ppm, lead, nickel, sodium, and silicon each at 1 ppm, calcium, chromium, magnesium, and manganese each at less than 1 ppm) for 6 days in air at 1000°C in a re-crystallized alumina boat. It has been reported7 that when Cu20 is prepared by heating copper sheet for 1 day the central plane of the blocks produced consists

Jan 1, 1967

By Lester G. Morrell

While developments in Australia dominated the minerals industry of the South Pacific area, New Caledonia's nickel, manganese ore from New Hebrides, gold from Fiji and New Guinea, and phosphate rock from several small islands were significant in world supplies of those materials. The total value of mineral commodities produced in this area in 1965 has been estimated at about $763 million an increase of nearly 16 percent over the value reported in 1964. Increases were recorded in mineral production value with respect to that of 1964 for all of the countries except Papua-New Guinea where lower gold output resulted in a drop of about $300,000 and in the several phosphate-producing islands that collectively recorded a value decline of around $1.3 million. Exploration and development activities continued at an intensified level, not only in Australia and New Zealand but also in the British Solomons, Bougainville, and Fiji. Substantial additions to world supplies of iron ore and bauxite are assured and recent discoveries of natural gas, manganese ore, and nickel combine to give Australia a brilliant mineral outlook. Important discoveries of copper on Bougainville Island and on Vanua Levu, the north island of the Fiji group, and a gold mine on Misma Island were being developed during the year, with plans for early production underway. In New Zealand progress has been made on the New Zealand Steel Company project, and preliminary appraisal of a new titano-magnetite beach sand resource on the South Island has aroused considerable industrial interest. Extensive geophysical investigations were carried out in the British Solomon Islands and on Fiji's goldfields. The expansion program that will double output of products by New Caledonia's Société Le Nickel continued through 1965, and several foreign private companies have expressed a desire to initiate additional industries based on nickel prospects in New Caledonia.

Jan 1, 1967

By Stanley A. Feitler

This Bureau of Mines report deals principally with the resources and economic aspects of feldspar in the United States east of the Mississippi River. Although in a strict sense, all phases of the feldspar industry affect its economic structure, emphasis in this study is on supply, demand, and marketing. Although feldspar was originally mined for use in the manufacture of pottery and other ceramics, the glass industry, which began to use feldspar in the mid-1920's, now consumes more than half of the annual output. Most mining is open cut, and the methods used are similar to those used in mining crushed stone. Excess plant capacity has been chronic, and production is usually about 50 percent of capacity fur the industry as a whole. Since 1947, feldspar consumption has grown more slowly than the average for all U.S. industry. This has fostered intense competition, especially for the glass market. Prices have not kept pace with inflation, and profits are small. The trend of consumption through 1.970 for glass feldspar is expected to be upward; less rapid growth in consumption of ceramic feldspar is anticipated.

Jan 1, 1967

By Edward A. Vitunac

The emerging importance of pneumatic conveying systems for bulk materials is becoming recognized by more persons responsible for materials management as consultants, at the corporate level and at the plant level. They have learned that the economic advantages of a pneumatic system are frequently decisive when compared to alternate methods. Included in these advantages are relative simplicity, ease of installation, flexibility, ease of maintenance, cleanliness, safety and ease of automation to the degree desired. In general, installed costs favor a pneumatic system when compared to competing mechanical systems if the transporting distances are long or to and from many points. In addition, supplemental use such as cooling, heating, or drying may supply the incremental value required to justify its selection. (1). The main disadvantages of a pneumatic system is the greater horsepower required per unit weight of material conveyed and material limits in abrasiveness and density. In addition, there is a tendency to increase material breakage at changes of direction and at any obstruction such as the imperfect butting of one, piece of pipe to another in the conveying line. Classification of the material at the discharge may also cause problems in dusting and segregation. Materials weighing less than 4 pounds per cubic foot tend to cause feeding and collecting problems although they can be conveyed easily. Material between 4 and 20 pounds per cubic foot can be handled with less problems but flow rate is hard to predict. The 20 to 60 pounds per cubic foot range offers best results; whereas, over 60 pounds per cubic foot, materials tend to drop out of the air stream and settle in the pipe line unless careful provisions are made to prevent it. (2).

Jan 1, 1967

By G. W. Phelps

The field of industrial minerals is concerned with both sieve size and distribution of sub-sieve particles. A great deal of work has been reported on the techniques designed to provide information of this work. The term sub-sieve is here considered to include particular material that will pass a 325-mesh testing sieve. Plant men require rapid, precise and simple testing techniques that are, if possible, inexpensive with respect to equipment and manpower. A number of particle-size procedures have been developed, based on the Stokes equation for streamline movement of a particle of diam D, moving at velocity V through a liquid of viscosity n. 1 Particles are considered to be rigid, smooth spheres, completely dispersed at low concentration and moving at low velocity through the suspending medium with no slippage between particle and liquid. In particle size determinations the particle moves either from natural gravitational forces or those provided by centrifugal means. The diagram of Fig. 1 shows a spherical particle of density S and diam D moving downward at velocity L/T (or V) through a liquid of density So and viscosity n. The forces of gravity G (natural) or Gc (centrifugal) cause the particle to move through the liquid, thereby creating a viscous drag F or Fc. Within the streamline flow

Jan 1, 1967

By M. J. Lempel

A theoretical study of the heat-transfer characteristics of a dilute gas-solids mixture in an externally heated tube is reported. Detailed equations are developed describing the system, and a numerical method is presented to solve the equations using a digital computer. The methods are applied to a system containing fine coal particles entrained in hydrogen, flowing through a hot tube. Heat-transfer coefficients and several other physical constants are evaluated in detail.

Jan 1, 1967

By Edmond F. Lawrence

The Calico area lies within the Walker Lane fault zone, six miles north of Schurz, Nevada. The mineralized area is overlain by a thick section of Tertiary tuffs and ash-flows, that have been intruded by a series of andesite plug, dikes, and sills. The pre-Tertiary rocks outcrops only in two areas at one to two miles distance from the drilling areas. Underlying the volcanics are sediments ranging from siltstones, sandstone, calcareous shales, to carbonates of the Luning sequence. These have been intruded by one or more phaneritic intrusives ranging in composition from quartz diorite to quartz monzonite, with the development of a skarn zone on the south flank that contains extensive mineralization consisting of magnetite, pyrrhotite, pyrite, and chalcopytite, with traces of sphalerite, galena, and molybdenite. The magnetite, pyrrhotite, and part of the pyrite appears to be contemporaneous with the skarn, while, part of the chalcopyrite, galena, sphalerite, molybdenite, quartz, and calcite, occurs as minute veinlets cutting the other minerals. This later mineralization may be associated with a late stage of the same sequence, or possibly associated with another intrusive to the southwest. Geophysical work has consisted of aerial magnetics, ground magnetics, gravity, seismic, and induced polarization surveys. Preliminary induced polarization surveys indicated anomalies at depth, both over the magnetic anomaly and to the northwest. Subsequent IP work confirmed this earlier anomaly, and drilling disclosed extensive mineralization at depths of 400 feet on the northwest end and over 1,000 feet to the southeast.

Jan 1, 1967

"Many advances in glass technology and processing are being made and the possibilities for glass as a material in the future appear unlimited. Float glass, glass-ceramics, high-strength sheet and container glass, glass-reinforced plastics, glass for electronic equipment, aerospace glass, glass fibres, glass vehicles, glasses with selective-reflective coatings and glare-reducing glasses, to name a few, provide areas of significance at present and for the future. There appear to be great opportunities, in certain localities of Canada, to develop new sources of raw materials for an expanding Canadian glass industry.New developments in the structural clay products industry have centered around facing brick as a structural load-bearing material, prefabricated brick panels, large-sized units, isostatic pressing of sewer pipe and auto-matic settmg of brick. Fast-firing techniques, using prefired or calcined raw materials, and the development of high-strength products will result in the use of a wider range of raw materials in the whiteware and structural clay products industries.Porcelain enamel, a material used for many years in domestic appliances and for sanitary ware, now is used extensively in architecture, agriculture, water tanks, highway signs and reflectors, and in products where resistance to corrosion-plus-temperature is important. Exotic composites of ceramics and metals, and specialized ceramic coatings applied on metals by various techniques such as flame spray, plasma jet, or vapour and chemical deposition have proved useful in materials for aircraft power plants, rockets, missiles and nuclear applications."

Jan 1, 1967

By O. M. McRae

The Courtland-Gleeson area is in Cochise County about 15 miles east of Tombstone in southeastern Arizona. Rocks exposed in the area range in age from Pre-cambrian to Quaternary. The Precambrian is repre-sented by the Pinal schist. Paleozoic rocks include the Cambrian Bolsa quartzite and Abrigo limestone, Mississippian Escabrosa limestone, and the Permo-Carboniferous Naco Group limestones. Rocks believed to be of Triassic and/or Jurassic age include the Copper Belle monzonite porphyry, Turquoise granite, and Gleeson quartz monzonite. The Cretaceous is represented by andesitic volcanics and various sedimentary rocks. Tertiary rocks include the intrusive and extrusive Sugarloaf quartz latite porphyry and numerous dikes of various rock types. Quaternary conglomerates cover the northern and eastern part of the area. The geologic structure is extremely complex. All rocks as old as early Tertiary have been involved in either tilting, normal faulting, high angle reverse faulting, imbricate thrusting or folding and overfold-ing. Major deformation was initiated during the first half of the Tertiary. Northeast-southwest compres-sional forces caused thrust plates containing lower Paleozoic rocks to override Cretaceous rocks. Subsequently, two large slide blocks of lower Paleozoic rocks, acting under the influence of gravity, moved eastward. The imbricate structure and the gravity slide blocks were then broken by late Tertiary normal faults. INTRODUCTION The Courtland-Gleeson area, or Turquoise Mining District, has long been recognized as an area of extreme structural complexity. Gilluly 2 referred to the entire district as a "gigantic thrust breccia". In 1962, Bear Creek Mining Company completed a two year program of detailed geologic mapping supported by exploration drilling. The purpose of this paper is to present some of the results of this investigation and to provide a structural interpretation based on these results. The geologic map that accompanies this report is generalized and shows only the major and significant features. The area was initially mapped on aerial photographs on a scale of 1 in. equals approximately 500 ft. These data were transferred to a planimetric base using a vertical sketch master. LOCATION The Courtland-Gleeson area is in central Cochise County, about fifteen miles east of Tombstone, and about twenty-two miles northeast of Bisbee in southeastern Arizona (Fig. 1). The area is readily accessible over graded gravel roads from both Tombstone and Elfrida. GENERAL GEOLOGY Rocks exposed in the area range in age from Pre-cambrian to Quaternary. wilson3 and Gilluly2 have published very detailed descriptions of the principal rock units exposed in the area. Only a summary description is provided in Table I. A great number of previously unmapped narrow Tertiary dikes and small irregular masses of hornblende andesite porphyry, lamprophyre, and aplite intrude the Gleeson quartz monzonite in the western part of the map area. The scale of the map prohibits showing them. The aplite dikes are related to, and bear the same structural relationships as, the Sugarloaf quartz latite dikes found in this area. For that reason, and because both the hornblende andesite porphyry and the lamprophyre are post-mineral and post-thrusting, their omission from the map is not considered significant. Because so many of the contacts in the district are fault contacts, because bedding faults appear to be prevalent but are difficult to recognize and map, and because igneous intrusions are so common throughout the sedimentary section, it is virtually impossible to measure an exact total thickness of any of the sedimentary rock units. Nevertheless, neither the field mapping program nor the diamond drilling provided any basis for suspecting that the thicknesses of the sedimentary units are significantly greater or less than what might be inferred from surrounding districts.

Jan 1, 1967

By E. A. Zawadzki

The problem of pollution of water by mine drainage is at least as old as the mining industry itself. However, research on the formation, composition, treatment, and abatement of mine water is a relatively recent historical event. At Bituminous Coal Research, Inc., acid mine drainage control has been an important area of work since 1944, at which time BCR began sponsorship of research at West Virginia University. The work at West Virginia University involved a detailed study of the acid mine drainage problem and led to the identification of iron oxidizing bacteria as important factors in the formation of acid mine water. The results of this research were summarized in 1954 by Temple and Koehler (1) who concluded that "no practical solution for the problem" of controlling acid mine drainage is yet known.?

Jan 1, 1967

By T. Kessler

The purpose of this investigation was to evaluate the application of a spark-source mass spectrograph equipped with a spinning-electrode system for the study of various high-molecular-weight materials derived from coal. Conclusions from the investigation of anthracene, phenanthrene, chrysene, coronene, truxene, a coal-tar pitch (800 to 850 C softening point), and anthracene-chrysene synthetic mixtures follow: 1. Simplified mass spectra of anthracene, phenanthrene, chrysene, coronene, and truxene, from which the molecular weights were easily determined, were obtained by the spinning-electrode system. 2. Eight structural types having molecular weights from 178 to 252 corresponding to compounds previously observed in an electron impact mass spectrum of a coal-tar pitch sample were affirmed by this technique. 3. Mass spectra obtained from synthetic mixtures of anthracene and chrysene demonstrated that the technique is applicable for semiquantitative analysis.

Jan 1, 1967

By R. B. Tippin

The heavy liquid separation (HLS) process was investigated by the Bureau of Mines to develop a means of concentrating minerals from natural ores, Various spodumene ores were tested in a 0.4-inch diameter cyclone using pure tetrabromoethane (TBE) as the heavy liquid. Studies were initiated to examine the influence of (1) pulp density (2) feed grade, (3) cyclone pressure, (4) cyclone apex opening size) (5) cyclone vortex finder opening sand (6) mineral particle size on the separation efficiency. Each of these factors was found to affect the heavy liquid separation in some degree; the mineral particle size exhibited the greatest effect and the ore feed grade the least. Conditions necessary to yield an 85 percent spodumene concentrate with an 85 percent recovery were determined to be: 70 psig pressure, 10 percent solids, 0.08-inch apex opening, 0.11-inch vortex finder opening and a minimum amount of minus 200-mesh fines in the feed. Operation of multiple cyclones in series resulted in spodumene concentrates assaying over 90 percent and indicated mineral recoveries exceed-in 90 percent.

Jan 1, 1967

This report presents depth and producing rate statistics pertaining to oil reservoirs (or fields) in each of the 14 States that produced more than 20 million bbl of oil during 1965. The combined oil production was about 2.6 billion bbl, or 96 pct of the U.S. total. Data are presented for each of the 14 States, each Texas Railroad Commission district, and four geographical areas of Louisiana. About 8 pct of the total oil produced in the 14 States was from depths of lees than 2,000 ft, 24 pct from 2,000 to 4,000 ft, 22 pct from 4,000 to 6,000 ft, 16 pct from 6,000 to 8,000 ft, and 30 pct from 8,000 ft and deeper. The average production per well in the 14 States ranged from 4.4 bopd for wells less than 2,000 ft deep to 57.6 bopd for wells 8,000 it and deeper. Data indicate that 9.5 pct of the 460,968 wells produced more than 1.2 billion bbl or 46.6 pct of the total oil. Oil production from reservoirs (or fields) not undergoing stimulative recovery operations, such as steam, air, gas, or water injection, wee about 1.1 billion bbl or 42.1 pct of the total.

Jan 1, 1967

By R. F. Shurtz

The problem of estimating the precision of systematic samples from a mineral deposit is attacked by interpolating the quality, or other attribute measured, by using Fourier approximation. Such approximation using trigonometric functions yields a particularly simple expression for the variance of the mean value of the attribute sampled. The increasing volume of publication in which the science of statistics has been applied to the problem of predicting the quality of an ore deposit from sets of samples taken from it might lead one to believe that engineering judgment can be replaced by statistics. There is, in fact, an implicit application of the principle of indifference or of "no advance knowledge" which has been discredited in modern statistical theory and practice. These pages will show that it is not always advantageous, efficient, or safe to apply this principle. This problem will be dealt with by using series of orthonormal functions to describe the distribution of the quality of ore in space as contrasted with the more commonly used distribution of quality as a frequency function. Mining engineers are rarely well acquainted with the use of such series or of the functions comprising them. These uses are commonplace in the fields of communication and information theory and it is not surprising that applications taken from these fields should be found appropriate for the analysis of the information contained in a set of samples from an ore deposit. It is hoped that presentation of the following basic, but incomplete, results will generate wider interest in this method and a fuller development of it as well as of the necessary computational techniques. FUNDAMENTAL PREMISES Random variables in the strictest sense are not very common in mine sampling. The sets of samples are almost always taken systematically and are, hence, not subject to all the laws governing random events. Therefore, unless there is indeed random experimental error in the determinations of quality, the treatment of systematic samples of n members as though they were random samples of n members often leads to calculation of confidence limits for the mean quality which are larger than they should be with the result that unnecessary additional sampling is done. The reason for this will emerge in the following discussion leading to Eq. 24 and its generalization. In order to inquire into such questions on a rigorous basis and at the same time avoid arithmetic complications that would obscure the concepts involved, a one dimensional distribution of quality will be assumed. The quality, Q, in suitable units is expressed as a function of the distance, x, along some straight traverse of the deposit. Such a function

Jan 1, 1967

By A. K. Snelgrove

At a time when water resource planning is proceeding on a continental scale, such as the proposed $100 billion North American Water and Power Alliance, which would redistribute water among three nations, including seven provinces of Canada, 35 of the United States, and three States of Mexico, the selection of a single river basin for study may seem to require an apologia. None is offered because of ( 1) the magnitude of the Indus , itself a part of the great Indo-Gangetic Plain drainage system, with Himalayan sources, upon which the thickly populated northern sub-continent of Indo-Pakistan depends for agriculture and hydroelectic power; (2) the extraordinary problems created by dismemberment of the world?s largest irrigation system through legal beheading of the Eastern Waters under the Indus Waters Treaty of 1960; and (3) the herculean effort to contain the twin encroachments of waterlogging and salinization in a basin which faces a shortage of fresh water. The British irrigation system of barrages and canals on the Indus was a venture admirable in conception. Unfortunately, it is now a legacy burdened with unwanted consequences, due to interference with the hydrological regimen, particularly the rise of water table occasioned by leakage.

Jan 1, 1967

By Y. Takahashi, I. Iwasaki, S. Tanabe

Supported by the vigorous capital investment of the heavy and chemical industries and by the ever-increasing demand for durable consumer goods in the past decade, Japan has now emerged as the world's third largest steel producer, surpassed only by the United States and the Soviet Union. In 1968, the crude steel production is expected to exceed 50 million tons; the per capita steel consumption at that time will reach 886 lb, approaching the level of Western Europe. Characteristics of the Japanese steel industry is the high dependence of raw materials on overseas sources. Before World War II the industry relied on North China and Manchuria for coking coal, and on middle China, Hainan Island, the Philippines and the Malayan Peninsula for iron ores. After the war, the major sources of iron ores were shifted to the Philippines and the Malayan Peninsula, supplemented by shipments from the United States, Canada, India and Goa. The United States, in addition, became the primary source of coking coal.

Jan 1, 1967

By James H. Russell

The Bureau of Mines used a statistical approach to evaluate the effects of temperature, current density, and composition of the electrolyte on the purity of boron prepared by electrolysis of a fused mixture of boric oxide in potassium fluoborate. The quadratic equation which best fits the data was calculated for a temperature of 650° to 850° C, a cathode current density of 40 to 1,150 amp/ft2,and a boric oxide content of 0.3 to 7.1 molal. The best products, better than 95 percent boron, were obtained when the current density was less than 2 amp/ft2 and the boric oxide content was less than 2 molal.

Jan 1, 1967

By C. A. Komar

The Bureau of Mines conducted experiments on one synthetic and three natural sandstone samples to investigate the effects of acoustic energy on the flow of brine in porous media. Ultrasonic energy at a frequency of 20 kc per second and an intensity of 55 watts per cm2 was irradiated in the direction of the fluid flow and in the opposite direction for distances of 1/2 and 2 inches between the vibrating device and the sample face and under conditions of suppressed and nonsuppressed cavitation. Forty tests were conducted: 32 with a pressure differential of 0.64 psi across the samples, 2 with 5 psi, and 6 with 15 psi. Acoustic waves altered the rate of flow of the brine through the samples, but this effect was observed only at low differential pressures and from a practical point of view was insignificant. As a result of irradiation, however, the samples exhibited reduced permeability. This reduction was probably caused by the shifting of solid particles dislodged by the acoustic waves.

Jan 1, 1967

Jan 1, 1967

By M. J. Mullikin, J. B. Conway

Equations capable of representing combined first -and second-stage creep behavior include the Andrade, Cottrell-Aytekin, Garofalo, and de Lacombe equations along with a third-degree polynomial in t1/3. Employing some recent high- temperature creep data for arc-cast tungsten the effectiveness of these expressions was evaluated. It was found that, in this instance, the most accurate representations were afforded by the third-degree polynomial in t1/3 and the de Lacombe equation. Also noted was the fact that the Andrade equation gave results just slightly inferior to those obtained with the third-degree polynomial, definitely better than those due to the Cottrell-Aytekin equation, and slightly superior to those furnished by the Garofalo equation. EXPRESSIONS designed to describe combined first -and second-stage creep behavior must possess certain specific characteristics. At time zero the equation must reduce to a strain value corresponding to the instantaneous deformation on loading. Then in the early moments following load application transient-creep behavior must be described to reflect a creep rate which constantly decreases with time. And finally at larger time values linear (or at least nearly linear) strain-time behavior must be accounted for to yield the steady state or minimum creep rate. Some equations, such as the one based on the parabolic creep law, yield fairly satisfactory results in transient analyses but are not effective at all when combined first- and second-stage data are to be analyzed. Other equations give equally accurate results in both instances although in general the complexity of the equation is slightly increased. For example the Andrade1 equation: has found fairly general application in expressing first-stage creep behavior. Furthermore the contribution of the exponential term becomes more and more prominent as the time increases and causes this equation to exhibit a point of inflection at large values of time. With a proper selection of equation constants the curve can be made fairly flat in the region of the inflection point indicating a desirable equation form for combined first- and second-stage creep analysis. Another equation form with the proper characteristic is that of Cottrell and Aytekin:2 e =a +bt1/3 +ct [2] Obviously as time increases the first derivative of this expression approaches a constant value to suggest application to combined first- and second-stage creep analysis. Similarly a third-degree polynomial in t1/3: e -a + bt1/3 + ct2/3 +dt [3] has the same characteristics. Expressions of this type have been shown3 to be very effective in the analysis of transient-creep behavior and the fact that the first derivative has the same characteristic as Eq. [2] suggests use in the combined analysis.

Jan 1, 1967