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By F. H. Wilson, E. W. Palmer

The solid solubility of iron in 2 to 10 pct cupro-nickels increases with temperature and nickel content. Property changes accompanying various heat treatments indicate typical precipitation hardening behavior. Iron content also affects softening temperature and sub-scale formation. These factors, as well as impingement corrosion resistance, influence the optimum iron content of commercial alloys. FOR many years Cu-Ni alloys have been used extensively in the form of tubes, pipes, and plates for the construction of salt-water lines and surface condensers on shipboard and in tidewater power stations. The 30 pct Ni alloy has been considered more resistant to rapidly flowing sea water than alloys of lower nickel content, and has been standard on ships of the U. S. Navy. Some ten years ago, the still better corrosion resistance obtained by modifying the 30 pct Ni alloy with approximately 0.5 pct Fe was recognized, and the iron-bearing alloy rapidly superseded the plain alloy as the standard material for severe service. In 1945, Tracy and Hungerford1 published a study of the effect of iron on the corrosion of various cupro-nickels in sea-salt solutions, and their data indicated that the 10 pct Ni alloy containing about 0.75 pct Fe was equivalent to the 30 pct Ni alloy containing 0.5 pct Fe. This was confirmed by LaQue in discussion of the above paper, and by results in an experimental condenser set up at the Kure Beach marine test station of The International Nickel Co., reported by Freeman and Tracy.' The 10 pct Ni iron-bearing alloy is now being very widely used in applications where the 30 pct Ni iron-bearing alloy was formerly considered standard. While this "substitution" has undoubtedly been stimulated by the present extreme shortage of nickel, it must be emphasized that it involves no loss of service performance, and would have occurred anyway in the course of time, for economic reasons. In view of the increasing use of the 10 pct alloy, it seems desirable to make generally available the results of several investigations of Cu-Ni-Fe alloys carried out in the Metallurgical Research Laboratory of The American Brass Co. in recent years. The present paper, deals with the constitution of these alloys in the copper-rich corner of the system, and with the variations in hardness and tensile properties resulting from the heat treatment of alloys containing various amounts of iron. Most of this work is concerned with alloys containing 10 pct Ni. With over about 0.75 pct fe, the 10 pct Ni alloy is suscep- Alloys Several series of cupro-nickel alloys containing iron were used in these investigations. Most of them were prepared in the laboratory, but two samples of commercially fabricated alloys were included. Series A—Nominally 2 and 5 pct Ni, each with 0 to 1.5 pct Fe. Series B—Nominally 10 pct Ni with 0.1 to 0.4 pct Fe. Series C—Nominally 1.0 pct Ni with 0 to 2 pct Fe. Series D—Nominally 10 pct Ni with 3 to 5 pct Fe. Series E—Nominally 10 pct Ni with 1 and 1.5 pct Fe.

Jan 1, 1953

By K. K. Clark, W. H. Somerton

The feasibility of reducing pressures needed to fracture formations by heating the borehole intensively has been investigated on a laboratory scale. Reductions in fracture pressures of heated Bandera, Berea and Boise sandstone cores were observed at various confining pressures, simulating reservoir stress conditions to a depth of 5,000 ft. Both permeable and impermeable borehole boundary conditions were tested. Three heating conditions were used in the tests. One group of samples was heated in a furnace to a temperature of 600C, cooled to room temperature., and then tested for fracture pressures. Two other groups of samples were heated with a borehole heater to maximum borehole wall temperatures of 625 and 792C, then cooled and tested. In all cases, heated samples showed substantial reductions in fracture pressures compared to unheated samples. The higher temperature borehole heated samples showed the greatest reduction, amounting to 70 per cent in the extreme case. In actual application to wells, it was concluded that fracture pressures may be reduced by 20 to 50 per cent by intensive borehole heating before fracturing. INTRODUCTION Hydraulic fracturing of oil and gas wells is an accepted and effective technique for increasing well productivity in many areas, but is notoriously unsuccessful in other areas. The technique becomes less interesting for production stimulation purposes when excessive fracture pressures are necessary. Formations which do fracture but require high pressures, probably form horizontal fractures. There is good evidence to indicate that some formations do not fracture at all, but yield plastically under high pressure. Thus, any technique which will make formations easier to fracture or will reduce fracture pressures is potentially interesting to petroleum producers. Horizontal fractures generally occur in planes of weakness, such as bedding planes, and at pressures equaling or exceeding the effective overburden stress. In the unusual case where planes of weakness do not exist, a slightly higher pressure must be applied to overcome the tensile strength of the rock. In general, high fluid-loss fracturing fluids are conducive to the formation of horizontal fractures.1 Vertical fractures, when they do occur, are initiated at pressures generally lower than overburden pressure and are favored by low fluid-loss fracturing fluids or impermeable boreholes. The pressure necessary to create a vertical fracture in an impermeable, elastic medium can be predicted from the so-called "thick-walled cylinder" equation: Pf = 2 or+ st.............(1) where pf = fracture pressure or = radial stress st = tensile strength of medium. This equation indicates that to fracture it is necessary to overcome a tangential compressive stress, induced by and equal to two times the radial confining stress, plus the tensile strength of the medium. If the above equation held strictly true for rocks, very little could be done to reduce fracture pressure. The tensile strength of the rock might be reduced somewhat, but any change in st would be small compared to the magnitude of the tangential stress at reasonable subsurface depths. Laboratory tests have shown that actual fracture pressures exceed values predicted from Eq. 1 by factors of 1.4 to 28.6.1,2 Eq. 1 thus does not properly describe the

Jan 1, 1966

By J. A. Thompson, M. A. Mayers

IN recent years, the problem of damage to coke-oven walls by expanding coal charges undergoing carbonization has engaged great attention on the part of research workers in this field, and has led to the development of many devices for estimating these pressures.1-14 Only in Russell's method11 and in the Koppers ovens7 are conditions quite similar to those in commercial ovens. Tests even in these ovens are empirical because no information has been published to permit an evaluation of "scale effects." Owing to the relatively large wall area in these test ovens, the average wall pressure determined may be lower than that existing in localized areas. This factor may be compensated for in part by the testing of coal charged into the test oven at a bulk density that is as high as the highest that is believed to exist in commercial ovens. Both of these lacks might be filled by the development of an adequate gauge for the direct measurement of wall pressure exerted by the charge in commercial coke ovens in normal operation. Previous attempts to elaborate such instruments7,15 have resulted in units which, because they had to be water-cooled, probably produced changes in the conditions of carbonization, and which had to be removed from the oven before carbonization was complete, to avoid their destruction. Late in 1941 the Coal Research Laboratory undertook to develop such a gauge, in which gas pressure was balanced against the charge pressure and which thus would not require water cooling, on a suggestion made in 1937 by one of the present authors and William B. Warren, a former member of the Laboratory staff. The gauge heads themselves were to be simple and cheap enough so that they might be discarded after each run if seriously damaged. This would permit them to be left in place throughout the carbonizing period, when they could be pushed out with the coke. The basis of the design, of which the latest exemplification is shown in Fig. I, was that as the internal gas pressure within a flexible metal envelope was increased, the flexible wall would move away from a stop when the gas pressure just overbalanced the charge pressure. If the stop were an insulated electrical contact, the point of balance could be indicated by the breaking of an electric circuit. It was anticipated that, while the instrument must operate at high temperature, the presence of a strongly reducing atmosphere throughout the carbonizing period would so reduce-the danger of scaling that mild steel could be used for the gauge. This expectation has been justified. Danger of attack on silica oven walls by the steel gauge body can be eliminated by cementing asbestos paper or an alundum or silica plate to the back of the gauge body. The gauge head itself has a relatively heavy mild-steel body, A, into which standard ¼ in. pipe B is screwed to conduct gas and electrical leads. The body is closed by a single bellows C. consisting of two annuli of 0.011-in. (0.28-mm.) cold-rolled shim-steel spot-welded together at their outside edges. The lower one is

Jan 1, 1944

By J. A. Thompson, M. A. Mayers

In recent years, the problem of damage to coke-oven walls by expanding coal charges undergoing carbonization has engaged great attention on the part of research workers in this field, and has led to the development of many devices for estimating these pressures.l-14 Only in Russell's method" and in the Koppers ovens7 are conditions quite similar to those in commercial ovens. Tests even in these ovens are empirical because no information has been published to permit an evaluation of "scale effects." Owing to the relatively large wall area in these test ovens, the average wall pressure determined may be lower than that existing in localized areas. This factor may be compensated for in part by the testing of coal charged into the test oven at a bulk density that is as high as the highest that is believed to exist in commercial ovens. Both of these lacks might be filled by the development of an adequate gauge for the direct measurement of wall pressure exerted by the charge in commercial coke ovens in normal operation. Previous attempts to elaborate such instruments7,15 have resulted in units which, because they had to be water-cooled, probably produced changes in the conditions of carbonization, and which had to be removed from the oven before carbonization was complete, to avoid their destruction. Late in 1941 the Coal Research Laboratory undertook to develop such a gauge, in which gas pressure was balanced against the charge pressure and which thus would not require water cooling, on a suggestion made in 1937 by one of the present authors and William B. Warren, a former member of the Laboratory staff. The gauge heads themselves were to be simple and cheap enough so that they might be discarded after each run if seriously damaged. This would permit them to be left in place throughout the carbonizing period, when they could be pushed out with the coke. The basis of the design, of which the latest exemplification is shown in Fig. I, was that as the internal gas pressure within a flexible metal envelope was increased, the flexible wall would move away from a stop when the gas pressure just overbalanced the charge pressure. If the stop were an insulated electrical contact, the point of balance could be indicated by the breaking of an electric circuit. It was anticipated that, while the instrument must operate at high temperature, the presence of a strongly reducing atmosphere throughout the carbonizing period would so reduce the danger of scaling that mild steel could be used for the gauge. This expectation has been justified. Danger of attack on silica oven walls by the steel gauge body can be eliminated by cementing asbestos paper or an alundum or silica plate to the back of the gauge body. The gauge head itself has a relatively heavy mild-steel body, A, into which standard ¼-in. pipe B is screwed to conduct gas and electrical leads. The body is closed by a single bellows C, consisting of two annuli of 0.011-in. (o.a8-mm.) cold-rolled shim-steel spot-welded together at their outside edges. The lower one is

Jan 1, 1944

By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy's law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By K. A. Johnson, F. H. Ellinger, C. C. Land

The Pu-In phase diagram has been determined by thevmal, filtvation, micrographic, and X-ray diffraction methods. This alloy system is characterized by 1) limited solubility of indium (-2 at. pet) in 6 and e plutonium, 2) one eutectic, and 3) fizte intermediate phases. Of the latter, PuIn and PuIn3 melt con-gruently, and Pu31n, Pu31n5, and the high-temperatuve 7 solid solution are formed peritectically. The n phase decomposes eutectoidally into Pu3In and PuIn at 865°C. Although the 6 phase can readily be retained to room temperature, it is not thermo-dynamically stable below 300°C. The Pu-In system has been investigated at Los Alamos as part of a study of the alloys of plutonium with the group 111-B elements. Constitutional studies of the Pu-A1 and Pu-Ga systems have been reported earlier.'9' To date, published information on the constitution of Pu-In alloys covers only the identification of the intermediate phases Pu3In and PuIn3.3,4 EXPERIMENTAL The alloys were prepared from five different lots of plutonium and three different lots of indium. The principal impurities in the plutonium differed from lot to lot within the following limits (in ppm): iron, 30 to 80; nickel, 30 to 60; aluminum, 15 to 30; silicon, 20 to 145: thorium, 50 to 300; carbon, 75 to 335; and oxygen, 20 to 135. Spectroanalysis of the indium showed that two of the lots were 99.9 wt pct pure, and the third was 99.98 wt pct pure. The alloys, in the form of about 5-g buttons, were prepared by arc melting in conventional equipment. The components for each alloy were weighed to the nearest 0.1 mg. In most instances the weight losses during melting were negligible; therefore confirmatory chemical analyses were usually not made. A few results are given in Table I. Density measurements of the arc-cast buttons were made by the liquid displacement of bromoben-zene. Heat treating was done in muffle furnaces controlled to +2°C. The alloy buttons were wrapped in tantalum foil before being enclosed in evacuated clear silica capsules. As a precaution against breakage, each capsule was in turn placed in a silica tube closed with a refractory wool plug prior to being charged into the furnace. For a moderately fast quench of the alloys, the outer protection tubes containing the capsules were plunged into cold water. Differential thermal analyses (DTA) in racuo were performed at heating and cooling rates of about 1.5°C per min. Tantalum crucibles having inverted thermocouple wells were used for most of the analyses. It was found micrographically, however, that the liquid alloys containing more than about 35 at. pct In reacted with the tantalum, resulting in contamination of the surface of the alloy. A search for a more satisfactory crucible material was not successful: tungsten and yttria behaved comparably to tantalum; thoria, vitrified magnesia, and vitrified alumina severely contaminated the alloys. So as to minimize the contamination by the crucible mater-

Jan 1, 1965

By R. W. Heckel

A method is described whereby the relationship of both the "at-pressure" powder compact density and the "zero-pressure" compact density to the applied pressure may be obtained from continuous measurements of punch movement during a single compaction operation. The rate of density increase with applied pressure for the metal powders is found to be proportional to the volume fraction of pores for pressures exceeding a lower limit which varies from 15,000 to 30,000 psi, depending on the powder. 1 HE compaction of powdered materials is carried out primarily to increase the density of the material. If the ultimate goal of the over-all process is the attainment of minimum porosity, compaction is responsible for most of the densification. For example, loose powdered metals have porosities of about 65 to 75 pct. Axial loading in a die or hydrostatic pressure may effectively reduce the porosity of most powders to 20 pct or lower with pressures of 50,000 psi and greater. The relationship between the density of a powder compact and the pressure needed to achieve that density is most commonly obtained by pressing several compacts, each at a different pressure. Measurement of the densities of the individual compacts when they are removed from the die then provides the density-pressure relationship. However, this method suffers from several disadvantages. Because a large number of compacts and pressing operations are required, it is inherently slow. Furthermore, since density measurements are made after the specimens are removed from the die, data obtained refer only to pressures greater than those necessary to form a coherent compact. The third disadvantage is the inability of this method to provide information about the compact density at the applied pressure in the die. Because the determination of density-pressure relationships has been a slow, tedious process, investigators have sought to express the compaction behavior of powders by other means. The general terms "comparability" and L'compressibility" have been used to rank powders qualitatively according to their compaction characteristics. To restore a quantitative nature to the subject and to prevent confusion, Schwarzkopf1 has proposed that compac-tibility be defined as the minimum pressure needed to produce a given green strength, while compressibility should be used to indicate the extent to which the density of a powder is increased by a given pressure. Probably the most widely used of the compaction parameters is the "compression ratio,'' which is generally defined as the ratio of the compact density obtained by pressing at a given pressure to the apparent density of the loose powder.2 However, the description of the compaction behavior of a powder by these parameters provides only limited information about the process because of their applicability to just one specific condition such as a given green strength or a given pressure. The method of obtaining density-pressure relationships which will be described in the present paper was designed to eliminate the shortcomings of the previous techniques while maintaining equivalent accuracy and precision. EXPERIMENTAL TECHNIQUES The general principle employed makes use of the fact that the linear movement of the punch during a

Jan 1, 1962

By F. E. Rizzo, L. R. Bidwell, D. F. Frank

THE poor high-temperature oxidation resistance of the refractory metals becomes an important problem as higher operating temperatures are sought. A meaningful analysis of their oxidation behavior requires a knowledge of the phases that can appear during oxidation as well as their relative stability. Although several extensive investigations have been carried out to obtain this information for the W-0 system,1-10 serious inconsistencies still remain. First, the standard free energies of formation (AG°) determined in recent studies which used the solid electrolyte galvanic cell technique6,7,9 differ significantly from those obtained primarily from gas equilibration measurements.1,3,4,10 The disagreement is especially large for the highest oxides. These data have been used to predict the decomposition temperatures of WO2. 72 and WO2.90.1 A considerable extrapolation is required, resulting in a large uncertainty in the decomposition temperatures. Second, Bousquet and perachon3 have presented convincing evidence, ob- tained by gas equilibration measurements, in support of the long-contested existence of W30. Phillips and chang,ll on the other hand, were not able to observe this phase under similar experimental conditions. The purposes of this work, which is part of a continuing investigation of the W-Mo system, were to resolve the discrepancies between the AGO measured by gas equilibration and solid electrolyte galvanic cell techniques, to extend the latter measurements to lower temperatures, to redetermine the WO2.72 and WO2.90 decomposition temperatures, and to apply the more sensitive electromotive-force method to the question of the existence of W3O. I) EXPERIMENTAL PROCEDURE The measurement of ?G° of reaction by the use of calcia-stabilized zirconia solid electrolyte galvanic cells has been described previously.12 The method is based on the measurement of the difference in chemical potential of oxygen between an electrode containing the two oxides of interest and a reference electrode of known oxygen activity. Two different types of cell holders were used in this study. The first type of apparatus has been described earlier." It consisted of two solid electrodes separated by a disc of electrolyte. Both electrodes were exposed to the same stream of purified helium. With this design a gaseous transport of oxygen between the two electrodes is possible. The second type of apparatus, which has also been described earlier,14 effectively separated the two electrode atmospheres. It utilized a closed-end impervious, calcia-stabilized zirconia tube that was open to the atmosphere. The tube served as an electrolyte for the cell and provided a means for separating the anode compartment, which was held under a static vacuum, from an air reference cathode. The cells and reactions of interest are described in Table I. High-purity tungsten metal was obtained from the Fansteel Metallurgical Corp. and the Allied Chemical Corp. Table II contains an analysis of each material. WO3 was prepared by oxidizing the metal in air at approximately 600°C in high-purity recrystallized alumina boats and by the dehydration of reagent-grade tungstic acid in alundum boats. The two methods of preparing WO3 resulted in slightly different purities.

Jan 1, 1968

After the explosion in the Black Heath pit, that company sent to England for some experienced miners to reopen the mine. The results of their work in this vicinity are mentioned in an advertisement for pit hands by the Mid-Lothian Co., as follows: "PIT HANDS WANTED.-In consequence of reports having been circulated of the insecurity of hirelings in the Mid-Lothian Mines, the Company deem it proper to make known, that the mines have recently been opened, and that not the slightest explosion from gas has occurred; the workings were laid out and are now progressing, ° under a plan furnished by Messieurs Foster & Hall, .two distinguished English Colliers, sent over from England to reclaim the Pits of the Black Heath Company after the recent explosion of gas-and the present under ground operations are now conducted under the management of one of the English foremen left here by these gentlemen, and supervised by Mr. Wm. Hall, who has under his superintendence the Black Heath Company's Works at present. The skill and capacity of those gentlemen, is fully evinced in their skilful reclamation of the Black Heath Mines, and their present successful working of said Pits; and their confidence in the safety of the hands in the Mid-Lothian Mines, will be seen, by reference to the annexed extract from the Plan left by Messrs. Foster & Hall for laying out and working the Mid-Lothian Mines, and from the Certificate of Mr. William Hall, as to the manner in which that plan is carried into effect. This publication has been deemed proper, as the Company are now in want of some ten or fifteen additional able-bodied, active Pit-hands, on hire by the year, for which they will give the most liberal hire. The Company have not hitherto spared any labor or expense, deemed necessary to secure the absolute safety and comfort of the hands in their mines; nor is it designed in future to omit any thing that can add to the security of their own hands, or the hired laborers of other persons-indeed they can, with great propriety, say, as far as they have progressed, that no mines in this country exhibit stronger, if as strong, evidence of general safety. The Company will receive on hire, no hands who do not voluntarily enter their service -and they request of those having hands to hire out, to remember that they will want upon hire, successively, at intervals of every ninety days, some additional four or five hirelings during the year, or to purchase, progressively, that number of healthy, able-bodied young men. "Owners of slaves at a distance from the Coal Mines, would do well to give some attention to the subject. There is no place in this country where slave labor commands as much, where their general health is better, and where the treatment and contentment of the slaves are surpassed. It is true that within the last few years several disastrous accidents have occurred, but from the scientific and practical skill attracted to the mines, these accidents will be of rare occurrence, it is to be hoped. A. S. WOOLDRIDGE, President, at the Mines in Chesterfield County.

Jan 1, 1942

By W. R. Bull, J. R. Roos

A method is described whereby the true financial value of each constituent of each concentrate can be calculated. Each value is then compared with what this value would be in a perfect separation. The difference in each case represents the loss incurred by each aspect of an inefficient separation. The relative magnitudes of these losses indicate those avenues of plant investigation and research that offer the highest potential reward. The metallurgical efficiency of a concentration operation is difficult to express because there are two criteria of performance, namely, grade and recovery. Neither of these alone gives any indication of the effectiveness of an operation and, if they are combined in some formula, it must be empirical and unreliable because of many external factors. Since milling is an operation performed as one step in the most profitable overall method of producing a metal or other end product, the main objective of mill operation should be to make a maximum contribution to this maximum profit. When concentrates are sold to custom smelters, the income from the operation, and the costs, may be calculated. When concentrates are further processed by another division of the same company, and there is no formal financial relationship between, say, the milling and smelting divisions of the company, the mill superintendent's job is less well defined. But even so, if the mill superintendent works as though he were selling his concentrates, and uses reasonable, if fictitious, conditions of sale, then he can get a good indication of the effectiveness of his operation by calculating his "Economic Recovery". ECONOMIC RECOVERY This is a method used as a basis of operation by several mills and has been described in the literature. Very briefly, the "standard" of operation is taken as that of a mill separating the ore into perfectly pure concentrates with 100% recovery of each mineral in its respective concentrate. For example, a 4%Pb, 4% Zn ore (galena and sphalerite), would provide a lead concentrate weighing 4.62% of the feed and assaying 86.6% Pb and a zinc concentrate weighing 5.97% of the feed and assaying 67.1 % zinc. These perfect concentrates are (hypothetically) shipped to the appropriate smelters, freight and treatment charges and payments calculated, and the net return obtained. This is the optimum financial return for the operation of the mill and is used as the standard. Now the return for the actual, real-life, mill operation is calculated in the same way, and the ratio of the two is termed the Economic Recovery. Many additions and modifications may be made in any particular case. For example, if the zinc mineral is marmatite, the optimum grade of the zinc concentrate may be set lower than 67.1%. If silver is present, it will be recovered 100% in the lead concentrate in the perfect operation. Similarly, cadmium will be recovered 100% with the sphalerite. Mr. Weiss' paper' mentions a case where, because of extremely fine intergrowth between the valuable mineral, chalcocite, and pyrite, the optimum grade of copper concentrate was taken as 45% Cu instead of the theoretical 80%. Each operation will present its own possibilities in this way.

Jan 1, 1970

By Raymond D. Sloan

During 1944, substantial gains were recorded in practically every phase of the petroleum industry in Oklahoma. With the spotlight of activity focused on other states during the more recent years, the production momentum that was achieved in Oklahoma through the discovery and development of such outstanding pools as Oklahoma City, Fitts. and major pools in the Seminole area during the late 1920's and early 1930's was practically spent by the end of 1943. However, with much of the industry's exploratory efforts greatly reduced in Illinois, Indiana and Kentucky, the strong demand for Mid-Continent crude and the optimism created by some discoveries in the state toward the end of 1943, Oklahoma has again become the recipient of much activity and interest, with its 1944 drilling activity, production and refinery runs to stills registering substantial gains over the preceding year. Development and Exploration Since the discovery of the West Edmond pool in April of 1943, with the substquent drilling and development boom, the scene of exploratory activity has shifted from the central. south and east portions of the state to the general trend of the . Granite Ridge, where leasillg and wild-catting were greatly activated within a wide radius of this high subsurface feature. Leasing activity, however, jumped the confines of the Granite Ridge trend and extended into all of the northwestern counties in the state. Seismograph activity at once began following and keeping pace with this shift in the leasing and exploration locale, by the concentration of a large number of seismograph crews in the area. At one time during the year,35 crews were concentrated in Oklahoma, the majority being west of the Granite Ridge and extending into the northwestern counties. To illustrate the increase in geophysical work done in the state during the year, records indicate that 377 crew months were worked in 1944, which is a 21 per cent increase over the 311.5 crew months activated in 1943. With the discovery in 1943 of several encouraging prospects and the finding of West Edmond as an incentive, drilling operations increased some 54.3 per cent, for a total of 1986 completions during the year. This is compared with a figure of 1287 for wells drilled in 1943, an increase of 699 wells. The industry, with a total of 1064 oil producers, enjoyed a success percentage of 53.6 per cent. Gas wells completed were 223, while 699 dry holes were drilled. In 1943, completions included 587 oil wells, 127 gas wells, and 573 dry holes. The number of oil producers completed during the Year was almost double the numher of wells in 1943. Of the total drilling wells completed in the state, 350, or 17.6 per cent, were wildcat operations—an increase of 5.1 per cent over the 194.3 total of 333. The wildcat success percentage was 13.4 per cent, 47 successful wells being completed for an average initial potential of 160 bbl. In the state, 23 gas wells were completed with an average initial production of

Jan 1, 1945

By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy's law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By T. B. Massalski, Horace Pops

The occurrence and the temperature dependence of the athermal martensitic transformation in bcc Cu-Zn ß-phase alloys have been studied by cold-state microscopy, differential thermal analysis, and electrical -resistivity measurements. CinenzatograpJzic studies have shown that in the majority of alloys the transformation occurs in two stages. A thermoelastic phase, having a 'needlelike" uppearance, forms initially at the MS temperature and grows relatively slowly, chiefly in the edge (lengthwise) direction. With further cooling, an additional martensitic phase forms in rapid bursts at a lower temperature, MB, Both martensitic phases appear to have the same cry stallographic habit hut their modes of formation and growth are different. For the composition range studied, between 38.55 and 41.49 wt pct Zn, the habit planes determined are close to the (2.17 ,12) plane of the matrix, in general agreement with the prediction of the phenomenological theory of martensite formation. Thermal cycling through the MB temperature produces permanent plastic deformation in the 0 matrix and gradutally eliminates the typical burst phenomena. Thermal cycling only through the MS temperature produces no noticeable deformation effects. THE bcc Cu-Zn ß-phase alloys tend to become unstable at low temperatures and undergo a martensitic transformation,'-3 but the details of the transformation have not been completely determined. Following earlier metal log raphic and X-ray work1 Tichener and ever' determined by means of electrical-resistivity measurements the temperature range of the martensite transformation during continuous cooling. The transformation temperature was found to decrease with increasing zinc content, becoming about -130°C for an alloy containing 40.04 wt pct Zn. Hull and Garwood3 made a metallo-graphic study of Cu-Zn 0 brasses at temperatures down to -160°C, and determined the habit plane of the transformation product for an alloy containing 38.88 wt pct Zn. No metallographic studies below liquid-nitrogen temperatures have been reported. The martensitic transformation in ß-brass alloys can also be induced by deformation.1,4 The MD temperature corresponding to the appearance of the strain-induced martensite is some 300°C higher than that observed without strain, and hence the transformation can be strain-induced in alloys containing a higher percentage of zinc. Massalski and Barrett4 found that alloys containing as much as 51.89 wt pct Zn could be transformed into a faulted hcp structure by cold working at liquid-helium temperature. Because the details of the MS temperature and morphology reported in the literature are somewhat incomplete, a further study has been made of some of the above features. A design of a cryogenic stage for optical metallography5 has permitted the examination of specimens at temperatures down to 4.2oK, and the use of a cinecamera has permitted a study of the morphology on cooling and heating. The particular aim of the present work was to examine the transformation temperatures, the habit planes, and the growth morphology over a wide composition range in the ß-phase field. The effect of thermal cycling upon the subsequent transformation was also examined.

Jan 1, 1964

By C. G. Dunn, F. W. Daniels, M. J. Bolton

IN recent papers on interface energies in metals¹,² the concept of an equilibrium of forces has been used in the measurement of interfacial tensions. Mathematically the equilibrium of three forces is given by the relations: where the 2's are the interfacial tensions (interface energies per unit area of interface) of three phases or grains meeting at angles 21 22 and 23 (212 relates to the 1-2 boundary formed by grains 1 and 2;223 to the 2-3 boundary, etc.). If these relationships are valid, one can calculate relative values of the interface energies from measured boundary angles on specimens which have been brought to equilibrium. Since Eq 1 may be derived through a mathematical process of minimizing the grain boundary energy under the restriction that the ?'s be independent of boundary orientation: the concepts of surface tensions and equilibrium of forces are not particularly essential. To deal with the general case involving dependence of boundary energy on boundary orientation, it becomes desirable to drop certain concepts formerly held (namely that energy per unit area is identical with force per unit length or surface tension) and to use the energy concept alone. It is appropriate, therefore, to use E in place of ? in deriving and using the more general equations that express the anisotropic nature of the grain boundary energy. Herring3# ' recently has derived the required general equations using the principle of minimization of energy. Specifying the boundary orientations in terms of angles (4) measured with reference to crystal axes within the grains, Herring's equations take the form E23 + E21 cos?8 + E12 cos?2 — sin ?12 + sin?2-?E12/?12 =O [2] where the partial derivatives are measured in the direction of counterclockwise rotation of the boundaries. Eq 2 implies that an infinitesimal displacement of the triple point along the 2-3 boundary produces no change in the boundary energy. Similar equations apply for infinitesimal displacements along each of the other two boundaries. From such equations Herring obtains the following general relationship (1 + E1 E2) sin?8 + (E2 — E1) cos?3 ________ E38______________ = (1+ E2 E8) sin ?1+ (E3— E2) cos ?1 __________^5____________[3] (1 + E sin ?2, + (E1 — E8,) COS ?2 1 E28 where E1 = 1/E23- E25 and PC and c8 have similar expressions. It is apparent that Eq 3 reduces to Eq 1 when the c's vanish. Eq 3 also reduces to Eq 1 when the E'S are all equal. Shockley and Read' have pointed out one limitation to these equations. When E plotted versus 4 appears as an energy cusp, as their theory requires, for example, for the energy near a twin boundary position, then Eq 3 (and therefore Eq 1 also) no longer applies if one boundary is in the minimum energy position. One of the equations of form Eq 2, however, applies if the infinitesimal displacement is along the boundary associated with the energy cusp. From the foregoing treatment it will be apparent that equilibrium angles alone are not sufficient in general for calculating relative interface energies.

Jan 1, 1951

By R. P. Dolan, W. M. Shedd, B. L. Buchanan

Analytical expressions are derived from empirical data relating the basic physical device parameters to the radiation dose. To put in perspective and justify the approach taken, the overall problem and methods of attempted solution of radiation damage to transistors in a missile or satellite environment is briefly examined. The main emphasis is on a new criteria for neutron radiation hardness and the device design implications resulting from using this criteria. Contrary to other derived criteria, the derived bipolar hardness relation depends mainly on the initial lifetime rather than the base transit time. It is shown, that contrary to previously accepted beliefs, the inherent attainable radiation tolerance of JFET's is at least a factor of ten greater than the radiation tolerance ofbipolars. Experimental results on JFET's designed for maximum neutron radiation tolerance are presented. The accuracy, utility, and range of possible validity of various published lifetime and carrier removal damage constants are discussed. It is well known that transistors are subject to damage due to radiation at much lower radiation levels than those which would cause structural damage to a missile or satellite. The three principal categories of radiation damage to transistors are displacement, ionization, and thermomechanical. The main cause of displacement damage is fast neutrons, and the main effects which permanently degrade transistor operation are minority carrier lifetime reduction and carrier removal. A second-order effect is mobility reduction. The main cause of ionization damage is gamma radiation which results in permanent effects due to charge build-up in the oxide and transient effects due to photo-current generation. The transient effects are usually handled by using circumvention techniques in the electronics system. The extent of the transistor degradation due to displacement and ionization damage depends strongly on the transistor type, whereas the extent of thermomechanical damage does not depend on the transistor type, but depends mainly on packaging and metallization which are common to all transistor types. The standard transistor types are categorized in Fig. 1 and typical cross-sections are shown in Fig. 2. The original reason for the designation of the two classes of transistors was that the unipolar operation depends on only one carrier (majority) and the bipolar operation depends on both minority and majority car- riers. The bipolar is then seriously degraded by minority carrier lifetime reduction, whereas the unipolar or field effect transistor is not. One of the two principle classes of field effect transistors, the junction field effect transistor (JFET), depends strongly on carrier removal. However, the insulated gate (MIS) is little affected by either carrier removal or lifetime changes, but is virtually eliminated as a radiation resistant device because of permanent charge build-up in the insulator caused by ionizing radiation. The bipolar and JFET suffer only minor effects due to charge build-up in the oxide passivation when compared1 to the MOS. This is because the active region of the MOS is adjacent to or part of the oxide layer. It is then the bipolar and JFET which are potentially resistant to permanent radiation damage. DERIVATION OF RADIATION TOLERANCE RELATIONS Criteria. The bipolar is by far the most widely used transistor type. The usual criteria for hardening bipo-

Jan 1, 1970

By John H. Hollomon, C. Zener

It is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect to rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. Earlier Investigations A clear analysis of the conditions necessary for plastic flow and for fracture was first given by LudwikI1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis. both a Flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracturc is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence of tlow stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated3 by the authors. According to this principle of equivalence, strain rate e and temperature T affect the flow stress only through a single parameter-p of the form: p = eeQ/RT 111 In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. article of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944

By R. H. Maes, R. E. de Strycker, J. J. Jacobs

A simple method, based upow density measurements, has been perfected in order to determine the critical temperature of liquid miscibility gaps. Applied to the Pb-Cu system, it yielded a value of 980"C for the critical tempevature of the miscibility gap in this system. In the Pb-Cu-As system, the immiscibility between lead and coppev evolves towards a miscibility gap be-tween lead and copper arsenides; the liquation temperatures were determined joy different avsenic contents and values up to 1065°C were found. Combining these results with those given by the clzemical analysis of liquid samples taken at dqj.event temperatures, it has been possible to make a cowzplete determination of the liquid miscibility gap in this ternary system. In the Pb-Cu-Fe-As system, a ternary miscibility gap has been discovered; for some compositions, the molten and slowly cooled alloys separated into three layers: an Fe-As alloy, a Cu-As alloy, and a lead-rich layer. ThE Pb-Cu-Fe-As system is of interest for the study of the behavior of speiss or arsenical alloys in the lead blast furnace. The speisses produced in lead metallurgy generally have complex compositions, but they may be considered, in a simplified way, as a mixture of copper, iron, nickel, and cobalt arsenides; there is often an excess of metallic constituants, and lead is also present. Speisses liquate from lead at various temperatures according to their composition; according to industrial experience, iron speisses are already distinctly separated from lead bullion at temperatures of the order of 1100°C, whereas copper speisses only begin to liquate from lead at much lower temperatures, near their solidification points, which were never accurately determined until now. Besides these considerations of practical interest, the present study is of importance for the knowledge of liquid miscibility gaps. Particularly the data of the literature about critical temperatures of liquation are incomplete and present sometimes considerable disparities; a method has been perfected in the present work to determine these temperatures with accuracy. MISCIBILITY GAP OF THE LEAD-COPPER SYSTEM Review of Literature. The generally admitted outline of the Pb-Cu equilibrium diagram is shown by Fig. 1. This figure, with its numerical indications, is taken from the review of Hansen and ~nderko;' compositions are given in weight percent, as will be the case in the remainder of this paper. Between 36 and 87 pct Pb, Pb-Cu alloys separate into two layers, in the liquid state. The critical temperature of liquation has been much disputed in earlier studies, where values up to 1500°C were claimed; but a reliable study of ~ohnen,' based upon differential thermal analysis, gave a value of 990°C; this rather low value was verified by a recent study of Schiirmann and Kaune? based upon thermodynamical properties of the Pb-Cu alloys, which predicted a value of 1002°C. Liquid miscibility gaps were also studied by means of chemical analyses. Satisfactory results were generally obtained with the method consisting in taking samples of the two liquid layers in equilibrium and submitting them to chemical analysis; however, this method becomes delicate near the critical temperature. With this technique, Friedrich and waehlerts ob-

Jan 1, 1968

By R. F. Hehemann, Darrell W. Smith

The kinetics of alloying- in W-5 rot pct Re powder compacts were investigated at temperature about the upper limit for the formation of the x phase, such that a single intermediate phase was involved in the process. The rates and directions of motion of the a-o and o-b interface were assessed as functions of tinze at the sintering teri7peraticve by quantitative izetallog-ralhic techtziques. The iiotion 01 these interjuces could be specified approxitnate1.y by u Parabolic )-ate law and deviations from this ,rate law were attribuled to a complex interaction between surface dif'fusion and volume diffusion during the initial stages of sintering. WHEN binary or more complex alloys are produced by sintering compacted blends of elemental powders, a complication is encountered which does not arise in the sintering of pure metals. In addition to concern for grain size and densification, the rate of inter diffusion of the component elements must be considered. The general problem of alloying during sintering has been treated by numerous investigators.'-7 These investigations have been concerned only with systems that form continuous series of solid solutions and a concentric-sphere diffusion model4 provides a useful description of homogenization in these stems.' Some controversy remains, however, over the contribution of surface and grain boundary diffusion to the homogenization process. Heckel% ePorts that homogenization can be described by volume diffusion at all temperatures, whereas other invetiators'' recognize the importance of surface and grain boundary diffusion, particularly at lower temperatures. Analysis of the homogenization process in partially miscible systems is complicated by the motion of the interfaces separating the individual phases. A simple analytical solution does not exist for such finite systems with spherical symmetry. It was the purpose of this work to examine the kinetics of the formation and dissolution of an intermediate phase in a binary system through an assessment of the motion of the interfaces separating this phase from the terminal solid solutions. PROCEDURE The W-Re system is an example of a partially miscible binary system and was selected for study because of its current importance in refractory-metal technology. The equilibrium phase diagram, Fig. 1, shows that the o phase will be formed by interdiffu-sion between tungsten and rhenium. At temperatures between approximately 2125" and 282O°C, the o phase will appear as the only intermediate phase in the diffusion system. In this work, a mixture of elemental powders containing 5 pct Re was employed. In such a mixture, the rhenium particles will be distributed randomly in a tungsten matrix. During sintering, a o-phase layer will form at the W-Re interface. The development and subsequent disappearance of the o phase are controlled by the relative rates and directions of motion of the 0-0 and a-p interfaces. The motion of these interfaces can be inferred from quantitative metallographic measurements of the average radii of the o shells surrounding rhenium particles. Elemental tungsten and rhenium powders of commercial purity were employed in these investigations. The rhenium powder was spheroidized from +200 mesh agglomerates by plasma-arc spraying and was then classified to yield a powder composed of essentially

Jan 1, 1967

By B. M. Larsen, K. Heindlhofer

THIS paper describes a relatively simple electrical apparatus that, through the close analogy between the flow of heat and of electricity, enables one to solve quickly and with satisfactory accuracy many complex problems in heat flow. This device, developed in 1935, has proved especially useful in the solution of certain practical problems relating to the design and efficiency of regenerators for an open-hearth furnace or coke oven, yielding within a few hours information that would take weeks or even months to acquire by mathematical1.2 or experimental3 methods of comparable accuracy. Its description now is prompted by growing interest in such analogues, as shown by several recent papers.4.5 The analogy between flow of heat and of electricity appears to have been recognized first by Maxwell who, in his famous Treatise on Electricity and Magnetism (1881) says: The analogy between the theory of the conduction of electricity and that of the conduction of heat is at first sight almost complete. If we can take two systems geometrically similar, and such that the conductivity. for heat at any part of the first is proportional to the conductivity for electricity at-the corresponding part of the second, and if we also make the temperature of any part of the first proportional to the electric potential at the corresponding point of the second, then the flow of heat across any area of the first will be proportional to the flow of electricity across the corresponding area of the second. .. Thus, in the illustration we have given, in which flow of electricity corresponds to flow of heat, the electric potential to temperature, electricity tends to flow from places of high to places of low potential, exactly as heat tends to flow from places of high to places of low. temperature He noted, however, that this analogy is restricted: ... there is, however, one remarkable difference between the phenomena of electricity and those of heat. Suspend a conducting body within a closed conducting vessel by a silk thread, and charge the vessel with electricity. The potential of the vessel and of all within it will be instantly raised, but however long and however powerfully the vessel be electrified, and whether the body within be allowed to come in contact with the vessel, or not, no signs of electrification will appear within the vessel, nor will the body within show any electrical effect when taken out. But if the vessel is raised to a high temperature, the body within will rise to the same temperature, but only after a considerable time, and if it is then taken out it will be found hot, and will remain so till it has continued to emit heat for some time. The difference between the phenomena consists in the fact that bodies are capable of absorbing and emitting heat, whereas they have no corresponding property with respect to electricity. According to this statement the application of the analogy would be limited to problems of steady flow that do not involve heat-capacity effects. In spite of this

Jan 1, 1945

By C. Zener, John H. Hollomon

It is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect to rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. Earlier Investigations A clear analysis of the conditions necessary for plastic flow and for fracture was first given by LudwikI1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis. both a Flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracturc is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence of tlow stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated3 by the authors. According to this principle of equivalence, strain rate e and temperature T affect the flow stress only through a single parameter-p of the form: p = eeQ/RT 111 In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. article of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944