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By W. A. Wood, W. H. Reimann, Maria Ronay

The basic mechanism of fatigue is studied in annealed a brass subjectecl to alternating torsion at room temperature, 100°, 200°, 300°, and 400°C, and in air. It is shown that the slip-zone micro-cracking which characterizes fatigue damage produced by small amplitudes at room temperature is progressively replaced by grain boundary cracking at elevated temperatures, replacement being complete at 400°C. Replacement occurs not because slip activity decreases hut because slip movements at elevated temperatures cease to concentrate in narrow zones and instead disperse. Decrease of amplitude at 400°C through permitting longer lives of specimens before fracture actually causes in- MOST studies of fatigue at elevated temperature have been concerned with data for design. Observations on the basic mechanism of fatigue have been largely incidental, though they have led to the interesting inference that this mechanism has features in common with that of creep.' This paper is concerned primarily with the mechanism itself. Advantage has been taken of mater- crease in pain boundary damage, an anomaly attributed to the greater difficulty at elevated tempwature of starting and propagating a crack. Surface corrosion was most pronounced along slip bands but since at elevated temperatures the slip hands showed no cracking the surface corrosion did not appear to influence onset and early spread of fatigue damage. Similarly the type of fatigue damage produced at room temperature by cyclic strain at large amplitudes, characterized by irregular mi-crocracks at zones between disoriented regions in a grain, was also replaced by mainly grain boundary cracking at elevated temperature, though not so completely. ials and procedures known to show readily how fatigue affects the microstructure of a metal at room temperature, so that direct comparison might be made with what the same procedures show when the material is subjected to fatigue deformation at higher temperatures. 1) MATERIAL This was 70/30 a brass, used extensively in previous studies at room temperature.' Specimens were turned from extruded rod to have parallel test portions 1-1/4 in. long and 7/32 in. diameter, annealed to a grain size -1/10 mm, and electro-

Jan 1, 1965

Jan 1, 1938

Jan 1, 1938

Jan 1, 1941

By Kung-Lee Wang, Brian W. Mackenzie, Warren E. Morrison, DeVerle P. Harris, George F. Sharrard

The term "mineral economics" is applied to a wide range of activities in the mineral industries. Earlier chapters have described the application of economic concepts to the mineral industries-supply, demand, conservation, tariffs, etc. The solution of mineral economics problems is often assisted by the application of quantitative methods. The purpose of this chapter is to describe a number of quantitative methods-econometric, operations research, and management science techniques-which find application in the analysis of mineral economics problems. These methods include input-output analysis, trend analysis, forecasting techniques, simulation, multivariate statistical analysis, mathematical programming, and market research techniques. The purpose of this introductory section is to provide a mineral economics framework for the application of these methods. Mineral economics is a subdivision of economics that is justified by a sufficient number of economic problems in the mineral industry requiring special experience and an unusual combination of skills. These problems are concerned with the conversion of minerals as geologic resources to minerals as economic goods. The mineral conversion process is outlined in Fig. 8.A.1. The physical occurrence of mineral deposits in nature and the market demand for mineral products in the economy provide the basic stimuli. The conversion process embodies a number of sequential stages-exploration, the development of mineral deposits, and mineral processing facilities and, consequently, productive activity to supply market demand. Changes in demand and the depletion of deposits illustrate the dynamics of the process. Mineral economics applies economic con-

Jan 1, 1976

By Sir Albert E. Kitson

The manganese ore deposits of the Gold Coast, British West Africa, occur in very ancient rocks, of both sedimentary and metamorphic types. In certain respects they have a strong resemblance to those of India and Brazil, as contrasted with those of Tertiary age in Georgia, but in this paper no careful comparison with them can be made. Viewed from the present condition of the manganiferous rocks, the oldest deposits are in the sediments. Later than these are the progressively metamorphosed representatives of these sediments. Youngest are the products of decay and degradation with the concentration of manganese oxide in the rocks of both groups. The oldest occurrences are in argillaceous and siliceous phyllites and slates, which show only a moderate degree of metamorphism. They belong to a series which also includes mudstones, sandstones, grits, conglomerates and subordinate limestones, with tuffs and lava-flows, largely of basic types. This has been named the Birrim System. Its age is unknown, for no definite fossils have been discovered in it. Since these non-fossiliferous strata at many plaees are of a character which in many parts of the world are suitable for the preservation of fossils, and which contain them, it is assumed that the Gold Coast deposits are pre-Cambrian. These rocks of the Birrim System have normally a northeast-southwest strike, and are folded, but not to any very great degree except in certain belts. From the Eastern Province of the Gold Coast they may be traversed diagonally across their strike for upwards of 600 miles, to the extreme northwestern corner of the Northern Territories. Thence they probably extend much farther into French territory.

Jan 1, 1927

By Walton J. Greer, System By John E. Owen

The guard electrode system measures the resistivity of formations by employing a thin disk of current which is caused to flow perpendicular to the bore hole. The control of this current disk is obtained in a brute force manner through the use of relatively long equipotential electrodes above and below the measuring electrode. The log obtained from the system is free of "lag," "plateau," "shadow," "reflection" and other distortions evident on conventional logs. The proportionate contributions of the hole size and invaded zone resistivity to the apparent resistivity reading are reduced when the mud and filtrate resistivities are lower. Thus, the guard system favors the use of conductive muds. The mathematical development of the theory is given in an appendix. Equations are derived to evaluate the effects of mud resistivity, hole size, invaded zone resistivity and depth, and the true formation resistivity. Sample logs from several provinces are reproduced and compared with conventional electric logs to illsutrate the much greater detailed lithology that can be presented by the guard electrode system. INTRODUCTION With increased ability of those in the petroleum industry to analyze formation characteristics from electrical resistivity data, there has become apparent the need for more precise measures of that parameter. The measurement of the resistivity of a homogeneous and isotropic material can be made simply when the body of the material is infinite in all dimensions and the measuring electrodes can be placed within the body. In such a case, the current leaving an electrode follows a spherical distribution and the mathematical expression for the potential level at any distance from that electrode can readily be derived.'.' If it is considered that the active electrodes are within a bore hole filled with mud of a resistivity different from that of the formation. the current does not flow in a spherical pattern near the current source or sink, and the calculations of potential levels become more difficult. The additional consideration of a section of formation invaded by mud filtrates, and thus having resistivity different from either that of the mud, the adjacent formations or of the undisturbed formation, makes the mathematical problem extremely complex. Should the vertical dimensions of the formations be considered as finite. the problem becomes so complex as to preclude reasonable solution. Yet, even these considerations have not described adequately the conditions encountered in a large proportion of the wells to be studied. In efforts to evaluate the effects of the various conditions. combinations of twn, three. and four electrode logging con- figurations of the conventional types have been used. The resulting logs have left much to be desired in some provinces. It has become apparent that the use of such configurations will not result in adequate measurements being made, particularly in cases where the formation is composed of thin sections. If all the current of a resistivity measuring circuit is made to flow through the formation opposite the exploring electrode, many of the shortcomings of the conventional measuring system are eliminated. In the guard electrode method of electrical well logging to be discussed in this paper, the current is so controlled by causing it to flow in a thin disk normal to the axis of the logging tool. EARLY HISTORY The guard electrode method of electrical well logging in its early years was a joint development by the Geophysical Research Corp. and the Amerada Petroleum Corp. The method was first experimentally investigated by means of model studies. The results of these studies indicated that current focusing systems properly applied to electrical well logging

Jan 1, 1951

By System By John E. Owen, Walton J. Greer

The guard electrode system measures the resistivity of formations by employing a thin disk of current which is caused to flow perpendicular to the bore hole. The control of this current disk is obtained in a brute force manner through the use of relatively long equipotential electrodes above and below the measuring electrode. The log obtained from the system is free of "lag," "plateau," "shadow," "reflection" and other distortions evident on conventional logs. The proportionate contributions of the hole size and invaded zone resistivity to the apparent resistivity reading are reduced when the mud and filtrate resistivities are lower. Thus, the guard system favors the use of conductive muds. The mathematical development of the theory is given in an appendix. Equations are derived to evaluate the effects of mud resistivity, hole size, invaded zone resistivity and depth, and the true formation resistivity. Sample logs from several provinces are reproduced and compared with conventional electric logs to illsutrate the much greater detailed lithology that can be presented by the guard electrode system. INTRODUCTION With increased ability of those in the petroleum industry to analyze formation characteristics from electrical resistivity data, there has become apparent the need for more precise measures of that parameter. The measurement of the resistivity of a homogeneous and isotropic material can be made simply when the body of the material is infinite in all dimensions and the measuring electrodes can be placed within the body. In such a case, the current leaving an electrode follows a spherical distribution and the mathematical expression for the potential level at any distance from that electrode can readily be derived.'.' If it is considered that the active electrodes are within a bore hole filled with mud of a resistivity different from that of the formation. the current does not flow in a spherical pattern near the current source or sink, and the calculations of potential levels become more difficult. The additional consideration of a section of formation invaded by mud filtrates, and thus having resistivity different from either that of the mud, the adjacent formations or of the undisturbed formation, makes the mathematical problem extremely complex. Should the vertical dimensions of the formations be considered as finite. the problem becomes so complex as to preclude reasonable solution. Yet, even these considerations have not described adequately the conditions encountered in a large proportion of the wells to be studied. In efforts to evaluate the effects of the various conditions. combinations of twn, three. and four electrode logging con- figurations of the conventional types have been used. The resulting logs have left much to be desired in some provinces. It has become apparent that the use of such configurations will not result in adequate measurements being made, particularly in cases where the formation is composed of thin sections. If all the current of a resistivity measuring circuit is made to flow through the formation opposite the exploring electrode, many of the shortcomings of the conventional measuring system are eliminated. In the guard electrode method of electrical well logging to be discussed in this paper, the current is so controlled by causing it to flow in a thin disk normal to the axis of the logging tool. EARLY HISTORY The guard electrode method of electrical well logging in its early years was a joint development by the Geophysical Research Corp. and the Amerada Petroleum Corp. The method was first experimentally investigated by means of model studies. The results of these studies indicated that current focusing systems properly applied to electrical well logging

Jan 1, 1951

By S. Grinsfelder

Although wildcatting was hampered by the general overproduction and low price of crude, several developments, worthy of note in the history of the petroleum industry in the Rocky Mountain region, were made in 1927. This district records production from six new fields, two of these having been heretofore productive of gas. Deeper pay horizons were found in two other oil fields. In order to facilitate transportation from fields, six new oil pipe lines were completed or in the course of construction at the end of the year, and one line is proposed for 1928. Four gas lines were completed, one was under construction, and one was proposed for 1928. The total production in 1927 in the Rocky Mountain district was 29,591,379 bbl.,' a decrease of 7,771,991 bbl., or 21 per cent., fro111 the previous year. This was occasioned by natural decline and the general curtailment of production and drilling. A review of the development by states follows. Colorado Production from horizons in the Morrison and Sundance at Craig and at Ilrs Dome, and the bringing in of the deepest producing well in the Rocky Mountain district on North McCalluin anticline (Waltlrn) in Jackson County are the outstanding developments for the year in Colorado. In March the Midwest Refining Co.'s Parkinson 21 SD, SW SE, Sec. 22 T p. 4 N R 92 W, Iles Domr, Moffat County Colorado, found gas in sands in the Morrison estimated at 15,000,000 cu. ft., and at 3242 ft. an oil sand was encountered in the Sundance. Initial production from this horizon was 2575 bbl. in this well. This structure previously was only productive of water in the sands of the Dakota group but has been producing shale oil from horizons in the Benton. The second well completed by the Midwest Refining Co., No. 18 SD in Sec. 23 was also productive of gas in the Morrison and made an initial of 300 bbl. from sands in the Sundance. By the end of the year three other wells wrrc nearing the completion stage but none of them indicate that they will be as big producers as the discovery. To date the productive area has

Jan 1, 1928

By R. V. Riley

IN the metallographic examination of the alloys of iron and silicon, several investigators1-' have reported on the occurrence of an unusual type of etched structure, particularly in the alloys of higher silicon content. This, the so-called "barley shell" structure, has been observed with iron-silicon alloys over a wide range of silicon content, and under certain circumstances it can be seen upon the micro-sections of pure iron. The barley shell structure may be demonstrated most easily with iron-silicon alloys in the range 8 to 20 pct Si after etching in a hydrofluoric acid base etchant. Two etchants which produce the structure are: Corson's reagent, which is 2 parts hydrofluoric acid, 1 part nitric acid, and 2 parts glycerol; and picric acid reagent, which is 1 part hydrofluoric acid and 1 part saturated solution of picric acid in alcohol. Both when freshly prepared and used for etching commercial silicon-iron alloys containing 14 to 16 pct Si, invariably produce the barley shell structure shown in Fig. la. It is now well known that the barley shell structure is a pseudomorph and the true structure of an alloy of this composition consists of a single phase of silico-ferrite together with graphite as shown in Fig. lb. Lower silicon alloys and even pure electrolytic iron may also be etched in the above reagents to give the barley shell provided the etchant has been either: 1—Stored in contact with glass or silica, or 2—used previously for etching an iron containing silicon. Pure iron etched in perfectly pure hydrofluoric acid base etchants free from silicon contamination gives a normal structure free from the barley shells. Therefore, although the hydrofluoric acid in the reagent primarily is responsible for the barley shells, silicon, or its compounds, also must be present, either in the etching reagent or in the specimen. It was of considerable interest to the author to read the paper by Wachtell,? in which the barley shell etch was deliberately used for the identification of the boundaries of high and low silicon areas in diffusion experiments made upon laminate bars of compacted and sintered pure iron and ferrosili-con powders. This method of utilizing the barley shell etch is novel and in the hands of the investigator gave a useful differentiation between the high and low silicon areas in those specimens. For the reasons already given, however, the technique is not to be regarded as of universal application. Misleading results might be obtained, for example, if two or more specimens were etched in the same etchant. Fresh pure reagents only must be used each time. Provided this is done and the investigators are well aware of the limitations of the method, then the barley shell pseudomorph can be made of limited use in distinguishing between higher and lower silicon areas in a microspecimen of a ferrous material. The greatest of care must be exercised in the interpretation of the results which may be regarded as qualitative only and may, in fact, not be specific to silicon alloys.

Jan 1, 1952

By H. L. Riley, B. W. Gandrud

A froth flotation unit was added to the DeBardeleben Coal Corporation's Empire washer at Empire, Alabama, in the fall Of I94O following an investigation of possible ways and means of recovering coal values from settling-tank overflow or slurry. Officials of the DeBardeleben corporation hoped that some practical and reasonably economical way could be found for recovering fine coal from overflow water, although there had as yet been very little progress along this line in the Alabama coal fields. The Bureau of Mines was asked to cooperate in the project through its Southern Experiment Station, at University, Alabama. This paper presents a brief description of the process and the installation that resulted from the investigation of the overflow water or slurry problem at the Empire mine. The experimental data include' as a Part of this Paper were obtained during the course of the investigation in 1940 Since that time, however, the flotation unit has been running more or less continuously without significant operational changes and is still Performing pretty much in accordance with the data obtained in 1940. Flowsheet at Empire and Type of Coal Treated The Empire mine is developed on the Black Creek bed near the the border of the Warrior field. The coal in this bed is extremely low-ash and although there is an almost complete absence of bone coal and partings, the bed is so thin that, with mechanized mining, a high percentage of rock from roof and floor inevitably gets into the run-of-mine coal. The thickness of the Black Creek bed throughout the part of the Warrior field in which it is mined extensively is rarely over 30 in. and probably would average about 25 in, the coal is of the high-volatile A rank and of excellent quality, but as a result of admixture of roof and floor material, the run-of-mine product usually contains I ; to 20 pct rock by weight. he following is a proximate analysis on an "as-received " basis of a typical seam sample from the Empire mine:' moisture, 3.0 pet; volatile, 34.6 fixed carbon 58.3; ash, 4.1 This sample shelved 15,070 Btu per pound and 0.9 pct sulphur on a moisture-and-ash-free basis. In the Empire preparation plant the lump sizes above 3 in. are removed and hand-picked on a Marcus conveying Screen, the 3 to ? -in. size is removed by vibrating screens and washed in two Montgomery single-cell jigs, and the ?-in. to o slack is cleaned on four diagonal

Jan 1, 1949

By H. R. Hanley

IT is a well-known fact that the solubility of zinc compounds decreases when these compounds are roasted in contact with iron compounds, but descriptions of tests to quantitatively express the fact have not appeared in the literature. Possibly such an expression cannot be uniformly and exactly duplicated by different operators because of the variation in the personal equation. In a general way, however, the reactions between zinc compounds and iron compounds under roasting conditions will show a certain trend with changing conditions and the approximate quantitative expression of this trend appears reasonably well established by experimental work conducted for this purpose.

Jan 1, 1929

By L. R. Jackson

THE idea presented in this paper is that the capacity of a metal for plastic flow before rupture is dependent on the type of stress system applied-that is, the absolute magnitude of the stresses are unimportant provided that they are large enough to produce continued flow; the important factor is the "type" of stress system. A term called the "triaxial stress ratio" is defined in such a way that this ratio can be used to characterize the "type" of system. The paper is divided into three sections. The first section discusses means of representing the effect of complex stresses on plastic flow and defines "triaxial stress ratio"; the second section discusses various methods of' obtaining complex stress distribution. The third section gives some experimental results showing the effect of types of complex stress on the capacity of various metals for flow. An appendix discusses some details on methods of obtaining complex stresses. I. REPRESENTATION OF COMPLEX STRESS SYSTEMS AND THEIR EFFECT ON PLASTIC FLOW Representation of Stresses It is convenient to have a consistent system of notation that will allow the representation of the entire range of complex stresses from hydrostatic compression to hydrostatic tension on plastic flow in a single diagram. Such a system is provided by making use of the fact that any complex stress system can be resolved into a hydrostatic tension or compression and a pure shear. Consider a stress system having the principal stresses [S1 S2 5 S3]. This system can be resolved into a new system consisting of the three components [ ] and three pure shears. If Sm is positive, the net stress effect is hydrostatic tension; if it is negative, the effect is hydrostatic compression. In order to produce a systematic notation, a quantity that will be referred to as the "triaxial ratio" will be defined by the equation [ ] Sm is given by Eq. I and S1 is the absolute magnitude of the largest principal stress without regard to sign. Table I lists the triaxial ratios for various common systems. [ ] Representation of Strains Strains will be plotted as "true" strains according to the system proposed by Ludwik.1

Jan 1, 1944

By A. R. Troiano, E. A. Steigerwald, F. W. Schaller

D. N. Williams(BatteZle Memorial Institute)-The authors have presented an extensive collection of arguments pertaining to the role of stress in hydrogen embrittlement. The basic assumption of these arguments is that stress is essential as a driving force for diffusion of hydrogen. However, in view of the rapid diffusion rate of hydrogen in steel at low temperatures as evidenced by the ability to alloy with hydrogen by electrolytic charging, it seems unlikely to me that stress acts in this manner. Instead, I would like to suggest that stress may be essential for the nucleation of hydrogen in steel. I believe that such an assumption would equally well satisfy the experimental data presented by the authors. I should also like to comment on the interpretation of the data presented in Figs. 5 and 6. Fig. 5 shows the effect of hydrogen content on ductility in a rupture test. The curve as drawn by the authors indicates an abrupt transition from ductile to brittle behavior at about 0.001 amp per sq in. (5 ppm). The data points would equally well support a gradual transition from ductile to brittle behavior extending over the range from 0.0008 to 0.02 amp per sq in. (4 to 8 ppm). A gradual transition would be the ex-

Jan 1, 1962

By C. H. Lee, R. Maddin

The diffusion rates of Ag110 in cylindrical single crystals of 99.99 pct pure silver, which were twisted to a total surface strain of 0.91 during the diffusion anneal at temperatures of 700°, 750°, and 800°C, were measured by sectioning and counting as a function of the strain rates. The ratio of the diffusivities while strain ing occurred (Ds) to those of the unstrained specimens varies linearly with the rate of twisting and attains values of near 100 for some of the rates used. The enhancement of diffusion by straining is inversely proportional to the temperature at which diffusion occurs. The activation energy for diffusion determined from the data plotted as a function of the rate of twisting decreases from 44,090 cal per mole for zero strain, to an asymptotic value of 21,000 cal per mole for the strain rates of 22 x it)"5 see-l. Qualitative explanation for the observations based on the generation of nonequilibrium number of defects by plastic deformation will be discussed. The initial research of Buffington and cohen1 on self-diffusion in a iron under compressive stresses contributed the first quantitative information concerning the effect of applied stresses on diffusion. These results were obtained from radioactive Fe55 plated on one of the horizontal surfaces and compressing the large-grained specimens while the diffusion-anneal was occurring. Enhancement of diffusion of a maximum of seventeen times was observed provided the strain was in the tertiary stage of creep and the rates of straining were at least as fast as rates used in the normal creep test. On the other hand, Darby, Tomizuka, and Balluffi,2 extending silver single crystals up to 30 pct elongation at rates of straining about equal to those used by Buffington and Cohen observed no effect. For the past two and a half years at the University of Pennsylvania, we have been investigating the effect or torsional strains on self-diffusion in silver single crystals. If enhancement is observed as has been reported1 a possible explanation may be based upon the generation of fairly large numbers of point defects and their role in the diffusion process. Hence, since torsion should produce an abundance3 of point defects, an increase in the diffusivity while the crystal is being twisted should easily be measured. EXPERIMENTAL PROCEDURE Our research uses single crystals of silver prepared from 99.99 Ag by the Bridgman method in a dynamic vacuum of less than 25 µ. As grown, they are about 25 cm long by 1.3 cm in diam. The crystals are cut into 7.5 cm lengths with a jeweler's saw and machined to the shape shown in Fig. 1. The test length of the crystal is machined to a 0.6 cm diam after which the ends are masked and the test section etched heavily in HNO3, and KCN:(NH4),S2Os , solution to remove the effects of machining. The specimen is then annealed in vacuum for 8 to 12 hr at 800°C to remove any residual stresses and also to recrystallize the end sections. The recrystallized ends are necessary since experiments showed that single-crystalline end sections are too soft to transmit the desired torque. Occasionally, recrystalliza-

Jan 1, 1960

By C. D. Locker

COMMON salt is mentioned in the most ancient writings as an impor-tant article of diet. It is fairly certain that it was used by men and animals long before the dawn of civilization. Its presence in natural springs has often been the determining factor in colonization; wars have been fought for possession of salt deposits; trade routes have been estab-lished expressly for the purpose of traffic in salt. Naturally this led men into adventures and discoveries that altered history and advanced civilization. In the early days the uses for salt were few and the methods of manu-facture were crude and the purity low when compared to salt of the pres-ent day. Then the salt came largely from springs, shallow wells or the ocean, while today deep wells must be drilled to the natural brines or beds of rock -salt and spacious shafts sunk so that the ancient deposits may be made to yield their supply of stored mineral.

Jan 1, 1936

By Walter R. Hibbard

ALTHOUGH extensive pole figure studies have been reported by Brick1 and others2,3 showing preferred orientations in rolled and annealed 70-30 alpha brass, and by Hermann and Sachs4 in 70-30 alpha brass cups, comparatively little information has been published on textures in drawn 70-30 alpha brass tubes. Crampton5 reported a (110), [III] texture in drawn brass tubes based on selected individual X ray photograms following the method of Norton and Hiller,6 but the extent and ease of developing this texture and the annealing texture have not been reported and pole figures of these structures were not found in the literature. The present investigation was further stimulated by the possible influence of textures on the mercury stress-corrosion cracking of brass tubes. According to Snoek,7 iron-nickel alloy sheet with a strong cubic texture was more resistant to corrosion than a randomly oriented sheet. Crampon5 reported that single crystals of 70-30 alpha brass drawn into tubes did not crack after 24 hr s in a standard mercurous nitrate test. Edmunds 12 found that single crystals of 70-30 alpha brass did not crack in a standard mercurous nitrate test but did crack when subjected to ammoniacal vapor. Wassermann reported a similar failure of a single crystal of brass in ammonia. A tube with a strong texture might approach single crystal behavior and tend to resist mercury cracking if the differences in orientation between adjacent grains were sufficiently slight. PREPARATION OF SPECIMENS Crampton's5 tubes drawn 28 pct reduction in area developed a slight degree of preferred orientation while in tubes drawn 48 pct it was more marked. Based on this information, in order to obtain specimens with markedly different degrees of preferred orientation but with the same final draw, two sets of 70-30 alpha brass tubes were made following the mill schedules shown in Table I. The final draw involved a large reduction in outside diameter, and a ratio of reduction in area to reduction in outside diameter similar to that reported by Crampton,5,10 to cause mercury cracking of brass tubes. The brass contained 71.31 pct copper, 0.01 pct lead, 0.01 pct iron and zinc by difference. DETERMINATION OF POLE FIGURES A 6-in. length from each tube was rotated rapidly by an electric stirrer in 25 pct nitric acid until the gauge was reduced to 0.003-0.005 in. The tubes were carefully cut longitudinally and the walls gently flattened. They were further etched in 25 pct nitric acid to 0.0015 in. thickness and (III) pole figures were determined using copper K-alpha radiation in the manner described by Brick.1 The three general types of pole figures

Jan 1, 1947

By W. R. Hibbard

Although extensive pole figure studies have been reported by Brick1 and others2,3 showing preferred orientations in rolled and annealed 70-30 alpha brass, and by Hermann and Sachs4 in 70-30 alpha brass cups, comparatively little information has been published on textures in drawn 70-30 alpha brass tubes. Crampton5 reported a (110) , [111] texture in drawn brass tubes based on selected individual X ray photograms following the method of Norton and Hiller,6 but the extent and ease of developing this texture and the annealing texture have not been reported and pole figures of these structures were not found in the literature. The present investigation was further stimulated by the possible influence of textures on the mercury stress-corrosion cracking of brass tubes. According to Snoek,7 iron-nickel alloy sheet with a strong cubic texture was more resistant to corrosion than a randomly oriented sheet. Crampton5 reported that single crystals of 70-30 alpha brass drawn into tubes did not crack after 24 hr in a standard mer-curous nitrate test. Edmunds12 found that single crystals of 70-30 alpha brass did not crack in a standard mercurous nitrate test but did crack when subjected to ammoniacal vapor. Wasserman11 reported a similar failure of a single crystal of brass in ammonia. A tube with a strong texture might approach single crystal behavior and tend to resist mercury cracking if the differences in orientation between adjacent grains were sufficiently slight. Preparation OF Specimens Crampton's5 tubes drawn 28 pct reduction in area developed a slight degree of preferred orientation while in tubes drawn 48 pct it was more marked. Based on this information, in order to obtain specimens with markedly different degrees of preferred orientation but with the same final draw, two sets of 70-30 alpha brass tubes were made following the mill schedules shown in Table I. The final draw involved a large reduction in outside diameter, and a ratio of reduction in area to reduction in outside diameter similar to that reported by Crampton,5, 10 to cause mercury cracking of brass tubes. The brass contained 71.31 pct copper, 0.01 pct lead, 0.01 pct iron and zinc by difference. Determination of Pole Figures A 6-in. length from each tube was rotated rapidly by an electric stirrer in 25 pct nitric acid until the gauge was reduced to 0.003-0.005 in. The tubes were carefully cut longitudinally and the walls gently flattened. They were further etched in 25 pet nitric acid to 0.0015 in. thickness and (111) pole figures were determined using copper K-alpha radiation in the manner described by Brick.' The three general types of pole figures

Jan 1, 1949

By W. R. Hibbard

Although extensive pole figure studies have been reported by Brick1 and others2,3 showing preferred orientations in rolled and annealed 70-30 alpha brass, and by Hermann and Sachs4 in 70-30 alpha brass cups, comparatively little information has been published on textures in drawn 70-30 alpha brass tubes. Crampton5 reported a (110) , [111] texture in drawn brass tubes based on selected individual X ray photograms following the method of Norton and Hiller,6 but the extent and ease of developing this texture and the annealing texture have not been reported and pole figures of these structures were not found in the literature. The present investigation was further stimulated by the possible influence of textures on the mercury stress-corrosion cracking of brass tubes. According to Snoek,7 iron-nickel alloy sheet with a strong cubic texture was more resistant to corrosion than a randomly oriented sheet. Crampton5 reported that single crystals of 70-30 alpha brass drawn into tubes did not crack after 24 hr in a standard mer-curous nitrate test. Edmunds12 found that single crystals of 70-30 alpha brass did not crack in a standard mercurous nitrate test but did crack when subjected to ammoniacal vapor. Wasserman11 reported a similar failure of a single crystal of brass in ammonia. A tube with a strong texture might approach single crystal behavior and tend to resist mercury cracking if the differences in orientation between adjacent grains were sufficiently slight. Preparation OF Specimens Crampton's5 tubes drawn 28 pct reduction in area developed a slight degree of preferred orientation while in tubes drawn 48 pct it was more marked. Based on this information, in order to obtain specimens with markedly different degrees of preferred orientation but with the same final draw, two sets of 70-30 alpha brass tubes were made following the mill schedules shown in Table I. The final draw involved a large reduction in outside diameter, and a ratio of reduction in area to reduction in outside diameter similar to that reported by Crampton,5, 10 to cause mercury cracking of brass tubes. The brass contained 71.31 pct copper, 0.01 pct lead, 0.01 pct iron and zinc by difference. Determination of Pole Figures A 6-in. length from each tube was rotated rapidly by an electric stirrer in 25 pct nitric acid until the gauge was reduced to 0.003-0.005 in. The tubes were carefully cut longitudinally and the walls gently flattened. They were further etched in 25 pet nitric acid to 0.0015 in. thickness and (111) pole figures were determined using copper K-alpha radiation in the manner described by Brick.' The three general types of pole figures

Jan 1, 1949

By L. H. Sjodahl, J. B. Conway

of each particle on grain boundary movement is proportional to the area it occupies on the grain boundary and this increases with the square of the particle radius. In contrast to the impression gained by Tiwari the effectiveness of a particle, as a grain boundary obstacle, increases rapidly as the particle size increases. The counterbalancing factor in a dispersion of constant volume (e.g., those considered by Zener) is of course the rapidly diminishing number of particles, a situation which does not exist in thoria dispersed materials where the volume fraction of thoria remains constant. Although it has been assumed that the Zener approach is valid for the sake of the above argument, it is open to the following objections: 1) It assumes that the effect of many small particles along a grain boundary is cumulative and does not take into account the possibility of each small particle being overcome separately. In this case the boundary will not be able to move forward until the largest particle on the boundary has been overcome. This means that the rate controlling factor will be the rate at which a few relatively large particles are overcome with the remaining small particles playing a negligible role. 2) When the dispersion consists of very small particles the interparticle spacing is usually small compared to the grain size and most particles are located away from grain boundaries where they can play no part. The most efficient dispersion, from a purely geometrical viewpoint, is one where the particle spacing is equal to the grain size so that all the particles are on grain boundaries. Tiwari's second point that voids cannot prevent re-crystallization seems to be unfounded as several workes20-23 have shown that voids alone can retard grain boundary movement and recrystallization. To further convince Tiwari, Fig. 17 shows a void in deformed TD Nichrome holding back a recrystallization interface. Tiwari's explanation for the effect of voids on recrystallization, i.e., they reduce local strain energy and hence lower the driving force for recrystallization may be valid in itself but is irrelevant to the present case where even complete recrystallization after ONE of the more recently proposed expressions for describing stress-strain behavior is that due to Voce.1,2 This equation is usually written: s =s8 ?(s8?so)e??/?c [l] where s is the true stress, ? is true strain, cC is a constant called the characteristic strain, s8 is the asymptotic stress approached at high strain values, and so is the threshold stress at which the plastic deformation begins. While this expression has not been universally accepted as yet it does contain certain features which are consistent with experimental stress-strain behavior. In a more recent publication Hsu, Davies, and Royles3 employed the concept of generalized strain proposed by seth4 and identified a method for linearizing the stress-strain plot. In this approach the generalized strain was given by: where 7 is the generalized strain, 1 is the instantaneous length, 1, the datum length, and n is a constant called the "coefficient of strain measure". A value of n was said to exist which would yield the linearity: s —s+ S[.-(tf] [3] In recent studies of both these approaches, it has been found that while the Voce equation and the gen-

Jan 1, 1970