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By C. A. Wert, M. G. Coleman

The Zener relaxation in alloys in the a! solid-solution region of the Cu-Ni-Zn ternary system has bear investigated. Of the binary solid solutions that bound this region, Cu-Zn and Ni-Zn exhibit measurable Zener peaks whereas Cu-Ni does not. At constant atomic percent copper, the Peak height drops uni.forinly from the value in the Cu-ZTL binary to zero in CIA-Ali. The cariation of peak ternperatuve with composition is linear. At constant atomic percent zinc, the peak height in the ternary alloys goes through a large maximum as compared with the binary values. The temperature of these peaks varies smoothly with composition. The half-width of the peaks in the ter nary alloys, however, are much larger than those in the binaries. A large enhancement of the relaxation strength of the Zener relaxation in ternary Au-Ag-Zn alloys as compared to the relaxation strengths in Au-Zn and Ag-Zn binary alloys was observed by Firson and ert.' Since this effect was unexpected, the present study was devised to investigate whether enhancement of the Zener relaxation in ternary alloys is a general feature or is particular to the Au-Ag-Zn system. We have chosen the Cu-Ni-Zn alloy system for this investigation. Measurable Zener relaxations are observed in both the Cu-Zn and the Ni-Zn binary systems, but not in the Cu-Ni binary system. A large solid-solution region extends to large concentrations of zinc, making it possible to vary composition of the alloys over a wide range without crossing phase boundaries. EXPERIMENTAL PROCEDURE Two series of alloys were prepared. the first at constant atomic percent copper, the second at constant atomic percent zinc. The compositions of these alloys are shown by the circles in Fig. 1. The alloys were prepared by melting the individual components, each of which had previously been vacuum-melted, in an evacuated quartz capsule in an induction furnace at 1500 C. The capsules containing the molten alloys were quenched in water to reduce coring. Any individual melt which exceeded 0.001 pct weight loss was discarded. The ingots were swaged to a 50 pct reduction of area and annealed for 1 week in an evacuated quartz capsule to aid homogenization. The alloys were then

Jan 1, 1967

By KENNETH CITTISGHAM

During the year 1945, the total number of wells drilled in Ohio, including the. non¬productive wells, was 1034. For the 10-year period ending with 1945, the average completions per year were 1125, the least number being 910 in 1938, and the maximum 1561 in 1941. The proportion of dry holes in 1945 was 37 per cent?about the same as for the year 1944 but exceeding the 10-year average, which was 34 per cent. The number of oil wells completed exceeded the number drilled in 1944 by about 30 per cent, the average initial per well being the same in both years. Gas-well completions were approximately 10 per Cent less than in 1944, with the average initial per well about 5 per cent greater. The difference in number of oil and gas wells in the two years was in Berea and Clinton completions, as the number of oil wells increased about 30 per cent, owing to greater activity in the two sands named, while the number of gas wells decreased because of fewer completions therein.

Jan 1, 1946

By J. E. Burke, C. W. Mason

In attempting to study precipitation from a tetragonal lattice, using solid solutione of bismuth in tin, it was found that although a Widmanstätten pattern is observed1,4 only a qualitative analysis of the orientation relationships is possible, because of the unusual structural changes that accompany the precipitation process. Microscopical Studies Alloys were made from Chempur tin (Standard samples 42b and 426, National Bureau of Standards), and bismuth (Kahl-baum C.P.) by melting weighed quantities together under palm oil, stirring well, and castilig in a heated graphite mold. The polishing and etching techniques employed largely govern the visibility of the structural changes. The preliminary surfacing operations were similar to those recommended by Villela and Bergekoff,5 through Behr-Manning 3/0 abrasive papers, lubricated by a solution of paraffin in kerosene. A rough metallographic polish was next given, using a thin cotton cloth charged with relevigated alumina (maximum particle size of about 4µ) and soap solution; repeated etching and polishing served to remove disturbed metal. For high-power examination better preparation was necessary. It was found that on such soft metals the threads of the fabric, rather than the abrasive, cause most of the scratching. Cotton outing flannel, which had been brushed so that the nap lay down, was fairly satisfactory, but a heavy grade of silk velvet (not the noncrushable kind) was found to be better, especially after some use. A better procedure was as follows: The metal lap was warmed slightly, and a 4-in. circle of woolen broadcloth was cemented to its center by a thin film of melted paraffin. The broadcloth was then moistened with water, and a 30 to 40 per cent solution of sodium hydroxide heated to about 50°C. was poured over it, allowed to stand for I to 2 min. and then washed off. It was neither necessary nor desirable to remove all the sodium hydroxide from the cloth, since its etching action aided in the removal of the flowed layer from the sample. The cloth was then charged with a paste of the relevigated alumina in water. Since this lap did not remove deep scratches, it was necessary previously to polish the specimen on some material such as the silk velvet. The sodium hydroxide softens and partly gelatinizes the woolen lap covering, permitting a scratch-free polish, but its action continues, and the cloth deterioratcs after about 24 hr. This is not serious, because a new lap can be prepared in about 5 min., and only small pieces of cloth are used. Etching with a strongly acid solution of ferric chloride was found satisfactory for removing the flowed layer. For the final etching, the most satisfactory reagent was that of Tafls,7 the formula for which is: FeC13.6H2O, 2 grams; HC1, 5 c.c.; H2O, 30 c.c.; C2H5OH (95 per cent), 60 C.C. This etchant reveals differences in com-

Jan 1, 1942

By J. E. Burke, C. W. Mason

In attempting to study precipitation from a tetragonal lattice, using solid solutione of bismuth in tin, it was found that although a Widmanstätten pattern is observed1,4 only a qualitative analysis of the orientation relationships is possible, because of the unusual structural changes that accompany the precipitation process. Microscopical Studies Alloys were made from Chempur tin (Standard samples 42b and 426, National Bureau of Standards), and bismuth (Kahl-baum C.P.) by melting weighed quantities together under palm oil, stirring well, and castilig in a heated graphite mold. The polishing and etching techniques employed largely govern the visibility of the structural changes. The preliminary surfacing operations were similar to those recommended by Villela and Bergekoff,5 through Behr-Manning 3/0 abrasive papers, lubricated by a solution of paraffin in kerosene. A rough metallographic polish was next given, using a thin cotton cloth charged with relevigated alumina (maximum particle size of about 4µ) and soap solution; repeated etching and polishing served to remove disturbed metal. For high-power examination better preparation was necessary. It was found that on such soft metals the threads of the fabric, rather than the abrasive, cause most of the scratching. Cotton outing flannel, which had been brushed so that the nap lay down, was fairly satisfactory, but a heavy grade of silk velvet (not the noncrushable kind) was found to be better, especially after some use. A better procedure was as follows: The metal lap was warmed slightly, and a 4-in. circle of woolen broadcloth was cemented to its center by a thin film of melted paraffin. The broadcloth was then moistened with water, and a 30 to 40 per cent solution of sodium hydroxide heated to about 50°C. was poured over it, allowed to stand for I to 2 min. and then washed off. It was neither necessary nor desirable to remove all the sodium hydroxide from the cloth, since its etching action aided in the removal of the flowed layer from the sample. The cloth was then charged with a paste of the relevigated alumina in water. Since this lap did not remove deep scratches, it was necessary previously to polish the specimen on some material such as the silk velvet. The sodium hydroxide softens and partly gelatinizes the woolen lap covering, permitting a scratch-free polish, but its action continues, and the cloth deterioratcs after about 24 hr. This is not serious, because a new lap can be prepared in about 5 min., and only small pieces of cloth are used. Etching with a strongly acid solution of ferric chloride was found satisfactory for removing the flowed layer. For the final etching, the most satisfactory reagent was that of Tafls,7 the formula for which is: FeC13.6H2O, 2 grams; HC1, 5 c.c.; H2O, 30 c.c.; C2H5OH (95 per cent), 60 C.C. This etchant reveals differences in com-

Jan 1, 1942

By Daniel D. Pollock

The il'lott and Jones theory of thermoelectricity predicts that the absolute thermoelectric power of alloys of transition and noble metals should be a maximum when the concentration of the noble metal is approximately 55 to 60 at. pct. An examination of the emf of a series of relatively pure alloys of copper and nickel shows that the predicted maximum occurs at about 57 at. pct Cu. This excellent agreement with the theory is considered to substantiate the Mott and Jones theory of thermoelectricity for binary alloys of transition elements. This theory is extended to show that the emf behavior of dilute, ternary copper-nickel base alloys, which contain approsimately 60 pct Cu and 40 pct Ni, may be described in terms of a scattering mechanism. The scattering effect of a third element is demonstrated to be a function of its valence and its period in the periodic table. Small amounts of solute elements have additive scattering effects upon the emf of the Cu-Ni base. The Mott and Jones equation is modified to include this scattering parameter. This adaptation accurately describes the thermoelectric behavior of ternary and quaternary CLL-Ni base alloys. An empirical form of the modified Mott and Jones equation is derived which permits the calculation of thermoelectric power with an average error of less than 0.4 pct at 500 "C. CONSTANTAN has long been used as a thermocouple element. Its approximate composition varies from 50 pct Cu, 50 pct Ni to 65 pct Cu, 35 pct Ni. Small amounts of manganese, iron, and other elements have been used to modify the composition in order that the resultant emf vs platinum conforms to nationally accepted table. Adjustments of this type are made on a purely empirical basis. Constantan was originally made in Germany and was imported into this country for thermoelectric and electrical resistance purposes. During World War I, the supply of this material became seriously depleted. The work of Bash4 was done in this period in order to develop a satisfactory substitute for the imported material. Bash's empirical work on Cu-Ni alloys is still the basis for all commercial constantans made in this country. No reexamination of the electrical properties of this system has been made, despite the fact that it is now well known that Bash's alloys contained impurities which strongly affected their thermoelectric behavior.

Jan 1, 1962

By H. A. Bedworth

ALLOYS of copper and silicon have been known for one hundred years or more but the commercial development of this type of alloy has taken place during the past few years. In 1905, Sperry1 proposed the use of copper-silicon alloys for springs and other purposes for which copper-tin bronzes were used. Some attention was given to this proposal at the time but no one succeeded in producing a practical alloy containing more than a fraction of a per cent. of silicon. The equilibrium relations of the copper-silicon system were studied first by Rudolfi2 and later by Sanfourche3 and Corson.4 The constitution of the system has also been recently investigated by Matuyama,5 and in the laboratories of the American Brass Co. by Smith.6 Some of the physical properties of the copper-silicon alloys have been investigated by Norbury7 and by Geiss and Van Liempt.8 Summarizing the results of various investigators of, the constitution of copper-silicon alloys, the solubility reaches its maximum value, 6.7 per cent. silicon, between 721° and 782° C. At 852° C. the solubility is 5.25 per cent., while at 400° C. it is only 4.1 percent. silicon. The copper-silicon alloy begins to get so hard at about 3 per cent. silicon that it is difficult to manage. It was found by Jacobs that the addition of manganese to this alloy considerably improved the working

Jan 1, 1929

[Trans. No. Place Date Vol. Page 1. Wilkes-Barre, Pa.* May, '71.. 1 3 2. Bethlehem. Pa Aug., '71.. 1 10 8. Troy, N. Y Nov., '71.. 1 1S 4. Philadelphia, PaFeb., '72.. 117 5. New York, N. Y.*May: '78.. 120 5. Pittsburgh, PaOct., '72.. 125 7. Boston, MassFeb., '78.. 128 8. Philadelphia, Pa.* May, '78.. 2 3 9. Easton, POct., '78.. 27 10. New York. N. YFeb.. '74.. 2 11]

Jan 1, 1946

By A. G. Raine

For the technological age in which we live, with the constant goal of further improvement in the efficiency of mechanized systems, the need for a replacement of the antiquated drill and blast method of shaft construction has been recognized. For over a decade now; the trend in shaft construction has been toward large diameter bored shafts using either raise boring methods or more flexible, rodless "down the hole" boring machine. The limits of conventional shaft sinking have been reached, the mining regulations are more stringent, and the environmental agencies more aggressive, all contributing to the growing need for development of the rodless shaft boring machine. In the last three years in the United States, world shaft construction records have been achieved using a V-Mole machine, designed by Mirth GmbH of West Germany, using American electrics and hydraulics. Shafts of 7.0 meters (23 feet) diameter, totaling 2,255 meters (7,400 feet) in depth have been constructed at high advance rates, yet with unusually low accident rates. Bearing in mind the high cost of today's mining labor and the inherent danger associated with conventional shaft sinking, this alternative method of shaft construction achieves a fast, competitive, low manpower requirement, whilst enhancing a safer environment for the labor force. Recent results have proven that program time savings of 50 percent over conventional shaft sinking can be achieved which can be directly translated into improved client cash flow projections and more accurate project budgeting.

Jan 1, 1984

By M. G. Jones

AT the Edwards mine a 4 by 81/2-ft two-compartment shaft is used for men and supplies in the older workings down to the 900-ft level. All ore is hoisted through a 5 by 15-ft three-compartment vertical shaft which extends to the 1500-ft level. Ore pockets are on the 1300- and 1500-ft levels. The two-compartment countershaft used below the latter level is 6 by 12 ft inclined at 42°. Ore from the countershaft is hoisted to the 1350-ft level where it flows by gravity to the 1500-ft level ore pocket. One-ton skips are used in balance in the countershaft and two-ton skips, also in balance, from the 1500-It level to the surface. These skips are slung under the man cages. Each level has an ore pocket of 200 tons' capacity. Development at Edwards is similar to that at Balmat except that haulage drifts are only 7 by 7 ft. They are mucked with Eimco-Finlay No. 12 loaders. A drill carriage similar to that used at Balmat is being tried out on the new 2300-ft level, the present bottom of the mine. Drifts are driven below grade and later raised 6 in. and ballasted with waste leaving a ditch 6 by 12 in. at one side for drainage. All development is done on an incentive bonus system, the miner paying for his explosives.

Jan 1, 1947

By Paul Berggreen

LIST OF PUBLICATIONS In the Bibliography titles of publications are replaced by corresponding symbols in this list. American A-1. Transactions of the American Institute of Mining Engineers, New York. A-2. Journal of the New York Microscopical Society, New York. A-3. Journal of the Franklin Institute, Philadelphia, Pa. A-4. The Metallographist, Boston, Mass. A-5. The Electrochemical and Metallurgical Industry, New York. A-6. Bulletin of the American Institute of Mining Engineers, New York. A-7. The Iron Trade Review, Cleveland, Ohio. A-8. The Journal of Physical Chemistry, Ithaca, N. Y. A-9. The Physical Review, New York. A-10. Van Nostrand's Electric Engineering Magazine, New York. English E-1. Proceedings of the Institution of Mechanical Engineers, London. E-2. Journal of the Iron and Steel Institute, London. E3. Proceedings of the Institution of Civil Engineers, London. E-4. Journal of the Chemical Society of London, London. E-5. Philosophical Magazine, London. E-6. Proceedings of the Royal Society of Edinburgh, Edinburgh., E7. Carnegie Scholarship Memoirs, London. E-8. Proceedings of the Royal Society of London, London. E-9. Chemical News, London. E-10. Philosophical Transactions of the Royal Society of London,, London. E-11. Transactions of the North-East Coast Institution of Engineers and Shipbuilders, Newcastle-on-Tyne E-12. Iron, London. E-13. Nature, London. E14. English Mechanic and World of Science, London.

Jan 6, 1914

By D. S. Bloom

RECENTLY a report has been published on an investigation of the MO-RU system by E. Raub.' In this report it is stated that below approximately 1200°C the system consists of two terminal solid-solution phases and the intervening two-phase field; at 1200°C and above, an intermetallic compound labeled Mo,Ru, makes an appearance. Along with some other little known systems in which it was considered possible for a u phase to form, the Mo-Ru system had been under investigation in this laboratory. Since molybdenum and ruthenium have very high melting points and also since ruthenium is expensive, the investigation was confined to X-ray diffraction by sintered powder compacts. The compositions which were studied were (in atomic percentages): 75 Mo-25 Ru, 67 Mo-33 Ru, 50 Mo-50 Ru, and 25 Mo-75 Ru. All compacts were made from the pure powders, and no chemical analyses were attempted. Each compact weighed about 5 g. All annealing was done in evacuated Vycor capsules, and even though the capsules completely collapsed at 1250°C, they still admitted no air. The results of this investigation in general corroborate the work of Raub. Up to 1150°C the two terminal solutions and the intervening two-phase field were found, and at 1200°C and above an intermetallic compound was found. However, the composition limits of the compound were estimated to lie close to 70 atomic pct Mo rather than 62.5 atomic pct Mo as Raub had reported. At least the X-ray diffraction results indicated that the 75 atomic pct Mo specimen consisted of the molybdenum solid solution plus the compound, while the 67 atomic pct Mo specimen consisted of the ruthenium solid solution plus the compound and the equiatomic composition contained only very little of the compound. The most interesting observation, however, was that the diffraction pattern of the compound was similar to that of the well known u phases, except that unusually large lattice constants were indicated. The d-values, or interplanar spacings, of the diffraction lines (as produced by filtered copper KCX radiation) of the compound are given in Table I, as determined from specimens annealed at 1250°C for 9 hr and then quenched in water. Also shown are the lines of the Mn-Mo u phase as given by Decker, Waterstrat, and Kasper,' the lines of the Fe-Mo a as given by Goldschmidt," and the lines of the Mo-Ru phase multiplied by constants in order to make comparison with the Mn-Mo and Fe-Mo patterns easier. These results indicate that the compound in the Mo-Ru system is apparently isomorphous with the other o- compounds. The rather large lattice constants of the Mo-Ru a phase are acceptable in view of the comparatively large size of the constituent atoms. The data in Table I for the Mo-Ru compound check quite well with those given by Raub, not shown here, though there are some discrepancies between the two sets of data in the estimated intensities of a few lines. Although very little is known at present about this u phase, there are some things which may be pointed out, mainly in comparison with other better known u phases. Even though molybdenum and ruthenium are in the same columns in the Table of Elements as chromium and iron, respectively, the Mo-Ru u phase contains much more molybdenum than ruthenium, while the Cr-Fe u phase centers around or very nearly around the equiatomic composition; furthermore, the Mo-Ru u is stable only above approximately 1200°C, but the Cr-Fe u is stable only below about 825 °C. With respect to its being unstable below 1200°C, the Mo-Ru u is similar to the other binary molybdenum u phases in the Co-Mo and Fe-Mo systems. Similar to the latter two systems, the Mo-Ru u apparently exists over a rather narrow composition range, whereas the Cr-Fe u at lower temperatures is stable over a much wider composition range. The Mo-Ru u thus is closer to the other molybdenum u phases than to the Cr-Fe cr phase. The most striking feature of the Mo-Ru u phase, however, is the absence of any of the transition elements of the First Long Period.

Jan 1, 1956

By H. R. Thresh, A. F. Crawley, D. W. G. White

The densities of liquid tin, lead, and Sn-Pb alloys have been measured over a range of temperature above the liquidus. In all cases, data can be adequately represented by an equation of the type p = a + bT. For pure tin, the values of a and b are, respectively, 7.139 and 7.125 x 10-4, and for pure lead, 11.060 and 12.220 x 10-4. At constant temperature, molar volumes in the Sn-Pb system vary linearly with composition. DURING the course of a long-term program at the Department of Energy, Mines and Resources, Ottawa, Canada, the densities of liquid tin, lead, and Pb-Sn alloys were studied. The work reported herein draws on two sets of results independently achieved by Thresh, on the one hand, and by Crawley and White, on the other. EXPERIMENT The method and apparatus were originated by Thresh and have been described in detail in Mines Branch reports.172 In operation, the 14 cu cm graphite pycnometer is put in the furnace as shown in Fig. 1 after a machined charge has been placed inside the pycnometer and the lid screwed down. The dimensions of the charge are such that, upon melting, a small excess of liquid metal is discharged through the capillary hole to displace the weighted float above. When the pycnometer has been equilibrated at the experimental temperature, the

Jan 1, 1969

By G. W. Elger, H. E. Bell, J. E. Tress, J. B. Wright

This paper describes laboratory techniques and subsequent results of US Bureau of Mines (USBM) research to produce chlorination-grade feed- stock from an abundant, low-grade, domestic, rock ilmenite ore. The research is part of the Bureau effort to devise technology that may help decrease US dependence on imported raw materials. A rock ilmenite containing about 46 wt % TiO2 was smelted in an electric arc furnace with coke, wood-chips, and Na2CO3 to separate most of the iron as pig iron and to form a low-iron, titanium-enriched slug. The slug was ground, pelletized, oxidized, and then sulfated with mixtures of SO2 and air in a continuous 4.5- to 9.1-kg/h (10- to 20-lb per hour) apparatus at 1023° to 122J0 K (1380° to 1740° F). The sulfated slug, containing 60% to 65% TiOb, was reground and leached in water at ambient temperature to decrease the combined levels of the troublesome calcium, magnesium, and manganese impurities from 7.0 to 1.7 wt 70. The final product was upgraded to about 8.4 wt % TiO2. This material is potentially suitable for chlorination in a fluidized bed reactor. The most favorable results were achieved with leached slug sulfated at a feed rate of 4.5 kg/h (10 lb per hour) and at temperatures of 1073° to 1123° K (1470° to 1560' F).

Jan 1, 1986

By T. F. Witherbee

It is proposed to give, first, a description of the works; second, a report of the first six months of the present blast; and third, such improvements as have been suggested by the practical working. The site selected for this furnace was, at the time of commencing work, October, 1872, entirely covered by the navigable waters of Lake Champlain. A coffer-dam was first built of cribs of round timber filled with stone, forming three sides, while the shore answered for the fourth. Considerable excavating was done with a steam-dredge, a hole being left for it to pass out. The opening was then built up, and the cribbing banked up with blue clay from the bottom of the lake, to render it water-tight and the dam pumped out; the remainder of the excavating being done by hand. All of the foundations, with the exception of the elevator-tower, and fifteen feet of the east side of hot blast, rest on the Potsdam sandstone, which forms the shore line, dipping into the lake at an angle of fifteen degrees. Owing to jogs in the formation, a much greater depth was found necessary than was at first anticipated, the foundation under the stack

By T. F. Witherbee

IT is proposed to give, first, a description of the works ; second, a report of the first six months of the present blast; and third, such improvements as have been suggested by the practical working. The site selected for this furnace was, at the time of commencing work, October, 1872, entirely covered by the navigable waters of Lake Champlain. A coffer-dam was first built of cribs of round timber filled with stone, forming three sides, while the shore answered for the fourth. Considerable excavating was done with a steam-dredge, a hole being left for it to pass out. The opening was then built up, and the cribbing banked up with blue clay from the bottom of the lake, to render it water-tight and the dam pumped out; the remainder of the excavating being done by hand. All of the foundations, with the exception of the elevator-tower, and fifteen feet of the east side of hot blast, rest on the Potsdam sandstone, which forms the shore line, dipping into the lake at an angle of fifteen degrees. Owing to jogs in the formation, a much greater depth was found necessary than was at first anticipated, the foundation under the stack

Jan 1, 1876

By William E. Ford, Edward Salisbury Dana

In their action upon the senses a few minerals possess taste, and others under some circumstances give off odor. 444. Taste belongs only to soluble minerals. The different kinds of taste adopted for reference are as follows: 1. Astringent: the taste of vitriol. 2. Sweetish astringent: taste of alum. 3. Saline: taste of common salt. 4. Alkaline: tast'e of soda. 5. Cooling: taste of saltpeter. 6. Bitter: taste of Epsom salts. 7. Sour: taste of sulphuric acid.

Jan 1, 1922

By Lennart Bergstedt, Olov Fägremo

Boliden Metall Aktiebolag, the prime base metal mining company of Sweden, treats some 10-10.9 t/y (11-12 stpy) of sulphide ore in nine concentrators. During the years considerable effort has been devoted to the development of all phases of the technology of ore prospecting, mining, milling, smelting and refining. This has been necessary due to the complex and low grade ores. The autogenous grinding technique was first studied within the company as early as 1945. Basic test work commenced during the early fifties, whereby the merits of pebble grinding could be evaluated. In parallel with the converting of the rod mill/ball mill grinding systems to rod mill/pebble mill systems, the development work concerning the feasibility of autogenous grinding went on resulting in the installation of a 8 6.7 x 2.1 m (8 22 x 7 ft.) cascade mill at the Vassbo lead mine in 1959. Long term tests at the Vassbo plant together with a number of pilot plant test involving low grade silicious ores and pyritic comples base metal ores successive led to a better understanding of the process of autogenous grinding. Before a two stage autogenous grinding system could be chosen for the expansion of the Aitik copper mine, a carefully planned survey concerning grinding characteristics and variances in the ore and flowsheet was undertaken. The expanded plant went on stream in 1972 and in the beginning of 1973 and since then has performed excellently.

Jan 1, 1979

By Bieniawski, Z. T.

The importance of understanding the phenomena associated with rock fracture has long been fully appreciated in rock mechanics. This is clearly apparent from the special attention paid to rock fracture in the comprehensive papers published within the past four years. These papers present a picture of how the knowledge of brittle fracture of rock was gradually enriched and also show that what was often taken for granted three or four years ago is no longer considered as valid today.

Jan 1, 1972

By N. L. Svensson

The model developed by Tuylor for the calculation of Polycrystalline yield strength has been applied to the case of an aggregate hawing a preferred orientation. In general this procedure requires the specification of texture by means of weighting factors applied to specific orientations. The problem to which the model has been applied is that of the yield-strength aniso-tropy of cold-rolled aluminum whose rolling texture was described as a combination of (110)[112] and (311) [112] In this case yield-strength anisotropy is defined by the rutio of yield strength measured at an angle 8 to the rolling direction to that measured along the rolling direction. The method of calculation of yield-strength ratio as a function of ? is described and the results show good agreement with experimental values. The orthotropic yield criterion suggested by Hill has been applied to the results and the strain ratio R also calculated as a function of ?. This has been compared with calculations using the method suggested by Elias, Heyer, and Smith which does not exhibit suck good agreement with observation. one deficietlcy of the method presented is that the strain ratios used by are those applying to iso-Irobic materials. The method should therefore be reg-clrded only as a first abbroximation to the prediction of anisotropy. THE problem of calculating the stress-strain characteristics of polycrystalline aggregates from the properties of single crystals has attracted attention for a number of years. The most important contributions to this study have been those due to: Sachs,' Cox and sopwith,2 Taylor,3 Kochendorfer,4 Batdorf and Budiansky,5 Calnan and Clews,6 Bishop and Hill,7,8 Kocks,9 Budiansky, Hashin, and sanders, 10 Kroner,11 Cyzak, Bow, and payne, 12 Budiansky and Wu,13 and Lin.14 While the earlier work has been largely superseded, recent developments tend to support Taylor's solution" within the restriction imposed by his assumptions. The essential features of Taylor's approach were: 1) the material is rigid-plastic; 2) each grain experiences the same strain components as the aggregate as a whole (the problem was that of uniaxial deformation with principal strain components in the ratio 3) all regions of each grain deform uniformly; 4) work hardening occurs equally on all slip systems. While Bishop and Hill7 have generally validated this approach, there has been some criticism offered. Kocks? as pointed out that since multiple slip must occur the single-crystal data must be determined from orientations arranged such that polyslip takes place. Boas and Hargreaves,15 and others, have shown experimentally that the strain distribution within grains is not uniform, the strains in the vicinity of grain boundaries being less than those in the center of the grains. Both of these criticisms can be largely offset by the suitable choice of single-crystal critical shear stress. However, for the problem analyzed below, the critical shear stress is not directly used and, consequently, these criticisms lose their importance. The more recent contributions have attempted to obtain a more complete analysis by considering an elas-toplastic material and considering interactions between grains of differing orientations. Lin14 has considered the early stages of yielding for a polycrystalline aggregate having specific regions of defined slip plane orientations. On the other hand, Budiansky and Wu13 have allowed for these interactions for randomly disposed grain orientations and have calculated the polycrystalline stress-strain curves for crystals exhibiting either elastic-ideally plastic or kinematic hardening characteristics. This work has shown that yielding commences when the macroscopic stress is 2.2 times the critical shear stress for slip in a single crystal (7,). The yield stress-strain curve then rises becoming asymptotic to a value of 3.072 7,. This is close to the value obtained by Bishop and Hill (3.06) in their confirmation of Taylor's method. This, of course, is to be expected since, at large strain values, the elastic strains are negligible and the rigid-plastic model is satisfactory. The results of Budiansky and Wu indicate that the result obtained by Taylor is 7.7 pct high at a plastic strain which is two times the elastic strain at the initiation of yield. By defining the anisotropy in terms of relative values, the ratio of yield strength at orientation ?, to that measured in the rolling direction, the effect of the discrepancy in Taylor's solution is considered to be of lesser consequence. Therefore, it is anticipated that an analysis based on Taylor's solution, which can be quite straightforward, should provide a reasonable estimation of the anisotropy of materials having a preferred orientation texture. OUTLINE OF TAYLOR'S METHOD In fee metals there are four possible slip planes (the octahedral planes) and in each there are three possible slip directions (the edges of the octahedron), that is a total of twelve possible slip systems. von Mises16 has shown that at least five independent slip systems must become operative in each grain of the polycrystalline aggregate in order to preserve continuity of strain. With this geometrical requirement as basis and the assumptions previously listed, Taylor determined the operative slip systems for a number of orientations of the tensile stress axis specified in the unit stereographic triangle. For the ith slip system, the critical shear stress

Jan 1, 1967

By AIME AIME

[The American Institute of -Mining Engineers does not assume responsibility for any statement of fact or opinion advanced in its papers or discussions.] A detailed list of the' papers contained in this section is given in the Table of Contents, pages i. and ii. Comments or criticisms upon all papers given in this section whether private corrections of typographical or other errors or communications for publication as "Discussions," or independent papers on the same or a related subject, are earnestly invited. ERRATA. The following corrections and. additions to papers contained in Bi-Monthly Bulletin No. 7, January, 1906,-were received too late for incorporation in the text of said papers ; but will be introduced in their: proper places: in the volume of the Transactions: These corrections are here published in order to bring them -promptly to the notice of the Institute. Page Line Cover, title-page and at the top of pages in the preliminary section "No. 1 " should be "No. 7 ". 1. Bottom For :" Dr. P. H. Shimer" read "Dr. P. W. Shinier " 69. Fig. 3. "N" of compass-record should be ?S". A new block for this illustration has been made as shown on p. xxxviii of this Bulletin. 78. 3 from bottom. For " slope " read " stope." 89. Fig. 2, small diagram in upper left-hand corner. Omit use 50 ft. to 1" scale ". For "Thro' 250 " read " Thro' 200 ". Add dotted line extend¬ing from upper right-hand corner of the square

Mar 1, 1906